diff --git a/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.json b/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.json new file mode 100644 index 0000000000000000000000000000000000000000..6bfb0241d1a85457a4588ae402dc72fc4c24ed51 --- /dev/null +++ b/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.json @@ -0,0 +1,30942 @@ +{ + "generated_at_utc": "2026-07-10T23:20:51.241026+00:00", + "model": "Qwen/Qwen3-4B-Instruct-2507", + "data_dir": "data/rl/ioling_qwen3_4b_manual_v1", + "splits": [ + "train", + "val" + ], + "iid_samples": 4, + "hint_samples": 4, + "solution_hint_samples": 4, + "groot_anchors": 1, + "groot_approaches": 4, + "max_tokens": 4096, + "planner_max_tokens": 2048, + "max_model_len": 16384, + "temperature": 1.0, + "planner_temperature": 0.7, + "top_p": 1.0, + "gpu_memory_utilization": 0.5, + "candidates": [ + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "iid", + "sample_index": 0, + "output": "We are asked to infer the theoretically possible Rotuman translations for **\"word\"** and **\"to exhaust\"**, based only on the given vocabulary and linguistic patterns.\n\nWe observe that the provided words do not contain \"word\" or \"to exhaust\" directly. However, we may look for patterns in how other concepts are formed — particularly via compounding, affixation, or root reuse.\n\nStep 1: Look for semantic or morphological patterns.\n- Rotuman uses root-based constructions.\n- Many words appear as compound constructions: e.g., *ha.fha.fu* = rocky (ha.fha = rocky, fu = something), *nu'suar tiro* = window (nu'suar = door, tiro = spectacles?), though that seems inconsistent.\n\nWait: *nu'suar tiro* — window; *nu‘sura* = door. So 'nu'suar' and 'nu‘sura' are similar, differing only in suffix. 'tiro' appears in 'maf tiro' = spectacles. So possibly 'tiro' is a root meaning \"lens\", \"eye\", or \"spectacle\". Could 'word' be related to 'pala' (pierce), or 'pogi' (night)? Unlikely.\n\nBut consider: many verbs are formed with prefixes or suffixes.\n\nLook at verbs:\n- ‘ele — to be near\n- ‘olo — to cut\n- ‘fau — year\n- ‘huli — to turn over\n- ‘pala — pierce\n- ‘piri — to curl\n- ‘puhra.ki — to boil\n- ‘hün kia — base of the neck\n- ‘ma.titi — coldness\n- ‘ma.tit mamasa — ice\n\nWe also have:\n- ‘huli — to turn over; could be related to 'rotate'?\n- ‘to‘a — hero; could be related to courage? ‘huag to‘a’ = courageous — so ‘to‘a’ is a root of hero/courage?\n\nNow, consider compounding:\n- *a‘öf fau* — year’s end → ‘a‘öf’ is likely a prefix meaning \"end of\", like “at the end of”.\n- *fäeag ‘u‘u* — to use sign language → ‘fäeag’ = to use, ‘u‘u’ = sign? Possibly.\n- *moafmofa* — littered with rubbish → ‘moa’ + ‘fmo’? Possibly reduplication for scattered state.\n\nNow, look at roots with high semantic features:\n- ‘is’ — sharp-pointed; ‘is susu’ = nipple — suggests ‘is’ has a core meaning related to point or shape.\n- ‘hün’ — base; ‘hün kia’ = base of neck → so ‘hün’ is a root for “base”.\n- ‘ma.titi’ = coldness; ‘ma.tit mamasa’ = ice → suggests ‘ma.titi’ + ‘mamasa’ = ice, a dense state of coldness.\n- ‘pala’ = pierce — could relate to “a hole” or “penetration”.\n\nNow, could \"word\" be a compound involving a \"sound\" or \"speech\"?\n\nWe have:\n- *pogi* = night\n- *fau* = year\n- *pulu* = glue\n- *ka.lu* = bracelet; to encircle\n- *riamrima* = shiny\n\nNow, check for any root that could mean \"sound\" or \"speech\". Not directly present.\n\nBut consider: **\"to exhaust\"** = to deplete, to use up completely.\n\nWe have the word *a‘öf fau* = year’s end — implies ‘a‘öf’ = end, ‘fau’ = year.\n\nWhat words involve use or consumption?\n\nWe have:\n- *fau* = year\n- *huli* = to turn over\n- *pala* = to pierce\n- *puhra.ki* = to boil, to bubble up — bubbling up → could involve depletion?\n- *huli* = turn over — maybe not.\n\nBut consider: 'to exhaust' might be formed via a root meaning “to use up” or “to consume”.\n\nDo we have any verb meaning \"to use\"?\n\n- *fäeag ‘u‘u* — to use sign language → ‘fäeag’ = to use → verb meaning ‘to use’ is present.\n\nSo ‘fäeag’ = to use.\n\nTherefore, “to exhaust” could be formed as “to use up” or “to consume completely”.\n\nPossible constructions:\n- ‘fäeag’ + root of “up” or “end”?\n- ‘a‘öf fau’ = year’s end → could suggest ‘a‘öf’ is a suffix or prefix meaning “end of”\n\nCould “to exhaust” be formed with a similar compounding structure?\n\nAlternatively, consider: *poagpoga = palpala* — “covered with holes” — so ‘poagpoga’ = covered with holes; possibly derived from ‘pog’ = hole?\n\n‘pala’ = pierce → hole? Possibly.\n\nSo ‘pala’ → hole → could be used to form “fill” or “empty”?\n\nBut no direct evidence.\n\nAnother clue: *lala* = deep → opposite of ‘el‘ele’ = shallow.\n\n‘el‘ele’ = shallow → suggests a root meaning “level” or “depth”.\n\nCould “word” be related to a “sound” or “utterance”?\n\nIn many languages, “word” is formed from “speech”, “utterance”, “sound”.\n\nWe have no direct word for speech or sound.\n\nBut we have:\n- *pala* = pierce — could be an analogy to “to pierce the air” = sound?\n- *piri* = to curl — not relevant\n- *rū huga* = stomach-ache — illness\n\nDo we have any word meaning “mouth” or “to speak”?\n\nNo.\n\nBut perhaps a compound: ‘to’ + ‘use’?\n\nWe have ‘fäeag’ = to use.\n\nCould “to exhaust” be a compound with ‘fäeag’ and a root meaning “end”?\n\nLike: ‘fäeag a‘öf’ = to use up to the end?\n\nBut ‘a‘öf fau’ = year’s end — so ‘a‘öf’ is used with ‘fau’.\n\nCould ‘fäeag a‘öf’ = to use to the end?\n\nThat seems plausible.\n\nSimilarly, “to exhaust” is \"to use up\".\n\nTherefore, a possible translation of **to exhaust** could be **fäeag a‘öf** — to use up to the end.\n\nAlternatively, if “word” is “something spoken”, perhaps “sound”?\n\nWe have no word for “sound”.\n\nBut we have:\n- *pala* = pierce → could be metaphorical for “to make a mark” or “to speak”?\n- *piri* = to curl → not relevant\n\nAnother possibility: in compound forms, words are formed with shared roots.\n\nNotice that:\n- *mamasa* = solid\n- *ma.titi* = coldness\n- *ma.tit mamasa* = ice → so ‘ma.titi’ + ‘mamasa’ = ice\n\nLikewise, could “word” be built from a root for “speech” or “sound”?\n\nWe have *pogi* = night; *fau* = year; *huli* = to turn over.\n\nWait: the structure *X + Y* appears often — e.g., *a‘öf fau*, *hün kia*, *ma.tit mamasa*.\n\nSo compound formation is common.\n\nNow, is there any root that means “to be” or “state”?\n\n‘ele’ = to be near — so verb.\n\nBut ‘is’ = sharp-pointed — noun?\n\n‘is susu’ = nipple — compound.\n\n‘huli’ = to turn over — verb.\n\nBut no match for “word”.\n\nPerhaps “word” is derived from “speech” → which may be absent in the data.\n\nSo what is the **theoretically possible** translation?\n\nThat means: based on the patterns observed, what forms could plausibly exist?\n\nFor **“word”**:\n- In many Austronesian languages, \"word\" is often derived from \"speech\" or \"sound\".\n- Words for \"sound\" might be formed from roots like “pala” (pierce) or “piri” (curl) — but not directly.\n- Alternatively, \"word\" could be a compound using “to speak” or “to utter”.\n- No such root is present.\n\nBut if we assume that “to use” = *fäeag*, and “to speak” is not present, then “word” may be unattested.\n\nBut the question asks for **theoretically possible** translations — so based on the structural patterns, what forms could be built?\n\nPattern: many compounds use prefixes, suffixes, or root stacking.\n\nFor “word”, possible forms:\n- Could be formed as *pala* + something → e.g., “to pierce” → “a sound”?\n- Or *pali* or *pali* something?\n\nBut no such word.\n\nAlternatively, “word” might be *pug* or *kala* — not present.\n\nBut we have *ka.lu* = to encircle → could “word” be encircled in a circle? Unlikely.\n\nAlternatively, language often has roots like *di* for “to say” or *sala* for “to speak” — not present.\n\nSo, **the only theoretical possibility** for “word” is a compound involving speech or sound — but no such root.\n\nThus, the only available morpheme for “to speak” or “to utter” is *fäeag* (to use), which could mean “to use language”.\n\nThus, *fäeag* might be used in a compound meaning “to speak”.\n\nTherefore, “word” might be a root or compound derived from a root meaning “sound” or “speech”.\n\nBut since nothing exists, the only plausible theoretical form would be something like *pala* — which means “to pierce”, and could metaphorically mean “a mark” or “a sound” — so perhaps “pala” is used for “word”?\n\nBut in the data, *pala* is “to pierce” — not “word”.\n\nAnother possibility: *lala* = deep — could “deep word” exist? Unlikely.\n\nCould “word” be *huli*? “To turn over” — not a word.\n\nThus, given that no form matches, the only reasonably constructed one is through use of existing roots.\n\nSince **“to use”** is represented as *fäeag*, and **“to exhaust”** involves using up, it could be formed as *fäeag a‘öf* → “to use up to the end”.\n\nAlso, in *a‘öf fau* = year’s end, *a‘öf* = end → so *a‘öf* suggests endpoint.\n\nThus, *fäeag a‘öf* = to use to the end → to exhaust.\n\nSimilarly, “word” — if “sound” is not present, but “speech” might be based on “to utter”, and “utter” is not directly present, but perhaps *pala* (to pierce) could mean “to make a sound”?\n\nIn some languages, “to pierce” can be metaphorical for “to make a sound”.\n\nSo *pala* could be a possible encoding of “word” via metaphor.\n\nAlternatively, no known root exists, so the only possible form is through derivative or compound formation.\n\nBut since the question asks for **theoretically possible**, we list what can be inferred from patterns.\n\nThus:\n- For “word”: the only available morpheme is *pala* (to pierce), which might be metaphorically applied to “a sound” or “a spoken mark”. So **pala** could be a theoretical possibility.\n- For “to exhaust”: *fäeag a‘öf* is plausible — “to use up to the end”.\n\nOther options? *huli* = to turn over — not relevant.\n\nNo word for “speech” is given, so we cannot form “word” directly.\n\nBut since “to exhaust” is “to use up”, and “to use” is *fäeag*, and “end” is *a‘öf*, then *fäeag a‘öf* is a compound that fits.\n\nTherefore, based on pattern:\n\nd.1 / word: pala \nd.2 / to exhaust: fäeag a‘öf \n\n(Note: we are not certain, but these are the only forms that can be built from existing roots through plausible morphological extension.)\n\n\\boxed{d.1: pala; d.2: fäeag a‘öf}", + "generated_tokens": 2777, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: pala; d.2: fäeag a‘öf", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9144.0, + "ioling_final_answer_chars": 26.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "iid", + "sample_index": 1, + "output": "We are asked to determine the theoretically possible translations of “word” and “to exhaust” into Rotuman, based only on the given word list. Since these two terms are not directly present, we must deduce possible forms by identifying patterns in the language.\n\n---\n\nStep 1: Look for patterns in compound words or combinations.\n\nObserve that many Rotuman words are formed via compounding or modification using affixes or root combinations.\n\nFor example:\n- ‘a‘öf fau’ → \"year’s end\"\n- ‘fau’ → \"year\"\n- ‘huli’ → \"to turn over\"\n- ‘huni’ → \"lower end\"\n- ‘is’ → sharp-pointed; ‘is susu’ → nipple → suggests “is” is a root with a noun suffix or modification\n- ‘nu‘suar tiro’ → window; ‘nu‘sura’ → door → shows possible noun formation via root + vowel + suffix\n\nNote: Many words are formed from roots with added elements (e.g., ‘nu’suar’ + ‘tiro’ → window). Suffixation appears consistent.\n\nAlso, some verbs are formed with grammatical elements:\n- ‘huag ‘el‘ele’ → impatient → uses root ‘huag’ + ‘el‘ele’\n- ‘huag to‘a’ → courageous → ‘huag’ + ‘to‘a’\n- ‘hün kia’ → base of the neck → ‘hün’ + ‘kia’\n- ‘pala’ → pierce; ‘pogi’ → night; ‘pulu’ → glue\n\nObserve root + noun or root + verb structure.\n\nNow look for potential roots that might build “word” or “to exhaust”.\n\n---\n\nStep 2: Consider the word “to exhaust”.\n\nIn English, “to exhaust” can mean:\n- to use up completely\n- to deplete\n- to overuse\n\nWhat other verbs in the list represent depletion or use?\n\n- ‘puruha.ki’ → to boil, to bubble up → reminiscent of going out or overflowing?\n- ‘pala’ → to pierce → not clearly related\n- ‘huli’ → to turn over → not directly related\n- ‘mamasa’ → solid; ‘ma.tit mamasa’ → ice → cold, hard\n- ‘poagpoga = palpala’ → covered with holes → suggests a state of being perforated\n\nHypothesis: “to exhaust” may involve “to use up” or “to consume”.\n\nLook at ‘fäeag ‘u‘u’ → to use sign language → “to use” is present.\n\n“Use” is expressed via ‘fäeag’ or ‘susu’?\n\nBut ‘is susu’ → nipple → not directly “use”\n\nAlternatively, “to use” might be derived from a root like ‘fäeag’ or even ‘to‘a’ → hero — no clear link.\n\nAnother possibility: “to exhaust” may be a verb involving consuming or emptying.\n\nIs “to boil” (puhra.ki) related? Boiling can imply using up or depleting a substance.\n\nBut boiling is usually a physical process.\n\nWhat about word “cover”? “covered with holes” → poagpoga.\n\n“pala” → pierce → might be related to penetration, not exhaustion.\n\nAlternative: “to exhaust” might come from a compound involving “to use up” → certain verbs in Rotuman may express consumption or depletion.\n\nNo clear verb like “to empty” or “to use up” exists directly.\n\nBut “to use” is in 'fäeag ‘u‘u’ → so perhaps “to use” is encoded in ‘fäeag’.\n\nHence, “to exhaust” might be a derived form of “to use up” → thus possibly involving ‘fäeag’ + a suffix, or compound like ‘fäeag’ + something.\n\nHowever, no such form appears.\n\nAlternative: could “to exhaust” be formed by compounding a root meaning “to empty”?\n\nDoes Rotuman have a root for “empty”?\n\nNot directly.\n\nBut consider: “lower end” = ‘huni’ → maybe “end” or “limit”?\n\n“Year” = ‘fau’, “year’s end” = ‘a‘öf fau’ → so ‘a‘öf’ means “end of”.\n\nSo ‘end’ is a semantic root.\n\n“end” may be fundamental.\n\nThen, “to exhaust” could be “to reach the end of” → to use all of something → to go to the end.\n\nSo “to exhaust” = to go to the end → use up → to reach end.\n\nThus, possible form: ‘a‘öf’ + a verb root meaning “to go”?\n\nBut no such verb.\n\nAlternatively, could “to exhaust” be a compound like ‘a‘öf’ + ‘pala’ → to pierce to the end?\n\nUnlikely.\n\nAnother possibility: observe that some words have repeated structure.\n\nFor example: ‘is susu’ → nipple; ‘lala’ → deep; ‘ma.tit mamasa’ → ice → compound root with descriptive quality.\n\nThus, Rotuman may form abstract concepts via nominal compounds.\n\nBut no direct word for “word”.\n\nConsider: are there any words that could be interpreted as “word”?\n\n“Sign language” → ‘fäeag ‘u‘u’ → language → relates to “word”?\n\n“Language” → sign language → contains “word”?\n\nIn that case, “word” may be implied in “language” → perhaps the word “word” is not a standalone, but part of “language” or “communication”.\n\nTherefore, could “word” be a compound form involving the root ‘fäeag’?\n\nAlternatively, is there a root meaning “to speak”?\n\nNot directly.\n\nBut “language” (‘fäeag ‘u‘u’) may contain the concept of word.\n\nHence, “word” might be related to ‘fäeag’ or ‘u‘u’.\n\nGiven that, the only plausible root for “word” is from ‘fäeag’ — which means “to use” (as in sign language).\n\nSo: the verb ‘to use’ may be central.\n\nTherefore, “word” might be a noun derived from “to use” → “used thing”?\n\nNo such form.\n\nAlternatively, in some languages, “word” is a root in a compound.\n\nBut Rotuman has no clear word for “word”.\n\nTherefore, the only possible theoretical translation based on affixation and root usage would involve compound formation.\n\nPossible structure:\n\n- “word” → possibly derived from a root like ‘fäeag’ (to use, to employ) → entity used → item → could be “a thing used” → so “word” as \"a thing used\" → so verb root ‘fäeag’ + noun suffix?\n\nNo direct suffix.\n\nAlternatively, consider “to exhaust” = to go to the end → as in “to reach the end” → so could be formed with ‘a‘öf’ (end) + a verb root.\n\nFor example, ‘a‘öf’ + ‘to go’?\n\nBut no “go” known.\n\nBut in the list, ‘huni’ = lower end → end-related.\n\n‘a‘öf fau’ = year’s end → clearly “end”.\n\nThus, “end” is a key concept.\n\nHence, “to exhaust” may be “to reach the end of” → so verb structure: ‘a‘öf’ + verb root.\n\nBut verbs like ‘huag’ are used with nouns.\n\nBut perhaps a verb meaning “to exhaust” could be formed as ‘a‘öf’ + ‘huag’ → “to reach end of something”?\n\nNot plausible.\n\nAlternatively, “to exhaust” may be derived from “to use up” → “to use” is ‘fäeag’ → so ‘fäeag’ + ‘to be used up’?\n\nBut no such.\n\nAlternatively, is there a root meaning “to fill” or “to empty”?\n\n‘pulu’ → glue → not related.\n\n‘to boil’ → may overflow or deplete.\n\nBut still weak.\n\nAnother possibility: in some languages, “to exhaust” is formed from a stem meaning “to spend” or “to consume”.\n\nNo such word.\n\nConclusion: since no direct word for “word” or “to exhaust” exists, we must rely on linguistic patterns.\n\nRoots in the language:\n- ‘fa’ or ‘fau’ → year\n- ‘a‘öf’ → end\n- ‘fäeag’ → to use\n- ‘huag’ → strong, to be brave or to act in a way\n- ‘pala’ → to pierce\n- ‘huli’ → to turn over\n\nPattern: many compound nouns are formed by combining two roots.\n\nExample: ‘huag ‘el‘ele’ → impatient → verb + noun → root + root\n‘huag to‘a’ → courageous → similar\n‘hün kia’ → base of neck → noun + noun\n‘fau’ + ‘a‘öf’ → year’s end → noun + noun\n‘nu‘suar tiro’ → window → root + root\n\nSo compounds are known: A + B → new concept.\n\nThus, “word” might be formed as a compound like:\n- ‘fäeag’ + ‘pala’ → to use and pierce? → no\n- ‘fäeag’ + ‘kia’ → to use the base? → no\n\nBut perhaps “word” is a nominalization of “to use” → so a thing that is used → “used thing” → which could be encoded as ‘fäeag’ + noun?\n\nBut no noun suffix provided.\n\nAlternatively, “to exhaust” might be formed using ‘a‘öf’ + verb root.\n\nBut in the list, ‘a‘öf fau’ is “year’s end” — so ‘a‘öf’ is a prefix or middle element.\n\nCould there be a verb like ‘a‘öf’ + ‘huli’ → to turn over to the end? → not meaningful.\n\nAlternatively, could “to exhaust” be a verb meaning “to be used up”?\n\nThen it could be a derived verb from “to use” → ‘fäeag’ + suffix?\n\nBut no suffix is clear.\n\nAre there any other words that indicate depletion?\n\n“moafmofa” → littered with rubbish → not directly.\n\n“lala” → deep → not helpful.\n\nAnother observation: all nouns are either single or compound. No single word for “word” or “to exhaust”.\n\nBut the question asks for the *theoretically possible* translations — not necessarily a direct match.\n\nSo, what would be possible, given the affixation and compounding patterns?\n\nSo:\n- “word” → likely related to communication, expression → so possibly derived from ‘fäeag’ (to use) → therefore, a possible translation: ‘fäeag’ or a compound involving ‘fäeag’\n- But since ‘fäeag’ means “to use”, and “word” is a thing that is used, perhaps “word” = ‘fäeag’ as a noun (zero-marking) — plausible?\n\nNo evidence.\n\nBut in a compound like ‘fäeag ‘u‘u’ → sign language → so “word” is part of that.\n\nTherefore, the only plausible root is ‘fäeag’.\n\nThus, the possible translation of “word” could be a compound like ‘fäeag’ or a nominalized form.\n\nBut is there anything else?\n\nAnother idea: “to exhaust” = to deplete → to go to the end → as in “year’s end”.\n\nSo “to exhaust” might be formed as ‘a‘öf’ + a verb root → but no such verb.\n\nBut words like ‘puhra.ki’ → to boil → could be associated with depletion.\n\nAlternatively, perhaps “to exhaust” is formed from the root ‘to use’ and a suffix denoting completion.\n\nBut no known suffix.\n\nConclusion based on pattern:\n\n- “word” is not directly in list → is likely derived from a root meaning “to use” → so ‘fäeag’ might be the root → so possible translation: ‘fäeag’\n- “to exhaust” may be formed from root meaning “end” → ‘a‘öf’ → so ‘a‘öf’ + verb → but no verb found\n\nBut ‘a‘öf fau’ = year’s end → so the pattern of ‘end’ is established.\n\nTherefore, to exhaust = to reach the end → so could be a verb with ‘a‘öf’ + something.\n\nBut no such word.\n\nPerhaps the only theoretically possible forms are:\n- “word” → ‘fäeag’ (as “to use” may imply “thing used”)\n- “to exhaust” → ‘a‘öf’ (as in “end”)\n\nBut both are verbs or nouns.\n\nBut “to exhaust” must be a verb.\n\nThus, theoretically, “to exhaust” could be a compound derived from ‘a‘öf’ + a verb root.\n\nBut which?\n\nOnly possible verb root available is ‘huli’ (to turn over), ‘pala’ (to pierce), etc.\n\nNo clear link.\n\nBut again, no direct match.\n\nTherefore, based on pattern, the only possible formations are nominalized or compound formations rooted in known elements.\n\nThus:\n\n- “word” → possibly: ‘fäeag’ (as it is involved in language)\n- “to exhaust” → possibly: ‘a‘öf’ (as “end” implies exhaustion)\n\nHowever, “a‘öf’” is not a verb.\n\nSo even “to exhaust” may be formed as ‘a‘öf’ + something.\n\nBut no such thing exists.\n\nTherefore, the only theoretically possible forms are derived from patterns:\n\n- “word” → must be based on “language” or “to use” → ‘fäeag’\n- “to exhaust” → based on “end” → ‘a‘öf’\n\nThus, the only plausible theoretical translations are:\n\nd.1: fäeag \nd.2: a‘öf\n\nBut are these correct?\n\n- ‘fäeag’ = to use → not directly “word”\n- ‘a‘öf’ = end → not directly “to exhaust”\n\nBut they are the only available roots that relate to the concepts.\n\nIn linguistic theory, when we say “theoretically possible”, we mean forms that can be constructed from prefix/suffix rules present.\n\nGiven the compound pattern, we can say that a word like “word” could be formed from ‘fäeag’ (to use) → so word as “a thing used” → possible.\n\nSimilarly, “to exhaust” could be formed by applying “end” to a process → so ‘a‘öf’ + root (e.g., ‘huag’) → but not present.\n\nSo without any known forms, the only possible candidates are built from established roots.\n\nTherefore, the theoretically possible translations are:\n\nd.1: fäeag \nd.2: a‘öf\n\nThis is the best step-by-step inference from the available patterns.\n\n\\boxed{d.1: fäeag; d.2: a‘öf}", + "generated_tokens": 3233, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: fäeag; d.2: a‘öf", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 11168.0, + "ioling_final_answer_chars": 21.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "iid", + "sample_index": 2, + "output": "We are given a list of Rotuman words and their translations, and asked to infer the theoretically possible translations of two English words: **'word'** and **'to exhaust'**. We are to determine what these might be in Rotuman, based on observed patterns.\n\n---\n\nFirst, analyze the structure of the provided words. Many of them combine elements, suggesting that compound or derived words are built from meaningful stems.\n\nNote possible patterns:\n\n1. **Words that are compound or derived from prefixes and roots**:\n - ‘a‘öf fau’ → year’s end → ‘a‘öf’ (perhaps “end of”) + ‘fau’ (year)\n - ‘faeag ‘u‘u’ → to use sign language → ‘faeag’ (to use) + ‘u‘u’ (sign)\n - ‘huni’ → lower end → similar to ‘huni’ as a root\n - ‘huli’ → to turn over\n - ‘pogi’ → night\n - ‘pala’ → pierce\n\n2. **Stems that may indicate common features**:\n - Many verbs are formed using a root with a prefixed element (e.g., huag ‘el‘ele’ → impatient → huag (to be) + el‘ele (shallow)? Not clear)\n - ‘hün kia’ → base of the neck → hün (base) and kia (neck?)\n - ‘ma.tit mamasa’ → ice → ma.tit (coldness) + mamasa (solid)\n - ‘poagpoga = palpala’ → covered with holes → seems compound, possibly poa’ (to cover) + gopoga (with holes)? Or ‘pal’ (to cover?) + ‘pala’? But pala is \"to pierce\"\n\n3. **Repetition and root reuse**:\n - ‘fau’ = year\n - ‘pala’ = pierce\n - ‘nu‘suar tiro’ = window → ‘nu‘suar’ (door/window) + ‘tiro’ (spectacles)?\n - ‘nu‘sura’ = door → suggests ‘nu’su’ may be root for “door” or “opening”\n\n4. **Common roots**:\n - ‘is’ → sharp-pointed; ‘is susu’ → nipple → suggests ‘is’ is a root meaning something sharp or pointed\n - ‘to‘a’ → hero → likely a root meaning \"brave\" or \"courageous\"\n - ‘huag to‘a’ → courageous → huag (to be?) + to‘a’ (hero)\n\nLet’s now consider the two missing items:\n\n---\n\n**What could 'word' be in Rotuman?**\n\nThere is no word for \"word\" directly given. But look for possible root-based patterns.\n\nWe see:\n- ‘to‘a’ → hero\n- ‘huli’ → to turn over\n- ‘pala’ → pierce\n- ‘faeag’ → to use\n- ‘pogi’ → night\n\nNo clear compound that includes \"word\" or \"speech\".\n\nBut in many Austronesian languages, words for “word” or “speech” are formed from roots meaning “to speak” or “to say”. We see:\n- ‘pala’ = pierce — could it mean “to speak” by analogy? Not obviously.\n- ‘ka.lu’ = bracelet; to encircle — might suggest something around? Could be metaphor for \"a word around\"?\n- ‘rū huga’ = stomach ache — no analogy.\n\nBut we observe compound formation:\n- ‘nu‘suar tiro’ = window → suggests ‘nu‘suar’ (portal/opening) and ‘tiro’ (spectacles)?\n- ‘poagpoga = palpala’ → covered with holes → possibly ‘poa’ (cover) + ‘gopoga’ (holes) or ‘pal’ + ‘pala’\n\nSo in some compounds, a root is used with a modifier like ‘-a’, ‘-u’, ‘-ti’, etc.\n\nWhat about the root for “speech”? Is there evidence of something like “to say”?\n\nWe see:\n- ‘faeag ‘u‘u’’ → to use sign language → implies ‘faeag’ = to use (as a verb root)\n- ‘pala’ = pierce — maybe not directly related\n- ‘puli’ → not in list\n\nBut no verb like “to say” or “to speak”.\n\nSo the only way to meaningfully build \"word\" is via a root that means “a thing that is said” or “an utterance”. That might be built from a root like “to speak” or “to utter”.\n\nBut no such verb is given.\n\nHowever, in many Austronesian languages, **\"word\"** might be formed from a root like *lau*, *tala*, or *palu*, which can mean “speech” or “utterance”.\n\nAlternatively, given that ‘pala’ means pierce, and ‘pala’ might be related to “to pass through” (like a word passing?), or “an opening” — something like “a hole”?\n\nBut ‘poagpoga = palpala’ means “covered with holes” — could “pal” be related to “hole”?\n\n‘pala’ = pierce — but piercing may also imply making a hole. So “pala” could mean “to poke” or “to create a hole”.\n\nThen “pal” or “pala” could be a root meaning “hole”, “opening”, and so “word” could be metaphorically an opening or an utterance?\n\nBut is there a better path?\n\nNote: “word” might be related to “sign” or “a thing that is used”.\n\nLook again: ‘faeag ‘u‘u’’ → to use sign language → here, ‘faeag’ = “to use”, ‘u‘u’ = sign\n\nAlso, ‘is susu’ → nipple — “susu” might be a root; if su = point or nipple, and word might be like “a thing that points”?\n\nBut not compelling.\n\nAlternatively: in compound words, form like X Y → meaning of X and Y combined.\n\nBut “word” is not derivable from any given pair.\n\nWe do have:\n- ‘fau’ = year\n- ‘huni’ = lower end\n- ‘lala’ = deep\n- ‘mamasa’ = solid\n- ‘ma.tit’ = coldness\n\nNothing suggests “utterance” or “speech”.\n\nSo we must conclude: the word “word” is not directly present and not derivable from any given stems. But question asks: what would the **theoretically possible** translations be?\n\nSo what are the plausible forms based on linguistic patterns?\n\nIn Austronesian languages, compound words are common. Since we have:\n- ‘nu‘sura’ = door\n- ‘nu‘suar tiro’ = window → probably “door/window” or “opening”\n- ‘pala’ = pierce\n- ‘pala’ could be used in verbs or nouns\n\nCould “word” be something like “a thing that is spoken”?\n\nWe have ‘pala’ as a verb: “to pierce” — could it mean “to speak” via metaphor? (as if speaking pierces)? Unlikely.\n\nBut is there a word in the list that could be related?\n\n‘pogi’ = night — not related.\n\n‘to‘a’ = hero\n\n‘ka.lu’ = bracelet; to encircle — circular, like a ring\n\nCould “word” be a circular thing? Like a ring?\n\nIn some languages, “word” is linked to “ring” — for example, “a ring of speech”? Not clear.\n\nAlternatively, in Polynesian languages, “kau” (to say) or “lau” (speech) are roots.\n\nBut not in list.\n\nHowever, we see a root in the form **‘is’**, used in:\n- ‘is’ = sharp-pointed\n- ‘is susu’ = nipple\n\n“Nipple” is a body part — could a “word” be a “point”?\n\nAlternatively, could a word be formed from the root *tala* or *lau* — not given.\n\nBut without direct evidence, we can only consider plausible forms based on construction.\n\nPossible constituents:\n- Stems with *-a*, *-u*, *-ti*, *-su*, *-fa*, *-nu*, *-ma*, *-hun*, *-pala*\n\nA plausible stem for \"word\" might be **‘tala’** or **‘palu’**, but those are not in the data.\n\nAlternatively, from compound: ‘nu‘suar’ → door/window → so opening. “An opening” could be a metaphor for a “word” — something that opens up or reveals?\n\nBut we have no word for “opening” in the data.\n\nAlternatively, look at ‘poagpoga = palpala’ → covered with holes → so “holes” is a concept.\n\n“Holes” could be a metaphor for “words” (as in “words in a hole”)? Unlikely.\n\nIn absence of evidence, the only plausible route is that “word” might be formed from a root like **‘pal’** or **‘pala’** — with “pala” meaning both pierce and possibly “a thing pierced” or “an opening”.\n\nThus, **pala** is a sound or thing that enters or pierces — could “word” be a misspelled or morphed form?\n\nBut we have no support.\n\nAlternatively, note that “word” might be built from a root like *tul* (to say), *ula* (to speak), not here.\n\nBut is there a possibility that **‘mamasa’** = solid → “solid thing” → could “word” be something solid?\n\nNot directly.\n\nBack to compounds: in the list, several words are compound and use a root + modifier.\n\nExample:\n- ‘a‘öf fau’ → year’s end\n- ‘hün kia’ → base of neck\n- ‘huli’ → to turn over\n- ‘ma.tit mamasa’ → ice\n\nSo: root + noun or adjective\n\nThus, a word like \"word\" could be:\n- **‘palu na’** — if *palu* = word, *na* = thing?\nBut not supported.\n\nAlternatively, could “word” be a compound like ‘nu‘suar’ → door → and a door is something that opens — so a word could be something that opens?\n\nPerhaps a form like **nu‘suar** or **nu‘sura**?\n\nBut these mean “door” or “window”.\n\nStill not close.\n\nWithout any stem directly related to speech, the most plausible theoretical form based on construction patterns is that **word** might be derived from a root meaning “opening” or “speech”.\n\nGiven that:\n- There is no verbal root for “to speak”\n- But “pala” = pierce → as in “to pierce the air” or “to speak”?\n- In some cultures, “to speak” is linked to “to pierce” (as in piercing the air)\n\nNot convincing.\n\nBut in absence of any evidence, the only reasonable inference is that **“word”** might be a noun built from a root denoting an “utterance” or “entity”, possibly using a root like **pala** or **tala**, which is common in Austronesian languages.\n\nHowever, based on only the given words, we have no data supporting “word” being literally or metaphorically formed from any known part.\n\nTherefore, the **theoretically possible** translation must be one that fits a pattern — possibly a compound with a known root.\n\nLooking again: we have **‘pala’** = pierce — could a noun like “pala” mean “a word” in a figurative sense?\n\nAlternatively, **‘ka.lu’** → bracelet — circular, symbolic — could be associated with \"word\" (as in ring of sign)?\n\nBut no.\n\nAnother possibility: ‘huli’ = to turn over — so something that turns over — like a \"turn\" of speech? Not clear.\n\nWe are not finding evidence.\n\nBut the question says: \"you cannot translate 'word' and 'to exhaust' into Rotuman with certainty\" — so we must find the **theoretically possible** translations — i.e., forms that could arise through linguistic regularity.\n\nSo for “word”, consider that in many Polynesian languages, “word” is given by:\n- ‘tā’ (to speak), ‘loka’ (word), etc.\n\nBut in Rotuman, based on patterns we see:\n\nAll verbs end in a stem, e.g., ‘to‘a’ = hero (a noun), but verbs are like ‘huli’ = to turn over, ‘pala’ = to pierce.\n\nSo motion or action — perhaps “word” is not a verb.\n\nCould it be a noun?\n\nWe see both nouns and verbs.\n\nSo a noun like “a thing”?\n\nBut known nouns: ‘fau’ (year), ‘huni’ (lower end), ‘lala’ (deep), ‘mamasa’ (solid), ‘rū’ (stomach ache), ‘pogi’ (night), ‘niu’ (copra), ‘pulu’ (glue), ‘ka.lu’ (bracelet)\n\nSo “a thing” not given.\n\nBut what about ‘nu‘sura’ = door → could “word” be a “door” of speech?\n\nNo.\n\nGiven the lack of evidence, and the need to provide a *theoretically possible* form, a plausible compound would be one built from a known morpheme.\n\nFor instance, **'palu'** or **'tala'** might be used, but not in list.\n\nBut from the list: we have ‘pala’, and it's used as a verb and a noun?\n\nNot clearly.\n\nBut since we see that compound stems are built with a root + modifier (like a‘öf fau), perhaps “word” could be **‘talo’** or **‘pala’**, but again, not in data.\n\nWait — another candidate: **‘ka.lu’** = bracelet, to encircle — could a “word” be something that encircles? Like a ring?\n\nIn some languages, words are represented as “rings” — e.g., in “word of power”.\n\nThus, **ka.lu** (to encircle) — could “word” be a verb using that root?\n\nSo perhaps: **ka.lu** meaning “to encircle” — could “to say” be derived from that? Not directly.\n\nBut could “word” be **‘ka.lu’** as a noun? Meaning “a thing that encircles” — like a ring?\n\nPossible.\n\nAlternatively, in compound form, **‘ku lu’**? Unlikely.\n\nAnother idea: both ‘huli’ and ‘pala’ involve motion or action. But not leading to “word”.\n\nAt this point, the only resonant pattern is that in Austronesian languages, “speech” or “word” is often related to the body or gestures.\n\nWe see: ‘faeag ‘u‘u’’ = to use sign language — the root ‘faeag’ = to use.\n\nCould “word” be formed from a root meaning “to be used” or “to hold”?\n\nWe have ‘faeag’ = to use.\n\nSo “to use” — could a word be “something used”?\n\nBut “used thing”?\n\nWe have no such word.\n\nStill, if “word” is something used, could it be **‘faeag’**? But that means “to use”, not “a thing used”.\n\nNo.\n\nFinal thought: since we cannot derive it with certainty, the **theoretically possible** translation must be a form that fits a pattern of construction.\n\nGiven that many words are compound: A + B, where A is a root and B is a modifier — and many roots are shared or used with suffixes.\n\nFor “word”, a plausible form could be **‘pala’**, or **‘palu’**, or **‘talo’**.\n\nBut are any of these present? No.\n\nBut **‘pala’** is present in the list and means “to pierce” — which might be metaphorically related to “a sharp thing” — a word might be sharp?\n\nBut ‘is’ = sharp-pointed — so “sharp” is a root.\n\nSo “sharp thing” → possible for “word”?\n\nNot convincing.\n\nAlternatively, the root **‘fa’** appears in ‘a‘öf fau’ — meaning “end”, so “end of year”.\n\nCould “word” be an “end” of something?\n\nWe have ‘huni’ = lower end — so “end” is used.\n\nSo “word” might be “end of speech”? Like “the end”?\n\nWe have no word for “speech” or “finish”.\n\nBut “huni” = lower end — could be used to form “lower end of speech”?\n\nNot plausible.\n\nThus, after careful analysis, the only possible theoretical forms based on stems in the list are:\n\n- “word” could be **‘pala’** — due to metaphorical use of piercing as speech (though weak)\n- or **‘nu‘sura’** — as a portal or opening\n- or **‘is’** — sharp point, as a sharp word?\n\nBut none are convincing.\n\nHowever, return to the second part: **“to exhaust”**\n\nWe have no direct word for “to exhaust”.\n\nPossible verbs in list:\n- ‘to‘a’ — hero\n- ‘huli’ — to turn over\n- ‘huni’ — lower end (not verb)\n- ‘hün kia’ — to blow (of a hurricane)\n- ‘pucha.ki’ — to boil, to bubble up\n- ‘pala’ — to pierce\n- ‘piri’ — to curl\n- ‘ka.lu’ — to encircle\n\n“to exhaust” might involve the idea of “to use up”, “to empty”, “to blow out”?\n\nWe see:\n- ‘hün kia’ — to blow (of a hurricane) → could be linked to “to blow out” → as in “exhaust” or “empty”?\n\nIn semantic fields, “to blow” can mean to exhaust — e.g., “to blow out a candle” (to extinguish) — which is to exhaust.\n\nSo “to blow” is a strong candidate.\n\nWe also have:\n- ‘puhra.ki’ — to boil, to bubble up — not exhaustion\n\nSo only ‘hün kia’ involves blow, which could be related.\n\nTherefore, **“to exhaust”** could be related to ‘hün’ or ‘hün kia’.\n\nThe root **‘hün’** means “to blow” — possibly in the context of a hurricane.\n\n“to blow” — could mean to exhaust by force — e.g., “to blow out of energy”.\n\nSo the theoretically possible translation for “to exhaust” is **‘hün kia’** or simply **‘hün’**.\n\nGiven that the original phrasing", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13867.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "iid", + "sample_index": 3, + "output": "We are given a list of Rotuman words and their English translations, and asked to infer the theoretically possible translations of two abstract concepts: *‘word’* and *‘to exhaust’*, despite the lack of direct equivalents.\n\nStep 1: Look for semantic clues or patterned word formation.\n\nFirst, observe compound words and derivational patterns:\n\n- ‘a‘öf fau’ = ‘year’s end’ → suggests ‘a‘öf’ (a variant of ‘a‘ö’?) + ‘fau’ (year) → possibly ‘end of year’\n- ‘fäeag ‘u‘u’ = to use sign language → ‘fäeag’ (to use?) + ‘u‘u’ (sign?) → suggests ‘fäeag’ might mean ‘to use’ or ‘to operate’\n- ‘hulu ha.fu’ = to blow (hurricane) → ‘hül’ (to blow) + ‘ha.fu’ (rocky)? — but ‘ha.fu’ is listed as rocky\n- ‘hün kia’ = base of the neck → ‘hün’ (base?) + ‘kia’ (neck?) — suggests ‘hün’ could relate to base or bottom\n- ‘huni’ = lower end → again, lower end\n- ‘lala’ = deep → similar to ‘lala’ being deep\n- ‘pala’ = pierce → a verb\n- ‘pogi’ = night → a noun\n- ‘puruha.ki’ = to boil → verb\n- ‘kala.lu’ = bracelet; also to encircle → a verb meaning “to encircle”\n- ‘riamrima’ = shiny → adjective\n\nStep 2: Identify possible derivational heads.\n\nNotably, several forms are built using:\n\n- Suffixes: ‘-a’, ‘-u’, ‘-fa’, ‘-ti’, ‘-kia’, etc.\n- Prefixes: ‘hu’, ‘ha’, ‘mā’, ‘niū’, etc.\n\nWe see that many verbs are formed with roots and affixes.\n\nLook for ‘to exhaust’ → this implies something like \"to use up\", \"to deplete\", \"to consume completely\".\n\nIn the given list:\n- ‘ele’ → to be near\n- ‘ele’ (also) → shallow\n- ‘holo’ not listed, but ‘hulu’ → to blow (hurricane), ‘hün’ → base of neck\n- ‘huni’ → lower end\n- ‘to‘a’ → hero\n- ‘mamasa’ → solid\n- ‘ma.tit’ → coldness\n- ‘ma.tit mamasa’ → ice → so ‘ma.tit’ + ‘mamasa’ = ice → compound formation\n\nSo compound formation: A + B → new meaning, often extending the semantic field.\n\nWhat could ‘to exhaust’ mean in Rotuman?\n\nPossibility: use up, use completely.\n\nWe see:\n- ‘fäeag’ → to use sign language → possibly ‘to use’\n- ‘pala’ → to pierce → not directly related\n- ‘puri’ not present, but ‘poagpoga’ = palpala = covered with holes → ‘poag’ + ‘poga’ = covered with holes → possible compounding or internal structure\n\nBut ‘to use’ appears in ‘fäeag’ → so if ‘to use’ is possible, then ‘to exhaust’ might be a stronger version: to use completely?\n\nThus, “to exhaust” → could be derived from ‘to use’ + some depletive suffix?\n\nBut no such suffix is plainly given.\n\nAlternatively, could ‘to exhaust’ be equivalent to ‘to use up’?\n\nWe see ‘niu’ = copra → copra is used, but not in a volume or use context.\n\nWe see ‘pala’ = pierce → not related.\n\nWhat about ‘huli’ = to turn over → could relate to a physical process, not exhaustion.\n\nAnother path: words with the pattern of semantic extension.\n\nLook at compounds:\n\n- ‘a‘öf fau’ → year’s end → ‘a‘öf’ (end?) + ‘fau’ → year\n- ‘nu‘suar tiro’ → window\n- ‘nu‘sura’ → door\n\n‘tiro’ appears in ‘maf tiro’ = spectacles → so ‘tiro’ is likely a noun meaning “spectacles” or “lenses”.\n\nAlso, ‘ka.lu’ = bracelet; to encircle → verb ‘to encircle’ → so ‘kala’ may be root.\n\nNo direct verb meaning ‘to exhaust’ or ‘word’.\n\nNow, consider word → what could a ‘word’ be?\n\nIn many Austronesian languages, a word may be expressed through a root or compound involving the verb of \"to speak\", or \"to name\", or \"to denote\".\n\nWe have:\n- ‘fäeag ‘u‘u’’ = to use sign language → so ‘fäeag’ is “to use”\n- ‘to‘a’’ = hero → not clearly related\n\nBut is there a root for “to say” or “to speak”?\n\nNot given.\n\nAnother possibility: Austronesian languages often use root compounds.\n\nFor example, ‘ele’ appears in both “shallow” and “to be near”.\n\nIs there a root meaning “to name” or “to say”?\n\nNot directly.\n\nBut in Rotuman, “to speak” may not be directly listed.\n\nThus, the only way to form ‘word’ is probably through compounding or derivation.\n\nPossible candidate: ‘ma.tit’ = coldness → ‘ma.tit’ is cold; ‘mamasa’ = solid; so ‘ma.tit mamasa’ = ice → cold solid.\n\nSo compound formation is acceptable.\n\nNow, for ‘to exhaust’, could it be formed from ‘to use up’?\n\nWe have:\n- ‘fäeag’ = to use → so perhaps ‘fäeag’ + a depletive suffix?\n\nBut no such suffix is given.\n\nAlternatively, could 'to exhaust' be the same as \"to burn out\", \"to consume\"?\n\nWe have ‘puhra.ki’ = to boil, to bubble up → not quite.\n\n‘pala’ = to pierce → could go into an object, not a process of depleting.\n\nBut: ‘moafmofa’ = littered with rubbish → suggests a lack, a state of disorder.\n\nBut no verb of “to exhaust”.\n\nLikewise, no noun meaning “word”.\n\nTherefore, both words are not directly represented.\n\nBut the question asks: What would the *theoretically possible* translations be?\n\nSo not direct translations, but hypothetical based on root patterns and semantic fields.\n\nStep 3: Hypothesize based on available roots.\n\nFor ‘word’: \nIn many Austronesian languages, 'word' is derived from a root meaning \"to speak\" or \"to name\". \nWe have ‘fäeag’ = to use — which could be a base for \"to use (a thing)\", and \"to use\" might extend to \"to use a word\".\n\nSo “word” might be formed using a verb root like ‘fäeag’ or ‘to name’ or ‘to speak’.\n\nBut no direct root given.\n\nBut we also see:\n- ‘nu‘sura’ = door → compound of ‘nu’ + ‘su’ + ‘ra’\n- ‘nu‘suar tiro’ = window → same root\n\nSo compound formation is common.\n\nCould ‘word’ be something like ‘u‘u’? → ‘u‘u’ appears in ‘fäeag ‘u‘u’’ → meaning sign language.\n\n‘u‘u’ might mean “sign” → so sign language = language using signs.\n\nSo perhaps ‘u‘u’ = sign → and ‘word’ might be expressed as ‘word’, or a root meaning “unit of language”.\n\nAlternatively, is there a root meaning “thing” or “object”?\n\nWe have ‘fau’ = year → a concept.\n\n‘kia’ = neck → body part.\n\nNo clear “thing” root.\n\nBut: ‘huli’ = to turn over → could relate to a piece of something being flipped.\n\nAlternatively, given that no word for ‘word’ exists, and no direct translation, the only plausible candidates are derived from semantic roots.\n\nBut since no verb means “to say”, we cannot directly form ‘word’.\n\nThus, the only theoretically possible translations would be either compounds or derived forms involving roots that relate to language or naming.\n\nFor instance:\n- A word might be formed as *u‘u* (sign) or *fa* (related to year?) — no.\n\nBut given that *fäeag* means “to use”, and *u‘u* means sign, and signs are used in language, perhaps “word” is related to sign or name.\n\nSo, possibly: *u‘u* could be a possible candidate for a word (as sign), though not literal “word”.\n\nAlternatively, is there a root for “name”?\n\nNot listed.\n\nBut perhaps, abstractly, a possible word could be formed using a verb like *to name*, or *to speak*.\n\nBut no such root.\n\nSo: the only possible expressions are culturally or semantically grounded.\n\nBut the question is not to guess, but to give the *theoretically possible* translations.\n\nThus: based on patterns, what could a word be?\n\nPossibility: in Austronesian languages, words are often formed from verbs or nouns with affixes.\n\nWe see:\n- ‘pala’ = pierce\n- ‘piri’ = to curl\n- ‘poagpoga’ = covered with holes — compound\n\nCould ‘word’ be formed as a compound? Like ‘to say + thing’?\n\nNot evident.\n\nBut observe: ‘fau’ = year → a time-based concept.\n\nNo clear link.\n\nThus, both are missing.\n\nBut the logically possible translations, based on linguistically plausible derivation, are:\n\n- ‘to exhaust’ → could be derived from ‘to use up’ → which might be formed with a depletive suffix, or from ‘to use’ with an intensifier.\n\n‘to use’ appears in ‘fäeag’ → so if ‘to use’ is established, then ‘to exhaust’ = to use completely.\n\nSo → possible form: *fäeag* + something depletive.\n\nBut what depletive? No such suffix in examples.\n\nWe have: ‘moafmofa’ = littered with rubbish → state of being filled with, not exhausting.\n\nAnother path: linguistic pattern in compounding.\n\nWe have:\n- ‘ma.tit mamasa’ = ice → cold + solid\n- So multiple roots can compound\n\nThus, for ‘to exhaust’, could be: *to use* + *base* or *to consume*\n\nBut we have no such word.\n\nAlternatively, could ‘to exhaust’ be equivalent to ‘to use up’ → so based on ‘fäeag’, possibly *fäeag* with a depletive suffix.\n\nBut no suffix is in evidence.\n\nWhat about ‘to blow’? → ‘hül ha.fu’ → to blow (of hurricane)\n\nCould ‘to blow out’ be a form of ‘to exhaust’?\n\nPerhaps in metaphorical sense.\n\nBut no clear link.\n\nThus, the theoretically possible translations are:\n\n- For ‘word’: since there is no direct word, but language is based on signs and use, and ‘u‘u’ (sign) appears in ‘sign language’, a possible word could be *u‘u* (sign), or *fau* (year), but no better match. The strongest candidate is *u‘u*, as it relates to language.\n\nBut ‘u‘u’ = sign → not “word”.\n\nCould there be a root for “speech”?\n\nNot listed.\n\nAlternatively, a root like *kala* → encircle → could be used for “to speak in a circle” — not likely.\n\nSo, no direct candidate.\n\nBut in the absence of direct information, and given that in Austronesian languages, “word” may be expressed through a root with a meaning related to naming or sign, and “sign” is present as *u‘u*, it is plausible that *u‘u* could be used as a substitute or referent for “word” in a loose sense.\n\nSimilarly, for “to exhaust”, meaning \"to consume completely\", could be derived from a root like “to use”, which is *fäeag*, so possibly *fäeag* + depletive element.\n\nBut depletive isn't present.\n\nAlternative: perhaps “to exhaust” is the same as “to burn” — but we have ‘puhra.ki’ = to boil, to bubble — not burn.\n\nBut if boiling is involved in a state of being used up, it's weak.\n\nThus, based on the material, the only theoretically possible translations are:\n\n- ‘word’ → possibly *u‘u* (a sign, as in sign language) — a representation of a unit of language\n- ‘to exhaust’ → possibly *fäeag* (to use), extended to “to use up”, meaning to exhaust\n\nThus, the possible forms are:\n\nd.1: u‘u \nd.2: fäeag\n\nBut is *u‘u* a word? It appears in ‘fäeag ‘u‘u’’ — so yes, it's a known word.\n\nIs it a word in the sense of “word”? Possibly — as in the unit of language.\n\nAnd for ‘to exhaust’ — if ‘to use’ is the base, and that’s the only verb, then ‘to use’ could be the base, and “to exhaust” would be a stronger form.\n\nBut is there any indication of a depletive form?\n\nNo.\n\nBut in the absence of more, the most plausible forms based on available roots are:\n\n- Word → u‘u’ (as sign)\n- To exhaust → fäeag (to use, used up)\n\nAlternatively, could ‘to exhaust’ be formed with ‘to blow’? — no.\n\nThus, the only plausible base forms are those in the given data.\n\nTherefore:\n\nd.1: u‘u \nd.2: fäeag\n\nFinal answer:\n\n\\boxed{d.1: u‘u}; d.2: fäeag}", + "generated_tokens": 3037, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": false, + "boxed_error": "text_after_boxed_answer", + "boxed_text": "d.1: u‘u", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10468.0, + "ioling_final_answer_chars": 8.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "iid", + "sample_index": 0, + "output": "We are given a set of Jaqaru words and their English translations. Our task is to translate three words from Jaqaru into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe analyze the given data to find patterns.\n\nFirst, observe the structure of the known translations:\n\n- aq”ipsa — \"the cave too\" \n- aq”na — \"in the cave\" \n- qucxap”a — \"through the lake\" \n- qucxst”psa — \"from our1+2 lake too\" \n- chushp”a — \"his corner\" \n- chushuntxi — \"is it in the corner?\" \n- ishinhna — \"in my bed\" \n- marka — \"the town\" \n- markp”t”a — \"from his town\" \n- markstxi — \"is it our1+2 town?\" \n- ishma — \"your bed\" \n- utamt”a — \"from your house\" \n- p”ak”u — \"the pot\" \n- p”ak”unhpsa — \"my pot too\" \n- qaqat”a — \"from the cliff\" \n- yapsanpsa — \"in our1+2 field too\"\n\nWe note a recurring pattern involving “our1+2”, which implies a plural possessive form (likely \"our\" including speaker and hearer).\n\nWe also see that certain words have suffixes that appear to indicate \"in\", \"from\", \"is it\", \"too\", or \"our1+2\".\n\nLet’s identify the component markers.\n\nLook at:\n- chushp”a = \"his corner\"\n- chushuntxi = \"is it in the corner?\" → \"is it\" + \"in the corner?\"\n- marka = \"the town\"\n- markp”t”a = \"from his town\" → \"from\" + \"his town\"\n- markstxi = \"is it our1+2 town?\" → \"is it\" + \"our1+2 town?\"\n- utamt”a = \"from your house\"\n- p”ak”u = \"the pot\"\n- p”ak”unhpsa = \"my pot too\" → \"my\" + \"pot\" + \"too\"\n\nNote: \"too\" appears in:\n- aq”ipsa → \"the cave too\"\n- p”ak”unhpsa → \"my pot too\"\n- qucxst”psa → \"from our1+2 lake too\"\n- yapsanpsa → \"in our1+2 field too\"\n\nThe suffix -psa appears in:\n- aq”ipsa → \"the cave too\"\n- qucxst”psa → \"from our1+2 lake too\"\n- yapsanpsa → \"in our1+2 field too\"\n\nSo “-psa” seems to mark “too” or “also”.\n\nAlso, “-ntxi” appears in:\n- chushuntxi → “is it in the corner?” → includes “is it in?”\n- ishinhna → “in my bed” → contains “in”\n- markstxi → “is it our town?” → contains “is it”\n- utnhantxi → unknown\n\n“-ntxi” seems to mark a question form, often with “is it” or “in” or “from”.\n\nFor example:\n- chushuntxi = “is it in the corner?” → contains “in” and “is it”\n- markstxi = “is it our town?” → contains “is it”\n- utnhantxi → may be “is it in my house?”\n\nSimilarly:\n- ishinhna → “in my bed” → has “in”\n- utnha → “my house” → has “my”\n- utamt”a → “from your house” → has “from”\n\nSo the structure of the language seems to have:\n\n- A base noun (e.g., bed, house, pot, field, town, lake, cliff, corner)\n- Possessive prefixes: my, your, his, our (1+2)\n- Question form: “is it” + (in/through/from) + noun?\n- “too” suffix: -psa\n\nNow, look at each of the target forms:\n\n1. utnhantxi \n- Base: utnha = “my house” \n- -ntxi suggests a question: “is it in my house?” \n- So utnhantxi = “is it in my house?”\n\n2. yapp”psa \n- Base: yaputxi = “is it the field?” \n- yapp”psa: likely “the field too” → base “yapu” + “-psa” \n- yaputxi = “is it the field?” \n- So yapp”psa = “the field too”\n\n3. yapup”psa \n- yaputxi = “is it the field?” \n- yapup”psa: replaces “is it” with “the field too”? \n- But -p“psa seems to be the “too” suffix \n- yapu = field? \n- So yapup”psa = “the field too” → same as yapp”psa?\n\nWait — what is different?\n\nCompare:\n- yapp”psa → “the field too”?\n- yapup”psa → “the field too”?\n\nBut yapp”psa lacks the “in” or “is it” structure.\n\nLet’s reexamine the pattern.\n\nIn qucxst”psa → “from our1+2 lake too” \n→ “from our lake too” = “from” + “our lake” + “too”\n\nIn yapsanpsa → “in our1+2 field too” = “in” + “our field” + “too”\n\nSo the suffix -psa means “too”\n\nSimilarly:\n- aq”ipsa → “the cave too” → “the cave” + “too”\n- p”ak”unhpsa → “my pot too” → “my pot” + “too”\n\nSo if a word has -psa, it means “[noun] too”\n\nNow look at:\n- yapp”psa → likely “the field too” → so “the field” + “too”\n- yapup”psa → could be a variant?\n\nBut “yapup” might stem from “yapu” (field), so “yapup”psa = “the field too”\n\nBut why two forms?\n\nWait: perhaps the possessive or location is missing.\n\nAlternative: perhaps yapp”psa and yapup”psa are both about “the field” with different possessives?\n\nBut no possessive prefixes.\n\nyapp”psa: “yap” + “p” + “psa”? \nyaputxi = “is it the field?” → contains “utxi” → likely a question form\n\nSo compound words seem to have different suffixes.\n\nNow compare:\n\n- yaputxi → “is it the field?” → has “utxi” (probably marks question)\n- yapsanpsa → “in our1+2 field too” → has “san” = in + our\n\nWhat about:\n- yapp”psa → could be “the field too”\n- yapup”psa → could be “in the field too”?\n\nBut “in” is marked by “san” in yapsanpsa.\n\nBut in yapsanpsa, we have:\n- yapsa → “in our field”\n- -npsa → “too” → so “in our field too”\n\nSimilarly, if we have:\n- yapp”psa → “the field too”\n- yapup”psa → “in the field too”?\n\nBut no “in” in the suffix.\n\nBut observe: in aq”ipsa, we have “cave too” — “cave” with -psa → “too”\n\nIn qucxst”psa → “from our lake too” → “our lake” with -psa\n\nIn yapsanpsa → “in our field too” → “our field” with -psa\n\nSo -psa = “too” added to the noun phrase.\n\nNow, the base forms:\n- p”ak”u → “the pot”\n- p”ak”unhpsa → “my pot too” → “my pot” + “too”\n- aq”ipsa → “the cave too” → “the cave” + “too”\n\nSo the pattern is: noun + too → (base noun) too\n\nTherefore, yapp”psa → likely “the field too” \nyapup”psa → possibly miswritten or a variant?\n\nWait — what if “yapu” is “field”, so “yapup”psa = “the field too”?\n\nSame as yapp”psa?\n\nBut they differ in the prefix.\n\nyapp”psa vs. yapup”psa — different infix.\n\nBut in the known list, we have:\n- yaputxi = “is it the field?”\n- yapsanpsa = “in our field too”\n\nSo “yap” is stem.\n\nNow, in p”ak”u: “the pot” \np”ak”unhpsa: “my pot too” → “my” + “pot” + “too”\n\nSimilarly, aq”ipsa: “the cave too” → “the cave” + “too”\n\nSo “too” is suffix -psa.\n\nThus: any word ending in -psa means “[base noun] too”\n\nSo:\n\n1. utnhantxi \n- utnha = “my house” \n- -ntxi = in the house? or “is it in my house?” \n- chushuntxi = “is it in the corner?” → pattern: “is it in the [noun]?” \n- ishinhna = “in my bed” → “in my bed” \n- markstxi = “is it our town?” → “is it” + “our town” \n- so utnhantxi = “is it in my house?”\n\n2. yapp”psa \n- yapu = field \n- yapp”psa = “the field too” → “the field” + “too”\n\n3. yapup”psa \n- yapu = field \n- yapup”psa = “the field too” → same?\n\nBut the only difference is “p” vs “up” — could be a typo?\n\nWait — in the list, we have:\n- yaputxi = “is it the field?”\n- no direct form with “up”\n\nBut note: yapsanpsa = “in our1+2 field too” \n→ “in our field too” → so -npsa for “in our field too”\n\nBut here, yapp”psa and yapup”psa — both have -psa\n\nSo both should be “the field too”?\n\nBut why two forms?\n\nPossibility: the infix indicates possessor?\n\nLet’s look at the structure:\n\n- qucxst”psa → “from our1+2 lake too” — “from” + “our lake” + “too”\n- markstxi → “is it our town?” — “is it” + “our town”\n- chushp”a → “his corner”\n- chushuntxi → “is it in the corner?”\n\nSo “ntxi” marks question (is it in?), and “psa” marks “too”\n\nNow, in utnhantxi → “utnha” + “ntxi” → “my house” + “ntxi” → question like chushuntxi → so “is it in my house?”\n\nSimilarly, yapp”psa → “yap” + “p” + “psa” → could be “the field too” \nyapup”psa → “yap” + “up” + “psa” → could be “the field too”\n\nBut is there a difference?\n\nWait — perhaps “up” is a variant of “in”?\n\nBut in yapsanpsa, “san” = “in”\n\nAlso, yapsanpsa = “in our field too” → “in” + “our field” + “too”\n\nSo “san” = “in”\n\nBut here, no “san” — so not “in”\n\nTherefore, yapp”psa and yapup”psa both likely mean “the field too”\n\nBut the two words differ in infix — possibly a copying error?\n\nWait — check the original:\n\nIn the problem:\n\na. Translate into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa\n\nLook at the original words:\n\n- yapsanpsa → “in our1+2 field too”\n\nSo the “san” may be “in”\n\nBut “p” and “up” — no direct parallels.\n\nBut “yapu” appears in the known form in yaputxi = “is it the field?”\n\nSo “yapu” = field\n\nThen:\n\n- yapp”psa = “the field too”\n- yapup”psa = “the field too”\n\nThus, both mean the same thing.\n\nBut is there a reason to distinguish?\n\nPossibly typo or linguistic error? But more likely, the infix “p” vs “up” may be for different aspects.\n\nBut no such pattern is visible.\n\nAnother thought: maybe the possessive is formed differently.\n\nBut “yapp”psa” and “yapup”psa” — if “up” = in, then “yapup”psa = “in the field too”\n\nBut in yapsanpsa = “in our field too” → “in” + “our field” + “too”\n\n“in” is marked by “san”\n\nSo “up” does not mean “in”.\n\nTherefore, “yapup”psa” likely retains the same meaning as “yapp”psa” → “the field too”\n\nBut let’s look at the base form.\n\nIs there a word like “p” or “up” in the known list?\n\nWe have:\n- p”ak”u = “the pot”\n- p”ak”unhpsa = “my pot too”\n\nNo “p” or “up” compounds.\n\nTherefore, safest inference:\n\n- -psa = “too”\n- yapp”psa = “the field too”\n- yapup”psa = “the field too”\n\nBut wait — opposite: perhaps “yapu” is not “field”?\n\n“yaputxi” = “is it the field?” — so “yapu” is field.\n\nYes.\n\nSo both yapp”psa and yapup”psa are “the field too”\n\nBut why two forms?\n\nPossibly a typo — or one is possessive.\n\nBut no possessive marker.\n\nAnother idea: perhaps “p” vs “up” reflects a different suffix, but no such distinction is in the data.\n\nTherefore, it is plausible both are “the field too”\n\nBut let’s confirm:\n\n1. utnhantxi → “my house” + “ntxi” → “is it in my house?”\n\n2. yapp”psa → “the field too”\n\n3. yapup”psa → “the field too”\n\nYes.\n\nFinal translations:\n\n1. is it in my house? \n2. the field too \n3. the field too\n\nBut is there a difference between “yapp”psa and “yapup”psa?\n\nPerhaps “up” is a possessive?\n\nNo evidence.\n\nAll data shows that -psa = “too”\n\nThus, both are “the field too”\n\nAlternatively, is “yapup”psa = “in the field too”?\n\nThen we would need a “in” marker.\n\nBut “san” is used in yapsanpsa.\n\nNo “in” in yapp”psa or yapup”psa.\n\nSo it is not “in”.\n\nTherefore, both mean “the field too”.\n\nThus:\n\na.1: is it in my house? \na.2: the field too \na.3: the field too\n\n\\boxed{a.1: is it in my house?; a.2: the field too; a.3: the field too}", + "generated_tokens": 3513, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: is it in my house?; a.2: the field too; a.3: the field too", + "score_fraction": 0.3333333333333333, + "exact": 0.0, + "matched_units": [ + "a.1" + ], + "missed_units": [ + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.3333333333333333, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 1.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.3333333333333333, + "ioling_strict_substring_reward": 0.3333333333333333, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9839.0, + "ioling_final_answer_chars": 63.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "iid", + "sample_index": 1, + "output": "We are given a set of Jaqaru words and their English translations, and we are to translate three new words into English.\n\nLet’s analyze the patterns step by step.\n\nFirst, look at the known forms:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- chushuntxi = is it in the corner? \n- marka = the town \n- markp”t”a = from his town \n- ishinhna = in my bed \n- markstxi = is it our1+2 town? \n- ishma = your bed \n- utamt”a = from your house \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n\nWe now look at the target words:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nObserve the structure of known words:\n\n- \"ishinhna\" = in my bed → \"in\" + \"my\" + \"bed\" \n- \"markstxi\" = is it our1+2 town? → \"is it\" + \"our1+2\" + \"town\" \n- \"yaputxi\" = is it the field? → \"is it\" + \"the\" + \"field\" \n- \"yapsanpsa\" = in our1+2 field too → \"in\" + \"our1+2\" + \"field\" + \"too\"\n\nWe see that \"is it X?\" is formed with \"xstxi\" or \"utxi\" or \"p”psa\", etc., and these often follow a verb-like structure.\n\nBut more importantly, we can observe:\n\n- \"ishinhna\" → \"in my bed\" \n- \"ishma\" → \"your bed\" \n- \"utamt”a\" → \"from your house\" \n- \"utnha\" → \"my house\" \n- \"p”ak”unhpsa\" → \"my pot too\"\n\n\"unhpsa\" appears in \"p”ak”unhpsa\" = my pot too \n\"na\" in \"aq”na\" = in the cave \n\"t”a\" in \"markp”t”a\" = from his town \n\"stxi\" in \"markstxi\" = is it our town?\n\nSo the pattern of \"is it X?\" seems to be formed with \"-stxi\" or \"-utxi\".\n\nFor example:\n- chushuntxi → is it in the corner? \n- markstxi → is it our town? \n- yaputxi → is it the field?\n\nSo general pattern: X + \"utxi\" → \"is it X?\"\n\nTherefore:\n- yaputxi = is it the field?\n\nNow, look at the target words:\n\n1. utnhantxi \n - \"utnha\" = my house \n → \"utnhantxi\" likely = is it my house?\n\n2. yapp”psa \n - \"yap\" is in \"yaputxi\" and \"yapsanpsa\" → \"yap\" likely = the field \n - \"p”psa\" = ? \n Compare: \n - \"p”ak”u\" = the pot \n - \"p”ak”unhpsa\" = my pot too \n - \"yapsanpsa\" = in our1+2 field too → \"in our1+2 field\" \n → So \"p”psa\" may be a variant of \"pot\"? But in \"yapp”psa\", it's \"yap\" + \"p”psa\" \n\nWait — in \"yapsanpsa\" = in our1+2 field too → \"in + our1+2 + field + too\" \nCompare with \"p”ak”u\" = the pot \nSo \"p”ak”u\" = the pot, \"p”ak”unhpsa\" = my pot too → \"my + pot + too\"\n\nSimilarly, \"yapsanpsa\" = in + our1+2 + field + too\n\nNow, \"yap\" appears in:\n- yaputxi = is it the field?\n- yapsanpsa = in our1+2 field too → so \"yap\" = field\n\nSo \"yap\" = field\n\nThen:\n- yapp”psa → \"yap\" + \"p”psa\" \nWhat is \"p”psa\"?\n\nWe have \"p”ak”u\" = the pot → so \"p”ak”u\" = the pot \nIf \"p”psa\" is a form similar to \"pot\", perhaps without “ak”? Then maybe \"p”psa\" = the pot?\n\nBut that doesn’t make sense — \"p”ak”u\" = the pot, so why would \"p”psa\" be that?\n\nPerhaps it’s a different noun.\n\nCompare: \n\"utnha\" = my house \n\"utamt”a\" = from your house \n\"p”ak”u\" = the pot \n\"p”ak”unhpsa\" = my pot too \n\n\"unhpsa\" = my too? \n\"unh\" may be a particle meaning \"my\"\n\nSo in \"p”ak”unhpsa\" = my pot too → my + pot + too\n\nSimilarly, in \"utnha\" = my house\n\nSo \"unh\" = my\n\nNow \"utnhantxi\" → \"utnha\" + \"ntxi\"? \n\"utnha\" = my house \n\"ntxi\" = ? \n\"chushuntxi\" = is it in the corner? → \"chushu\" + \"ntxi\"\n\n\"markstxi\" = is it our town? → \"mark\" + \"stxi\" \n\"yaputxi\" = is it the field? → \"yap\" + \"utxi\"\n\nWait — this suggests that \"-ntxi\" might be an alternative to \"-stxi\" or \"-utxi\"?\n\nBut \"chushuntxi\" = is it in the corner? \n\"markstxi\" = is it our town? \n\"yaputxi\" = is it the field?\n\nSo in each case, the word ends with -stxi, -utxi, -ntxi?\n\n\"chushuntxi\" — ends with -ntxi \n\"markstxi\" — ends with -stxi \n\"yaputxi\" — ends with -utxi \n\"yapsanpsa\" — ends with -anpsa → different\n\nBut \"yaputxi\" and \"yapsanpsa\" have \"yap\" + \"utxi\" or \"yap\" + \"anpsa\"\n\nNotice:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too\n\nSo \"yap\" = field\n\nSimilarly, \"p”ak”u\" = the pot\n\nSo if \"yap\" = field, then \"yapp”psa\" = field + p”psa?\n\nPossibly, \"p”psa\" = pot?\n\nBut \"p”ak”u\" = the pot → with \"ak\" \n\"p”psa\" may be a simpler form or without the determining affix?\n\nBut we don’t have a word \"the pot\" without \"ak\".\n\nWait — maybe the \"p”psa\" is a form of \"the\" or \"field\"?\n\nBut no.\n\nAnother idea: the base form is attached to determiners and particles.\n\nLook at the patterns:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- aq”na → \"in\" + \"cave\" \n- aq”ipsa → \"the cave too\"\n\n\"psa\" and \"na\" are different particles.\n\nFrom the examples:\n- \"p”ak”unhpsa\" = my pot too → my + pot + too \n- \"markp”t”a\" = from his town → from + his + town \n- \"qucxst”psa\" = from our1+2 lake too → from + our1+2 + lake + too \n- \"yapsanpsa\" = in our1+2 field too → in + our1+2 + field + too \n\nSo we see the pattern:\n[Locative or question form] + [determiner] + [noun]\n\nAlso, the suffixes like “stxi”, “utxi”, “ntxi” seem to mark questions.\n\nSpecifically:\n- \"-ntxi\" in \"chushuntxi\": is it in the corner? \n- \"-stxi\" in \"markstxi\": is it our town? \n- \"-utxi\" in \"yaputxi\": is it the field?\n\nSo the pattern for \"is it X?\" is: [noun] + [stxi/ntxi/utxi]?\n\nWait — \"chushuntxi\" = is it in the corner? \nBut “chushp”a” = his corner → so “chushp”a” = his corner \nThen “chushuntxi” = is it in the corner? → perhaps \"in the corner\" → \"in\" + \"corner\"?\n\nBut the structure of the question isn’t just \"is it X?\" directly.\n\nAlternatively, consider the form:\n\n- “chushp”a” = his corner \n- “chushuntxi” = is it in the corner? \n→ “chush” + “untxi” → like \"in\" + \"corner\"? \n\nBut “ishinhna” = in my bed → \"in my bed\" \n\"ishma\" = your bed \n\"marka\" = the town \n\"markp”t”a\" = from his town → \"from his town\"\n\n\"markstxi\" = is it our town? → \"is it\" + \"our\" + \"town\"?\n\nSo again, \"is it X\" = [X] + stxi\n\nSimilarly:\n- yaputxi = is it the field? → \"yap\" + \"utxi\"\n\nSo: [noun base] + [stxi/utxi/ntxi] → is it [noun]?\n\nNow, the base nouns:\n- chushp”a” = his corner → base: chush + p”a\n- ishinhna = in my bed → base: ishin + hna → \"in my bed\"\n- ishma = your bed → \"your bed\"\n- utnha = my house\n- p”ak”u = the pot\n- marka = the town\n- qucxap”a = through the lake → \"through\" + \"lake\"\n- qucxst”psa = from our1+2 lake too → \"from\" + \"our\" + \"lake\" + \"too\"\n\nSo the question forms seem to be built on:\n\n[base noun] + [stxi/utxi/ntxi] → \"is it [noun]?\"\n\nAlso, \"in\", \"from\", \"through\" are locative prefixes.\n\nNow look at the target:\n\n1. utnhantxi \n→ utnha = my house \n→ \"ntxi\" instead of \"stxi\" or \"utxi\"? \nBut in \"chushuntxi\" → \"in the corner\" → used \"ntxi\" \n\"chushuntxi\" = is it in the corner? \n→ contains \"ntxi\"\n\nBut \"markstxi\" = is it our town? → \"stxi\" \n\"yaputxi\" = is it the field? → \"utxi\"\n\nSo which suffix is used?\n\n- \"ntxi\" → seems to appear in context with \"in\"?\n- \"stxi\" → with \"our\"?\n- \"utxi\" → with \"the\"?\n\nBut \"yaputxi\" = is it the field? → \"field\" with \"utxi\"\n\n\"chushuntxi\" = is it in the corner? → \"in\" + corner? → \"ntxi\"\n\n\"markstxi\" = is it our town? → \"stxi\"\n\nSo likely:\n- \"utxi\" = is it X? (the X)\n- \"ntxi\" = is it in X?\n- \"stxi\" = is it our X?\n\nBut check: \n\"markstxi\" = is it our town? → yes \n\"chushuntxi\" = is it in the corner? → yes \n\"yaputxi\" = is it the field? → yes\n\nNow, the suffix:\n- \"utxi\" = is it the X?\n- \"ntxi\" = is it in the X?\n- \"stxi\" = is it our X?\n\nNow, look at the first target: \n1. utnhantxi \n\n\"utnha\" = my house \nSo utnhantxi = is it in my house?\n\nBecause:\n- \"in\" + \"my house\" → \"ntxi\"\n\nThus, utnhantxi = is it in my house?\n\nSimilarly, \n2. yapp”psa \n\"yap\" = field \n\"p”psa\"? What is p”psa?\n\nWe have:\n- \"p”ak”u\" = the pot → pot \n- \"p”ak”unhpsa\" = my pot too → my pot too\n\nSo the base noun \"pot\" is formed with \"p”ak”u\"\n\nBut \"yapp”psa\" — does \"p”psa\" = pot?\n\nPossibly, but \"p”ak”u\" = the pot — so \"p”ak”\" might be the full form, \"p”psa\" might be a variant?\n\nBut in \"yapsanpsa\" = in our1+2 field too → in + our1+2 + field + too \n\"yap\" = field \n\"p”psa\" might be \"the pot\", but \"yapp”psa\" = field + p”psa?\n\nWait — perhaps \"p”psa\" is not a noun, but a locative?\n\nBut all forms have a noun base and a suffix.\n\nAlternatively, compare to \"chushp”a\" = his corner → noun \n\"marka\" = the town → noun\n\nSo \"p”psa\" may be a form of \"the pot\" or \"the field\"?\n\nBut \"yap\" is field.\n\nPerhaps the \"p”psa\" is a suffix or auxiliary?\n\nAlternatively, consider that in \"yapsanpsa\" = in our1+2 field too → \"in\" + \"our1+2\" + \"field\" + \"too\"\n\nBut \"yapsanpsa\" ends with \"anpsa\"\n\nNow, \"yapp”psa\" ends with \"p”psa\"\n\n\"yap\" + \"p”psa\" — might this be \"is it the field too\"?\n\nBut \"yaputxi\" = is it the field?\n\nSo \"yap\" + \"p”psa\" = is it the field too?\n\nThen \"p”psa\" = too?\n\nBut where is \"too\" in the other forms?\n\nExamples:\n- aq”ipsa = the cave too → \"too\"\n- p”ak”unhpsa = my pot too → \"too\"\n- qucxst”psa = from our1+2 lake too → \"too\"\n- yapsanpsa = in our1+2 field too → \"too\"\n\nSo \"too\" is marked by suffix: -psa?\n\nYes:\n- aq”ipsa → ends with \"ipsa\" — \"ipsa\" might be base\n- p”ak”unhpsa → ends with \"unhpsa\" → \"hpsa\"\n- qucxst”psa → ends with \"st”psa\" → \"st”psa\"\n- yapsanpsa → ends with \"anpsa\"\n\nSo the suffix “-psa” marks \"too\"?\n\nIn \"aqpipsa\" → \"the cave too\" → so \"-psa\" = too\n\nIn \"p”ak”unhpsa\" → \"my pot too\" → \"unhpsa\" → \"-hpsa\", but \"hpsa\" could be \"too\"\n\nIn \"qucxst”psa\" → \"from our1+2 lake too\" → \"-st”psa\" → so \"-psa\" is a marker for \"too\"\n\nIn \"yapsanpsa\" → \"in our1+2 field too\" → \"-anpsa\"\n\nThus, \"-psa\" or \"-hpsa\", \"-st”psa\", \"-anpsa\" → all contain \"psa\" and mean \"too\"\n\nTherefore, any word ending in \"-psa\" has \"too\"\n\nNow, back to target:\n\n2. yapp”psa \n\"yap\" + \"p”psa\" → \"p”psa\" = too? \nSo yapp”psa = the field too?\n\nBut \"yap\" = field → \"the field too\"\n\nSimilarly, 3. yapup”psa → yap + up”psa → \"up”psa\" = too → \"the field too\"?\n\nWait — both end with \"psa\" → so both mean \"too\"?\n\nBut is \"yapp”psa\" or \"yapup”psa\" a question?\n\nOnly if the suffix is -utxi, -ntxi, or -stxi.\n\n\"yaputxi\" = is it the field?\n\n\"yapp”psa\" does not end with \"utxi\" or \"stxi\" or \"ntxi\" → it ends with \"p”psa\" → which is \"too\"\n\nSo this is not a question — it is an affirmation with \"too\"\n\nSimilarly, \"yapup”psa\" = the field too?\n\nBut is there a similar form?\n\n\"p”ak”unhpsa\" = my pot too \n\"aq”ipsa\" = the cave too \n\"qucxst”psa\" = from our1+2 lake too\n\nSo \"too\" is marked by -psa\n\nTherefore:\n- yapp”psa = the field too \n- yapup”psa = the field too?\n\nBut \"yapp”psa\" and \"yapup”psa\" — both have \"yap\" + \"p”psa\" or \"up”psa\"?\n\nBut \"up”psa\" → could it be an error?\n\nWait — the word is \"yapup”psa\" — perhaps \"up”\" is a variant of \"the\"?\n\nBut look at \"yaputxi\" = is it the field?\n\nMaybe \"up”\" is distinct.\n\nBut we have no other word.\n\nAlternatively, could \"up”\" be a form of \"our", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10493.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "iid", + "sample_index": 2, + "output": "We are given a set of Jaqaru words and their English translations, and asked to translate three new words into English.\n\nFirst, analyze the patterns in the given data:\n\n1. \"aq”ipsa\" = \"the cave too\" \n \"aq”na\" = \"in the cave\" \n \"qucxap”a\" = \"through the lake\" \n \"qucxst”psa\" = \"from our1+2 lake too\" \n → \"our1+2\" appears in \"qucxst”psa\", \"markstxi\", \"yapsanpsa\"\n\n2. \"chushp”a\" = \"his corner\" \n \"chushuntxi\" = \"is it in the corner?\" \n \"marka\" = \"the town\" \n \"markp”t”a\" = \"from his town\" \n \"markstxi\" = \"is it our1+2 town?\" \n → \"our1+2\" appears with possessive markers\n\n3. \"ishinhna\" = \"in my bed\" \n \"ishma\" = \"your bed\" \n \"p”ak”u\" = \"the pot\" \n \"p”ak”unhpsa\" = \"my pot too\" \n \"qaqat”a\" = \"from the cliff\" \n \"yaputxi\" = \"is it the field?\" \n \"yapsanpsa\" = \"in our1+2 field too\"\n\nWe observe that:\n- Possessive markers: \n - \"my\" → appears in ishinhna (my bed), p”ak”unhpsa (my pot too) \n - \"your\" → ishma \n - \"his\" → chushp”a \n - \"our1+2\" → in qucxst”psa, markstxi, yapsanpsa\n\nStructure of phrases: \n- \"Xstxi\" seems to be a question: “is it X?” \n → chushuntxi = \"is it in the corner?\" \n → ishinhna = \"in my bed\" (not a question) \n → markstxi = \"is it our1+2 town?\"\n\nSo: \n- “…stxi” → likely means “is it…” (question form) \n- “…hpsa” → added after a noun, often with \"too\" \n → aq”ipsa = “the cave too” \n → p”ak”unhpsa = “my pot too”\n\nThus:\n- \"hpsa\" = “too” \n- \"stxi\" = “is it?”\n\nNow look at the verbs or expressions:\n- \"yaputxi\" = “is it the field?” → “yap” + “utxi” → “is it the field?” \n- \"yapsanpsa\" = “in our1+2 field too” → “in” + “our1+2” + “field” + “too” \n\nSo:\n- \"yap\" + \"utxi\" = is it the field? \n- \"yap\" + \"san\" + \"p”sa\" = in our1+2 field too? \nBut yapsanpsa = in our1+2 field too → so \"san\" likely means \"our1+2\"\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → \"qucx\" = from lake; \"st\" = our1+2? \nBut “qucxst”psa” has “st”, which parallels “san” in “yapsanpsa”\n\nSo:\n- “st” → our1+2 possession \n- “san” → our1+2 possession? \nWait: “qucxst”psa” has “st” → “from our1+2 lake too” \n“markstxi” → “is it our1+2 town?” \n“yapsanpsa” → “in our1+2 field too” \n\nSo: \n- “st” has \"our1+2\" when attached to a noun in a locative or possessive context \n- “san” also appears in “yapsanpsa” → maybe “san” = “our1+2”? \nBut “qucxst”psa” has “st”, “markstxi” has “st”, “yapsanpsa” has “san” — consistent? \n\nAlternatively, \"st\" and \"san\" are similar? Or one is a variant?\n\nWait: “qucxst”psa” → from our1+2 lake too \n“yapsanpsa” → in our1+2 field too \n\nSo both have “our1+2” and “too” (hpsa) \nBut:\n\n- “qucxst”psa” = from + our1+2 lake + too \n- “yapsanpsa” = in + our1+2 field + too \n\n“st” and “san” are different suffixes.\n\nCould it be that:\n- “st” = from (in locative) \n- “san” = in (in locative)\n\nCheck:\n\n- “qucxst”psa” = from our1+2 lake too → “qucx” = lake, “st” = from → so “st” = from \n- “yapsanpsa” = in our1+2 field too → “yap” = field, “san” = in → so “san” = in\n\nBut “markstxi” = is it our1+2 town? → “st” is in “town” — not “in” or “from”\n\nAlternatively, consider:\n- “markstxi” = is it our1+2 town? → “st” appears \n- “utamt”a” = from your house → “utam” = house, “t” = from → so “t” = from?\n\nWait: “utamt”a” = from your house \n“utnha” = my house \n“utamt”a” = from your house → has “t” at end \n\nSimilarly, “qucxst”psa” = from our1+2 lake too → has “st” \n“qucxap”a” = through the lake → “ap” = through\n\nSo maybe:\n- “t” = from → in “utamt”a” \n- “st” = from → in “qucxst”psa” \n- “st” also in “markstxi” → is it our1+2 town? → so “st” = from or possessive?\n\nBut “markstxi” is a question: “is it our1+2 town?” → not “from our1+2 town”\n\nThus, “st” is not exclusively “from”.\n\nWait — the structure of “acq”na = “in the cave” \n“chushp”a” = his corner \n“ishinhna” = in my bed → “in” + “my bed”\n\nPossibility:\n- “in” = “ih” or “an”? \nWe see:\n- ishinhna → “in my bed” \n- ishma → your bed \n→ could “inh” be “in”?\n\nSimilarly, “markstxi” → “is it our1+2 town?” → “st” appears, but with “is it”\n\nCompare:\n- chushuntxi → “is it in the corner?” → “untxi” → “in”?\n\n→ This is promising.\n\nchushuntxi = “is it in the corner?” \n→ So “unt” + “xi” = “is it in the corner?”\n\nSimilarly:\n- ishinhna = “in my bed” → “inh” + “na” \n- ishma = “your bed” → “ish” + “ma” \n→ So “inh” might be “in”\n\nAnd “unt” in chushuntxi → “in”?\n\nYes — \"unt\" and \"inh\" both seem to be forms of “in”\n\nSo:\n- “unt” → in (in chushuntxi) \n- “inh” → in (in ishinhna)\n\nSo “in” is encoded as either “inh” or “unt”? Why?\n\nchushuntxi → “is it in the corner?” → “unt” + “xi” \nishinhna → “in my bed” → “inh” + “na”\n\nNot exactly the same. But perhaps the “in” marker is fixed and follows the noun.\n\nNow consider the questions:\n- “yaputxi” = is it the field? → “yap” + “utxi” → so “utxi” = “is it the field?” \n- “chushuntxi” = is it in the corner? → “chushuntxi” → “untxi” = is it in the corner?\n\nSo likely:\n- “untxi” = “is it in X?” \n- “yaputxi” = “is it the field?” → so “yap” + “utxi” = is it the field?\n\nWait — “yap” is field, “utxi” = is it?\n\n→ so “utxi” = “is it?”\n\nSimilarly, “chushuntxi” = “is it in the corner?” → “untxi” = “is it in the corner?” — so the marker “unt” = in?\n\nThen “utxi” = “is it?”\n\nYes — consistent.\n\nSo pattern:\n- “x + utxi” = “is it x?” \n- “x + st” = “our1+2 x” \n- “x + hpsa” = “x too” \n- “x + t” = “from x?” → e.g. “utamt”a = from your house\n\nNow check:\n- “utamt”a” = from your house → “utam” = house, “t” = from \n- “qucxst”psa” = from our1+2 lake too → “qucx” = lake, “st” = our1+2, “psa” = too\n\nWait — “qucxst”psa” has “st” and ends in “psa”\n\n“psa” appears in:\n- aq”ipsa” = the cave too → “ipsa” = the cave too \n- p”ak”unhpsa = my pot too → “unhpsa” = my pot too \n- qucxst”psa” = from our1+2 lake too → “st” + “psa” = “from our1+2 lake too” \n- yapsanpsa = in our1+2 field too → “san” + “psa” = in our1+2 field too\n\nSo “psa” = “too”\n\nThus:\n- “psa” = “too”\n- “utxi” = “is it?”\n- “inh” or “unt” = “in”\n- “st” or “san” = “our1+2”\n\nNow, exponents:\n- “st” = “our1+2” → appears in “qucxst”psa”, “markstxi” \n- “san” = “our1+2” → in “yapsanpsa”\n\nSo both “st” and “san” denote “our1+2” — possibly variants?\n\nBut we need to see how the base nouns work.\n\nNow translate the target:\n\n1. utnhantxi\n\nBreak it down:\n- “utn” + “ha” + “t” + “xi” ?\n\nBut “utnha” = “my house” → so “utnha” = my house \n“utamt”a” = from your house → “utam” = house → “t” = from\n\n“utnhantxi” → “utn” + “ha” + “t” + “xi”\n\nBut “utnha” = my house → so “utnh” = my house?\n\nThen “t” + “xi” → “from is it?” — not likely.\n\nWait: “utnha” = my house → so “utnh” = my house with suffix “a”?\n\nBut “utnha” = my house \n“utamt”a” = from your house → “utam” = your house\n\nSo:\n- “utna” = house? \n- “utnha” = my house \n- “utamt”a” = from your house \n\nThen “utnhantxi” = (my house?) + “t” + “xi”\n\nBut “t” = from? \nSo “from my house?” → but “utamt”a” is “from your house”\n\nSo perhaps “t” is used with “from” and specifically with “your”?\n\nBut we don’t have “from my house” in the examples.\n\nAlternatively, is “utnhantxi” = “is it in my house?”?\n\nLook — “ishinhna” = in my bed → “in” + “my bed” \nSo “in” = “inh” or “unt”?\n\nIn “chushuntxi” → “in the corner” → “untxi”\n\nIn “ishinhna” → “in my bed” → “inh” + “na” → so “inh” is “in”\n\nBut “in” appears in:\n- in my bed → in\n- is it in the corner? → in\n\nSo the “in” marker is a prefixed element.\n\nNow, “utnhantxi” — does it contain “t”?\n\nPossible split:\n- “utnha” = my house \n- “t” = from? \n- “xi” = is it?\n\nBut “t” in “utamt”a” = from your house — so “t” = from\n\nSo “utnhantxi” → “from my house?” or “is it from my house?”\n\nBut no such phrase.\n\nAlternatively: is “utnha” = the house, and “t” + “xi”?\n\nBut “utnha” + “t” + “xi” → from my house?\n\nBut we don’t have a word for “from my house” — only “from your house”\n\nWait — “utnha” = my house → so “t” signifier must be “from”\n\nSo “utnhantxi” = from my house is it? → “is it from my house?”\n\nBut the example “utamt”a” = from your house — so “from your house” is expressed via “utam” + “t” + “a”\n\nBut here it is “utnha” + “t” + “xi”\n\nSo could “utnhantxi” be “is it from my house?”\n\nYes — because “xi” = “is it?” \nAnd “t” = from\n\nNow check if construction is consistent.\n\nWe have “utamt”a” = from your house \n→ structure: noun (your house) + t + a \n“utnha” = my house → noun with “ha” \nSo “utnhantxi” = my house + t + xi → “from my house is it?” → “is it from my house?”\n\nThat makes sense.\n\nSimilarly:\n2. yapp”psa\n\n“yap” = field \n“p”psa” → what?\n\n“yaputxi” = is it the field? → so “yap” + “utxi” \n“yapsanpsa” = in our1+2 field too → “yap” + “san” + “psa”\n\n“psa” = too \n“san” = our1+2\n\nSo “p”psa” → could be “yap” + “p”psa” → but “p” might be possession?\n\n“p” not seen.\n\nAlternatively, “yapp”psa” = field + “p” + “psa”\n\nBut “p” is not seen.\n\nWait — “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” = my, “psa” = too\n\nSo “hpsa” = too\n\nSo “psa” is likely a suffix meaning “too”\n\nIn “yapsanpsa” → “san” + “psa” = in our1+2 field too\n\nSo “psa” = too\n\nNow, “yapp”psa” = yap + p + psa → what?\n\nCould “p” be “my”?\n\nThen “my field too”?\n\nYes — because:\n- “p”ak”unhpsa” = my pot too → “unh” = my, “psa” = too \n- “unh” might be “my”\n\nBut “yapp”psa” is “yap” + “p” + “psa” → not “unh”\n\nSo does “p” = my?\n\nNo — in “p”ak”u” = the pot → “ak” is pot, “p” is beginning?\n\n“p”ak”u” → “p” + “ak” → pot \n“p”ak”unhpsa” → “p” + “ak” + “unh” + “psa” → my pot too\n\nSo “unh” = my\n\nBut “yapp”psa” = “yap” + “p” + “psa” → where is “unh”?\n\nPossibly a typo or mismatch?\n\nWait — is it “yap + p + psa” or “yap + p” + “psa”?\n\nCould “p” be a possessive?\n\nWe have only one other possessive: “unh” = my\n\n“t” = your? \n“utamt”a” = from your house → “your” house → “utam” = your house?\n\nYes — so “utam” = your house\n\n“utnha” = my house\n\n“chushp”a” = his corner\n\nSo only “my”, “your”, “his”, “our1+2”\n\n“yapp”psa” → no possessive — so what?\n\nPossibly “the field too”?\n\nBut “yaputxi” = is it the field?\n\n“yapsanpsa” = in our1+2 field too\n\nSo “yap” + “psa” = the field too?\n\nBut “psa” is “too”\n\nSo “yap” + “psa” = the field too?\n\nBut the word is “yapp”psa” — with “p” between?\n\nCould it be a typo in the problem? Or is “p” the possessive?\n\nBut we don’t have “p” = my.\n\nAlternative — perhaps the “p” is part of a root?\n\nGiven that “p”a” is used in “p”ak”u”, but is not used as a standalone possessive.\n\nAnother possibility: “yapp”psa” = in our1+2 field too?\n\nBut “yaps", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10256.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "iid", + "sample_index": 3, + "output": "We are given several Jaqaru words and their English translations. Our task is to translate three new Jaqaru words into English: \n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nStep 1: Look for patterns in the given data.\n\nBase forms and their meanings:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- ishinhna → in my bed \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishma → your bed \n- utamt”a → from your house \n- utnha → my house \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nStep 2: Identify the structure of questions.\n\nNote that:\n- chushuntxi → \"is it in the corner?\" \n- markstxi → \"is it our1+2 town?\" \n- yaputxi → \"is it the field?\" \n- yapsanpsa → \"in our1+2 field too\" \n\nSo, \"xptxi\" appears in questions like “is it in X?” \n- chushuntxi = is it in the corner? \n- markstxi = is it our1+2 town? \n- yaputxi = is it the field? \n\nSo the pattern: \n“X + txi” = “is it in X?” or “is it X?” \n\nAlso, “X + npsa” = “in our1+2 X too” \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n\nSo “X + npsa” → “in our1+2 X too” or “my X too”?\n\nBut “p”ak”unhpsa” = my pot too → “unh” may mark “my” and “psa” marks “too”?\n\nWait: the pattern of “X + psa” for “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nSo: \n- “X + psa” → “too” (with some modifier)\n\nBut “unh” appears in p”ak”unhpsa → likely “my” \n- utnha → my house \n- utamt”a → from your house \n\nSo “unh” = my, “t” = your?\n\nAlso: \n- markp”t”a → from his town → “p”t”a” → his \n- chushp”a → his corner → “chushp”a” \n→ “p””a” → his? \n→ “t” → your? \n→ “unh” → my?\n\nThus, possessive markers: \n- unh → my \n- t → your \n- p → his? (in chushp”a → his corner) \n- p”t”a → from his town → his? \n→ markp”t”a → from his town \n\nSo there are possessive affixes: \n- “unh” → my \n- “t” → your \n- “p” → his \n\nAlso, “x + txi” = is it in X? \n- chushuntxi = is it in the corner? \n- ishinhna = in my bed → not a question \n- markstxi = is it our1+2 town? \n- yaputxi = is it the field? \n\nSo “x + txi” = “is it in X?” \n\nNow, “x + npsa” = in our1+2 X too \n\nBut note: \n- aq”ipsa = the cave too \n- qucxst”psa = from our1+2 lake too \n- yapsanpsa = in our1+2 field too \n→ So “X + npsa” = in our1+2 X too \n\nSimilarly, “X + psa” = the X too? \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n\nSo different markers for “too” depending on possession?\n\nNow look at target words:\n\n1. utnhantxi \n - “utnha” → my house \n - “utnhantxi” → likely “is it in my house?” \n → because “utnha” + “txi” → is it in my house? \n → similar to “ishinhna” = in my bed, “markstxi” = is it our1+2 town? \n → “utnha” + “txi” = is it in my house?\n\n2. yapp”psa \n - “yap” → the field? \n - yaputxi = is it the field? \n - yapp”psa → “yap” + “p” + “psa” \n - Could this be “the field too”? \n → Compare to “yapsanpsa” = in our1+2 field too \n → But “yapp”psa” = “yap” + “p” + “psa” \n → Not “yap” + “psa” \n → “yap” + “p” → his field? \n → But “p” is possessive (his), “psa” = too \n\nSo “yapp”psa” = his field too?\n\nBut no direct translation. But we have: \n- “p”ak”u” → the pot \n- “p”ak”unhpsa” → my pot too \n- “p”ak”u” + “unh” + “psa” → my pot too \n- “yap” → the field? (from yaputxi) \n- “yaputxi” = is it the field? \n- “yapsanpsa” = in our1+2 field too → “yap” + “san” + “psa” → “san” = our?\n\nBut “yapp”psa” → “yap” + “p” + “psa” → “p” = his → so “his field too”?\n\nIs that consistent?\n\nYes: \n- “chushp”a” = his corner \n- “markp”t”a” = from his town \n- So “p” = his \n→ So “yap” + “p” + “psa” = his field too \n\n3. yapup”psa \n- “yap” + “u” + “p” + “psa” → “u” = ?\n\nIs “u” a possessive?\n\nPossessive markers so far:\n- unh → my \n- t → your \n- p → his \n- Qu? → “qucx” → lake? \n- No “u” in existing examples.\n\nCould “up” be a form of “our”?\n\nIn “yapsanpsa” → in our1+2 field too \n→ “s” might be possessive for “our” → “san”?\n\nSimilarly, in “qucxst”psa” → from our1+2 lake too → “st”?\n\nNo, “qucxst”psa” — likely “st” = our?\n\nBut in “markstxi” → is it our1+2 town? → “st” = our?\n\nYes! \n- markstxi → is it our1+2 town? → “st” = our \n→ Similarly, “qucxst”psa” → from our1+2 lake too → “st” = our \n→ “yapsanpsa” → in our1+2 field too → “san” = our? But “san” is a different form?\n\n“san” vs “st”? Could be variant spelling or different possessive.\n\nBut in “yapsanpsa”, the possessive part is “san” → possibly “our”.\n\nSimilarly, “yapup”psa” → “yap” + “up” + “psa” \n→ If “up” = our → then “our field too”?\n\nBut “yapsanpsa” = in our1+2 field too → with “san”\n\nIs “san” and “up” same?\n\nPossibly “up” is a variant of “our” or equivalent?\n\nWait — possible affixes: \n- unh → my \n- t → your \n- p → his \n- st → our1+2 \n- But “san” appears in “yapsanpsa” → might be a form of “our”\n\n“up” is not in any existing word.\n\nBut look at structure:\n\n- yaputxi = is it the field? → “yap” + “utxi” \n- yapsanpsa = in our1+2 field too → “yap” + “san” + “psa” \n- yapup”psa = “yap” + “up” + “psa”\n\nPossibility: “san” and “up” are both “our” in different forms?\n\nBut \"san\" is in \"yapsanpsa\", \"up\" is in \"yapup”psa\"\n\nAlternatively, is “up” a combining form?\n\nNote that in the word “yapp”psa”, we have “p” = his → so his field too\n\nIn “yapup”psa”, if “up” = our → then our field too\n\nSupport: \n- “qucxst”psa” → from our1+2 lake too — “st” likely = our \n- “markstxi” → is it our1+2 town? — “st” = our \n- “yapsanpsa” → in our1+2 field too — “san” = our \n\nSo “san” and “st” are both possessive for “our”\n\nAre “san” and “up” the same?\n\nPossibly a typo or morphological variation?\n\nBut “up” does not appear in any known possessive.\n\nWait — could “up” be a mistake for “us” or “our”?\n\nLook at spelling: \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n- yapup”psa → our field too? \n\nPossibility: “up” is a possessive form of “our” used in “too” constructions.\n\nBut we have no such construction. Only “san” for “our”.\n\nAlternatively, is there a pattern for “too”?\n\n“X + psa” → too \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” adds “too” → so “yap” + “psa” → the field too? \nBut “yap” alone = the field? (from yaputxi)\n\nSo “yap” = the field \n“yap + psa” = the field too \nBut “yapp”psa” = yap + p + psa → not “yap + psa” \n\nSimilarly, “yapup”psa” = yap + up + psa \n\nSo if “p” = his → yapp”psa” = his field too \nif “up” = our → yapup”psa” = our field too \n\nBut we need to check if “up” = our.\n\nDo we have another word with “up”?\n\nNo.\n\nBut “st” and “san” are both used for “our” — perhaps “up” is a variant?\n\nAlternatively, “up” is a reduplication or affix for “our”?\n\nBut “yapup”psa” doesn't resemble any known form.\n\nWait — look at: \n- utnhantxi → utnha (my house) + txi → is it in my house? \n→ consistent pattern \n- yapp”psa → yap (field) + p (his) + psa (too) → his field too \n- yapup”psa → yap (field) + up? + psa (too) \n\nBut if “up” is not a possessive, then it may be a mistake.\n\nAlternative: could “up” mean “in”? \n\nNo — “yaputxi” = is it the field? → so “utxi” = question \n“yapsanpsa” = in our1+2 field too → so “san” + “psa” = in our field too \n\nSo the “in” is already there — only “psa” adds “too”.\n\nThus, “yap + up + psa” must be a possession + “too”\n\nBut no “up” in base.\n\nWait — is “up” actually “us” or “our”?\n\nIn the word “yapsanpsa”, the “san” might be an alternate form for “our”.\n\nSimilarly, in “yapup”psa”, “up” might be a variant of “san” or “us”.\n\nBut the spelling differs.\n\nPerhaps “up” is a typo or morphological variant of “our”.\n\nNote: the problem uses “our1+2” — so “our” is 1+2 → inclusive group.\n\nThus, “our” is used in “qucxst”psa”, “markstxi”, “yapsanpsa”\n\nSo when “our” is used, we have “st” or “san”\n\nIn “yapup”psa”, “up” may be a form of “our” for the possessive.\n\nIs there any structural similarity?\n\nCompare:\n- yapsanpsa = in our1+2 field too \n- yapup”psa = ? → likely in our1+2 field too? \nBut the structure is “yap + up + psa” — not “yap + san + psa” \n\nBut “up” and “san” are both possessive? Possibly “up” = our\n\nAlternatively, is “up” a marker for “in”?\n\nUnlikely — because “yaputxi” = is it the field? — not in\n\nThus, “up” most likely is a possessive for “our”\n\nSo:\n\n1. utnhantxi → is it in my house? \n2. yapp”psa → his field too \n3. yapup”psa → our field too \n\nBut “our” = “up”?\n\nBut “up” is not in possessive forms elsewhere.\n\nWait — in “markstxi” → “our” → “st” \nIn “yapsanpsa” → “san” → “our”\n\nSo “st” and “san” both mean “our” — perhaps “up” is a spelling variant?\n\nBut “up” is not in any other word.\n\nAlternatively, could “up” be a mistake for “san”?\n\nBut the problem says “yapup”psa” — so it is written as “up”.\n\nAnother idea: “p” and “up” — is “up” formed from “p”?\n\nNo.\n\nPerhaps a morphological merger.\n\nBut in “yapp”psa”, “p” = his \nIn “yapup”psa”, “up” = our\n\nGiven that “san” and “st” are used for “our”, and “up” is used in the target, it may be that “up” is a different possessive form.\n\nBut in absence of other data, we must conclude from structure.\n\nPattern for “too”:\n- X + psa → too (with possessive)\n\nSo:\n- yapp”psa → yap + p + psa → the field (yap) + his (p) + too → his field too \n- yapup”psa → yap + up + psa → field + our + too → our field too \n\nBut is “up” possessive?\n\nWe have no word with “up” but with “our” — but we have “san” and “st”\n\nPossibility: “san” = our, “up” = our \n→ Possibly in different dialects or forms.\n\nBut the pattern of “our” is consistently marked by “st” or “san” — not “up”.\n\nThus, “up” may not be possessive.\n\nAlternative: is “up” a prefix meaning “in” or “to”?\n\nBut “yaputxi” = is it the field? — not “in the field”\n\n“yapsanpsa” = in our1+2 field too — “in” is already in the base.\n\nThus, “up” likely is possessive.\n\nGiven that only “p” is explicitly possessive (his), and “t” (your), “st” (our) appears in “markstxi”, we can conclude:\n\n- “p” → his \n- “t” → your \n- “unh” → my \n- “st” → our \n- “san” → our (in “yapsanpsa”) \n→ So “up” may be a variant or mistake.\n\nBut in the word “yapup”psa”, if “up” is not possessed, then what?\n\nPerhaps “up” is “in” + “our”?\n\nNo evidence.\n\nBest available inference: \nThe affix “psa” adds “too” \nThe possessive affix is attached before “psa”\n\nIn:\n- yapp”psa → “p” → his → his field too \n- yapup”psa → “up” → likely “our” → our field too \n\nSince “san” and “st” are used for “our”, and “up” appears in a position similar, it is plausible that “up” is a form of “our”.\n\nTherefore:\n\n1. utnhantxi → utnha + txi → is it in my house? \n2. yapp”psa → yap + p + psa → his field too \n3. yapup”psa → yap + up + psa → our field too \n\nFinal answers:\n\n1. is it in my house? \n2. his field too \n3. our field too \n\n\\boxed{a.", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10962.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "iid", + "sample_index": 0, + "output": "We are given 17 sentences in Dyirbal with their English translations. We are to translate three more (17, 18, 19) into English, based on patterns in the earlier sentences.\n\nStep 1: Identify core structure.\n\nLook at the verb and noun patterns.\n\nIn sentence 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\" \n→ \"Booze is making the man that is always being blamed tired.\"\n\nStructure: [A] [B] [C] [D] [E] → [A] is doing something to [C], where [C] has a modifier and becomes [E].\n\nKey verbs:\n- \"baNgu\" → \"is making\" (causative)\n- \"baNgul\" → \"is following\" or \"is carrying\"\n- \"gabu\" or \"gurugu\" → related to \"tired\"\n- \"yaóaNgu\" → \"is always being blamed\"\n- \"biman\" → \"is healthy\", \"is fat\", etc.\n\nStep 2: Identify key predicates.\n\nLooking at sentence 1: \n\"bayi\" → \"booze\" → causes \"biNgunman\" (tiredness) → via \"baNgu\" → \"making\"\n\nSentence 4: \n\"bala yila wura baNgul bargandu biNgundu guniñu\" \n→ \"The tired wallaby is searching for the little feather.\"\n\n\"baNgul\" = \"is searching for\" \n\"bala\" = subject \n\"baNgul\" is followed by object and direction.\n\nImportant: \"baNgul\" appears with a noun + \"baNgul\" + noun → \"is searching for [X]\"\n\nSimilarly:\n- \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" → \"The strong man is blaming the mother that is always following death adders.\"\n\n\"baNgul\" = \"is blaming\" or \"is following\"?\n\nWait: \"blaming\" vs \"following\"\n\nCompare:\n- Sentence 11: \"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" → \"The mother that is always being ignored is carrying the sugar.\"\n\n\"baNgun\" = \"is carrying\"\n\nSentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"The dragonfly is searching for the stinging tree.\"\n\n\"baNgul\" = \"is searching for\"\n\nSo: \"baNgul\" + noun → \"is searching for\"\n\nSentence 9: \"bala garan baNgul biñéiriñéu banéan\" → \"The lizard is following the smoke.\"\n\n\"baNgul\" = \"is following\"\n\nSo this suggests: \n\"baNgul\" is used in a causative or instrumental form with a direction: either \"is following\" or \"is searching for\", depending on context.\n\nAlso:\n- \"baNgu\" is \"is making\" — causative effect.\n\nStep 3: Reduce to templates.\n\nTemplate A: [A] baNgu [B] [modifier] [result] → [A] is making [B] [result] \ne.g., 1: booze is making the man always blamed → tired\n\nTemplate B: [A] baNgul [B] → [A] is [searching/following] [B]\n\nIn sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"The mother-in-law that is always pushing stones is looking at the smoke.\"\n\n\"baNgun\" = \"is looking at\"\n\nSo \"baNgun\" = \"is looking at\" or \"is carrying\" — context-sensitive.\n\nWait: \"garan\" = lizard, \"baNgun\" = \"is looking at\", \"waymindu\" = always pushing, \"dibanbilmbal...\" = stones.\n\nSo \"baNgun\" = \"is looking at\"\n\nSimilarly: \"bala garan baNgun...\" → the lizard is looking at the smoke.\n\nSo: \"baNgun\" → \"is looking at\", \"is carrying\", \"is following\"?\n\nBut in sentence 11: \"bala éuga baNgun yabuNgu...\" → mother is carrying sugar → \"baNgun\" = \"is carrying\"\n\nSo \"baNgun\" and \"baNgul\" are both used as causative verbs with \"is doing something to X\".\n\nNow examine sentence 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ \"The big grasshopper is searching for the bent spear.\"\n\n\"baNgay\" = big \n\"waóu\" = grasshopper \n\"baNgun\" = is searching for\n\nSo: \"baNgun\" = \"is searching for\"\n\nBut in sentence 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke → \"baNgul\" = \"is following\"\n\nHence: \n- \"baNgul\" → \"is following\" or \"is searching for\" \n- \"baNgun\" → \"is carrying\", \"is looking at\", \"is searching for\"\n\nThis is inconsistent. But look at the object:\n\nIn sentence 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nFirst, parse parts.\n\n\"bayi\" = booze \n\"bargan\" = ? \n\"baNgul\" = followed by \"yaóaNgu\" → \"always being blamed\"? \n\"gubimbuluNunéanaymuNagu\" → \"the man that is always being offended\"? \n\"banéan\" = the smoke?\n\nBut in sentence 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" → \"Booze is making the tired doctor fall asleep.\"\n\n\"gubimbulu\" → \"tired\" \n\"biNgun\" → \"is tired\"\n\n\"baNgu\" → \"is making\" \n\"baNgul\" → not used.\n\nWait, in sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"baNgul\" → \"offending\"? But \"guli\" → \"strong\", \"baNgul\" + \"yaóaNgu\" → \"is being followed\"?\n\nSeems off.\n\nPerhaps \"baNgul\" is a verb of movement or action.\n\nBack to sentence 19:\n\n\"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nWe have:\n- \"bayi\" = booze\n- \"bargan\" = unknown\n- \"baNgul\" = verb\n- \"yaóaNgu\" = always being blamed\n- \"gubimbuluNunéanaymuNagu\" = the man that is always being offended? (from \"gubimbulu\" = tired? or \"offended\"?)\n\nIn sentence 8: \"gubimbulu\" → \"tired doctor\"\n\nIn sentence 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" → \"Booze is making the tired doctor fall asleep.\"\n\nSo \"gubimbulu\" = \"tired\"\n\n\"biNgun\" = \"is tired\"\n\nSo \"gubimbulu\" = \"tired\"\n\nNow \"gubimbuluNunéanaymuNagu\" → likely \"the man that is always being tired\" or \"the man that is always being offended\"?\n\n\"unéanaymuNagu\" may be a relative clause.\n\nCompare sentence 1: \"NunéaymuNa\" → \"that is always being blamed\"\n\n\"yaóaNgu\" → \"always being blamed\"\n\nSo \"yaóaNgu\" = \"is always being blamed\"\n\nSimilarly, \"guli\" → \"strong\"\n\nSo \"Numa guli\" → \"the man that is strong\"\n\n\"baNgul yaóaNgu\" → \"is being blamed\"\n\nSo the structure of relative clauses is:\n\n[subject] [modifier] [baNgul yaóaNgu] → [subject] that is always being blamed\n\n\"Numa guli baNgul yaóaNgu\" → \"the man that is strong and is always being blamed\" → but sentence says \"the man that is always being followed\"\n\nWait: sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"baNgul yaóaNgu\" → \"is being followed\"?\n\nBut \"yaóaNgu\" was used for \"blamed\", not \"followed\".\n\nSo maybe \"yaóaNgu\" is not always \"blamed\".\n\nPerhaps it's fixed to a root.\n\nLet’s look at the pattern of doubling.\n\nIn sentence 1: \n\"baNgu gurugugu biNgunman\" → making tired\n\nIn sentence 2: \n\"baNgul yaóaNgu guliNgu\" → blaming mother\n\nIn sentence 3: \n\"baNgun éugaNgu\" → carrying sugar\n\nIn sentence 5: \n\"babanaymuNagu\" → perhaps \"is always searching\"? Not clear.\n\nNow sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nBreak it down:\n- \"balan\" = strong man?\n- \"ñalNga\" = quiet boy?\n- \"baNgul\" = verb\n- \"NumaNgu\" → the man that is strong?\n- \"guniymuNagu\" → the thing that is always being quiet? \"guli\" = strong, \"guni\" = quiet?\n- \"bambunman\" = fat?\n\nSo: strong man is doing something to \"man that is always quiet\"? and the result is \"fat\"?\n\nBut in sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet \n\"biNgun\" = is tired \n\"baNgul\" = is looking at \n\"ñalNgaNgu\" = quiet boy? \n\"mugurugu\" = the one that is hiding? \n\"buóan\" = the smoke?\n\nSo: \"baNgul\" = \"is looking at\"\n\nThus: \"X baNgul Y\" → X is looking at Y\n\nIn sentence 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ \"big grasshopper is searching for the bent spear\"\n\n\"baNgun\" = is searching for\n\nSo verb differs: \"baNgul\" vs \"baNgun\"\n\nBut both involve motion or action toward an object.\n\nNow in sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n\"balan\" = strong man \n\"ñalNga\" = quiet boy? (from sentence 15) \n\"baNgul\" = verb \n\"NumaNgu\" = the man that is strong (status) \n\"guniymuNagu\" = likely \"the one that is always quiet\" → \"gani\" = quiet \n\"bambunman\" = fat\n\nSo: \"strong man\" [verb] \"strong man that is always quiet\" → becomes fat?\n\nBut \"fat\" is \"bambunman\"\n\nIs there a pattern of cause-effect?\n\nIn sentence 3: \"balan waymin bambun baNgu éugaNgu éamiman\" \n→ \"Sugar is making the healthy mother-in-law fat.\"\n\n\"baNgu\" = is making \n\"bambun\" = fat \n\"baNgun\" = is making \n\"éugaNgu\" = healthy mother-in-law → \"bambun\" → fat\n\nSo \"X is making Y fat\"\n\nIn sentence 1: \"boozing is making man always blamed → tired\"\n\nSo: [A] baNgu [B] [modifier] → [B] becomes [result]\n\nSo: [A] is making [B] [status] → [result]\n\nNow in sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n\"baNgul\" is not \"baNgu\"\n\nBut \"baNgul\" is used with object like \"following\" or \"searching\"\n\nSo perhaps \"balan ñalNga\" is the subject, and \"baNgul\" is the verb.\n\n\"NumaNgu\" = man that is strong \n\"guniymuNagu\" = man that is always quiet? (guni = quiet)\n\nBut \"guni\" — in sentence 15: \"biñéiriñ\" = quiet, so \"guni\" is quiet\n\nSo \"guniymuNagu\" = the one that is always quiet\n\nSo: \"strong man\" [verb] \"strong man who is always quiet\" → becomes fat?\n\nBut \"bambunman\" = fat → result?\n\nBut in previous patterns, result is attached after, and the verb is \"baNgu\" for causative.\n\nHere, verb is \"baNgul\", not \"baNgu\"\n\nSo not causative.\n\nWait — is \"baNgul\" used as a directional verb?\n\nIn sentence 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ \"The offended father is carrying the booze.\"\n\n\"baNgul\" = carrying\n\nIn sentence 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke.\n\nSo \"baNgul\" = following\n\nIn 10: \"balan duNan baNgul yiriñéilagu guniñu\" → dragonfly is searching for stinging tree.\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → big grasshopper is searching for bent spear → \"baNgun\", not \"baNgul\"\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke → \"baNgun\" = looking at\n\nSo, two types:\n- \"baNgul\" = \"is searching for\", \"is following\"\n- \"baNgun\" = \"is carrying\", \"is looking at\"\n\nBut in sentence 17, we have \"baNgul\" with a relative clause.\n\nPossibility: \"X baNgul Y\" → X is following Y\n\nWhere Y has a modifier like \"strong man that is always quiet\"\n\nBut then what is \"bambunman\"? Is it the result?\n\nIn sentence 3: \"bambun\" = fat — used as result after \"baNgu\"\n\nBut here, after \"baNgul\", we have \"bambunman\"\n\nSo perhaps \"bambunman\" is not a result.\n\nBut in sentence 2: \"baNgul yaóaNgu guliNgu Nunéañu\" → \"blaming mother\" — \"guliNgu\" = strong, \"Nunéañu\" = death adders\n\nSo \"baNgul\" + [modifier] = \"is [blaming/following] [object]\"\n\nThus, \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n→ \"The strong man is (searching for/following) the man who is strong and always quiet, and becomes fat\"?\n\nBut fat is not in the verb structure.\n\nAlternatively, could \"bambunman\" be the subject?\n\nNo — \"baNgul\" acts on a noun phrase.\n\nLet’s try to find a noun for \"ñalNga\".\n\nSentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\nSo \"ñalNga\" = boy, \"biñéiriñ\" = quiet\n\nSo \"ñalNga\" = boy.\n\nIn sentence 17: \"balan ñalNga\" → strong man and quiet boy? Unlikely.\n\n\"balan\" = strong man \n\"ñalNga\" = boy?\n\nSo \"strong man and quiet boy\"?\n\nBut \"baNgul\" → is following?\n\n\"NumaNgu\" = the strong man \n\"guniymuNagu\" = the one who is always quiet\n\nSo: strong man and quiet boy is following the strong man who is always quiet and becoming fat?\n\nDoesn't make sense.\n\nAlternative: \"balan\" = strong man \n\"ñalNga\" = quiet boy (but not an object)\n\n\"baNgul\" = verb \n\"NumaNgu\" = strong man \n\"guniymuNagu\" = person who is always quiet \n\"bambunman\" = fat\n\nSo perhaps: \"The strong man is following the strong man who is always quiet, and he is becoming fat\"?\n\nBut then \"bambunman\" is the result.\n\nBut in previous sentences, when there is a causative like \"is making\", the result follows.\n\nHere, verb is \"baNgul\", not \"baNgu\"\n\nSo it must be a different structure.\n\nPerhaps \"baNgul\" here is \"is causing to become\" or \"is making\", but with different form.\n\nBut in sentence 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" \n→ \"booze is making the tired doctor fall asleep\"\n\n\"baNgu\" = causative\n\n\"biNgun\" = tired\n\n\"baNgul\" not used.\n\nSo \"baNgul\" is not causative.\n\nLet’s try sentence 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = the one that is always pushing stones? (from sentence 13) \n\"baNgun\" = is looking at \n\"biñéiriñéu\" = the quiet lizard \n\"guniñu\" = little feather?\n\nSo: \"The fat doctor is looking at the quiet lizard\"\n\nYes — matches sentence 1", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12015.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "iid", + "sample_index": 1, + "output": "We are given 17 sentences in Dyirbal (a central dialect) with English translations. Our task is to translate three new sentences (17, 18, 19) into English, based on identifying patterns in the original data.\n\nStep 1: Identify word classes and patterns.\n\nLook at recurring structure.\n\nMany sentences follow a subject–verb–object structure. Often, the structure is:\n\n[Adjective-modifier] [noun] [is making/being] [noun] [adjective-modifier]\n\nOr:\n\n[Adjective-modifier] [noun] [is] [verb] [object]\n\nFor example:\n- (1) bayi yaóa NunéaymuNa baNgu gurugugu biNgunman \n → \"Booze is making the man that is always being blamed tired.\"\n\nHere, \"bayi\" = booze; \"yaóa\" + \"NunéaymuNa\" → \"the man that is always being blamed\"; \"baNgu\" = is making; \"gurugugu\" = tired.\n\nPattern: \n[Agent] is making [Patient] [adjective]\n\nAnother:\n- (2) balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu \n → \"The strong man is blaming the mother that is always following death adders.\"\n\n\"blaming\" = verb; structured as [subject] [verb] [object].\n\n- (3) balan waymin bambun baNgu éugaNgu éamiman \n → \"Sugar is making the healthy mother-in-law fat.\"\n\nAgain: [Agent] is making [Patient] [adjective]\n\nSo: possessive modifier (like \"the strong\", \"the healthy\") often comes after a noun.\n\nStep 2: Observe how adjectival phrases appear.\n\nIn (1): \"NunéaymuNa\" → \"always being blamed\"\n\nIn (3): \"éugaNgu éamiman\" → \"fat\" (modifies \"mother-in-law\")\n\nIn (8): \"gurugugu éagunman\" → \"tired doctor\" → \"éagunman\" = tired?\n\nWait: in (8): “Booze is making the tired doctor fall asleep.”\n\n\"gurugugu éagunman\" → \"tired doctor\" → not just \"tired\", but \"tired doctor\".\n\nIn (5): \"malayigara baNgu garandu biNgunman\" → \"The smoke is making the scorpion tired.\"\n\n→ \"biNgunman\" = tired\n\nIn (3): \"éugaNgu éamiman\" → \"fat\"\n\nSo adjectives are often formed by combining a root with a suffix.\n\nLook at:\n- \"Nunéañu\" → always following death adders → \"Nunéan\" similar to \"NunéaymuNa\"\n\nIn (15): \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet \n\"biNgun\" = tired \n\"ñalNga\" = lizard? → \"ñalNgaNgu\" = tired lizard?\n\nWait: \"ñalNgaNgu\" is \"lizard\", but \"biNgun\" = \"tired\" → \"tired lizard\"?\n\nBut here: “quiet boy is looking at the tired lizard.”\n\nSo structure: [subject] is [verb] [object with adjective]\n\nKey pattern:\n- A noun modified by an adjective is formed: [adjective] + [noun] \n- The adjective appears as a separate root + suffix, often ending in -Nga, -NaymuNa, -Nuné, etc.\n\nAlso, verbs:\n- \"baNgul\" = \"blaming\" or \"carrying\"? \n (2): \"blaming\" \n (11): \"carrying\" \n (12): \"pushing\" → \"bilmban\" = pushing? \n (13): \"looking at\" → \"garan\" = following / looking?\n\nIn (9): \"bala garan baNgun biñéiriñéu banéan\" → \"The lizard is following the smoke.\"\n\n\"garan\" = following\n\nIn (14): \"bala éagun baNgul\" → \"the big grasshopper is searching\" → \"waóu\" = big → \"waóu\" likely modifies \"grasshopper\"\n\nIn (15): \"biñéiriñ\" = quiet → adjectival\n\nSo: adjectives come before or modify nouns.\n\nNow, look at sentence 17:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak it down:\n\n- \"balan\" = strong man (from (2): \"balan yabu\" → strong man)\n- \"ñalNga\" = lizard (in (15): \"biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\")\n → \"ñalNga\" = lizard\n- \"baNgul\" = blaming \n → this is the verb, like in (2)\n- \"NumaNgu\" = the one that is always being followed → from (16): \"The man that is always being followed is offending the strong father\"\n → \"Numa\" = always being followed → \"NumaNgu\" = the one always being followed\n- \"guniymuNagu\" → possibly \"guni\" + \"ymuNagu\" → \"following\"?\n In (2): \"guliNgu Nunéañu\" = following death adders → \"guli\" = following?\n In (14): \"bala baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"the big grasshopper is searching for the bent spear\"\n → \"guniñu\" = searching for?\n\nWait: \"guni\" seems to be \"searching\" or \"following\".\n\nIn (14): \"guniñu\" = searching\n\nIn (2): \"guliNgu Nunéañu\" → “following death adders”\n\nSo \"guli\" = following?\n\n\"Numa\" = always being followed → \"Numa\" is an adjective stem.\n\n\"NumaNgu\" = the one that is always being followed.\n\n\"guniymuNagu\" → possibly \"following\" + [some root]?\n\n\"guniymuNagu\" — perhaps \"following the one that is always being followed\"?\n\nWait: \"guni\" = follow; \"ymuNagu\" → maybe \"the one\"?\n\nBut in (14): \"guniñu\" → \"searching for\"\n\n\"guni\" = searching?\n\nIn (14): \"bala baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for the bent spear\"\n\nSo \"guniñu\" = searching for\n\nSimilarly, in (15): \"biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → “quiet boy is looking at the tired lizard”\n\n\"baNgul\" = looking at\n\nSo:\n- \"baNgul\" = looking at, or blaming\n\nBut in (3): \"baNgu\" = making\n\n\"baNgul\" appears in multiple forms: blaming, looking at, carrying?\n\nFrom (2): \"baNgul yaóaNgu guliNgu\" → \"is blaming\"\n\nFrom (9): \"baNgun\" → \"is following\" → \"garan\" → \"following\"\n\nWait: \"baNgun\" vs \"baNgul\" — possibly suffixes indicate different verbs.\n\nIn (3): \"baNgu\" → making \nIn (2): \"baNgul\" → blaming \nIn (9): \"baNgun\" → following?\n\nActually, (9): \"bala garan baNgun biñéiriñéu banéan\" → \"The lizard is following the smoke.\"\n\nSo \"garan\" = following, \"baNgun\" = verb? Or is \"baNgun\" attached to \"biñéiriñéu\"?\n\nWait: \"baNgun\" is used with a noun: \"baNgun biñéiriñéu\" = \"is following the smoke\"?\n\nYes → \"baNgun\" = verb \"to follow\"\n\nBut in (2): \"baNgul yaóaNgu guliNgu Nunéañu\" → \"is blaming the mother that is always following death adders\"\n\n\"baNgul\" here is the verb → \"blaming\"\n\nSo verb is \"baNgul\" → blaming \nVerb \"baNgun\" → following?\n\nBut sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n- \"balan\" = strong man \n- \"ñalNga\" = lizard \n- \"baNgul\" = verb? \nBut \"baNgul\" is the verb of \"blaming\" — would \"the strong man is blaming the lizard\"?\n\nThen: \"NumaNgu\" = the one that is always being followed → the person being followed? \nBut if \"guniymuNagu\" means \"following\", then \"the strong man is blaming the one who is always being followed, who is following the fat one\"?\n\nWait: \"guniymuNagu\" — likely \"the one who is following\" \n\"bambunman\" = fat?\n\nYes: \"bambunman\" → fat (from (3): \"éugaNgu éamiman\" → fat mother-in-law)\n\nSo:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The strong man is blaming the one who is always being followed, who is following the fat one?\n\nBut structure:\n\n[Subject] [is] [verb] [object with modifier]\n\n\"NumaNgu\" = the one always being followed \n\"guniymuNagu\" = the one who is following \n\"bambunman\" = fat?\n\nWait: \"guniymuNagu\" may be \"following the fat one\"?\n\nBut “guniymuNagu” = likely “following” + “bambunman”?\n\nBut “bambunman” is an adjective? → fat → so \"following the fat one\"?\n\nYes.\n\nSo: The strong man is blaming the one who is always being followed (who is following the fat one).\n\nWait — is it \"the one who is always being followed\" is following the fat one?\n\nYes.\n\nSo: The strong man is blaming the one who is always being followed (who is following the fat one).\n\nBut “NumaNgu” = the one who is always being followed \n“guniymuNagu” = the one who is following the fat one?\n\nBetter: “NumaNgu guniymuNagu” → the one who is always being followed and is following?\n\nBut likely a chain:\n\nThe strong man is blaming [the one who is always being followed] [who is following] [the fat one].\n\nBut \"guniymuNagu\" may be \"the one who is following\" — but what is being followed?\n\n\"guniymuNagu\" likely contains the object — “guni” = following, “ymuNagu” = the one?\n\n“ymuNagu” → “the one” → so “following the one”?\n\nBut “bambunman” is fat → so maybe “following the fat one”?\n\nSo perhaps “guniymuNagu” → following the fat one?\n\nBut “bambunman” is the adjective.\n\nStructure: [subject] + [verb] + [object with attribute]\n\nSo likely:\n\nThe strong man is blaming the one who is always being followed, who is following the fat one.\n\nYes.\n\nNow, sentence 18:\n\n18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n\n- \"bala\" = the lizard? Or \"the fat one\"? \n- \"diban\" = fat → (12: \"fat doctor\") → \"diban\" = fat \n- \"bilmbalmuNa\" = the one who is always pushing stones → from (12): \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"the fat doctor is pushing the big stone\" \n → “bilmbal” = pushing stones? \n → “bilmbalmuNa” = the one who is always pushing stones \n- \"baNgun\" = verb \"to follow\" → \"is following\" \n- \"biñéiriñéu\" = the quiet one? → from (15): \"biñéiriñ\" = quiet → \"biñéiriñéu\" = the quiet one \n- \"guniñu\" = searching for\n\nSo: The fat one (specifically, the one who is always pushing stones) is following the quiet one who is searching for something?\n\nWait: “is following the quiet one who is searching for something”\n\n“guniñu” = searching — but what? Not specified.\n\n\"biñéiriñéu guniñu\" → the quiet one who is searching?\n\nSo: [bala diban bilmbalmuNa] is following [biñéiriñéu guniñu]\n\n→ The fat one who is always pushing stones is following the quiet one who is searching.\n\nYes.\n\nSo English: The fat one who is always pushing stones is following the quiet one who is searching.\n\nNow, sentence 19:\n\n19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\n- \"bayi\" = booze (from (1)) \n- \"bargan\" → ? \nIn (15): \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\" \n\"baNgul\" = looking at \nBut here: \"bargan\" → not in that list.\n\nIs “bargan” a verb?\n\nIn (19): \"bargan\" → possibly a verb like \"following\"?\n\nBut earlier, \"garan\" = following.\n\nLook at (9): \"bala garan baNgun biñéiriñéu banéan\" → lizard following the smoke\n\nSo \"garan\" = following \n\"bargan\"? → similar?\n\nPossibly a variant.\n\n\"bargan\" → perhaps \"is following\"?\n\nThen: \"bayi bargan\" = \"booze is following\"? Unlikely — agent is often a noun.\n\nBut \"bayi\" is also subject — \"booze is making\" or \"is following\"?\n\nIn other cases, \"bayi\" is subject of a verb.\n\nCould \"bargan\" be part of the object?\n\nLook: \"baNgul yaóaNgu\" = blaming? \n\"yaóaNgu\" = mother that is always being blamed? → \"yaóaNgu\" is a noun phrase\n\nIn (1): \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → \"booze is making the man that is always being blamed tired\"\n\nHere: \"yaóaNgu\" → mother that is always being blamed? → \"yaói\" + \"NunéaymuNa\" → but \"NunéaymuNa\" meaning \"always being blamed\"\n\nIn (16): \"The man that is always being followed is offending the strong father\" → \"Numa\" = always being followed\n\nSo patterns:\n\n- \"Numa\" → always being followed \n- \"Nuné\" → always being blamed \n- \"guli\" → following \n- \"yaó\" → the one that is always being blamed? → yaóaNgu → mother that is always being blamed\n\nSo \"yaóaNgu\" = the mother that is always being blamed\n\n\"baNgul\" = verb → \"blaming\"\n\nSo sentence 19: bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\n\nStructure:\n\n\"bayi\" = agent (booze) \n\"bargan\" = verb? \n\"baNgul\" = verb? \nConflict: two verbs?\n\nWait — perhaps \"bargan\" is a verb, and \"baNgul\" is another?\n\nBut in previous, \"baNgul\" was the main verb.\n\nPossibility: \"bargan\" is a noun?\n\nNo — in (19), no clear noun.\n\nPossibility: typo or variant?\n\nCompare with (1): \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → \"booze is making the man that is always being blamed tired\"\n\nHere: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nPossibly: \"booze is following [the mother that is always being blamed, who is always being followed by the one who is searching?]\" — but doesn’t fit.\n\nAlternative: maybe \"bargan\" = \"making\" or \"causing\"?\n\nBut in (1): \"baNgu\" = making \n\"baNgul\" = blaming \n\"baNgun\" = following\n\nSo perhaps \"bargan\" is a form of \"making\"?\n\nUnlikely — not in data.\n\nWait — perhaps \"bargan\" is a noun?\n\nLike \"the one who is following\"?\n\nIn (9): \"garan\" = following\n\nBut \"bargan\" might be a misspelling?\n\nPossibility: in (15): \"biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at the tired lizard\"\n\nSo \"baNgul\" = looking at\n\nIn (19), \"baNgul\" appears with another noun.\n\nAnother idea: \"bargan\" = the one who is following?\n\nBut \"bargan\" is not in known noun phrases.\n\nLook at (7): \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → \"the death adder that is always searching for scorpions is following the possum\"\n\n\"midin\" = always searching?\n\n\"bimab-...-inaymuNagu\" → always searching?\n\n\"midin\" → searching?\n\nIn (19): \"gubimbuluNunéanaymuNagu\" — possibly \"the one who is always searching for scorpions\"?\n\n\"gubimbulu\" — similar to \"midin\"?\n\nIn (7): \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12325.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Identify the core structure of the Dyirbal sentences.\n\nAll sentences follow a pattern with two main components:\n- A subject (A) doing something (verb) to a second entity (B).\n- The verb is typically in the form [Actor] [verb] [object].\n\nStep 2: Identify common verb forms and associated nouns.\n\nLook at verbs like:\n- bayi → \"booze is making\"\n- balan → \"the strong man is blaming\"\n- bala → \"the [something] is following\"\n- bima → \"is making\" (e.g., \"making tired\")\n- biñéiriñ → \"looking at\"\n- gurugugu → \"tired\"\n- yaóa → \"is always being blamed\"\n- éuga → \"sugar is making\"\n- waymin → \"is making fat\"\n- garan → \"is following\"\n- diban → \"fat\"\n- buóan → \"smoke\"\n- Numa → \"always being followed\"\n- mundu → \"offending\"\n- guli → \"following\"\n- etc.\n\nStep 3: Extract the patterns for each sentence.\n\nSentence 1: \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ Booze is making the man that is always being blamed tired. \nPattern: [boozing] + [subject] + [is always being blamed] + [to] + [tired]\n\nSentence 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ The strong man is blaming the mother that is always following death adders. \n→ \"blaming\" + [object] + [is always following] + [death adders]\n\nSentence 3: \"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n→ [Sugar] + [is making] + [healthy mother-in-law] + [fat]\n\nSentence 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" \n→ The tired wallaby is searching for the little feather. \n→ \"is searching for\" → wura = searching for\n\nSentence 5: \"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n→ [Smoke] + [is making] + [scorpion] + [tired]\n\nSentence 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ The offended father is carrying the booze. \n→ [offended father] + [is carrying] + [booze]\n\nSentence 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" \n→ The death adder that is always searching for scorpions is following the possum. \n→ [death adder] + [is always searching for] + [scorpions] + [is following] + [possum]\n\nSentence 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" \n→ Booze is making the tired doctor fall asleep. \n→ [booze] + [is making] + [tired doctor] + [fall asleep]\n\nSentence 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n→ [lizard] + [is following] + [smoke]\n\nSentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n→ [dragonfly] + [is searching for] + [stinging tree]\n\nSentence 11: \"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" \n→ The mother that is always being ignored is carrying the sugar. \n→ [mother that is always being ignored] + [is carrying] + [sugar]\n\nSentence 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" \n→ The fat doctor is pushing the big stone. \n→ [fat doctor] + [is pushing] + [big stone]\n\nSentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n→ [mother-in-law that is always pushing stones] + [is looking at] + [smoke]\n\nSentence 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ The big grasshopper is searching for the bent spear. \n→ [big grasshopper] + [is searching for] + [bent spear]\n\nSentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ The quiet boy is looking at the tired lizard. \n→ [quiet boy] + [is looking at] + [tired lizard]\n\nSentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ The man that is always being followed is offending the strong father. \n→ [man that is always being followed] + [is offending] + [strong father]\n\nStep 4: Identify relevant structural patterns.\n\nPattern for verb + noun + [modifier] = [subject] + [verb] + [modifier] + [object]\n\nSpecifically:\n\n- \"baNgul\" → \"is following\"\n- \"yabu\" → \"is making fat\"\n- \"gurugugu\" → \"tired\"\n- \"malayigara\" → \"smoke\"\n- \"bargan\" → ??? \n- \"diban\" → fat\n- \"biñéiriñ\" → looking at\n- \"Numa\" → always being followed\n- \"guli\" → following\n\nNow, sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\nBreak it down:\n- \"balan\" → the strong one (agent)\n- \"ñalNga\" → similar to \"ñalNgaNgu\" in sentence 15: \"quiet boy\"\n- \"baNgul\" → is following\n- \"NumaNgu\" → always being followed\n- \"guniymuNagu\" → ??? (variant of \"guli\" or \"guniñu\"?)\n- \"bambunman\" → fat → from \"bambun\"\n\n\"bambunman\" = fat\n\n\"Numa\" = always being followed → \"is always being followed\"\n\n\"guniymuNagu\" → likely a variant of \"guli\" → \"following\"\n\nSo: \nThe strong one (what?) is following the one that is always being followed, who is (possibly) following (guniymuNagu?) and who is fat?\n\nBut \"guniymuNagu\" → may be \"guli\" with variant. \"guli\" = following, \"guniñu\" = searching for\n\nWait — in sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"quiet boy is looking at the tired lizard\"\n\n\"ñalNga\" → quiet boy \n\"biñéiriñ\" → looking at \n\"ñalNgaNgu\" → object (tired lizard)\n\n\"mugurugu\" → tired\n\nThus: \n\"ñalNga\" = quiet boy \n\"biñéiriñ\" = looking at \n\"biNgun\" = the tired \n\"baNgul\" = following? But here it's \"biñéiriñ\", not \"baNgul\"\n\nWait — confusion: \"baNgul\" is \"following\", not \"looking at\"\n\nIn sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ Is looking at smoke → \"biñéiriñéu\"\n\nSo \"biñéiriñ\" = looking at\n\n\"baNgul\" = following\n\nSo:\n- \"biñéiriñ\" = looking at\n- \"baNgul\" = following\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n→ [the strong one] + [is following] + [the one that is always being followed] + [who is (guniymuNagu) and fat]\n\nguniymuNagu — likely \"guli\" or \"guli\" variant → \"following\"\n\nSo: \"who is following and fat\"\n\nSo: The strong one is following the one who is always being followed and who is following (someone) and is fat?\n\nBut who is following? Who is the object?\n\nThe structure is: \n[Actor] + [is following] + [subject with attribute] + [attribute]\n\n→ \"The strong one is following the one who is always being followed and who is following and is fat?\"\n\nBut that's redundant.\n\nWait — perhaps \"guniymuNagu\" = \"guli\" = \"following\" → but \"following what\"?\n\nIn sentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"searching for\"\n\n\"yiriñéilagu\" = searching for something → \"stinging tree\"\n\nSo \"guniñu\" = searching for\n\nIn sentence 17: \"guniymuNagu\" — likely \"guniñu\" with a variant (\"ymu\" vs \"ñu\")?\n\n\"guniymuNagu\" → possibly \"searching for\" + something?\n\nLook at \"guli\" = following → \"guli\" appears in sentence 16: \"Numa guli\" → \"is following\"\n\n\"Numa\" = always being followed\n\n\"guli\" = following\n\nSo \"Numa guli\" = \"is following\"\n\nNow \"guniymuNagu\" — perhaps it's a stretch, but likely \"guli\" with a modification.\n\nAlternatively: \"guniymuNagu\" = \"is searching for\" → guniymu = guni + ym?\n\nCompare to sentence 10: \"yiriñéilagu guniñu\" → \"searching for stinging tree\"\n\n\"guniñu\" = searching for?\n\nNo — \"yiriñéilagu\" = searching for, \"guniñu\" = stinging tree?\n\nNo — sentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"dragonfly is searching for stinging tree\"\n\nSo \"yiriñéilagu\" = searching for \n\"guniñu\" = stinging tree\n\nSo \"guniñu\" is the object.\n\nTherefore, \"guniymuNagu\" might be an object noun?\n\nBut in sentence 17: \nguniymuNagu → object phrase?\n\n\"bambunman\" → fat\n\nSo: The strong one is following the one that is always being followed and who is (fat) and (guniymuNagu)?\n\nBut \"guniymuNagu\" = nothing?\n\nAlternative: perhaps \"guniymuNagu\" is a noun phrase meaning \"the one who is following\", i.e., a role.\n\nBut in sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ man that is always being followed is offending the strong father\n\n\"Numa\" = always being followed \n\"guli\" = following \n\"baNgul\" = is following \n\"yaóaNgu\" = the one being blamed\n\nSo \"Numa guli\" = the one that is always being followed, is following?\n\nAnd \"baNgul\" = is following — seems nested.\n\nWait — structure of sentence 17 is: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nSplit: \n- balan → strong one \n- ñalNga → subject (similar to \"quiet boy\") \n- baNgul → is following \n- NumaNgu → one that is always being followed \n- guniymuNagu → ??? \n- bambunman → fat\n\nSo: The strong one is following the one who is always being followed and who is [guniymuNagu] and is fat?\n\nBut what is \"guniymuNagu\"?\n\nCompare to sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ quiet boy is looking at the tired lizard\n\n\"biñéiriñ\" = looking at \n\"biNgun\" = tired \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired\n\nSo \"biNgun\" + \"mugurugu\" = both describe lizard\n\nIn sentence 17: we have \"guniymuNagu\", which may be like \"guni\" + \"ym\" → could be \"following\"?\n\nBut \"numa\" already has \"following\"\n\nPossibly, \"guniymuNagu\" is a noun meaning \"the one who is following\" — but that's what \"Numa\" is.\n\nAlternatively, perhaps \"guniymuNagu\" is a noun meaning \"stinging tree\" or some object.\n\nBut no object is specified.\n\nClosest parallel: sentence 14 → \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear\n\n\"waóu\" = searching for \n\"bundiñéu\" = bent spear \n\"guniñu\" = stinging tree? No — \"bundiñéu\" = bent spear\n\n\"guniñu\" = is not used as object.\n\nSo \"guniñu\" is not a verb or object.\n\nNow notice: \"guniymuNagu\" — could be \"guni\" (a root) + \"ymu\" → perhaps a typo or variant?\n\nAlternatively, check all \"guni\" variants:\n\n- guniñu → in sentence 14, object — \"bent spear\"\n- guniymuNagu → in sentence 17 — object?\n\nPossibly \"guniymuNagu\" = \"the one who is following\" — but redundant.\n\nPattern in sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ mother-in-law that is always pushing stones is looking at the smoke \n\"waymindu\" — pushing \n\"dibanbilmbalNaymuNagu\" — always pushing stones \n\"buóan\" — smoke\n\nSo \"dibanbilmbalNaymuNagu\" = object modifier\n\nSimilarly, sentence 17: \"NumaNgu guniymuNagu bambunman\" \n→ could be \"one that is always being followed and following and is fat\"\n\nBut \"guniymuNagu\" might be \"is following\" as a verb, with \"Nagu\" → possessor?\n\nWait — \"Numa\" = always being followed \n\"NumaNgu\" = the one that is always being followed\n\n\"guniymuNagu\" = the one that is following? or doing \"guni\"?\n\nBut is there a verb \"guni\" in the data?\n\nOnly in \"guli\", not \"guni\".\n\n\"guni\" not listed.\n\nBut in sentence 10: \"yiriñéilagu guniñu\" → verb + object\n\n\"yiriñéilagu\" = search for \n\"guniñu\" = stinging tree\n\nSo \"guniñu\" is object.\n\nSimilarly, \"guniymuNagu\" → could be object?\n\nBut what object?\n\n\"bambunman\" = fat — adjective\n\nSo likely: the one that is always being followed and is fat and (is searching for/doing something)\n\nBut missing.\n\nWait — perhaps \"guniymuNagu\" is a typo for \"guli\" or \"guni\" — but not found.\n\nLook at sentence 19: \n\"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\n\"bargan\" → ???\n\nIn sentence 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" \n→ death adder (always searching for scorpions) is following possum\n\n\"midin\" → always searching for \n\"malayigaraguninaymuNagu\" → scorpions\n\n\"banéan\" → possum\n\nSo \"midin\" = always searching for\n\nIn sentence 19: \"bargan\" → could be similar?\n\n\"bargan\" → new verb?\n\nNo parallel.\n\nBut \"bargan\" — in sentence 19: \"bayi bargan\" → \"the death adder is doing something\"\n\n\"bargan\" = might be \"being blamed\" → \"yaóa\" = being blamed\n\nBut \"gubimbuluNunéanaymuNagu\" → \"the one that is always being blamed\"?\n\n\"gubimbulu\" = \"tired\" or \"offended\"?\n\nIn sentence 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" → \"booze is making the tired doctor fall asleep\"\n\n\"gubimbulu\" = tired\n\nSo \"gubimbulu\" = tired\n\n\"gubimbuluNunéanaymuNagu\" → the one that is always being tired?\n\nBut \"NunéanaymuNagu\" → similar to \"NunéaymuNa\" → \"always being blamed\"?\n\nSentence 1: \"yaóa NunéaymuNa\" → \"is always being blamed\"\n\nSo \"NunéanaymuNagu\" → always being blamed\n\nSo \"gubimbuluNunéanaymuNagu\" → one that is always being tired?\n\nBut \"gubimbulu\" = tired, so \"the tired one that is always being tired\"?\n\n\"banéan\" → possum\n\nSo sentence 19: \"death adder is doing [bargan] to the one that is always being tired and is being blamed, and is following possum?\"\n\nNo — structure: \"bay", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12114.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the core structure of the Dyirbal sentences. Most sentences follow a pattern: [agent] [verb] [object/possessor] [modifier].\n\nLook at sentence 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → \"Booze is making the man that is always being blamed tired.\" \nSo: [agent] = bayi (booze); \"is making\" = verb; [result] = man that is always being blamed → \"biNgunman\" \n\"biNgunman\" = \"the man that is always being blamed\" → \"being blamed\" is a passive state.\n\nStep 2: Notice that passive states (e.g., being blamed, being ignored, being followed) are marked by suffixes like:\n- -Nunéan → \"that is always being [X]\" \n- -bimabanéal → \"that is always following\" \n- -yaóa → \"that is always being blamed\"\n\nCheck sentence 2: \n\"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\" \n\"bimabanéalNaymuNa\" = mother that is always following \n\"yaóaNgu\" = death adders → object\n\nSo \"that is always following\" → suffix \"-bimabanéal...\"\n\nIn sentence 3: \"bambun baNgu éugaNgu éamiman\" → \"sugar is making the healthy mother-in-law fat\" \n→ \"éamiman\" = healthy \n→ quality adjectives → often derived from roots\n\nStep 3: Identify the verbs and their correspondences.\n\nVerb roots:\n- bayi → booze (agent)\n- balan → strong man (agent)\n- bala → lizard or tired entity \n- bala → one that follows (e.g., in 9: \"the lizard is following the smoke\")\n- bayi → in 8: \"booze is making the tired doctor fall asleep\" → \"gurugugu\" = tired\n\nNote: “making” is expressed via verb + object + result modifier.\n\nStructure: \n[agent] + [verb] + [object] + [modifier (passive/predicative)] + [result]?\n\nBut let's look at the forms of verb + noun:\n\nExample: \nSentence 1: bayi yaóa → \"booze is making\" \nSentence 2: balan yabu → \"strong man is blaming\" → modifies \"mother that is always following death adders\" \nSo the verb corresponds to an action.\n\nNow, look at sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak down: \n\"balan\" → strong man \n\"baNgul\" → \"is carrying\" or \"is following\" (cf. sentence 2: balan yabu bimabanéalNaymuNa → strong man blaming the mother that is always following) \n\"NumaNgu\" → a man (cf. sentence 16: \"The man that is always being followed\") \n\"guniymuNagu\" → ?? \n\"bambunman\" → \"fat\" or \"healthy\" → possibly refers to the object being described.\n\nFrom sentence 3: \"bambun\" = sugar → \"fat\" \n\"éama\" = healthy → \"éamiman\"\n\nSo \"bambunman\" = fat \n\"bambun\" → fat\n\n\"guniymuNagu\" → possibly a passive participle? Compare:\n\nSentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"the quiet boy is looking at the tired lizard.\" \n\"biñéiriñ\" = quiet boy \n\"baNgul\" = is looking at \n\"ñalNgaNgu\" = tired lizard \n\"mugurugu\" = tired — redundant? Or \"mugurugu\" = tired, \"ñalNgaNgu\" = the one who is tired?\n\nWait — in sentence 15: \"ñalNgaNgu\" → tired lizard → so \"ñalNga\" = tired\n\nIn sentence 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for bent spear\" \n\"baNgay\" = big \n\"baNgun\" = is searching for \n\"bundiñéu\" = bent spear\n\nSo \"baNgul\" = \"is carrying\" or \"is looking at\"\n\nSentence 9: \"bala garan baNgun biñéiriñéu banéan\" → \"lizard is following smoke\"\n\nSo \"baNgun\" = following\n\nSentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → dragonfly is searching for stinging tree → \"baNgul\" = \"is searching for\"\n\nMultiple uses of \"baNgul\" with different meanings:\n- following (9: bala garan baNgun ...) \n- carrying (6: bala gurugu baNgul NumaNgu munduNgu dimbañu → \"offended father is carrying booze\") \n- searching for (10,14,16)\n\nSo \"baNgul\" is context-dependent.\n\nBut let’s look at sentence 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"the man that is always being followed is offending the strong father\" \n\"Numa\" = man \n\"guli\" = that is always being followed \n\"baNgul\" = offending? → verb that means \"offending\" or \"is offending\"?\n\nWait: \"baNgul yaóaNgu\" → is offending the strong father? But \"yaóaNgu\" = death adders? \nWait — the translation says: \"offending the strong father\" — so \"baNgul\" must carry the verb of \"offending\".\n\nBut in sentence 16, the verb \"baNgul\" appears with \"yaóaNgu\" (death adders) — contradiction?\n\nNo: sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\" \nBut \"yaóaNgu\" = death adders? That contradicts.\n\nWait — translation says: \"offending the strong father\", not death adders.\n\nPossibly a translation error?\n\nReview the original: \n\"16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman. \nThe man that is always being followed is offending the strong father.\"\n\n\"yaóaNgu\" → if it's \"the strong father\", then it must be a misread.\n\nBut in sentence 2, \"yaóaNgu\" = death adders. \nOnly in sentence 16 is \"yaóaNgu\" used, and it's translated as \"strong father\".\n\nPossibility: \"yaóaNgu\" can mean \"strong father\" in this context?\n\nOr is \"yaóaNgu\" a disguised form?\n\nNo — in sentence 2: \"guliNgu Nunéañu\" = death adders \nIn sentence 16: \"banéalmuNagu\" = strong father? — wait: \"banéalmuNagu\" = strong father?\n\nCheck: sentence 16: \"banéalmuNagu munduman\" = strong father\n\nSo \"baNgul yaóaNgu\" — is the verb? But it's not matching.\n\nWait — sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\"\n\nStructure: \n\"the man that is always being followed\" \n\"is [verb]ing the strong father\"\n\nSo \"baNgul\" = verb (offending), \"yaóaNgu\" = strong father?\n\nBut in sentence 2, \"yaóaNgu\" = death adders — so \"yaóaNgu\" is not \"strong father\".\n\nWait — unless \"yaóaNgu\" is \"a man\" or \"the man\"?\n\nIn sentence 2: \"baNgul yaóaNgu guliNgu\" → \"blaming the mother that is always following death adders\"\n\n\"yaóaNgu\" = object → death adders\n\nIn sentence 16: \"baNgul yaóaNgu banéalmuNagu\" → \"offending the strong father\" → so \"yaóaNgu\" = strong father?\n\nThat would mean \"yaóaNgu\" has different meanings depending on context — which is odd.\n\nAlternatively, perhaps a typo — maybe it's \"banéalmuNagu\" instead?\n\nBest inference: \"baNgul\" is a verb meaning \"to offend\", \"yaóaNgu\" = \"the strong father\" — so the form \"yaóaNgu\" can mean \"strong father\".\n\nBut in sentence 2: \"yaóaNgu\" → death adders → so it's a noun.\n\nSo perhaps \"yaóaNgu\" = \"death adder\", \"banéalmuNagu\" = \"strong father\".\n\nThus, \"baNgul yaóaNgu\" is not \"offending the death adder\", but \"offending the strong father\" — so likely \"yaóaNgu\" is a mistake in our parsing.\n\nWait — sentence 16: \"baNgul yaóaNgu banéalmuNagu munduman\" → perhaps \"baNgul\" affects the object?\n\nMore likely: \"baNgul\" is the verb (offending), and \"yaóaNgu\" is the object (strong father)? But it's not listed as such.\n\nAnother possibility: \"yaóaNgu\" = \"strong father\", \"baNgul\" = \"is making\" or \"is causing\".\n\nBut in sentence 1: \"bayi yaóa\" — \"booze is making\" → so \"yaóa\" is an intransitive verb?\n\nWait — in sentence 1: \"bayi yaóa\" — agent + verb → \"is making\" \nIn sentence 2: \"balan yabu\" → \"is blaming\" \nIn sentence 3: \"bambun baNgu\" — sugar is making → \"baNgu\" = making?\n\nSo verbs like \"yaóa\", \"yabu\", \"baNgu\" are verbs of causation.\n\nSo \"baNgul\" may be a different causative verb.\n\nIn sentence 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ \"the offended father is carrying the booze\"\n\nSo \"baNgul\" = carrying\n\nSentence 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke → \"baNgul\" = following\n\nSentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → dragonfly is searching for stinging tree → \"baNgul\" = searching\n\nSo \"baNgul\" is used with different verbs: \n- following \n- carrying \n- searching \n- offending?\n\nIn sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"the man that is always being followed is offending the strong father\" \nSo \"baNgul\" = \"offending\" \n\"yaóaNgu\" → object = strong father? But only if \"yaóaNgu\" = strong father — which is not standard.\n\nBut in sentence 2, \"yaóaNgu\" = death adder — so likely not.\n\nUnless \"yaóaNgu\" is a misanalysis.\n\nWait — sentence 16: \"baNgul yaóaNgu banéalmuNagu munduman\" → perhaps \"baNgul\" modifies the noun, meaning \"the one that is offending\"?\n\nNo — it's \"baNgul\" as verb, \"yaóaNgu\" as object.\n\nBut no noun for strong father in the verb form.\n\nThis suggests that in sentence 16, \"yaóaNgu\" is not the object, but part of a locative or epithet.\n\nAlternative: perhaps the structure is [agent] [modifier] [verb] [object]\n\nWait — sentence 1: \"bayi yaóa NunéaymuNa\" → \"booze is making the man that is always being blamed\"\n\nSo: [agent] [verb] [object with modifier]\n\nSimilarly, sentence 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" \n→ \"the tired wallaby is searching for the little feather\" \n\"yila\" = tired → modifier \n\"wura\" = little feather → object? \n\"baNgul\" → is searching for\n\nSo pattern: \n[agent] + [modifier] + [verb] + [object] + [result]\n\nOr: [agent] + [verb] + [object with modifier]\n\nIn 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n\"balan\" = strong man \n\"ñalNga\" = tired? (like in sentence 15: \"biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at the tired lizard\") \n\"baNgul\" = carrying or following \n\"NumaNgu\" = man \n\"guniymuNagu\" = ? \n\"bambunman\" = fat\n\nLikely: \"the strong man is making the man that is always being tired fat\"?\n\nBut \"guniymuNagu\" — compare to \"guli\", \"gurugugu\", \"gurugugu\"\n\nIn sentence 8: \"bayi gurugugu biNgun baNgu gurugugu éagunman\" → \"booze is making the tired doctor fall asleep\" \n\"gurugugu\" = tired\n\nSo \"gurugugu\" = tired\n\n\"guniymuNagu\" — might be a variant of \"guri\" or \"guri-\"\n\nPossibly \"guni\" = tired? Or \"guni\" = following?\n\nNo — in sentence 10: \"yiriñéilagu\" = stinging tree\n\nBack to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nBreak: \n\"balan\" → strong man \n\"ñalNga\" → tied or tired (modifier) \n\"baNgul\" → verb: carrying or following \n\"NumaNgu\" → man \n\"guniymuNagu\" → [that is always being] ... \n\"bambunman\" → fat\n\nSo: \"the strong man is [doing something] to the man that is always being [X] to become fat\"\n\nWhat is \"guniymuNagu\"? \nCompare to sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at the tired lizard\" \n\"ñalNgaNgu\" = tired lizard \n\"mugurugu\" = tired — redundant?\n\n\"mugurugu\" = tired — and \"ñalNga\" = tired? Possibly overlapping.\n\nIn sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law that is always pushing stones is looking at the smoke\"\n\n\"waymindu\" = pushing \n\"bibanbilmbalNaymuNagu\" = pushing stones (with infix or suffix)\n\nSo adverbial modifiers (passive/continuous) are marked by -NaymuNa, -Nunéan, -bimabanéal, etc.\n\nIn sentence 17: \"guniymuNagu\" → likely \"that is always being [something]\"\n\n\"guniymuNagu\" → compare to \"guli\" → in sentence 16: \"Numa guli\" → \"man that is always being followed\"\n\nSo \"guli\" = being followed\n\nSo \"guniymuNagu\" = man that is always being [some action]\n\nWhat action? \"guni\" = follow?\n\n\"guni\" → follow → \"guniymuNagu\" = man that is always being followed?\n\nYes — possible.\n\nSo: \"the strong man is carrying the man that is always being followed to become fat\"\n\n\"bambunman\" = fat\n\nSo translation: \"The strong man is making the man that is always being followed fat.\"\n\nBut in that case, \"baNgul\" = making?\n\nEarlier we saw \"baNgul\" = carrying or searching — not always causative.\n\nBut in sentence 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" → \"offended father is carrying the booze\"\n\nSo \"baNgul\" = carrying\n\nIn sentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → searching for\n\nIn sentence 1: \"bayi yaóa\" — is making\n\nSo \"baNgul\" seems to vary.\n\nBut in sentence 17: the object is \"NumaNgu\" (a man), and \"guniymuNagu\" = man that is always being followed.\n\nThus, the strong man is carrying the man that is always being followed, and he becomes fat?\n\nBut \"bambunman\" = fat — so this is the result of the action.\n\nSo \"baNgul\" = causative verb → \"is making [him] fat\"?\n\nBut in sentence 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"tired wallaby is searching for little feather\"\n\n\"biNgundu\" = little feather — not a result.\n\nIn sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law that is always pushing stones is looking at the smoke\" → result not mentioned.\n\nOnly in causal cases (1,3,5,8) is a result given.\n\nIn sentence 3: sugar is making the mother-in-law fat → result\n\nSentence 5: smoke is making the scorpion tired → result\n\nSentence 8: booze is making the tired doctor fall asleep → result\n\nSo when a result is given, it is marked by a modifier like \"biNgunman\" = tired, \"bambunman\" = fat, \"éagunman\" = falling asleep.\n\nSo in sentence", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12557.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "iid", + "sample_index": 0, + "output": "We are given verb forms in Menominee and their English translations. We need to translate four specific English sentences into Menominee.\n\nStep 1: Identify known forms and their patterns.\n\nLook for verbs involving \"begin\", \"walk\", \"dig\", \"lay flat\", \"bite\", \"cut\", \"open\", \"take out\", etc.\n\nFrom the table:\n\n- \"kewǣpeqtaq\" = we1+2 begin → *kewǣp- + -eqtaq* → \"begin\"\n- \"kewǣpānæhkæq\" = we1+2 begin to dig → *kewǣpānæhkæq* → \"begin to dig\"\n- \"kekǣtohnæq\" = we1+2 walk out → *kekǣt- + -ohnæq*\n- \"pahkǣsam\" = he cuts it off → \"cuts off\"\n- \"tawǣsam\" = he cuts a hole in it → \"cuts a hole\"\n- \"nekāweqtam\" = I lie down\n- \"pāhkeqtaw\" = he opens up\n- \"kekēskahtæq\" = we1+2 bite it through\n- \"kepītahtæq\" = we1+2 come eating it; bring it in mouth\n- \"wǣpohnæw\" = he begins walking\n- \"nektāwahtæq\" = we1+2 bite, gnaw a hole in it\n- \"ketǣnam\" = he takes it out by hand\n- \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it\n- \"kēskenam\" = he breaks it through by hand\n- \"pītenam\" = he passes it here\n- \"pāhkaham\" = he opens it by tool (by raising lid)\n\nWe need:\n\n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out\n\nStep 2: Translate each.\n\n1. \"I begin to eat it\" \n- \"begin\" is in *kewǣpeqtaq* (we1+2) \n- \"begin\" also appears in *wǣpohnæw* (he begins walking) → *wǣp-*, so *wǣp-* = begin \n- \"eat\" is not directly given, but \"bite\" or \"gnaw\" is present. \n- \"kepītahtæq\" = we1+2 come eating it → implies \"eating\" as part of action \n- \"kepītahtæq\" has \"come eating\" and \"bring in mouth\" \n- \"bite\" and \"gnaw\" action: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it \n- So, \"begin to bite it\" or \"begin to eat it\" might be derived from \"begin\" + \"bite\" \n- \"begin\" = *kewǣp-* or *wǣp-* \n- \"to eat\" is not directly present, but \"gnaw\" is a verb for eating (especially of food) \n- \"I begin to eat it\" likely = \"I begin to gnaw it\" \n- Pattern: *kewǣp-* + *-tahtæq*? \n- Wait: *ketāwahtæq* = we1+2 bite, gnaw a hole in it → but it's \"bite\" not \"begin to eat\" \n- Perhaps \"begin to eat\" is formed from *kewǣp-* + *-tahtæq* or similar \n- Look for structure: Verb + suffix indicating eating \n- Compare: *kekēskahtæq* = we1+2 bite it through → \"bite through\" \n- *kepītahtæq* = we1+2 come eating it; bring in mouth → \"come eating\" \n- \"begin to eat\" = start to consume → likely *kewǣp-* + *-tahtæq* \n- \"I\" = first person singular \n- In Menominee, \"I\" is marked in root or suffix \n- From \"nekāweqtam\" = I lie down \n- \"nekāwāhpem\" = I fall over laughing \n- So \"I\" = *ne-*, *ne-*, *ne-*\n\nThus, \"I begin to eat it\" → likely: *ne + begin + eat* \n- \"begin\" root = *wǣp-* (from *wǣpohnæw* = he begins walking) \n- \"eat\" = \"gnaw\" = from *ketāwahtæq* \n- So \"begin to gnaw\" → *ne + wǣp-* + *-tahtæq*? \n- But *ketāwahtæq* has *kew*? No → \"ketāwahtæq\", not *kew* \n- \"kew\" only in \"kewǣpeqtaq\", \"kewǣpānæhkæq\" \n- Is there a root for \"eat\"? Not directly. \n- But \"come eating\" in *kepītahtæq* → perhaps \"eat\" is encoded in *-tahtæq* \n- \"begin to eat\" → likely from *kewǣp-* + *-tahtæq* \n- But \"we1+2\" version: *kepītahtæq* → already contains \"come eating\" \n- So \"I begin to eat\" = *ne + wǣp- + tahtæq* → *newǣptahæq*? \n- Check: *kewǣpeqtaq* = we1+2 begin → if \"begin\" is *wǣp-* then *wǣp-* + *-eqtaq* = begin \n- \"begin to bite\" = *wǣp-* + *-tahtæq*? \n- No direct form. \n- What about *kewǣp-* ? *kewǣp-* is in \"we1+2 begin\" \n- So for \"I begin to eat\", perhaps: *ne + wǣp-* + *-tahtæq* → *newǣptahæq* \n- But no such form given. Alternatively, use \"gnaw\" form with \"begin\" prefix \n- Alternative: in *kepītahtæq*, \"we bring it in mouths\" → implies \"eating\" \n- So maybe \"begin to eat\" = *kewǣp-* + *-tahtæq* = we1+2 begin to eat → not \"I\" \n- So we need first person \n- \"I\" = *ne-*, so likely *ne + wǣp-* + *-tahtæq* \n- So *newǣptahæq* \n\nBut no clear example. Try to find \"lay it flat by hand\"\n\n2. \"we1+2 lay it flat by hand\" \n- \"lay flat\" → flat? What verb? \n- \"walk here\" = *nepītohnæm* \n- \"pass here\" = *pītenam* \n- \"break it through by hand\" = *kēskenam* \n- \"take it out by hand\" = *ketǣnam* \n- \"open it by hand\" = *pāhkeqtaw* \n- \"cut it off\" = *pahkǣsam* \n- \"cut a hole\" = *tawǣsam* \n- \"pry it out by tool\" = *nekǣtahan* \n- Is there a verb for \"lay flat\"? \n- \"lay\" may be similar to \"place\" or \"set\". \n- \"Walk here\" – could \"lay\" be a type of setting? \n- Also, \"by hand\" → no tool \n- \"begin to dig\" → *kewǣpānæhkæq* \n- So no \"lay flat\" verb. \n- But \"lay flat\" might be formed from \"set down\" \n- Look at \"we1+2 walk out\" = *kekǣtohnæq* \n- \"we1+2 walk out\" = *kekǣtohnæq* \n- What about \"we1+2 come eating\" = *kepītahtæq* \n- Nothing clearly matches. \nWait — \"we1+2 lay it flat by hand\" → could be from \"set down\" → compare to \"walk\" or \"pass\"? \n- \"walk here\" = *nepītohnæm* \n- No \"set\" or \"lay\" verbs. \n- But \"begin to dig\" → *kewǣpānæhkæq* → dig \n- \"dig a hole\" is separate — see below \n- Perhaps \"lay flat\" is not a direct verb; could it be \"set down\"? \n- But no form. \nAlternative idea: \"lay flat\" → similar to \"place\" \n- \"open it\" = *pāhkeqtaw* \n- \"break it through\" = *kēskenam* → by hand \n- So \"by hand\" might be in *-næm*, *-næq*? \n- \"walk here\" = *nepītohnæm* → ends in -næm \n- \"break it through by hand\" = *kēskenam* → ends in -næm \n- \"take it out by hand\" = *ketǣnam* → ends in -nam \n- So \"by hand\" often ends in -næm or -nam \n- \"lay it flat by hand\" → likely root + -næm \n- What root? \"lay\" — similar to \"set\", \"place\" \n- Is there a verb for \"place\"? \n- No direct example. \n- Perhaps from \"walk\" → can \"walk flat\" be used? Unlikely. \n- Could \"lay\" be from \"set\" — maybe *kew*? \n- Wait: \"walk here\" = *nepītohnæm* → \"nepī\" might be root \n- \"nepī\" → walk \n- What about \"set\"? No. \n- Another thought: \"dig a hole\" → *tawǣsam* = he cuts a hole in it → \"cut a hole\" \n- So digging = \"dig\" → is there \"dig\" verb? \n- No verb directly says \"dig\", but \"begin to dig\" = *kewǣpānæhkæq* \n- \"dig a hole\" = likely *tawǣsam* or *kewǣpānæhkæq*? \n- But *tawǣsam* is \"he cuts a hole in it\" — not \"dig\" \n- \"dig\" may be similar to \"cut\" \n- So \"he digs a hole\" → perhaps *tawǣsam*? But that's \"cuts a hole\" \n- So could be the same. \n- In some contexts, \"cut a hole\" ≈ \"dig a hole\" \n- So \"he digs a hole\" → *tawǣsam*? \n- But *tawǣsam* is \"he cuts a hole in it\" → matches \"digs a hole\" in meaning? \n- Possibly. \n- So \"he digs a hole\" → *tawǣsam* \n\n3. \"he digs a hole\" → likely *tawǣsam* \nBecause: \"tawǣsam\" = he cuts a hole in it → “cuts” likely means “digs” in context. \nIn many languages, \"cut a hole\" = \"dig a hole\" \n\n4. \"he walks out\" → directly given \nIn list: *kekǣtohnæq* = we1+2 walk out → so \"he walks out\" → need 3rd person \nBut in list: only \"we1+2 walk out\" = *kekǣtohnæq* \nIs there a 3rd person \"he walks out\"? \nWe have \"he walks roundabout\" = *wackōhnæw* \nNo \"walks out\" for \"he\" \nBut \"we1+2 walk out\" = *kekǣtohnæq* \nSo likely, \"he walks out\" = *kekǣtohnæq* with 3rd person marker? \nBut no such form given. \nSimilarly, \"he\" appears in: \n- kawāham → he fells it \n- kēskenam → he breaks it \n- pahkǣsam → he cuts it off \n- tawǣsam → he cuts a hole \n- pāhkaham → he opens it \n- wackōhnæw → he walks roundabout \n- ketǣnam → he takes it out by hand \n- nepītohnæm → I walk here \n- pītenam → he passes it here \n\nSo for \"he walks out\", no direct form. \nBut \"we1+2 walk out\" is *kekǣtohnæq* \n\"we1+2\" = we and you \nSo for \"he walks out\", might be *kekǣtohnæq* with third person? \nBut no known marker. \nPerhaps the verb is the same, and \"he\" is implied. \nBut in the original list, only one form for \"walk out\". \nPossibly, the verb is *kekǣtohnæq* regardless of person? \nBut \"I\" and \"he\" have different roots or suffixes. \nWait — what about \"he walks out\" = *kekǣtohnæq*? But that's first person? \nNo — *kekǣtohnæq* is for \"we1+2\" \nSimilarly, \"he walks out\" is not in list. \nBut \"he begins walking\" = *wǣpohnæw* \n\"walks out\" is different — goes away \n\"walks roundabout\" = *wackōhnæw* \nSo \"walks out\" is not directly given. \nBut \"we1+2 walk out\" = *kekǣtohnæq* \nSo likely, for \"he walks out\", it is *kekǣtohnæq* with third person suffix \nBut no such form. \nLook at \"he takes it out by hand\" = *ketǣnam* \n\"takes it out\" — similar to \"walks out\" \n\"walks out\" may be \"takes out\" in movement \nBut \"takes out\" of a container — different \n\"walks out\" = leaves place \n\"kepītahtæq\" = we1+2 come eating → not relevant \nAnother idea: \"walk out\" = *kekǣtohnæq* \nEven though it's \"we1+2\", perhaps it's the only verb for \"walk out\", and for \"he\", it's the same root \nSo we accept *kekǣtohnæq* for \"he walks out\" \nMultiple forms suggest that the verb root *kekǣ- + -tohnæq* covers \"walk out\" for both we and he \nIn the list, only \"we1+2\" is given \nBut in context, likely the verb is *kekǣtohnæq* \n\nNow back to \"I begin to eat it\" \nWe have no \"eat\" verb \nBut \"gnaw\" = *ketāwahtæq* → we1+2 bite, gnaw \n\"begin to gnaw\" = *kewǣp-* + *-tahtæq* \n\"kewǣp\" is used in \"begin\" with \"we1+2\" → *kewǣpeqtaq* \nSo *kewǣp-* → begin \nSo \"begin to gnaw\" = *kewǣptahæq* \nThen for \"I\" — first person → *ne- + kewǣp-* + *-tahtæq* → *newǣptahæq* \nBut is *-tahtæq* used for \"bite/gnaw\"? \nYes — *ketāwahtæq* → we1+2 bite, gnaw \nSo \"I begin to eat it\" → *newǣptahæq* \n\nNow \"we1+2 lay it flat by hand\" \nWhat verb? \nCompare to \"pass it here\" = *pītenam* \n\"break it through by hand\" = *kēskenam* \n\"set down by hand\" — possible root? \nNote: \"walk here\" = *nepītohnæm* → *nepī* → walk \n\"lay it flat\" — might be from \"put\" or \"place\" \nBut not present \nAlternative: \"by hand\" → suffix *-næm* → in *kēskenam*, *ketǣnam*, *nepītohnæm* \nSo likely ends in *-næm* \nRoot: \"lay flat\"? \nDo we have a verb meaning \"lay down\" or \"set\"? \nNot directly \nBut \"we1+2 come eating\" = *kepītahtæq* \nNo \nWait — \"lay it flat\" could be similar to \"set it\" \nBut no. \nAnother possibility: from \"dig\" or \"cut\"? \nNo \nPerhaps it's a missing form, but likely from context.\n\nAlternatively, is \"lay it flat\" a form of \"place\" — and \"place\" might be derived from another root.\n\nBut no such verb.\n\nWait — \"we1+2 walk here\" = *nepītohnæm* \n\"walk here\" — could \"lay\" be \"set\" in place? \nNot directly.\n\nBut in Menominee, some verbs are minimal.\n\nAlternatively, perhaps \"lay it flat\" = *nepītohnæm* with different meaning? \nUnlikely.\n\nAnother idea: look at \"he opens it\" — *pāhkeqtaw* \n\"lay\" is not equivalent.\n\nBut perhaps \"lay flat\" is not a standard verb.\n\nWait — in the list, no verb for \"lay flat\".\n\nBut in the verb list, is there \"set\" or \"place\"? \nNo.\n\nPerhaps we must infer from patterns.\n\nAnother clue: \"by hand\" appears in several verbs: *kēskenam*, *ketǣnam*, *nepītohnæm*, *pītenam* — all end in -næm or -nam\n\nSo likely, \"lay it flat by hand\" → some root + -næm\n\nRoot: \"lay flat\" — what root?\n\nWe have:\n\n- \"walk here\" = *nepītohnæm* \n- \"break through by hand\" =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10747.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Identify the relevant verb forms from the given list that match the meaning of the target sentences.\n\n1. \"I begin to eat it\" \n→ The form \"kewǣpeqtaq\" means \"we1+2 begin\" — this is \"begin\", not \"eat\". \nWe need a verb meaning \"begin to eat\". \nLooking for a form with \"begin\" + \"eat\". \nWe have: \"kepītahtæq\" → \"we1+2 come eating it; we1+2 bring it in our mouths\" \nThis includes \"eating it\", but is in third person (we1+2), and it's about bringing in mouths, not beginning to eat. \nWe have \"ketāwahtæq\" → \"we1+2 bite, gnaw a hole in it\" — close to eating but not \"begin to eat\". \nBut \"begin to eat\" may be a semantic variant. \nIs there a verb for \"begin to eat\"? \nLooking at \"kewǣpānæhkæq\" → \"we1+2 begin to dig\". \nBut no direct form for \"begin to eat\". \nPerhaps \"begin\" is key. \nWe have \"kewǣpeqtaq\" — \"we1+2 begin\" \nAnd \"wǣpohnæw\" — \"he begins walking\" \nSo \"begin\" is expressed by \"kewǣp-\", \"wǣp-\", etc. \nSo \"I begin to eat it\" could be a variant of \"begin\" + food-related action. \nBut there's no direct \"eat\" verb. \nWait: \"kepītahtæq\" = \"we1+2 come eating it\" — this is continuous, not beginning. \nBut \"begin to eat\" might be best captured by \"begin\" + \"eat\" — we don't have a bare \"eat\" verb. \nIs there a verb like \"begin biting\" or \"begin eating\"? \n\"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" — could be used metaphorically? \nBut \"bite\" is not the same as \"eat\". \nAnother candidate: \"kewǣpānæhkæq\" = \"we1+2 begin to dig\" — initiating motion. \nPerhaps \"begin to eat\" is not directly available. \nBut look at \"kepītahtæq\" — \"we1+2 come eating it\" — which implies an action of eating, possibly initiated. \nMaybe the verb \"come eating\" is interpreted as \"begin to eat\" in context. \nAlternatively, is there a form for \"eat\" that is used with \"begin\"? \nNo direct form. \nBut observe: in Menominee, verbs often combine action + manner or instrument. \nAnother thought: \"kepītahtæq\" is \"we1+2 come eating it\" — which might cover \"begin to eat\" in meaning. \nBut it's third person (we1+2), not first person. \nTarget is \"I begin to eat it\". \nSo we need first person singular. \nNo \"I begin to eat\" form. \nBut perhaps \"begin\" is a root: \"wǣp-\" = \"begin\" in \"wǣpohnæw\" = \"he begins walking\". \nCould \"wǣp-\" be used with food? \nUnlikely. \nAlternative: is there a verb for \"eat\" that is missing? \nWait — \"ketāwahtæq\" is \"we1+2 bite, gnaw a hole in it\" — very close to \"bite\" rather than \"eat\". \n\"keskenam\" = \"he breaks it through by hand\" — not eating. \n\"pahkǣsam\" = \"he cuts it off\" — not directly related. \nLook at \"pekāwāhpem\" = \"I fall over laughing\" — unrelated. \nNo verb for \"eat\" appears in the list. \nBut \"kepītahtæq\" = \"we1+2 come eating it\" — this suggests that \"coming to eat\" = \"begin to eat\" in some sense. \nCould \"kepītahtæq\" be used for \"I begin to eat it\"? \nBut subject is \"we1+2\", not \"I\". \nWe need first person. \nPerhaps the root \"kepī-\" means \"come to eat\" — maybe it can be used with \"I\". \nBut no form is given. \nWait — is there a version that can be adapted? \nNo clear form. \nBut note: the form \"kewǣpeqtaq\" is \"we1+2 begin\" — so \"begin\" is a root. \n\"begin to eat\" likely means \"start eating\". \nIs there a verb for \"start to eat\"? \nWe cannot find it directly. \nBut look at the list: \"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" — again, gnaw. \n\"kewǣpānæhkæq\" = \"we1+2 begin to dig\" — so \"begin\" is formed with \"kewǣp-\", and \"to dig\". \nSimilarly, perhaps \"begin to eat\" would be \"kewǣp-\" + \"eat\". \nBut there's no \"eat\" verb. \nAlternative: perhaps \"eat\" is implied in \"come eating it\". \nBut \"come eating\" is a continuous action. \n\"begin to eat\" is a starting point. \nPerhaps the closest is \"kepītahtæq\" — but it's plural. \nBut the verb \"kepī-\" might be used in first person. \nNo such form. \nAnother idea: perhaps \"begin to eat\" is formed with the root \"kewǣp\" (begin) and the action of \"eaten\" or \"eating\". \nBut nothing in the list supports that. \nWait — is there a form like \"begin to bite\"? \n\"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" — could be used as \"begin to bite\"? \nBut again, not \"eat\". \n\"eat\" is broader than \"bite\". \nBut perhaps in the absence of a direct word, the only possible translation from the list is based on verb roots. \nLook at other sentences — maybe we can infer the pattern.\n\n2. \"we1+2 lay it flat by hand\" \n→ \"by hand\" = \"by hand\" → contextually, \"by hand\" appears in: \n\"kēskenam\" = \"he breaks it through by hand\" \n\"nekǣtahan\" = \"I pry it out by tool\" \n\"pāhkaham\" = \"he opens it by tool\" \n\"pītenam\" = \"he passes it here\" — no tool. \nSo \"by hand\" is associated with actions like breaking or prying. \n\"lay it flat\" — what do we have? \n\"kepītahtæq\" = \"we1+2 come eating it\" — not flat. \n\"kekǣtohnæq\" = \"we1+2 walk out\" — not laying. \n\"pahkǣsam\" = \"he cuts it off\" — cutting. \n\"pāhkeqtaw\" = \"he opens up\" — opening. \nNo verb for \"lay flat\". \nBut \"lay flat\" might be \"place it down\" — could be \"put down\" or \"spread\". \nIs there a verb for \"place\" or \"set\"? \nNo. \nBut \"by hand\" suggests an action without tool. \nLook at \"kēskenam\" = \"he breaks it through by hand\" — \"by hand\" is the manner. \nSo the structure is [verb] + [by hand]. \nSo for \"we1+2 lay it flat by hand\" → we need a verb meaning \"lay flat\", with \"by hand\". \nBut no such verb. \nBut is there a form that means \"place\" or \"set\"? \n\"pāhkeqtaw\" = \"he opens up\" — no. \n\"kekēskahtæq\" = \"we1+2 bite it through\" — not. \nWait: \"pītenam\" = \"he passes it here\" — move to a place. \nNot laying. \nPerhaps \"lay flat\" is not a standard verb. \nAlternatively, is \"lay flat\" a form of \"place down\"? \nBut no such form. \nWait — could \"we1+2 come eating it\" be used to mean \"we begin eating\"? \nBut not laying. \nAnother possibility: \"kepītahtæq\" might be the only relevant one, but it's not about laying. \nBut note: \"we1+2 come eating it\" — perhaps \"come\" means \"start\" or \"begin\", and \"eating\" is the action. \n\"Come eating\" might be used as \"begin to eat\". \nBut \"lay flat by hand\" — is there a verb that means \"place\"? \n\nWait: look at \"nekāweqtam\" = \"I lie down\" — lying down. \n\"pāhkeqtaw\" = \"he opens up\" — opening. \nNo verb for placing. \nBut consider: \"pāhkaham\" = \"he opens it by tool\" — opening. \n\"pahkǣsam\" = \"he cuts a hole in it\" — cutting. \nBut perhaps \"lay flat\" is equivalent to \"place it level\". \nIs there a verb for \"put\" or \"set\"? \nNo. \nBut note: \"by hand\" appears in two forms: \"by hand\" in \"kēskenam\" and \"nekǣtahan\". \n\"nekǣtahan\" = \"I pry it out by tool\" — tool. \n\"pāhkaham\" = \"by tool\". \n\"kēskenam\" = \"by hand\". \nSo \"by hand\" is used with breaking. \nThus, if we have \"lay it flat by hand\", we need a verb meaning \"lay\" with \"by hand\". \nBut no such verb. \nPerhaps \"lay flat\" is not a verb in that list. \nBut is there a verb that implies placing or spreading? \nNone directly. \n\n3. \"he digs a hole\" \n→ we have: \"kewǣpānæhkæq\" = \"we1+2 begin to dig\" \n\"we1+2 begin to dig\" — so \"begin to dig\" is there. \nBut for \"he digs a hole\" → first person singular? \n\"he digs a hole\" → third person singular. \nSo we need a form for \"he digs a hole\". \nWe have \"kewǣpānæhkæq\" — \"we1+2 begin to dig\" → plural. \nWe have no verb for \"he digs\" alone. \nBut \"begin to dig\" is there — so perhaps \"dig\" is the root. \nSo for \"he digs a hole\", perhaps it's just \"dig\" + \"hole\" — but no hole-specific form. \nThe verb \"dig\" is present in \"kewǣpānæhkæq\" — so \"dig\" is the verb. \nThus, \"he digs a hole\" could be the form with \"dig\" in third person. \nSo it must be \"kewǣpānæhkæq\" but in third person. \nBut no such form. \nWait — the list has \"pahkǣsam\" = \"he cuts it off\" — not digging. \n\"tawǣsam\" = \"he cuts a hole in it\" — cuts a hole. \n\"tawǣsam\" = \"he cuts a hole in it\" — very close to \"he digs a hole\" — cutting a hole. \nIn some linguistic contexts, \"dig a hole\" and \"cut a hole\" can be used interchangeably. \nSo \"he digs a hole\" ≈ \"he cuts a hole in it\" → tawǣsam \nYes — likely. \nSo \"he digs a hole\" → tawǣsam\n\n4. \"he walks out\" \n→ we have \"kekǣtohnæq\" = \"we1+2 walk out\" \nSo \"we1+2 walk out\" is given. \nWe need \"he walks out\" — third person. \nSo the verb root is \"walk out\", with \"we1+2\" → for \"he\", we need third person singular. \nIn Menominee, verb forms change for subject. \nSo we need a form like \"he walks out\" → from \"we1+2 walk out\" → likely \"kekǣtohnæq\" but for third person. \n\"kekǣtohnæq\" is \"we1+2 walk out\" — so \"he\" would be \"ke-kǣ-tohnæq\" with a different subject marker. \nBut no such form in list. \nWait — in the list, we have \"wǣpohnæw\" = \"he begins walking\" — begins walking, not \"walks out\". \n\"kekǣtohnæq\" is the only form for \"walk out\" — so \"he walks out\" must be a variation of that. \nBut the given list has only \"we1+2 walk out\" — so we infer that \"he walks out\" is a subject-specific form, possibly with a different affix. \nSince subject is \"he\", and only \"we1+2 walk out\" is given, we assume that \"he walks out\" is formed by changing subject to third person. \nBut no form in list. \nHowever, in the list, \"kawāham\" = \"he fells it by tool\" — so third person verb with \"he\" is given. \nSimilarly, \"pāhkeqtaw\" = \"he opens up\" — so third person verbs exist. \nThus, \"he walks out\" should be a third-person singular form of \"walk out\". \nSince \"kekǣtohnæq\" is \"we1+2 walk out\", we infer that the verb \"walk out\" has a third-person form, likely with a different subject marker. \nBut it's not listed. \nSo cannot extract exactly. \nBut perhaps the translation is based on pattern. \nMaybe \"he walks out\" is directly \"kekǣtohnæq\" but with subject changed — but we have to use only the given forms. \nWait — is there a verb for \"walk out\" in third person? \nNo. \nBut we have \"wǣpohnæw\" = \"he begins walking\" — starts walking. \n\"kekǣtohnæq\" = \"we1+2 walk out\" — literal. \nSo for \"he walks out\", perhaps it's not directly available. \nBut the only verb with \"walk out\" is in plural. \nSo likely, the translation is to use the verb form for \"walk out\" and adjust subject. \nBut the instruction is to translate using the given forms. \nRe-examining the list: \n\"kekǣtohnæq\" → we1+2 walk out \n\"pītenam\" → he passes it here \n\"ketǣnam\" → he takes it out by hand \n\"ketāwahtæq\" → we1+2 bite, gnaw a hole in it \n\"kepītahtæq\" → we1+2 come eating it \n\nNow, \"he takes it out by hand\" is \"ketǣnam\" — so \"takes it out\" is used. \n\"walk out\" is a movement. \n\"takes it out\" might be used for \"walk out\" as well? \nBut \"hold it out\" vs \"walk out\". \nPossibly not. \nBut \"walk out\" may be equivalent to \"move out\" or \"exit\". \nWe have no direct form. \nBut perhaps \"kekǣtohnæq\" is the only verb for \"walk out\", and subject is flexible. \nBut the task is to translate into Menominee — using the pattern from the list. \nSo for \"he walks out\", we could use a form derived from \"kekǣtohnæq\" with third person. \nBut no such form. \nPerhaps \"he walks out\" is \"ke-kǣ-tohnæq\" with the subject marker for \"he\". \nBut in the list, no such form. \nBut maybe the pattern is that verbs are subject-marked. \nSo for \"I begin to eat it\", we need a first person verb for \"begin to eat\". \nWe have \"kewǣpeqtaq\" — \"we1+2 begin\" \nSo for \"I begin\", it might be \"kewǣp\" + first person. \nBut no first person \"begin\" verb. \nWe have \"wǣpohnæw\" = \"he begins walking\" → so \"he begins\" = wǣpohnæw \nSimilarly, \"I begin walking\" would be \"ne-wǣpohnæw\"? \nBut no such form. \nSo the verb root \"wǣp-\" means \"begin\". \nSo \"begin to eat\" = wǣp + eat. \nBut no \"eat\" verb. \nHowever, \"kepītahtæq\" = \"we1+2 come eating it\" — which includes \"eating\" — so perhaps \"come eating\" can be used as \"begin to eat\". \nBut it's plural. \nIs there a first person form? \nNo. \nBut perhaps the verb is \"kepītahtæq\" with subject changed. \nBut again, no. \nAlternatively, \"begin to eat\" may be inferred from \"begin to dig\" or \"begin to bite\". \nBut \"begin to bite\" is not given. \nLook at the list: \n\"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" — so \"bite\" is there. \n\"begin to bite\" may be formed from \"kewǣp\" + \"bite\". \nBut not available. \nBut perhaps \"begin to eat\" is expressed by \"wǣp\" + \"eat\", and since \"eat\" is not in list, maybe the only available verb is from \"come eating\". \nBut \"come eating\" is not \"begin to eat\". \n\"Come eating\" suggests gradual action. \n\"begin to eat\" suggests starting point. \nDifferent. \nAnother idea: perhaps \"begin to eat\" is equivalent to \"come eating\" in some contexts. \nIn some languages, \"come to eat\" = \"begin to eat\". \nSo perhaps \"kepītahtæq\" can be used. \nFor \"we1+2 lay it flat by hand\" — is there a verb for \"lay flat\"? \nWe have \"kēskenam\" = \"he breaks it through by hand\" — \"by hand\" is used. \n\"lay flat\" might be \"place it down", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12576.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Identify relevant verb forms in the given list that match the semantic and grammatical patterns in the translation tasks.\n\nTask 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" paired with \"eat\". \nIn the list: \n- \"kewǣpeqtaq\" = we1+2 begin → \"begin\" with subject we1+2 \n- \"kewǣpānæhkæq\" = we1+2 begin to dig → \"begin\" with “dig” \n- \"wǣpohnæw\" = he begins walking → \"begin\" with \"walk\" \nThe verb \"begin\" is present in \"kewǣpeqtaq\", and \"begin to eat\" would likely be a variant with \"eat\" as the object. \nBut no direct \"begin to eat\" is given. \nHowever, \"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths → this has \"eating\" in the sense of consuming. \nStill not \"begin to eat\". \nBut \"begin to eat\" likely combines \"begin\" (start) with \"eat\". \nWe have no form for \"eat\", but \"kepītahtæq\" is about eating. \nPossible inference: \"begin to eat\" = \"begin\" + \"eat\" → the verb \"begin\" must be used with a verb for eating. \nBut no exact form. \nWait: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\" \n\"bite\" is closely related to \"eat\". \nBut \"begin to eat\" might be formed from \"begin\" + \"eat\" → if \"begin\" is \"kewǣpeqtaq\", and the verb for eating is not present, perhaps we can use \"kewǣpeqtaq\" in a derived way. \nBut we lack a form for \"eat\". \nAnother possibility: is there a form for \"begin to eat\" in a separate structure? \nNote: \"kepītahtæq\" is \"we1+2 come eating it\" → eating is part of the action. \nBut \"I begin to eat it\" → subject is \"I\", not \"we\", and the action is initiating. \nSo we need a verb with \"begin\" (root) + \"eat\". \nNo direct form. But look at \"kewǣpeqtaq\" = \"we1+2 begin\" → base. \nFor \"I begin to eat it\", we need the 1st person singular \"begin\" + \"eat\". \nBut \"eat\" is absent. \nWait — is \"ketāwahtæq\" used? That's \"we1+2 bite, gnaw\" → not \"eat\". \nBut perhaps \"bite\" is used as a generic form of \"eat\" in this context? \nNo, not convincing. \nWait — is there a verb that means \"start\" and is used with food? \n\nAlternative: look at \"kepītahtæq\" = \"we1+2 come eating it\" → implies eating during movement. \nStill not \"begin to eat\". \n\nCheck the verb for \"begin\" in 1st person: \n- \"kewǣpeqtaq\" is for \"we1+2\" \n- \"wǣpohnæw\" is \"he begins walking\" → \"begin\" with \"walk\" \n→ So \"begin\" is a verb, attached to a complement. \nSo likely, \"begin to eat\" would be an inflected form of \"begin\" with \"eat\". \nBut no such form exists. \nUnless we assume that eating is implied or that \"begin to eat\" is formed from a verb root like \"eat\" with \"begin\". \n\nBut we don't have \"eat\" as a verb. \nHowever, note: in Menominee, verbs are often transitive, and many action verbs are compound. \nLook back: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → suggests \"gnawing\" \n\"bite\" may be used in eating contexts. \nBut still, no \"begin to eat\". \n\nPossible error: perhaps \"begin to eat\" is formed from \"begin\" + \"eat\", and if \"eat\" is not present, there’s a missing verb. \nBut maybe the verb \"kepītahtæq\" is the closest — \"come eating\" — so beginning the action of eating. \nBut subject is \"we1+2\", not \"I\". \n\nWait — the verb \"kewǣpeqtaq\" is for \"we1+2 begin\". \nWe need \"I begin to eat it\". \nIs there a 1st person form? \nNo direct form in list. \nBut perhaps the root for begin is \"kewǣp-\", and \"eat\" is implied. \nStill no. \n\nAlternative idea: perhaps \"begin to eat\" = \"begin\" + \"eat\", but in Menominee, \"eat\" is not a standalone verb. \nLooking at the list: \n\"kepītahtæq\" = we1+2 come eating it → \"eating\" \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → eating a hole? \n\"Not clear\". \n\nBut recheck: there is no verb for \"eat\". \nSo perhaps \"begin to eat\" is formed from \"begin\" and \"eat\" — but no verb for eat. \nThen maybe the translation must be based on existing roots. \n\nWait — is there a verb form for \"begin\" in 1st person? \nNot in list. \n\"kewǣpeqtaq\" is we1+2. \n\"wǣpohnæw\" is \"he begins walking\". \nSo \"begin\" is not a standalone verb; it is attached. \n\nConclusion: likely, \"I begin to eat it\" → use the root \"kewǣp\" for \"begin\", and apply to \"eat\", but no \"eat\" verb. \n\nBut perhaps \"bite\" is used as \"eat\" in a loose sense. \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → this is not \"eat\". \n\"begin to bite\" would be \"begin biting\", not \"begin to eat\". \n\nBut in some contexts, \"bite\" implies eating. \nStill, not convincing. \n\nAlternative: look at \"kepītahtæq\" → \"we1+2 come eating it\" → perhaps \"come eating\" implies \"start to eat\"? \nBut subject is plural, not \"I\". \n\nSo perhaps \"I begin to eat it\" is not directly available. \nBut maybe the base verb is \"kewǣpeqtaq\" — \"begin\" — and we can use the 1st person present for \"begin\" with the object \"it\". \nBut no such form exists in the list. \n\nWait — what about \"we1+2 begin to eat\" — is there a form? \nNo. \n\nBut observe: there is a form \"kewǣpānæhkæq\" = we1+2 begin to dig → \"begin\" + \"dig\" \nSimilarly, \"kekǣtohnæq\" = we1+2 walk out \nSo \"begin to dig\" has the structure: \"begin + verb\" → and the verb is \"dig\". \n\nSo perhaps \"begin to eat\" = begin + eat → but eat is missing. \n\nBut \"eat\" might be implied by \"bite\" or \"gnaw\". \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — \"bite\" includes eating. \n\nSo perhaps \"begin to eat\" is directly rendered as \"kewǣp\" + \"eat\", but since eat is not present, and bite is used for eating, we can use \"begins to bite\" — but that's not \"eat\". \n\nBut in Menominee, language may use \"gnaw\" or \"bite\" for eating. \nHowever, the intended solution may be to use the \"begin\" verb with a verb for eating. \n\nBut we have no such form. \n\nWait — perhaps the verb \"kepītahtæq\" = \"we1+2 come eating it\" — is this used for \"begin to eat\"? \n\"Come eating\" might imply initiation. \n\nBut again, subject is plural. \n\nSo perhaps \"I begin to eat it\" uses the root \"kewǣp\" with object \"it\", and the verb for eating is missing. \n\nBut notice: in the list, \"nektāwāhtæq\" is not listed — wait, given is \"ketāwahtæq\" — yes. \n\nWait — is there a form like \"kewǣp[eat]\"? \n\nNo. \n\nAlternative approach: look at the other tasks first. \n\nTask 2: \"we1+2 lay it flat by hand\" \nLook for \"lay flat\" or \"place flat\". \n\"nektāwāhtæq\" is not in list — given is \"nekāwāhpem\" = I fall over laughing \n\"pāhkeqtaw\" = he opens up \n\"kepītahtæq\" = we1+2 come eating it \n\"pītenam\" = he passes it here \n\"kekēskahtæq\" = we1+2 bite it through \n\"pahkǣsam\" = he cuts it off \n\"kekǣtohnæq\" = we1+2 walk out \n\"nektāwāhtæq\" — not present. \n\nIs there a verb for \"place\" or \"lay\"? \n\"nektāwāhtæq\" — missing. \nBut \"kekāwahtæq\" — not in list. \n\nWait — \"pāhkeqtaw\" = he opens up → opening \n\"pītenam\" = he passes it here → passing \n\"nekāweqtam\" = I lie down \n\"pekāwāhpem\" = I fall over laughing \n\nNo verb for \"lay\" or \"place\". \n\nBut \"lay it flat by hand\" → \"place\" with \"flat\" and \"by hand\" → \"hand\" is a common modifier. \n\nLook at: \"nepītohnæm\" = I walk here → \"walk\" \n\"pāhkaham\" = he opens it by tool → \"by tool\" \n\"nekǣtahan\" = I pry it out by tool → \"by tool\" \n\"ketǣnam\" = he takes it out by hand → \"by hand\" \n\nAh! \"ketǣnam\" = he takes it out by hand → \"by hand\" is used. \nAlso, \"by hand\" is used in \"he takes it out by hand\". \n\nSo \"by hand\" is a modifier. \n\nSimilarly, \"by tool\" is used in \"pāhkaham\", \"nekǣtahan\". \n\nSo \"lay it flat by hand\" likely uses a verb like \"place\" or \"set\" with \"by hand\". \n\nBut no such verb exists in the list. \n\nWait — is there a form for \"place\"? \n\nLook at \"kepītahtæq\" = we1+2 come eating it — \"come\" with eating \n\"kekǣtohnæq\" = we1+2 walk out — \"walk out\" \n\"pahkǣsam\" = he cuts it off \n\"kekēskahtæq\" = we1+2 bite it through \n\nNo. \n\nBut \"begin to dig\" is in list — \"kewǣpānæhkæq\" = we1+2 begin to dig \n\nSo \"dig a hole\" → \"dig\" is a verb, and \"a hole\" is the object. \n\nSo \"he digs a hole\" → likely \"pahkǣsam\"? No — \"pahkǣsam\" = he cuts a hole in it → cutting a hole. \n\n\"dig a hole\" = digging a hole. \n\nLook for \"dig\" verb. \n\"kewǣpānæhkæq\" = we1+2 begin to dig → \"begin to dig\" \nSo \"dig\" is possible — \"dig\" = \"pāhka?\" or \"pāhkā\"? \n\n\"pāhkaham\" = he opens it by tool → not dig. \n\"pahkǣsam\" = he cuts a hole in it → close to digging. \n\nBut \"cut a hole\" vs \"dig a hole\" — different. \n\"dig\" is not directly available. \n\nBut \"begin to dig\" is in list, so \"dig\" must be a verb root. \n\nSo for \"he digs a hole\", use \"dig\" verb. \nBut which form? \n\nWe have no \"he digs\" form. \nWe have \"we1+2 begin to dig\" = kewǣpānæhkæq \nWe have \"he begins walking\" = wǣpohnæw \n\nSo for \"he digs\", no direct form. \n\nBut perhaps \"dig a hole\" is formed with the root \"pahk\" → from \"pahkǣsam\" which is \"he cuts a hole in it\" — close. \n\nSo perhaps \"he cuts a hole\" is a good proxy for \"he digs a hole\"? \nIn context, \"cut a hole\" can mean \"dig a hole\". \n\nSimilarly, in many languages, \"cut a hole\" = \"dig a hole\". \n\nSo possible: \"pahkǣsam\" → \"he cuts a hole in it\" → could be used for \"he digs a hole\" — with slight semantic shift. \n\nBut the instruction is to translate based on the patterns. \n\nTask 3: \"he walks out\" \n\"kekǣtohnæq\" = we1+2 walk out → \"we1+2 walk out\" \nSo \"he walks out\" — subject is \"he\", not \"we\". \n\nWe have \"wǣpohnæw\" = he begins walking → \"he begins walking\" \n\"kekǣtohnæq\" = we1+2 walk out → includes \"walk out\" for plural. \n\nSo for \"he walks out\", we need a form for \"he\" + \"walk out\". \n\nBut the only close form is \"kekǣtohnæq\" = we1+2 walk out. \n\nSo maybe the form is \"kekǣtohnæq\" with subject \"he\"? \n\nBut in the list, no 3rd person singular \"he walks out\". \n\nSo perhaps the pattern is that \"walk out\" is a fixed verb form, and it is used in both \"we1+2 walk out\" and \"he walks out\" if the verb is shared. \n\nIn native languages, some verb forms are invariable. \n\nSo \"kekǣtohnæq\" is the verb for \"walk out\" — and it may be used with different subjects. \n\nBut subject is marked: \"we1+2\" for that one. \n\nWe need to find the root. \n\nNow, back to \"I begin to eat it\". \n\nAfter reevaluation: perhaps \"begin to eat it\" is best formed by using \"begin\" + \"eat\", and based on the pattern, \"kewǣpeqtaq\" is \"we1+2 begin\", so \"I begin\" would be a different form. \n\nBut no such form. \n\nIs there a form that means \"eat\"? \n\nLook at: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — could \"bite\" imply \"eat\"? \nPossibly. \n\n\"come eating\" — \"kepītahtæq\" — this may mean \"start to eat\". \n\n\"come eating\" = when you arrive and begin eating. \n\nSo perhaps \"I begin to eat it\" = \"kewǣp\" + \"eat\", but we lack the verb. \n\nBut in the list, \"kepītahtæq\" = \"we1+2 come eating it\" → so \"come eating\" is a verb. \n\n\"come eating\" = start to eat. \n\nSo maybe \"I begin to eat it\" = \"I come eating it\"? \nBut \"come\" is not \"begin\". \n\n\"come\" and \"begin\" are different. \n\nBut in some contexts, \"come\" can mean \"start\". \n\nStill, not strong. \n\nThen what about \"begin\" + \"eat\" as a compound? \n\nNo such form. \n\nBut observe: \"wǣpohnæw\" = he begins walking → \"begin\" is with \"walk\" \n\"kewǣpānæhkæq\" = we1+2 begin to dig → \"begin\" with \"dig\" \nSo the structure is: \"begin + verb\" for the main action. \n\nSo \"begin to eat\" = \"begin + eat\" → verb for eat must exist. \n\nBut eat is not listed. \n\nUnless \"gnaw\" or \"bite\" is used as \"eat\". \n\n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" can include \"eat\" in food context. \n\nSo perhaps \"I begin to eat it\" is \"kewǣp\" + \"bite it\" → but no such form. \n\nThe only verb form with \"begin\" and a food-related action is missing. \n\nTherefore, likely the intended solution is: \n- \"I begin to eat it\" → \"kewǣp\" + \"eat\" — but not present \nPerhaps the verb is \"kepītahtæq\" — but subject is wrong. \n\nWait — is there a verb for \"begin\" in 1st person? \n\nNo. \n\nAnother possibility: perhaps the verb for \"begin\" is used in the form of \"kewǣp\" with the object, and the object \"eat\" is not present. \n\nBut we have to go with given forms. \n\nPerhaps the pattern is that \"begin\" is used with a verb root, and for \"eat\", the closest is \"bite\" or \"gnaw\". \n\nBut still not. \n\nLet’s try the others. \n\nTask 2: \"we1+2 lay it flat by hand\" \nWe have \"ketǣnam\" = he takes it out by hand → \"by hand\" \nSo \"by hand\" is used. \n\nIs there a verb for \"lay flat\"? \n\n\"pāhkeqtaw\" = he opens up \n\"pītenam\" = he passes it here \n\"nepītohnæm\" = I walk here \n\"kepītahtæq\" = we1+2 come eating it \n\nNo. \n\nBut perhaps \"lay it flat\" is not direct. \n\n\"lay flat\" could be \"place on a surface\". \n\nBut no such form. \n\n\"Walk here\" is \"nepītohnæm\" — not relevant. \n\n\"walk out\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12302.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the verb patterns in the provided verb forms.\n\nLook for verbs related to \"begin\", \"lay flat\", \"dig a hole\", and \"walk out\".\n\n1. \"I begin to eat it\" → \"begin\" is already present in \"kewǣpeqtaq\" (we1+2 begin) and \"wǣpohnæw\" (he begins walking). \n \"to eat\" is not directly given, but \"kepītahtæq\" means \"we1+2 come eating it; we1+2 bring it in our mouths\". \n This suggests \"eating\" is associated with \"come eating\" or \"bring in our mouths\". \n But we need \"begin to eat it\". \n The verb “begin” appears in \"kewǣpeqtaq\" and \"kewǣpānæhkæq\" (we1+2 begin to dig). \n \"begin to dig\" uses \"kewǣpānæhkæq\". \n “begin” is a root with a prefix and suffix. \n “begin to eat” → derivative of “begin” + “eat”.\n\n But no direct form for \"eat\" is given. However, “kepītahtæq” involves eating, and the structure includes “come eating”. \n Perhaps the verb “begin to eat” is formed with the root \"kewǣp\" (begin) + \"eat\" as a derived action. \n Is there a form with “begin” + “eat”?\n\n Observe that “kepītahtæq” = we1+2 come eating it → implies eating is the action. \n So \"begin to eat\" would require a verb with “begin” + “eat”.\n\n But none of the entries have \"eat\".\n\n However, note that “kepītahtæq” = we1+2 come eating it → the verb may be based on \"kewǣp\" root, and \"come eating\" implies starting the eating process. \n Possibly, “begin to eat” is a transformation of the root \"kewǣp\" + \"eat\" → but no such form.\n\n Wait: “kewǣpeqtaq” = we1+2 begin → “kewǣp” root. \n “kewǣpānæhkæq” = we1+2 begin to dig → so “kewǣp” + “dig”.\n\n So for “begin to eat”, we may use \"kewǣp\" + \"eat\". But \"eat\" is not in the forms. \n Alternative: \"kepītahtæq\" includes \"come eating\", which may be the same root.\n\n Maybe the base verb “begin” is “kewǣp”, and the action is derived. \n But no form with \"eat\" exists.\n\n Wait — perhaps “eat” is implied in a verb like “kepītahtæq”, but that means “come eating”, not “begin to eat”.\n\n No direct match.\n\n Let’s look for “lay it flat by hand”.\n\n2. “we1+2 lay it flat by hand” → “lay flat” is parallel to “walk here”, “walk out”, etc.\n\n What verbs involve \"lay\" or \"place\" flat?\n\n “nepītohnæm” = I walk here (to this place) \n “pāhkeqtaw” = he opens up \n “pekāwāhpem” = I fall over laughing — not relevant.\n\n No “place” or “lay” verbs.\n\n But note “pāhkaham” = he opens it by tool → “open” \n “nekǣtahan” = I pry it out by tool → “pry” \n “pahkǣsam” = he cuts it off \n “tawǣsam” = he cuts a hole in it\n\n Nothing suggests “lay flat by hand”.\n\n But recall “kepītahtæq” = we1+2 come eating it → implies bringing in mouth → not laying.\n\n Is there any verb with “place”?\n\n Wait: “ketǣnam” = he takes it out by hand → “take out” \n “ketāwahtæq” = we1+2 bite, gnaw a hole in it → “bite”\n\n Still not matching.\n\n Alternate idea: use the root for “begin” in combination with the verb for “eat”.\n\n But no verb for “eat” is given.\n\n However, look at “kepītahtæq” — it includes “come eating it” → perhaps “eating” is the verb. \n Could “begin to eat” be formed by adding “begin” prefix to “eating”?\n\n But the forms show that “begin” has a different root: “kewǣp”.\n\n Another possibility: the verb “begin” is used as a root, and the other part is derived.\n\n In “kewǣpānæhkæq” = we1+2 begin to dig → “kewǣp” + “dig”\n\n So “begin to eat” = “kewǣp” + “eat”\n\n But we don’t have “eat” in the forms.\n\n Wait — is there a verb with “eat”?\n\n “kepītahtæq” = we1+2 come eating it → implies “eating” is the verb, and “come” is part of it.\n\n Possibly, “begin to eat” is not directly listed, but “begin” and “eat” are separate.\n\n Could “eat it” be represented by a verb that means “bring in mouth” or “consume”? \n That might be \"kepītahtæq\", but it's \"come eating\", not \"begin to eat\".\n\n What if we suppose that “begin to eat” uses the root \"kewǣp\" combined with a form for “eat”?\n\n But no form for “eat” is given.\n\n Perhaps “eat” is a verb that behaves like “cut”, “break”, etc.\n\n However, the only verb involving consumption is “kepītahtæq” → “come eating”.\n\n No “lay flat” verb either.\n\n3. \"he digs a hole\" → “dig a hole”\n\n Look: “kewǣpānæhkæq” = we1+2 begin to dig \n “pahkǣsam” = he cuts it off \n “tawǣsam” = he cuts a hole in it → “cuts a hole” \n “pāhkaham” = he opens it by tool \n “nekāweqtam” = I lie down\n\n “tawǣsam” = he cuts a hole in it → very close to “dig a hole”\n\n So “he digs a hole” → “tawǣsam”\n\n This seems plausible.\n\n4. “he walks out” → “walk out”\n\n There is “kekǣtohnæq” = we1+2 walk out → “we1+2 walk out”\n\n So “he walks out” must be the third person singular form.\n\n In Menominee, person marking: \n “we1+2” = we and you \n “I” = singular first person → appears in “nepītohnæm”, “nekāweqtam”, “nekǣtahan” \n “he” = third person → “kawāham”, “kēskenam”, “pahkǣsam”\n\n So from “kekǣtohnæq” = we1+2 walk out → the verb for “walk out” is “kekǣtohnæq” \n Then “he walks out” → must be third person singular form.\n\n We need to find a form with “he” and “walk out”.\n\n Is there a derived form?\n\n The root for “walk” appears in:\n - nepītohnæm = I walk here\n - kekǣtohnæq = we1+2 walk out\n - wǣpohnæw = he begins walking\n\n “wǣpohnæw” = he begins walking → not “walks out”\n\n “kekǣtohnæq” = we1+2 walk out\n\n No third person singular “walk out”.\n\n But perhaps the root is “kekǣtoh” + “næq” → “walk out”\n\n Then “he walks out” = he + walk out → likely “kekǣtohnæq” with third person prefix?\n\n In the list:\n - “nepītohnæm” = I walk here → first person\n - “kekǣtohnæq” = we1+2 walk out → second person inclusive\n - “wǣpohnæw” = he begins walking → not “walk out”\n\n So perhaps the verb for “walk out” is not marked by person in the given list.\n\n But the form “kekǣtohnæq” is for “we1+2 walk out” → so for “he walks out”, it may be a derived or inflected form.\n\n However, the pattern suggests that for “walk out”, the verb is “kekǣtohnæq”, and for singular, it might be “kekǣtohnæ” or “kekǣtoh”? Not given.\n\n But in the list, there is no third person singular verb for “walk out”.\n\n However, notice “wǣpohnæw” = he begins walking → “begins walking” → different from “walks out”\n\n “wǣpohnæw” = he begins walking → “begins walking”\n\n So “begin walking” is available.\n\n “walk out” is something else.\n\n But in the list, “kekǣtohnæq” = we1+2 walk out → so the base form is “kekǣtoh”?\n\n Then “he walks out” would require the third person singular form.\n\n But the forms do not show person marking for “walk out”.\n\n Only one verb for “walk out” is provided: “kekǣtohnæq” → we1+2.\n\n So perhaps the verb is “kekǣtohnæq” for all, with person marking by context? \n But that’s not likely.\n\n Alternatively, the root “kekǣtoh” might be used with different suffixes.\n\n Wait: “nepītohnæm” = I walk here → base “nepītoh” + “næm” → “næm” = here\n\n “kekǣtohnæq” = walk out → “næq” = out?\n\n So “walk out” = kekǣtohnæq\n\n For “he”, it may be formed similarly.\n\n But no direct third person singular.\n\n In Menominee, verb structure often involves root + directional or manner suffixes.\n\n Since the form “kekǣtohnæq” is given for “we1+2 walk out”, and “he” is a third person, perhaps the verb for “he walks out” is formed by a different root or suffix.\n\n However, another verb: “wǣpohnæw” = he begins walking → shows that “begin walking” exists.\n\n No “walk out” for he.\n\n But perhaps “he walks out” is just “kekǣtohnæq” with the person marked by context or inflection not shown.\n\n But that doesn’t make sense.\n\n Wait — is there a verb: “he walks” without direction?\n\n We have:\n - “nepītohnæm” = I walk here\n - “kekǣtohnæq” = we1+2 walk out\n\n So “walk” has different directional components.\n\n So “he walks out” must be “kekǣtohnæq” with third person singular.\n\n But that form is given only for “we1+2”.\n\n No such form listed.\n\n So perhaps the translation uses “kekǣtohnæq” as the base, and for “he”, it is inferred.\n\n But we must use the listed forms.\n\n All verbs have person and number marking.\n\n So for “I begin to eat it” → must be first person singular with “begin to eat”\n\n First person: I\n\n “kewǣpeqtaq” = we1+2 begin → so for “I begin”, it may be “kewǣp” + something.\n\n But no first person “begin”.\n\n “nepītohnæm” = I walk here → first person\n\n So “begin” is not marked in first person.\n\n Wait — is there a verb “I begin”?\n\n No form is given.\n\n The only “begin” forms are plural.\n\n “kewǣpeqtaq” = we1+2 begin \n “kewǣpānæhkæq” = we1+2 begin to dig\n\n So perhaps “begin” is not marked for first person.\n\n For “I begin to eat it”, perhaps it is formed from the root “kewǣp” + “eat”.\n\n But no “eat” verb.\n\n However, the verb “kepītahtæq” = we1+2 come eating it → “come eating”\n\n So perhaps “eating” is the base verb, and “begin to eat” is not directly available.\n\n But we have one verb that involves “come eating”.\n\n Alternative idea: “begin to eat” = “kewǣp” + “eat” → but no “eat” form.\n\n Is there a verb that means “take in mouth” or “consume”?\n\n “kepītahtæq” = we1+2 come eating it → implies consuming.\n\n So “begin to eat it” might be derived from this.\n\n But no.\n\n Wait: perhaps “begin to eat” is “kewǣp” + “kepītaht” → but not in the list.\n\n Unclear.\n\n Let's reexamine.\n\n For “he digs a hole” → \"tawǣsam\" = he cuts a hole in it → matches.\n\n For “he walks out” → “kekǣtohnæq” is for “we1+2 walk out” → so “he walks out” → likely the third person singular, which is not listed.\n\n But in the list, no verb for “he walks out”.\n\n However, in Menominee, verbs are often marked by person.\n\n So perhaps “he walks out” is formed with a third person prefix.\n\n But the only form with “walk out” is “kekǣtohnæq”.\n\n Unless the form “kekǣtohnæq” is used for all, and the person is implied.\n\n But that seems weak.\n\n Alternatively, look for verbs with “walk” and “out”.\n\n Only “kekǣtohnæq”.\n\n So we must accept that for “he walks out”, the form is “kekǣtohnæq” with person marked.\n\n But no such form.\n\n Perhaps “walk out” is not present — unless the verb is “kekǣtohnæq” for all.\n\n But the language has person marking.\n\n Another verb: “wǣpohnæw” = he begins walking → not walking out.\n\n “ketǣnam” = he takes it out by hand → “takes out”\n\n “ketāwahtæq” = we1+2 bite, gnaw a hole in it → “bite”\n\n No “walk out”.\n\n Only one verb has “out”: “kekǣtohnæq”.\n\n So likely, “he walks out” = kekǣtohnæq.\n\n Similarly, for “we1+2 lay it flat by hand” — nothing in the list.\n\n But “lay flat” — “flat”?\n\n “walk here” is “nepītohnæm” — “here”\n\n “lay flat” — possible derivation from “place”?\n\n No verb.\n\n “pāhkeqtaw” = he opens up → not “lay flat”\n\n “nekāwāhpem” = I fall over laughing\n\n No.\n\n So how to form “we1+2 lay it flat by hand”?\n\n “by hand” is common in some verbs.\n\n For example:\n - “kāwāham” = he fells it by tool → “by tool”\n - “nekǣtahan” = I pry it out by tool → “by tool”\n - “pāhkaham” = he opens it by tool → “by tool”\n - “nekāweqtam” = I lie down — not relevant\n\n So “by hand” might be a suffix or marker.\n\n What verbs have “by hand”?\n\n “ketǣnam” = he takes it out by hand → “by hand”\n\n Yes! “ketǣnam” = he takes it out by hand\n\n So “by hand” is used.\n\n So “we1+2 lay it flat by hand” → “lay it flat” + “by hand”\n\n What is “lay it flat”?\n\n Is there a verb for “lay”?\n\n No direct verb.\n\n But perhaps “lay flat” is formed by a root for “place” or “put”.\n\n Not in list.\n\n But “kepītahtæq” = we1+2 come eating it → “come eating”\n\n Still not.\n\n Wait — “nepītohnæm” = I walk here — directional.\n\n Perhaps “lay flat” is not directly present.\n\n Alternative: is there a verb for “place” or “set”?\n\n Not given.\n\n But “kepītahtæq” has “bring in mouth”, which is a form of “consume”.\n\n No.\n\n Perhaps “lay it flat” is not a direct translation, but derived.\n\n But we must use the verbs given.\n\n Let's go back to one that is clear:\n\n \"he digs a hole\" → “tawǣsam” = he cuts a hole in it → \"cuts a hole\" → fits.\n\n \"he walks out\" → only form is “kekǣtohnæq” for “we1+2 walk out” → no form for he.\n\n However, in the list, “kekǣtohnæq” is for “we1+2 walk out” — it's a specific verb.\n\n Could it be used for “he walks out” in a simplified form?\n\n Unlikely.\n\n But is there a verb that means “he walks out”?\n\n No.\n\n So perhaps the verb is “kekǣtohnæq” with a third person prefix.\n\n But no such form is given.\n\n However, in the problem, the verb forms given are all that are provided — so we must use them.\n\n For “he walks out” → the closest match is “kekǣtohnæq” — even if it's for plural.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12572.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "iid", + "sample_index": 0, + "output": "We are given several sentences in Nooni from different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, which is a day in the Nooni week.\n\nWe must infer the linguistic pattern, especially regarding time references and how days are named and referenced, to correctly translate these.\n\n---\n\nStep 1: Identify the days mentioned\n\nFrom the examples:\n\n- Bvutfu: mentioned multiple times\n- Bvusɔw: mentioned in (2), (4), (5), (6), (7)\n- Bvuzhi: (3)\n- Bvuŋka: (4), (5), (6), (7), (13), (14)\n- Bvuŋkaden: appears in (8), (9), (10), (11)\n\nWe are told the sentences are spoken on **Bvuŋkaden**, so we need to interpret them based on how time expressions are formed.\n\n---\n\nStep 2: Analyze time expressions\n\nWe observe patterns of time references:\n\n- \"The day after tomorrow is Bvutfu\" → (5) → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n - So: \"day after tomorrow\" = \"ntfǔː\" (cf. \"ntfǔː\" = tomorrow in (8)? \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\")\n\n- \"The day before yesterday was Bvuŋka\" → (11) → \"kefwé cí nú bvûŋka\"\n - \"kefwé\" = day before yesterday → so \"day before yesterday\" = \"kefwé\"\n\n- \"Today\" = \"wɔ̀ tɔ̀\" (in 6: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → You(sg) heard the thief a long time ago)\n\n- \"Tomorrow\" = \"ntfǔː\" (in 8: \"Tomorrow is Bvuŋkaden\")\n\n- \"The day after tomorrow\" = \"fɔ̀ shě ntfǔː\" → (5): \"The day after tomorrow is Bvutfu\"\n\nSo:\n- Today = wɔ̀ tɔ̀\n- Tomorrow = ntfǔː\n- The day after tomorrow = fɔ̀ shě ntfǔː\n- The day before yesterday = kefwé\n- Yesterday = cǐ (in 1: \"Yesterday was Bvumbon\")\n\nThus, time reference markers:\n- cǐ = yesterday\n- kefwé = day before yesterday\n- ntfǔː = tomorrow\n- fɔ̀ shě ntfǔː = day after tomorrow\n- wɔ̀ tɔ̀ = today\n\nAlso, these are used with speaker’s day to reference other days.\n\n---\n\nStep 3: Reflexive time expressions\n\nNote that the day name is embedded in the sentence as a noun (e.g., \"On Bvutfu\", \"On Bvusɔw\")\n\nIn example (5): \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nSimilarly, (8): \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n\nSo structure: [time expression] + nú + [day]\n\nThus, structure is: [reference] nú [day]\n\n---\n\nStep 4: Translate each sentence on Bvuŋkaden\n\n**16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː**\n\n- \"bvúsɔ̀w\" = \"On Bvusɔw\"\n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n- So: \"On Bvusɔw, the day after tomorrow\"\n\nWait — but that doesn't make sense. \"On Bvusɔw, the day after tomorrow\" is awkward.\n\nAlternatively, could \"bvúsɔ̀w\" be a verb?\n\nLook back: sentence (2) is: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you(sg) will steal the yam\"\n\nSo \"bvúsɔ̀w\" is a day.\n\nSimilarly, (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nSo all are of form: [on [day]] [predicate]\n\nSo 16: \"On Bvusɔw, the day after tomorrow\" — still awkward.\n\nWait — could \"fɔ̀ shě ntfǔː\" be something else?\n\nIn (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = day after tomorrow\n\nThus, sentence 16: \"On Bvusɔw, the day after tomorrow\" → ungrammatical.\n\nIs there a different interpretation?\n\nWait — maybe it's \"On Bvusɔw, [something] happens on the day after tomorrow\"?\n\nBut there's no verb.\n\nCould it be \"On Bvusɔw, [someone] will steal the yam\"?\n\nBut no verb.\n\nLook at the verb forms:\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you(sg) will steal the yam on Bvusɔw\"\n\nSo structure: [Subject] [verb] [object] [on day]\n\nIn (17): \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me\" = I \n\"nú\" = on \n\"ŋgéː\" = will/going to \n\"nyɛ́n\" = the man \n\"kèŋkfǔ\" = the yam \n\"lé\" = steal \n\"ɛ̀bɛ̀n\" = the woman\n\nSo \"I will steal the yam from the woman\" — or \"I will take the yam from the woman\"?\n\nBut \"nyɛ́n\" = man, \"kèŋkfǔ\" = yam → \"the man will steal the yam\"?\n\nBut \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → likely: \"I will steal the yam from the man\" or \"the man\" is object?\n\nWait — more likely: \"I will steal the yam from the woman\"?\n\nBut \"kèŋkfǔ\" = yam, \"lé\" = steal, \"ɛ̀bɛ̀n\" = woman → so \"steal the yam from the woman\"?\n\nBut \"nyɛ́n\" = man → so \"from the man\"? Or is \"nyɛ́n\" the subject?\n\nPossibly misanalysis.\n\nBetter to see: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\nCompare to (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you(sg) will steal the yam on Bvusɔw\"\n\nSo pattern: [subject] [verb] [object] [on day]\n\nSo: me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\n\n→ \"I will steal (the yam) (from the man) [on something]\"\n\nNo day mentioned → unless \"nú\" is connecting to a day?\n\nIn structure, \"nú\" is used only before a day, not after.\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" — no nú\n\nOnly in (4), (5), (8), (9), (12), (13), (14), (15) do we see \"nú\"\n\nIn (12): \"me nú nfí dìɛ̀msɛ̌n\" → \"On Bvutfu, I am about to help the man\"\n\nSo \"nú\" introduces the day.\n\nSo: in sentences with \"nú\", we have a day after \"nú\"\n\nThus, in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → does not contain \"nú\"\n\nSo this may not have a day in the usual \"on X\" form.\n\nBut \"bvúsɔ̀w\" is a day, so probably it's: \"On Bvusɔw, [something is happening] on the day after tomorrow\"\n\nBut \"fɔ̀ shě ntfǔː\" = day after tomorrow — how can it be the time of an event on another day?\n\nWait — is \"fɔ̀ shě ntfǔː\" acting as a day?\n\nNo, in (5), \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → the day after tomorrow is Bvutfu → so it's a time reference, not a day name.\n\nSo the structure is: [time reference] nú [day]\n\nTherefore, in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — the day \"Bvúsɔ̀w\" is paired with the time \"the day after tomorrow\"?\n\nNot clear.\n\nBut perhaps it's a misreading.\n\nWait — could \"nǔ\" be a verb?\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you(sg) will steal the yam on Bvusɔw\"\n\nSo \"nǔ\" = will\n\n\"nǔ\" is a future marker.\n\nSimilarly, in (17): \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"nú\" = on (preposition for day)\n\n\"ŋgéː\" = will\n\nSo two verbs: \"nǔ\" and \"nú\"\n\nIn (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" = will\n\n\"bvúsɔ̀w\" = on Bvusɔw\n\n\"fɔ̀ shě ntfǔː\" = the day after tomorrow?\n\nBut \"the day after tomorrow\" cannot follow \"on Bvusɔw\" as object.\n\nUnless \"fɔ̀ shě ntfǔː\" is the object.\n\nBut what is \"fɔ̀ shě ntfǔː\"?\n\nFrom (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = the day after tomorrow (possessing a value)\n\nSo sentence 16: \"On Bvusɔw, the day after tomorrow\"\n\nStill ungrammatical.\n\nAlternative: Could \"fvúsɔ̀w\" be \"will steal\"?\n\nBut that would require a translation of \"bvúsɔ̀w\" as a verb.\n\nFrom (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you(sg) will steal the yam on Bvusɔw\" — so \"bvúsɔ̀w\" = day\n\n\"nǔ\" = will\n\nSo \"nǔ\" is future, \"bvúsɔ̀w\" is day.\n\nThus, in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — \"on Bvusɔw, will [something] the day after tomorrow\"?\n\nNo verb.\n\nUnless \"fɔ̀ shě ntfǔː\" is a verb?\n\nNo — it's a time expression.\n\nConclusion: likely misreading.\n\nBut let's go back to (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo: \"cǐ nɔ̂ː yɛ᷅n wáy é\" → \"on Bvutfu, the woman saw the market\"\n\nSo the verb is \"saw\"\n\nTherefore, in (16): no verb\n\nUnless \"nǔ\" is the verb?\n\n\"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nIf \"nǔ\" = will, then \"will Bvúsɔ̀w the day after tomorrow\"?\n\nNo.\n\nPerhaps \"bvúsɔ̀w\" is the subject?\n\nBut in (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" — \"you(sg) will steal the yam on Bvusɔw\" — \"bvúsɔ̀w\" is day.\n\nIn (17): \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"I will steal the yam from the man\" on a day? But no day.\n\nUnless the day is implied from the day of speaking.\n\nSpeaking on Bvuŋkaden.\n\nWe are to translate sentences spoken on Bvuŋkaden.\n\nSo each sentence is spoken on Bvuŋkaden, and we are to interpret them with respect to that day.\n\nSo likely, the day is implicit.\n\nNow, go sentence by sentence.\n\n---\n\n(16) bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\n\nAssume \"nǔ\" = will (future)\n\n\"bvúsɔ̀w\" = on Bvusɔw — day\n\nBut then \"fɔ̀ shě ntfǔː\" = the day after tomorrow — do we assign it as object?\n\nBut no verb like \"steal\", \"saw\", etc.\n\nIn (2): verb is \"cɔ́ŋ\" = steal\n\nIn (13): \"yɛ᷅n wáy\" = saw\n\nIn (3): \"fí\" = help\n\nIn (6): \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"he killed the woman\"\n\nSo verb is \"bɛ̂ː\" = kill\n\nSo every sentence has a verb.\n\n(16) has no verb — only \"nǔ\" which is a future auxiliary.\n\nSo must be a typo or misreading.\n\nWait — is it \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — \"On Bvusɔw, [the day after tomorrow] will happen\"?\n\nNo.\n\nAlternative: is \"fɔ̀ shě ntfǔː\" the day name?\n\nBut \"fɔ̀ shě ntfǔː\" is not a day name — in (5), it's used as \"the day after tomorrow\"\n\nIn (8): \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"tomorrow is Bvuŋkaden\"\n\nSo \"fɔ̀ shě ntfǔː\" is not a day.\n\nSo the only possibility is that the sentence is: \"On Bvusɔw, [something will happen on the day after tomorrow]\"\n\nBut no verb.\n\nPerhaps it's missing the verb.\n\nMaybe \"nǔ\" is not future — in (2), it is.\n\nIn (17): \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me\" = I \n\"nú\" = on \n\"ŋgéː\" = will \n\"nyɛ́n\" = the man \n\"kèŋkfǔ\" = the yam \n\"lé\" = steal \n\"ɛ̀bɛ̀n\" = the woman\n\nSo likely: \"I will steal the yam from the man\" on a day — but no day.\n\nUnless the day is implied.\n\nBut in this sentence, \"nú\" is used, so likely a day is intended.\n\nSimilarly, (18): \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\"\n\n\"wvù\" = he \n\"tɔ̀\" = heard \n\"yɛ᷅n\" = the thief \n\"bèsèn\" = the woman \n\"ě\" = (in) \n\"bvúmbòn\" = yesterday\n\nSo: \"He heard the thief in the woman yesterday\"?\n\n\"bèsèn\" = the woman, \"ě\" = in?\n\n\"bèsèn ě\" = in the woman? — unlikely.\n\n\"bèsèn\" = the woman, \"ě\" = a preposition?\n\nIn (14): \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSo \"bèsèn\" = the woman or \"we\"?\n\nIn (14): \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" — so \"bèsèn\" may be a subject or object.\n\n\"bèsèn\" = the woman\n\n\"nǔ\" = on or will\n\n\"géː\" = will\n\n\"cɔ́ŋ\" = steal\n\n\"mutù\" = the car\n\n\"ɛ̀bɛ̀n\" = the woman?\n\nNo — \"mutù ɛ̀bɛ̀n\" → the car the woman?\n\nSo \"we (the woman and others) will steal the car from the woman\"?\n\nUnlikely.\n\nMore likely: \"the woman will steal the car from the woman\" — not grammatical.\n\nMust be: \"we will steal the car\" — \"bèsèn\" = subject.\n\nIn Nooni, \"bèsèn\" may be used as \"we\" or \"they\".\n\nSimilarly, in (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo \"bɔ́\" = they\n\n\"nɔ̂ː\" = saw\n\n\"yɛ᷅n\" = the thief\n\n\"me\" = I\n\n\"lé\" = at\n\n\"fɔ̀wǎy\" = the market\n\nSo verb \"saw\"\n\nBack to (16): no verb — only \"nǔ\"\n\nUnless \"bvúsɔ̀w\" is a verb.\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" — \"you will steal the yam on Bvusɔw\"\n\nSo \"bvúsɔ̀w\" = day\n\nSo not a", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10182.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Identify the pattern in how days are referenced in Nooni. \nFrom the given sentences, we see that days are named (e.g., Bvutfu, Bvusɔw, Bvuŋka, Bvuzhi), and references to time are expressed using relative markers: \n- “Yesterday” → \"cǐ nú\" (in sentence 1) \n- “Tomorrow” → \"ntfǔː nú\" (sentence 8) \n- “The day after tomorrow” → \"fɔ̀ shě ntfǔː\" (sentence 5) \n- “Today” → \"wvù tɔ̀\" (sentence 4, 6) \n- “The day before yesterday” → \"kefwé cí nú\" (sentence 11)\n\nThese show a consistent pattern: \n- Present day = \"wvù tɔ̀\" \n- Today = present, marked by \"wvù tɔ̀\" \n- Tomorrow = \"ntfǔː nú\" \n- Yesterday = \"cǐ nú\" \n- The day after tomorrow = \"fɔ̀ shě ntfǔː\" (literally \"after tomorrow\" or \"two days after today\") \n- The day before yesterday = \"kefwé cí nú\" (literally \"two days before today\")\n\nNote: \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" → \"ntfǔː\" = future day \nSimilarly, \"kefwé cí nú\" = two days earlier.\n\nStep 2: Identify how relative days are used in temporal constructions. \nEach sentence uses the day name + a relative temporal marker. \nFor example: \n- \"On Bvutfu, I came to the market\" → \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" \n- \"On Bvusɔw, you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \nSo, the structure is: [subject] + [verb] + [relational phrase] + [day name]\n\nPattern: The day name is referenced with or after a relative temporal construction. \nBut in many sentences, the day name is used in a present/future context with a time reference.\n\nStep 3: Work on sentence 16: \n\"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n→ \"On Bvúsɔw, the day after tomorrow\" \nWait — this seems grammatically odd. \"On Bvúsɔw, the day after tomorrow\"? That can’t mean the day after tomorrow is Bvúsɔw. \nInstead, perhaps it's a verb with a day: \n\"bvúsɔ̀w\" = \"on Bvúsɔw\" \n\"nǔ\" = you (sg) \n\"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" → so \"you will be on the day after tomorrow\" \nBut that doesn't make sense.\n\nWait — perhaps \"fɔ̀ shě ntfǔː\" is not a relative day, but a fixed reference.\n\nFrom sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\"\n\nAh! So \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" \n\"ntfǔː nú\" = \"tomorrow\" \n\"ntfǔː\" = \"tomorrow\" \n\"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n→ \"on Bvúsɔw, you will be on the day after tomorrow\"? Doesn’t parse.\n\nWait — perhaps the structure is:\n[day] + [verb] + [relative day]\n\nBut in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \nThis might mean: \"On Bvúsɔw, you will be on the day after tomorrow\" — still odd.\n\nAlternative: Could it be that \"fɔ̀ shě ntfǔː\" is an event? Or could this be a misordering?\n\nCheck the target: \"spoken on Bvuŋkaden\" — so the sentence is being spoken on Bvuŋkaden.\n\nNow, the day names: \nWe see the following day names appear: \n- Bvutfu \n- Bvusɔw \n- Bvuzhi \n- Bvuŋka \n- Bvuŋkaden (new)\n\nFrom earlier: \n- Bvutfu = day 1 (spoken on Bvutfu) \n- Bvusɔw = day 2 \n- Bvuzhi = day 3 \n- Bvuŋka = day 4 \n- Bvuŋkaden = day 5 (spoken on Bvuŋkaden)\n\nSo the days are in sequence: \nDay 1: Bvutfu \nDay 2: Bvusɔw \nDay 3: Bvuzhi \nDay 4: Bvuŋka \nDay 5: Bvuŋkaden\n\nSo relative days from today (Bvuŋkaden): \n- Today = Bvuŋkaden \n- Tomorrow = Bvuŋkaden+1 = ? (no such name) \nBut we see names like Bvutfu (day 1), Bvusɔw (day 2), so the days are fixed.\n\nBut in sentence 8: \"Tomorrow is Bvuŋkaden\" → so tomorrow is Bvuŋkaden (when spoken on Bvukema) \nSimilarly, sentence 11: \"The day before yesterday was Bvuŋka\" → so day before yesterday = Bvuŋka\n\nSo using relative timing from a reference day:\n\nFrom sentence 11: \"kefwé cí nú bvûŋka\" = \"the day before yesterday was Bvuŋka\"\n\nSo: \n- Today = T \n- Yesterday = T-1 \n- Day before yesterday = T-2 → Bvuŋka \n- Tomorrow = T+1 \n- Day after tomorrow = T+2\n\nNow, in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo T+2 = Bvutfu \nBut Bvutfu is the first day. \nSo T+2 = Bvutfu → so T = Bvutfu - 2 → 3 days before Bvutfu.\n\nBut days cycle? No — from context, days are linear, not cyclic.\n\nWait — maybe the days are fixed and ordered. \nList days in order of appearance:\n\n- Bvutfu → day 1 \n- Bvusɔw → day 2 \n- Bvuzhi → day 3 \n- Bvuŋka → day 4 \n- Bvuŋkaden → day 5 \n\nSo sequence: \nDay 1: Bvutfu \nDay 2: Bvusɔw \nDay 3: Bvuzhi \nDay 4: Bvuŋka \nDay 5: Bvuŋkaden \n\nSo on day 5 (Bvuŋkaden), what are the relative days?\n\n- Today = Bvuŋkaden \n- Yesterday = Bvuŋka \n- Day before yesterday = Bvuzhi \n- Tomorrow = ? (no name) \n- Day after tomorrow = ? \n\nBut in sentence 8: on Bvukema, \"tomorrow is Bvuŋkaden\" → so tomorrow = Bvuŋkaden → so when on Bvukema (day 3), tomorrow = day 4 → Bvuŋka? Wait — no:\n\nWait — sentence 8: \"Tomorrow is Bvuŋkaden\" — so if spoken on Bvukema, tomorrow is Bvuŋkaden.\n\nBut if Bvuŋkaden is day 5, then tomorrow from day 3 is day 4 → not 5.\n\nSo contradiction.\n\nWait — perhaps the day names are not in a strict linear sequence, but the relative time markers are consistent.\n\nLet’s fix the reference point.\n\nEach sentence is spoken on a specific day.\n\nSentence 1: spoken on Bvutfu \n→ \"Yesterday was Bvumbon\" \n→ So on Bvutfu, yesterday was Bvumbon\n\nSentence 2: on Bvusɔw \n→ \"On Bvusɔw, you will steal the yam\" → time of event is Bvusɔw\n\nSentence 3: on Bvuzhi \n→ \"On Bvuzhi, the woman will help me\"\n\nSentence 4: on Bvusɔw \n→ \"On Bvuŋka, he found the book\" → event on Bvuŋka, when speaking on Bvusɔw\n\nSo when speaking on Bvusɔw (day 2), an event is on Bvuŋka (day 4)\n\nSo Bvuŋka is two days after Bvusɔw → two days later.\n\nSimilarly, sentence 5: \"The day after tomorrow is Bvutfu\" → spoken on Bvusɔw \nSo from Bvusɔw, day after tomorrow is Bvutfu — which is day 1 → so Bvutfu is before Bvusɔw? Contradiction.\n\nWait — unless the days are cyclic or not in order.\n\nBut from sentence 1: on Bvutfu, yesterday was Bvumbon → so Bvumbon is before Bvutfu\n\nSentence 5: on Bvusɔw, day after tomorrow is Bvutfu → so from Bvusɔw, +2 = Bvutfu\n\nSo Bvutfu = Bvusɔw + 2 days\n\nSentence 4: on Bvusɔw, he found the book on Bvuŋka → so Bvuŋka = Bvusɔw + 2 days\n\nSo Bvutfu = Bvusɔw + 2 \nBvuŋka = Bvusɔw + 2 → so Bvutfu = Bvuŋka?\n\nBut different names → contradiction.\n\nTherefore, must be error in interpretation.\n\nAlternative: \"fɔ̀ shě ntfǔː\" is not \"the day after tomorrow\", but part of a verb?\n\nBack to sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" \n\"ntfǔː\" = \"tomorrow\" \n\"fɔ̀ shě\" = \"after\" \n\"shě\" = \"after\", so \"fɔ̀ shě\" = \"after\" → \"fɔ̀ shě ntfǔː\" = \"after tomorrow\"\n\nBut \"after tomorrow\" = tomorrow + 1 = day after tomorrow\n\nYes — consistent. \nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo, when spoken on Bvusɔw, \"the day after tomorrow is Bvutfu\"\n\nSo Bvutfu = Bvusɔw + 2 days\n\nBut earlier: on Bvutfu, \"yesterday was Bvumbon\" → so Bvumbon = Bvutfu - 1\n\nSo sequence: \nBvumbon — Bvutfu — Bvusɔw — ? — Bvuŋka — ?\n\nFrom Bvusɔw, two days later is Bvutfu → so Bvutfu = Bvusɔw + 2 → Bvusɔw is two days before Bvutfu → so Bvusɔw < Bvutfu\n\nBut in sentence 1: on Bvutfu, \"yesterday was Bvumbon\" → Bvumbon = Bvutfu - 1\n\nSo days: \n... — Bvumbon — Bvutfu — Bvusɔw — ?\n\nBvusɔw is after Bvutfu? But from above, Bvusɔw is before Bvutfu.\n\nContradiction.\n\nUnless the marker is misread.\n\nSentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\"\n\nSo from Bvusɔw, day after tomorrow = Bvutfu\n\nSo Bvutfu = Bvusɔw + 2\n\nSentence 1: on Bvutfu, yesterday was Bvumbon → so Bvumbon = Bvutfu - 1\n\nSentence 2: on Bvusɔw, \"On Bvusɔw, you will steal\" → event on Bvusɔw\n\nSentence 3: on Bvuzhi, event on Bvuzhi\n\nSentence 4: on Bvusɔw, \"On Bvuŋka, he found the book\" → so on Bvusɔw, event is on Bvuŋka → so Bvuŋka = when?\n\nSo from Bvusɔw to Bvuŋka = some time\n\nSentence 5: from Bvusɔw, day after tomorrow is Bvutfu → so Bvutfu = Bvusɔw + 2\n\nSo Bvutfu > Bvusɔw by 2 days\n\nSo Bvusɔw +2 = Bvutfu\n\nThen from sentence 1, Bvumbon = Bvutfu -1 = Bvusɔw +1\n\nSo days: \nBvusɔw — Bvumbon — Bvutfu — ... \n\nSentence 3: on Bvuzhi — so Bvuzhi is after?\n\nThen sentence 4: on Bvusɔw, \"he found on Bvuŋka\" — so Bvuŋka is later.\n\nSentence 11: on Bvukema, \"the day before yesterday was Bvuŋka\" → so Bvuŋka = today - 2\n\nIf spoken on Bvukema, then Bvuŋka = Bvukema - 2\n\nSentence 4: on Bvusɔw, event on Bvuŋka → so Bvuŋka = Bvusɔw + x\n\nSo Bvusɔw + x = Bvukema - 2\n\nSo Bvusɔw + x + 2 = Bvukema\n\nNow, days are likely ordered: Bvusɔw, Bvumbon, Bvutfu, Bvuzhi, Bvuŋka, Bvukema?\n\nBut names are different.\n\nPerhaps the days are not in a fixed sequence, but the relative markers are consistent.\n\nWe can extract the pattern of time markers:\n\n1. \"cǐ nú\" = yesterday \n2. \"ntfǔː nú\" = tomorrow \n3. \"fɔ̀ shě ntfǔː\" = day after tomorrow \n4. \"kefwé cí nú\" = day before yesterday \n5. \"wvù tɔ̀\" = today \n6. \"me nú mbɛ̂ː\" = today (action) \n7. \"wvù tɔ̀\" = today \n8. \"ntfǔː nú\" = tomorrow \n9. \"me mbɛ̂ː\" = today \n10. \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" = the man is about to see him \n11. \"kefwé cí nú\" = day before yesterday\n\nNow for the target example, spoken on Bvuŋkaden.\n\nWe must translate:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ \"On Bvúsɔw, you will be on the day after tomorrow\"? No.\n\nPerhaps \"fɔ̀ shě ntfǔː\" is not a day, but a verb?\n\nBut in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\" — so \"fɔ̀ shě ntfǔː\" is a time expression.\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n→ \"On Bvúsɔw, you [will] have the day after tomorrow\" — doesn't work.\n\nAnother idea: maybe \"fɔ̀ shě ntfǔː\" = future event, but the structure is: [day] [subject] [event]\n\nBut what event?\n\nSimilarly, 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n→ \"I will see the thief the car\" — no.\n\n\"nyɛ́n\" = \"the\" \n\"kèŋkfǔ\" = \"the yam\"? (from sentence 2: \"you will steal the yam\" — \"cɔ́ŋ kèŋkfǔ\") \n\"kèŋkfǔ\" = \"the yam\" \n\"lé\" = \"the\" \n\"ɛ̀bɛ̀n\" = \"the woman\" (from sentence 6: \"he killed the woman\")\n\nSo \"nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam the woman\" — not grammatical.\n\n\"nyɛ́n\" might be \"will see\" or \"will meet\" — \"ŋgéː\" = \"to see\" (in sentence 15: \"they saw me\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\")\n\nSo \"ŋgéː\" = \"see\" \n\"nyɛ́n\" = \"the\" or \"will\" — in context, may be a marker.\n\n\"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" = \"I will see the [something] the woman\"\n\nPerhaps \"nyɛ́n\" is a definite article, so \"the yam the woman\" is odd.\n\nAlternatively, \"nyɛ́n\" = \"in\" or \"at\" — but not.\n\nAnother possibility: \"nyɛ́n\" is a future verb form.\n\nIn sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" = \"They saw me at the market just now\" — \"yɛ᷅n\" = \"at\", \"lé\" = \"the market\"\n\nSo \"nyɛ́n\" might be a place?\n\nBut \"kèŋkfǔ\" is \"the yam\", \"lé\" is \"the woman\"\n\nNo.\n\nPerhaps \"nyɛ́n\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10480.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "iid", + "sample_index": 2, + "output": "We are given a set of Nooni sentences spoken on different days of the Nooni “week”, with English translations. We are to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns in the earlier sentences.\n\n---\n\n### Step 1: Identify key temporal markers and their references\n\nThe days of the week in Nooni are:\n- Bvutfu (from sentence 1: \"Yesterday was Bvumbon\")\n- Bvusɔw (line 2, 4, 6, 7)\n- Bvuzhi (line 3)\n- Bvuŋka (line 4, 5, 6, 7, 13, 14)\n- Bvuŋkaden (target day: sentences 16–19)\n\nWe observe that in Nooni, time references are often built using expressions like:\n- “On X-day” → refers to a specific day\n- “Tomorrow” → +1 day\n- “Yesterday” → -1 day\n- “The day after tomorrow” → +2\n- “The day before yesterday” → -2\n- “Today” → current day\n\nLet’s extract temporal patterns.\n\n---\n\n### Step 2: Track day-of-week markers\n\nWe infer relative days from the context.\n\nFrom sentence 1: \n> \"Yesterday was Bvumbon\" → **Yesterday = Bvumbon**\n\nSentence 5: \n> \"The day after tomorrow is Bvutfu\" → **+2 = Bvutfu**\n\nSo:\n- Yesterday = Bvumbon\n- Day after tomorrow = Bvutfu\n\nThus, if we assume Bvutfu is two days after Bvumbon, then:\n- Bvumbon → -1\n- Bvutfu → +2 → so from -1 to +2 is 3 days → so Bvutfu is 3 days after Bvumbon?\n\nWait — but “yesterday was Bvumbon” and “day after tomorrow is Bvutfu” → so Bvutfu is **three days after** Bvumbon?\n\nBut Nooni days are cyclic, so likely follow a 7-day cycle.\n\nWe now know:\n- Bvumbon = yesterday\n- Bvutfu = day after tomorrow → two days from now → so Bvutfu = +2\n\nSo if yesterday = Bvumbon, then:\n- Today = Bvutfu − 2 = Bvumbon + 1\n- So today = one day after Bvumbon?\n\nBut sentence 2: “On Bvusɔw, you will steal the yam” and it’s spoken on Bvusɔw.\n\nSentence 3: “On Bvuzhi, the woman will help me” — on Bvuzhi.\n\nSentence 4: “On Bvuŋka, he found the book” — on Bvuŋka.\n\nSo we have the following days:\n- Bvumbon (yesterday)\n- Bvusɔw (present day? in sentence 2)\n- Bvuzhi\n- Bvuŋka\n- Bvutfu (day after tomorrow)\n- Bvuŋkaden (tomorrow? in sentence 8)\n\nNow, sentence 8:\n> \"Tomorrow is Bvuŋkaden\" → Tomorrow = Bvuŋkaden\n\nSo when sentence 8 is spoken, **tomorrow = Bvuŋkaden**\n\nSentence 8 is spoken on **Bvukema** — so when spoken on Bvukema, tomorrow is Bvuŋkaden.\n\nThus:\n- Bvukema → tomorrow = Bvuŋkaden → so Bvukema is the day before Bvuŋkaden\n\nSo:\n- Bvukema = -1\n- Bvuŋkaden = 0 (today in this context)\n\nNow, we are to translate sentences spoken **on Bvuŋkaden** — so we are now evaluating those from **the perspective of Bvuŋkaden**.\n\nWe need to interpret relative days from Bvuŋkaden.\n\n---\n\n### Step 3: Pattern in sentence structure\n\nLook at the verb forms and constructions.\n\nExample: \nSentence 5: \"The day after tomorrow is Bvutfu\" \n→ \"fɔ̀ shě ntfǔː nú bvútfu᷅\" \nStructure: “fɔ̀ shě ntfǔː” = “The day after tomorrow is” → then “Bvutfu”\n\nSimilarly, sentence 8: \"Tomorrow is Bvuŋkaden\" → “ntfǔː nú bvûŋka᷆ːde᷆n”\n\nSo pattern: \n[Temporal expression] + [day name] = time expression\n\nWe see:\n- “fɔ̀ shě” → “the day after tomorrow”\n- “ntfǔː” → “tomorrow”\n- “kwɔ᷆ːn cǐ” → “on [day]”\n- “wvù tɔ̀” → “he found” \n- “me nú” → “I will” / “I am” \n- “nǔ” → “you (sg)” \n- “cɔ́ŋ” → “steal” \n- “bóy” → “help” \n- “bɛ̂ː” → “killed” \n- “wɔ̀” → “you (sg)” \n- “nɔ̂ː” → “heard” \n- “cɔ̌ŋ” → “thief” \n- “bèsèn” → “will” \n- “tɔ́” → “will” \n- “fɔ̀wǎy” → “market”\n\nNow, look at sentence 10: \n> \"The man is about to see him\" → \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" \n→ “dìɛ̀msɛ̌n” = man; “nú” = about to; “yɛ́n” = see; “wvù” = him\n\nSentence 12: \"I am about to help the man\" → \"me nú nfí dìɛ̀msɛ̌n\" \n→ \"me nú nfí\" = I am about to → \"nfí\" = help → \"dìɛ̀msɛ̌n\" = man\n\nSo \"nú\" = about to (future, imminent)\n\n\"Sentence 15\": \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" \n→ \"bɔ́\" = they; \"nɔ̂ː\" = saw; \"yɛ᷅n\" = me; \"lé\" = at; \"fɔ̀wǎy\" = market\n\nSo \"just now\" = recent past\n\nNow, sentence 13: \"On Bvutfu, the woman saw the market\" \n→ \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" \n→ \"kwɔ᷆ːn\" = woman; \"cǐ\" = on; \"nɔ̂ː\" = saw; \"yɛ᷅n\" = the market? → \"wáy\" = market; \"é\" = at → so “saw the market”\n\nFrom sentence 5: “The day after tomorrow is Bvutfu” → so Bvutfu is +2 from current day\n\nNow, we are at **Bvuŋkaden** (which we have established is tomorrow from Bvukema, and spoken on Bvukema, so now we are speaking on Bvuŋkaden).\n\nWe are to translate 16–19.\n\n---\n\n### Sentence 16: \n> \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nBreak it down:\n- \"bvúsɔ̀w\" → day name (Bvusɔw)\n- \"nǔ\" → you (sg)\n- \"fɔ̀ shě ntfǔː\" → “the day after tomorrow is” → “fɔ̀ shě” = the day after tomorrow; “ntfǔː” = Bvutfu?\n\nWait — actually, in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → “the day after tomorrow is Bvutfu”\n\nSo the structure is:\n- [Temporal phrase] + [day name] → “the day after tomorrow is Bvutfu”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, the day after tomorrow is [something]”?\n\nBut “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu”?\n\nWait — this would be redundant.\n\nBut perhaps the day name is not Bvusɔw but is used in a temporal expression.\n\nBetter: maybe the structure is:\n- [Day name] + [subject] + [temporal expression] → “On Bvusɔw, you (sg) will have the day after tomorrow” → that doesn't make sense.\n\nAlternative: \nFrom sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\"\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” → so the phrase \"fɔ̀ shě ntfǔː\" is a full expression meaning “the day after tomorrow is [day]”\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) [have] the day after tomorrow” — no.\n\nWait — more likely:\nIn sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → “On Bvusɔw, you will steal the yam”\n\nSo structure: [Day] + [subject] + [verb] + [object] → “On X, you will steal Y”\n\nSo 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\n“bvúsɔ̀w” = day name \n“nǔ” = you (sg) \n“fɔ̀ shě ntfǔː” = “the day after tomorrow is [something]” → but that's a noun phrase?\n\nWait — perhaps \"fɔ̀ shě ntfǔː\" is meant to be “will be” or “had”?\n\nNo, in sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow is” → it's a time expression.\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow”? — doesn't make sense.\n\nWait — perhaps the structure is: [Day name] + [subject] + [temporal expression]\n\nBut there is no verb here.\n\nAnother idea: perhaps “fɔ̀ shě ntfǔː” is a verb form?\n\nBut in the example, “fɔ̀ shě ntfǔː” is used as “the day after tomorrow is” — not a verb.\n\nIn fact, looking back at sentence 1: “fɔgò cǐ nú bvúmbòn” → “Yesterday was Bvumbon”\n\nSo “fɔgò” = yesterday; “cǐ” = was; “nú” = Bvumbon\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě” = the day after tomorrow → “ntfǔː” = is → “nú” = Bvutfu\n\nSo the structure is: [temporal phrase] + [verb] + [day name]\n\nBut here: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — starts with day name.\n\nCompare to sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you (sg) will steal the yam” → so day at start.\n\nSentence 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “On Bvuzhi, the woman will help me”\n\nSo pattern: **On [day], [subject] [verb] [object]** when the verb is an action.\n\nBut in 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — has no verb, only a time expression.\n\nWait — perhaps “fɔ̀ shě” is a verb meaning “will be”?\n\nBut in sentence 5, “fɔ̀ shě ntfǔː” is “the day after tomorrow is” — it's a noun phrase.\n\nWait — perhaps the sentence is:\n“On Bvusɔw, you will have that day” → no.\n\nAnother idea: perhaps “fɔ̀ shě ntfǔː” is meant to be interpreted as “on the day after tomorrow” or “the day after tomorrow” as a day name.\n\nBut Bvusɔw is already a day name.\n\nAlternatively, could it be:\n“On Bvusɔw, you will be that day” — no.\n\nLet’s consider sentence 17.\n\nSentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\nBreak it down:\n- \"me\" = I\n- \"nú\" = about to / will\n- \"ŋgéː\" = see / observe\n- \"nyɛ́n\" = the thief\n- \"kèŋkfǔ\" = steal\n- \"lé\" = at\n- \"ɛ̀bɛ̀n\" = the woman\n\nWait — \"kèŋkfǔ lé ɛ̀bɛ̀n\" → “steal the woman”? no — “kèŋkfǔ” = steal; “lé” = at; “ɛ̀bɛ̀n” = woman → so “at the woman” — but that's awkward.\n\nWait — sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → “you will steal the yam”\n\nSo \"cɔ́ŋ kèŋkfǔ\" → “steal the yam”\n\nSo \"kèŋkfǔ\" = steal; object is implied.\n\nSo \"nyɛ́n kèŋkfǔ\" = “the thief will steal” — but “nyɛ́n” is the subject?\n\n“me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “I will see the thief steal at the woman”?\n\nThat doesn’t make sense.\n\nAlternative: \"kèŋkfǔ\" = to steal; \"lé ɛ̀bɛ̀n\" = “at the woman” → so “steal at the woman” → maybe “rob the woman”?\n\nBut sentence 2 says “steal the yam” — so “kèŋkfǔ” + object (yam) = “steal the yam”\n\nSo “kèŋkfǔ” is the verb; object is what follows.\n\nBut in 17: \"nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → “the thief steal at the woman” — seems off.\n\nBut “lé” might mean “the” or “at” — so perhaps “the thief stole the woman” — but “steal the woman” is a person.\n\nBut in context, in sentence 2, it's “steal the yam” — so object is a thing.\n\nSo “kèŋkfǔ” must have a direct object.\n\nPossibility: “kèŋkfǔ” is used with “the woman” → perhaps “steal [the] woman” — but that would mean to take her — possible.\n\nBut sentence 17: “I will see the thief steal at the woman” → still odd.\n\nAnother idea: maybe “kèŋkfǔ” is not “steal” but something else?\n\nNo — in sentence 2: “you will steal the yam”.\n\nSo likely, “kèŋkfǔ” = steal.\n\nSo “the thief steal at the woman” → likely “the thief stole from the woman” or “the thief stole at the woman” → but “at” is literal.\n\nBut in sentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “you heard the thief”\n\nSo “cɔ̌ŋ” = the thief.\n\nSo likely, “kèŋkfǔ” = steal.\n\nNow, sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “I will see the thief steal at the woman”\n\nStill awkward.\n\nWait — perhaps “kèŋkfǔ lé” is a fixed phrase → “steal from the woman”?\n\nBut “lé” means “at” or “from”?\n\nIn sentence 2: “cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “steal the yam”\n\nSo “kèŋkfǔ” + “object” → “steal [object]”\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “steal at the woman” → not standard.\n\nPossibility: “kèŋkfǔ” = to steal, and “lé” = the, “ɛ̀bɛ̀n” = woman → so “the woman is stolen”?\n\nNo — not grammatical.\n\nAnother possibility: typo or misrendering?\n\nIn the original: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\nBut in sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you will steal the yam\"\n\nSo \"cɔ́ŋ\" = steal; \"kèŋkfǔ\" = yam?\n\nNo — \"cɔ́ŋ\" and \"kèŋkfǔ\" are both used — in 2: \"yúː cɔ́ŋ kèŋkfǔ\" → probably \"yúː\" = will; \"cɔ́ŋ\" = steal; \"kèŋkfǔ\" = yam\n\nAh! Big insight:\n\nIn sentence 2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10421.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "iid", + "sample_index": 3, + "output": "We are given sentences in Nooni spoken on different days of the week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in the earlier sentences.\n\nFirst, let's look at the structure and time reference patterns across the examples.\n\n---\n\n**Step 1: Identify time reference patterns**\n\nWe see the day names indexed with adverbial or temporal expressions like:\n- \"Yesterday was Bvumbon.\" → \"fɔgò cǐ nú bvúmbòn\"\n- \"On Bvusɔw, you will steal the yam.\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"The day after tomorrow is Bvutfu.\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n- \"Tomorrow is Bvuŋkaden.\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n- \"The day before yesterday was Bvuŋka.\" → \"kefwé cí nú bvûŋka\"\n\nThese show that:\n- \"ntfǔː\" = tomorrow\n- \"fɔ̀ shě\" = the day after tomorrow\n- \"fɔgò\" = yesterday\n- \"kefwé cí\" = the day before yesterday\n- \"wvù tɔ̀ nɔ̂ː\" = today\n- \"me nú\" = I will (future)\n- \"kwɔ᷆ːn\" = the woman\n- \"bèsèn\" = we will\n- \"wɔ̀\" = you (sg)\n- \"cɔ́ŋ\" = steal, take\n- \"kèŋkfǔ\" = yam\n- \"é\" = the market\n- \"mutù\" = car\n- \"bɔ́ŋ\" = find\n- \"bóy\" = woman\n- \"yɛ᷅n\" = saw\n- \"wáy\" = market\n- \"lě\" = him\n\nWe are to interpret sentences from **Bvuŋkaden**, which is mentioned as \"tomorrow is Bvuŋkaden\" (sentence 8).\n\nSo we are working in a frame where the days of the week are ordered:\n- Bvutfu (from sentence 1: \"yesterday was Bvumbon\")\n- Bvusɔw (sentence 2)\n- Bvuzhi (sentence 3)\n- Bvuŋka (sentence 4, 5, 6, 7)\n- Bvuŋkaden (target day)\n\nFrom the observed pattern:\n- \"ntfǔː\" = tomorrow\n- \"fɔ̀ shě\" = day after tomorrow\n- \"fɔgò\" = yesterday\n- \"kefwé cí\" = day before yesterday\n\nSo, relative to the current day (Bvuŋkaden), we can determine the days:\n- Bvuŋkaden = current day\n- The day before yesterday = Bvuŋka (sentence 11)\n- The day after tomorrow = Bvutfu (sentence 5: \"The day after tomorrow is Bvutfu\")\n- The day after today = Bvutfu? Wait — contradiction?\n\nWait! Sentence 5 says:\n> \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nThis is **spoken on Bvusɔw**.\n\nSo on Bvusɔw, day after tomorrow is Bvutfu.\n\nThat gives a reference point: **Bvusɔw → Bvutfu (day after tomorrow)**\n\nSimilarly, sentence 11: \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\" — spoken on Bvuŋkaden.\n\nThus:\n- On Bvuŋkaden, the day before yesterday was Bvuŋka.\n\nSo sequence is:\n- Bvuŋkaden (today)\n- Bvuŋka (yesterday)\n- Bvutfu (day after tomorrow?) — no.\n\nWait: \"day after tomorrow\" is Bvutfu — spoken on Bvusɔw.\n\nLet’s build a timeline.\n\nUse sentence 5 (spoken on Bvusɔw):\n\n> \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo on Bvusɔw, day after tomorrow is Bvutfu → thus:\n- Bvusɔw → Bvutfu (in +2 days)\n\nSimilarly, sentence 11: \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\" → spoken on Bvuŋkaden\n\nSo:\n- On Bvuŋkaden, day before yesterday was Bvuŋka → so Bvuŋka = two days before Bvuŋkaden\n\nSo Bvuŋkaden → Bvuŋka (yesterday)\n→ Bvuŋka → day before yesterday → two days before today\n\nSo days:\n- Bvuŋkaden = today\n- Bvuŋka = yesterday\n- Bvummbon = day before yesterday? No → sentence 1 says \"Yesterday was Bvumbon\" (spoken on Bvutfu)\n\nWait — sentence 1: \"fɔgò cǐ nú bvúmbòn.\" — \"Yesterday was Bvumbon\", spoken on Bvutfu\n\nSo:\n- On Bvutfu, yesterday was Bvumbon → so Bvumbon = day before Bvutfu\n\nSo sequence:\n- Bvutfu\n- Bvumbon (yesterday)\n- ?\n\nFrom sentence 5: On Bvusɔw, day after tomorrow is Bvutfu → so:\n- Bvusɔw → day after tomorrow → Bvutfu → so Bvutfu is two days after Bvusɔw\n\nThus:\n- Bvusɔw → Bvutfu (in +2)\n\nSimilarly:\n- On Bvuŋkaden: day before yesterday was Bvuŋka → so Bvuŋka is two days before Bvuŋkaden\n\nNow, day after tomorrow on Bvuŋkaden would be two days after Bvuŋkaden → let’s call that X\n\nWe know from sentence 5 (on Bvusɔw): day after tomorrow is Bvutfu\n\nSo if Bvusɔw → Bvutfu in +2, then relative days are fixed.\n\nBut we are to infer temporal expressions in sentences on Bvuŋkaden.\n\n---\n\nNow analyze each sentence:\n\n**(16) bvúsɔ̀w nǔ fɔ̀ shě ntfǔː**\n\n\"bvúsɔ̀w\" = Bvusɔw (day name)\n\"nǔ\" = you (sg)\n\"fɔ̀ shě\" = the day after tomorrow\n\"ntfǔː\" = tomorrow\n\nBut the structure is: \"On Bvusɔw, the day after tomorrow is tomorrow?\"\n\nNo — that doesn’t make sense.\n\nWait — likely a verb or construction.\n\nLook at sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" is \"the day after tomorrow is [day]\"\n\nTherefore, in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → likely \"On Bvusɔw, the day after tomorrow is tomorrow?\"\n\nBut that’s illogical.\n\nWait — perhaps the structure is \"on [day], [event] happens\"\n\nCompare sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam.\"\n\nSo structure: [temporal marker] + [subject] + [verb] + [object] + [day]\n\nIn (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nNote that \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is tomorrow\" — contradiction.\n\nUnless \"fɔ̀ shě\" is a verb meaning \"to be\", and \"ntfǔː\" is a day.\n\nBut sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" + \"nú\" + day = \"The day after tomorrow is X\"\n\nIn (16): no \"nú\" — just \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" = you\n\nSo \"you the day after tomorrow is tomorrow\"?\n\nNo.\n\nCould it be a misordering?\n\nIs it \"you (will) see (the day after tomorrow) is tomorrow\"?\n\nUnlikely.\n\nAlternative: perhaps \"fɔ̀ shě\" is a temporal noun phrase.\n\nBut from sentence 5, \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is [day]\"\n\nBut here, it's not followed by a day.\n\nWait — sentence 16 might be: \"On Bvusɔw, you will see the day after tomorrow\" — but doesn't match.\n\nCheck sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nPattern: \"On X, subject verb object\"\n\nSo likely, sentence 16: \"On Bvusɔw, you will [something]\"\n\nSo what is \"fɔ̀ shě ntfǔː\"?\n\nFrom sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo perhaps \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nBut here, no \"is\" or \"nú\"\n\nPerhaps it's a verb: \"to be\" or \"to see\"?\n\nBut \"nǔ\" = you\n\nSo perhaps \"you (will) (be) the day after tomorrow\" — nonsense.\n\nWait — look at sentence 9: \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → \"Today, I chose the book\"\n\n\"me\" = I\n\"mbɛ̂ː\" = chose\n\"nca᷅w\" = the book\n\"ɛ̀bɛ̀n\" = the woman\n\nSo \"I chose the book (the woman)\" → probably \"the woman\" is the object\n\nSo likely, \"you will (do something) on Bvusɔw\"\n\nBut the phrase is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCould it be: \"On Bvusɔw, you will [see the day after tomorrow]\"?\n\nBut \"see\" is not in the root.\n\nAnother idea: in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"the woman saw the market on Bvutfu\"\n\nSo \"nɔ̂ː yɛ᷅n\" = saw\n\n\"yɛ᷅n\" = saw (intransitive)\n\nSo perhaps \"fɔ̀ shě\" is \"saw\"?\n\nBut \"fɔ̀ shě\" in sentence 5 is part of \"the day after tomorrow is\"\n\nBut \"fɔ̀ shě ntfǔː\" is a phrase.\n\nCompare to sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → \"On Bvuŋka, he found the book\"\n\nSo: \"On X, he found the object\"\n\nSo for sentence 16: \"On Bvusɔw, you [did] something\"\n\nWhat action?\n\n\"nǔ fɔ̀ shě ntfǔː\" — \"you the day after tomorrow\"\n\nSo perhaps a mistranslation or misreading.\n\nWait — maybe it's \"you saw the day after tomorrow\" — \"nǔ yɛ᷅n fɔ̀ shě ntfǔː\"?\n\nBut it's written as \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCould it be \"On Bvusɔw, you will see the day after tomorrow\"?\n\nBut \"see\" is not there.\n\nAlternatively, in sentence 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"You(sg) heard the thief a long time ago\"\n\n\"nɔ̂ː\" = heard\n\nSo \"nɔ̂ː\" is a verb.\n\nIn sentence 16, \"fɔ̀ shě\" — could be a verb?\n\nBut in sentence 5, \"fɔ̀ shě\" is part of \"the day after tomorrow is\"\n\nSo likely a noun phrase.\n\nThus, most likely structure: \"On Bvusɔw, you will see [something]\"\n\nBut what?\n\nWait — sentence 19: \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n\"\n\n\"bèsèn\" = we will\n\"nǔ\" = you\n\"bóy\" = woman\n\"tɔ́\" = help? (in sentence 3: \"bóy fí me\" — woman helps me)\n\"fɔ̀wǎy\" = market\n\"bvúzhı᷇ːde᷆n\" = market? or Bvuzhi day?\n\n\"bvúzhı᷇ːde᷆n\" — look at sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nSo \"bvúzhí\" = Bvuzhi\n\n\"bvúzhı᷇ːde᷆n\" — likely \"Bvuzhid-en\" = Bvuzhi tomorrow?\n\nPossibly a day name with suffix.\n\nSimilarly, in sentence 8: \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"Tomorrow is Bvuŋkaden\"\n\n\"bvûŋka᷆ːde᷆n\" = Bvuŋkaden (tomorrow)\n\nSo patterns:\n- \"ntfǔː\" = tomorrow\n- \"fɔ̀ shě\" = the day after tomorrow\n- \"fɔgò\" = yesterday\n- \"kefwé cí\" = the day before yesterday\n\nSo \"ntfǔː nú X\" = \"Tomorrow is X\"\n\n\"kefwé cí nú X\" = \"The day before yesterday was X\"\n\n\"fɔ̀ shě ntfǔː nú X\" = \"The day after tomorrow is X\"\n\nNow, in sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nIt has no \"nú\", so likely not a day is being stated.\n\nBut it has \"nǔ\" = you\n\nSo possibly \"you will [something] on Bvusɔw\"\n\nBut what?\n\nCompare sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo structure: [day] + [subject] + [verb] + [object]\n\nHere: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nSo if \"fɔ̀ shě\" is object, but \"ntfǔː\" is not a noun.\n\nBut \"fɔ̀ shě\" might be the verb.\n\nNo — \"fɔ̀ shě\" is part of a temporal phrase.\n\nAlternative: perhaps it's \"On Bvusɔw, you will be the day after tomorrow\" — absurd.\n\nAnother possibility: in sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me nú\" = I will\n\"ŋgéː\" = see? (in sentence 13, \"yɛ᷅n\" = saw)\n\"nyɛ́n\" = the thief\n\"kèŋkfǔ\" = yam\n\"lé\" = the car\n\"ɛ̀bɛ̀n\" = the woman\n\nSo \"I will see the thief the yam the car the woman\"? Unlikely.\n\n\"nyɛ́n\" = the thief\n\"kèŋkfǔ\" = yam\n\"lé\" = car\n\nSo \"see the thief the yam the car\"?\n\nNo.\n\nIn sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"the woman saw the market on Bvutfu\"\n\nHere, \"yɛ᷅n\" = saw, \"wáy\" = market\n\nSo verb is \"yɛ᷅n\"\n\nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me nú\" = I will\n\"ŋgéː\" = see\n\"nyɛ́n\" = the thief\n\"kèŋkfǔ\" = yam\n\"lé\" = car\n\"ɛ̀bɛ̀n\" = woman?\n\nSo \"I will see the thief the yam the car the woman\"?\n\nPerhaps a misordering.\n\nBut likely: \"I will see [the thief] at [the yam] at [the car] at [the woman]\" — nonsense.\n\nPerhaps \"kèŋkfǔ\" is location, \"lé\" is object.\n\nBut yam and car are not locations.\n\nAnother idea: perhaps \"kèŋkfǔ\" = the market, \"lé\" = the car\n\nBut in sentence 13: \"wáy\" = market\n\n\"kèŋkfǔ\" = yam\n\nSo not matching.\n\nBut in sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSo \"géː\" = steal → so \"cɔ́ŋ\" = steal\n\nSo verb is \"cɔ́ŋ\"\n\nSimilarly, sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\n\"bɔ́\" = they\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10263.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "iid", + "sample_index": 0, + "output": "Step-by-step analysis of Inuktitut patterns from the given examples:\n\n1. Identify core verb patterns:\n- \"hurt\" appears in multiple sentences:\n - 3: Aanniqtutit → You hurt yourself.\n - 19: The shaman hurt you → likely \"Angatkuq aanniqtutit\" (shaman + hurt + you)\n - 10: Qingmiq iputujait → You speared the dog (spearing = injuring)\n - 5: Qingmiq iputujait → same verb form\n - 19: \"The shaman hurt you\" → subject is shaman, verb \"hurt\", object \"you\"\n\nPattern: \"aanniqtutit\" = hurt (base verb), often with subject and object marking.\n\n2. \"saw\" appears in:\n- 1: Qingmivit takujaatit → Your dog saw you → \"takujaatit\" = saw\n- 20: The teacher saw the boy → likely \"iluaqhaiji\" (teacher) + \"takujaatit\" (saw) + object (boy)\n\nPattern: \"takujaatit\" = saw (object in accusative)\n\n3. \"shot\" appears in:\n- 2: Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor → \"qukiqtanga\" = shot\n- 12: Angunahukti nanurmik qukiqsijuq → The hunter shot a polar bear → \"qukiqsijuq\" = shot\n- 22: You shot a dog → \"iputujait\" seems to be spearing, not shooting.\n\nBut \"qukiqtanga\" = shot (past tense), used with object.\n\nSo verb \"qukiqtanga\" = shot (with object)\n\nNote: \"qukiqtanga\" = shot (did not appear for \"you shot a dog\" – so must be in the same form)\n\n4. \"fell\" appears in:\n- 11: Ukiakhaqtutit → You fell → verb \"ukiakhaqtutit\" = fell\n- 21: Your wolf fell → \"iluaqhaiji\" (wolf) + \"ukiakhaqtutit\" → \"iluaqhaijivit ukiakhaqtutit\"\n\n\"vit\" may indicate \"your\" in genitive or possessive marking.\n\n5. \"cured\" appears in:\n- 4: Iluaqhaijiup aarqijaatit → the doctor cured you → \"aarqijaatit\"\n- 6: Angatkuq iluaqhaijimik aarqisijuq → shaman cured a doctor → \"aarqisijuq\"\n\nPattern: \"aarqijaatit\" = cured, object marked.\n\nVerbs: \n- aanniqtutit → hurt \n- takujaatit → saw \n- qukiqtanga → shot \n- ukiakhaqtutit → fell \n- aarqijaatit → cured \n\n6. Object marking:\n- The sentence structure generally follows subject + verb + object.\n- Possessive marking (e.g. \"your\") is marked via suffix like \"vit\" (your), \"up\" (of), etc.\n\n7. Use of \"up\" and \"vit\":\n- \"Qingmivit\" = your dog → \"vit\" = your\n- \"iluaqhaijivit\" = your doctor → \"vit\" = your\n- \"angunahuktiup\" = the hunter → \"up\" = [something] of? Seems \"up\" is used for certain constructions, possibly for an instrument or agent.\n\nBut in 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"iluaqhaijivit\" (your doctor), \"inuuhuktuit\" (shot), \"aarqijanga\" (cured)\n\nSo suffix patterns:\n- \"vit\" = your (possessive)\n- \"up\" may be used in sentences with more complex structure (e.g. 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → the boy shot the doctor → \"Inuuhuktuup\" = the boy)\n\n8. Constructing translations:\n\n19. The shaman hurt you \n→ Earlier, shaman + hurt → \"Angatkuq aanniqtutit\" \nBut from example 6: Angatkuq iluaqhaijimik aarqisijuq → shaman cured a doctor → so \"Angatkuq\" + object with marker \nHere, \"Angatkuq aanniqtutit\" → shaman hurt you → likely correct\n\n20. The teacher saw the boy \n→ \"iluaqhaiji\" = teacher → \"takujaatit\" = saw → \"up\" or \"vit\"? \nFrom 1: Qingmivit takujaatit → your dog saw you → \"takujaatit\" is verb \nSo: \"iluaqhaiji takujaatit\" → teacher saw → needs object? \nNo object — \"the boy\" → must be \"iluaqhaijivit\"? But \"vit\" is \"your\" \nBut \"the boy\" → likely \"inuuhukti\" or \"inuuhuktuit\"? \nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → \"inuuhuktuup\" = the boy \nSo \"inuuhuktuit\" (past form of boy) → could be boy? \nPossibly: \"iluaqhaiji takujaatit inuuhuktuit\" → teacher saw the boy\n\n21. Your wolf fell \n→ \"iluaqhaiji\" = wolf → \"vit\" = your → \"iluaqhaijivit\" → \"ukiakhaqtutit\" → fell \n→ \"iluaqhaijivit ukiakhaqtutit\"\n\n22. You shot a dog \n→ \"you\" = ukiakhaqtutit? No — \"you\" is subject in 1: Qingmivit takujaatit (your dog saw you) \n\"you\" is marked with \"takujaatit\" or \"aanniqtutit\"? \nFrom 1: \"Qingmivit takujaatit\" = your dog saw you — \"you\" is direct object → subject = your dog \nSo \"you\" is marked by lack of possessive? \nIn 11: \"Ukiakhaqtutit\" → you fell → so \"you\" = subject, verb \"ukiakhaqtutit\" \nSo \"you shot\" → \"takujait\" → no, \"qukiqtanga\" is shot \nSo: \"u\" = you → \"u\" is root, \"qukiqtanga\" = shot \nSo: \"uqukiqtanga\" or \"uqukiqtanga\"?\n\nBut no \"you\" in object form.\n\nExample 12: Angunahukti nanurmik qukiqsijuq → the hunter shot a polar bear → \"Angunahukti\" = hunter, \"nanurmik\" = a polar bear, \"qukiqsijuq\" = shot\n\nSo \"you\" → in 11: \"Ukiakhaqtutit\" = you fell → so subject\n\nThus: \"qukiqtanga\" is a verb if unmarked → for \"you shot a dog\" → \"uqukiqtanga\" → but no example shows \"you\" + \"shot\" in that form.\n\nBut 22: \"You shot a dog\" → likely \"uqukiqtanga\" + object → \"iluaqhaiji\" = dog\n\n→ \"uqukiqtanga iluaqhaiji\"\n\nBut is \"u\" used? In 1: \"Qingmivit takujaatit\" → \"your dog\" has \"vit\"\n\nWhere is \"you\" with a verb? Only in 11: \"Ukiakhaqtutit\" — \"you fell\"\n\nSo likely \"u\" = you → unmarked\n\nThus: \"uqukiqtanga iluaqhaiji\" — you shot a dog\n\n23. Your dog hurt a teacher \n→ \"your dog\" = Qingmivit → \"aanniqtutit\" = hurt → \"iluaqhaiji\" = teacher? \nBut \"iluaqhaiji\" is teacher → so object → \"iluaqhaiji\"\n\n→ \"Qingmivit aanniqtutit iluaqhaiji\"\n\n(possible)\n\nCheck consistency:\n\nExamples show:\n- \"your dog\" = Qingmivit\n- \"you hurt\" = aanniqtutit\n- \"teacher\" = iluaqhaiji\n- \"shot\" = qukiqtanga or qukiqsijuq (contextual)\n- \"fell\" = ukiakhaqtutit\n- \"saw\" = takujaatit\n\nThus:\n\n19. The shaman hurt you → Angatkuq aanniqtutit \n→ \"Angatkuq\" = shaman (as in 6), \"aanniqtutit\" = hurt (as in 3)\n\n20. The teacher saw the boy → iluaqhaiji takujaatit inuuhuktuit \n→ \"iluaqhaiji\" = teacher, \"takujaatit\" = saw (as in 1), \"inuuhuktuit\" = boy (past of \"inuuhukti\", e.g. 2)\n\n21. Your wolf fell → iluaqhaijivit ukiakhaqtutit \n→ \"iluaqhaijivit\" = your wolf, \"ukiakhaqtutit\" = fell (as in 11)\n\n22. You shot a dog → uqukiqtanga iluaqhaiji \n→ \"u\" = you, \"qukiqtanga\" = shot (same as 2), \"iluaqhaiji\" = dog\n\n23. Your dog hurt a teacher → Qingmivit aanniqtutit iluaqhaiji \n→ \"Qingmivit\" = your dog, \"aanniqtutit\" = hurt, \"iluaqhaiji\" = teacher\n\nAll verbs and possessives are consistent with the examples.\n\nFinal answers:\n\nb.1 / 19: Angatkuq aanniqtutit \nb.2 / 20: iluaqhaiji takujaatit inuuhuktuit \nb.3 / 21: iluaqhaijivit ukiakhaqtutit \nb.4 / 22: uqukiqtanga iluaqhaiji \nb.5 / 23: Qingmivit aanniqtutit iluaqhaiji\n\n\\boxed{b.1: Angatkuq aanniqtutit; b.2: iluaqhaiji takujaatit inuuhuktuit; b.3: iluaqhaijivit ukiakhaqtutit; b.4: uqukiqtanga iluaqhaiji; b.5: Qingmivit aanniqtutit iluaqhaiji}", + "generated_tokens": 2467, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: Angatkuq aanniqtutit; b.2: iluaqhaiji takujaatit inuuhuktuit; b.3: iluaqhaijivit ukiakhaqtutit; b.4: uqukiqtanga iluaqhaiji; b.5: Qingmivit aanniqtutit iluaqhaiji", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 6380.0, + "ioling_final_answer_chars": 167.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Identify the verb patterns from the given examples.\n\nLook at the verbs in the base forms:\n- \"saw\" → in sentence 1: *takujaatit* → (you saw me) → verb root *takuj* + suffix *-aatit* (3rd person, past, marked for object)\n- \"shot\" → sentence 2: *iluaqhaiji* → \"a doctor\" → \"shot\" is *qukiqtanga* → root *qukiq* + *-tanga* (passive/active? Not clear)\n- \"hurt\" → sentence 3: *aanniqtutit* → \"you hurt yourself\" → *aanniqt* + *-utit* → verb suffix *-utit* for past, 1st person, reflexive\n- \"cured\" → sentence 4: *iluaqhaijiup aarqijaatit* → \"cured you\" → *aarqijaatit* → root *aarqi* + *-jaatit* → past tense, object marked\n- \"speared\" → sentence 5: *Qingmiq iputujait* → \"you speared the dog\" → *iputujait* → root *iputuj* + *-ait* → past, object marked\n- \"came\" → sentence 7: *Nanuq qaijuq* → “came” → root *qaijuq* → simple past\n- \"cured\" → sentence 6: *Angatkuq iluaqhaijimik aarqisijuq* → “cured a doctor” → *aarqisijuq* → root *aarqi* + *-sij* + *-uq* → shows internal marking\n- \"speared\" → sentence 9: *Angunahuktiup amaruq iputujanga* → “shooter speared the wolf” → *iputujanga* → *iputuj* + *-anga* → object marked\n\nStep 2: Identify verb suffixes for object marking.\n\nCompare verb forms:\n- \"saw\": takujaatit → *-aatit* → object marked → \"saw you\"\n- \"hurt\": aanniqtutit → *-utit* → reflexive, no object → \"you hurt yourself\"\n- \"cured\": aarqijaatit → *-jaatit* → object marked → \"cured you\"\n- \"speared\": iputujait → *-ait* → object marked → \"speared dog\"\n- \"cured\" again: aarqisijuq → *-sijuq* → different object?\n\nWait: sentence 6: \"cured a doctor\" → *aarqisijuq* → suggests *aarqi* + *-sij* + *-uq* → object marking via *-sij* and *-uq*? (possibly possessed or extended)\n\nBut sentence 4: \"cured you\" → *aarqijaatit* → *-jaatit* → pattern: -jaatit = object marked → past tense, transitive\n\nIn sentence 8: *iluaqhaijivit inuuhuktuit aarqijanga* → “your doctor cured your boy” → “cured” verb: *aarqijanga* → *aarqi* + *-janga* → *-janga* = object marked, with possessive?\n\nIn sentence 10: *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"the dog hurt your teacher\" → *aanniqtanga* → *aanniqt* + *-anga* → object: \"your teacher\" → object marked with *-anga*\n\nAh! Pattern:\n\n- When object is marked → suffix like *-a*, *-i*, *-ng*, *-anga*, *-jaatit*, etc., depending on object pronoun\n- Reflexive → *-utit*\n- Possessive objects use possessive marker + ending\n- Subject is usually marked via the noun or a pronominal suffix\n\nNow, observe how object is marked in examples:\n\n1. \"Your dog saw you\" → *takujaatit* → *takuj* + *-aatit* → object is \"you\" → so *-aatit* = object marked\n2. \"The boy shot the doctor\" → *iluaqhaiji qukiqtanga* → \"qukiqtanga\" → *qukiq* + *-tanga* → object \"doctor\" → *-tanga*\n3. \"You hurt yourself\" → *aanniqtutit* → *aanniqt* + *-utit* → reflexive, object is self\n4. \"The doctor cured you\" → *iluaqhaijiup aarqijaatit* → *aarqijaatit* → *-jaatit* → object marked → \"you\"\n5. \"You speared the dog\" → *Qingmiq iputujait* → *iputujait* → *-ait* → object \"dog\" → *-ait*\n6. \"The shaman cured a doctor\" → *Angatkuq iluaqhaijimik aarqisijuq* → *aarqisijuq* → *-sijuq* → object \"a doctor\"\n7. \"The polar bear came\" → *Nanuq qaijuq* → no object → root verb *qaijuq*\n8. \"Your doctor cured your boy\" → *aarqijanga* → *-janga* → object \"your boy\" → possessive + object marking\n9. \"The hunter speared the wolf\" → *iputujanga* → *-janga* → object \"the wolf\" → possessive?\n10. \"The dog hurt your teacher\" → *aanniqtanga* → *aanniqt* + *-anga* → object \"your teacher\"\n\nSo in general:\n\n- For transitive verbs, object is marked by suffix: *-a*, *-it*, *-ng*, *-anga*, *-jaatit*, *-ait*, etc.\n- Suffix varies based on object type (possessive vs. personal)\n- Reflexive: *-utit*\n- Intransitive verbs: no object suffix (e.g., came)\n\nNow consider verb roots:\n\n- *takuj* → saw\n- *qukiq* → shot\n- *aanniqt* → hurt\n- *aarqi* → cured\n- *iputuj* → speared\n- *qaijuq* → came\n\nSo:\n- hurt → *aanniqt* → in example 3: *aanniqtutit* (reflexive)\n- cured → *aarqi* → in example 4: *aarqijaatit* (object marked), example 6: *aarqisijuq* (object \"a doctor\")\n- speared → *iputuj* → example 5: *iputujait*, example 9: *iputujanga*\n\nNow phrase each target:\n\n19. \"The shaman hurt you.\"\n- Subject: \"the shaman\" → from sentence 6: \"The shaman cured a doctor\" → \"Angatkuq iluaqhaijimik aarqisijuq\" → \"Angatkuq\" = shaman\n- Verb: \"hurt\" → root *aanniqt*\n- Object: \"you\" → requires object marking → from example 3: \"you hurt yourself\" → *aanniqtutit* → reflexive\n- But here, object is \"you\", not self → transitive\n- From example 10: \"dog hurt your teacher\" → *aanniqtanga* → object \"your teacher\"\n- So \"you\" → personal object → likely *-anga* or *-a*?\n- But in \"you hurt yourself\" → *utit*, reflexive\n- So when object is \"you\", and not reflexive → ? \n- In sentence 5: \"you speared the dog\" → *iputujait* → object = dog → *-ait*\n- In sentence 10: \"the dog hurt your teacher\" → *aanniqtanga* → object = \"your teacher\" → *-anga*\n- So personal object → predict *-anga*?\n- But \"you\" is subject → own pronoun\n\nWait: in sentence 3: \"You hurt yourself\" → *aanniqtutit* → object \"yourself\" → *-utit*\n\nIn sentence 10: \"The dog hurt your teacher\" → *aanniqtanga* → object \"your teacher\" → *-anga*\n\nSo \"you\" as object → not reflexive → must be marked with *-anga*?\n\nBut what about direct object possibility?\n\nNot in examples. Are there any examples where \"you\" is object?\n\nOnly in sentence 3: “you hurt yourself” → reflexive.\n\nAll others use possessive or specific persons.\n\nBut sentence 4: \"doctor cured you\" → *aarqijaatit* → \"you\" → marked with *-jaatit*\n\n→ So \"you\" as object → *-jaatit*?\n\nBut sentence 10: \"dog hurt your teacher\" → *aanniqtanga* → *-anga* → possessive object.\n\nDifference: \"you\" vs. \"your teacher\"\n\nSo:\n- \"you\" as object → use *-jaatit*? or *-anga*?\n\nIn sentence 4: \"cured you\" → *aarqijaatit* → has *-jaatit*\nIn sentence 10: \"hurt your teacher\" → *aanniqtanga* → *-anga*\n\nWhy difference?\n\nPossibility: *-jaatit* = object marked in some cases, *-anga* = possessive object?\n\nIn sentence 10: \"your teacher\" → \"your\" + \"teacher\" → possessive → *-anga*\n\nIn sentence 4: \"you\" → direct object → *-jaatit*\n\nBut \"you\" (direct) → should be *-jaatit*\n\nSo in sentence 19: \"the shaman hurt you\" → “you” → direct object → should be marked with *-jaatit*?\n\nBut “you” is also a personal pronoun — can it be used directly?\n\nRule: when object is someone (not self), use specific marking.\n\nSo try pattern:\n\n- hurt with object: *aanniqt* + suffix\n- For \"you\" → *-jaatit* → as in sentence 4\n- For \"your teacher\" → *-anga* → as in sentence 10\n\nSo \"the shaman hurt you\" → *Angatkuq aanniqtjaatit*\n\nBut is *aanniqtjaatit* supported?\n\nSentence 4: \"the doctor cured you\" → *aarqijaatit* → *aarqi* + *-jaatit*\n\nSo yes — *-jaatit* is used for direct object \"you\"\n\nSo 19: \"The shaman hurt you\" → *Angatkuq aanniqtjaatit*\n\nAdd subject: \"shaman\" → *Angatkuq* → matches sentence 6\n\nSo b.1 → *Angatkuq aanniqtjaatit*\n\n---\n\n20. \"The teacher saw the boy.\"\n\n- saw → root *takuj*\n- subject: \"the teacher\" → no direct example, but \"boy\" → sentence 2: \"the boy shot doctor\" → \"iluaqhaiji\" = boy\n- \"teacher\" not named\n- But sentence 10: \"dog hurt your teacher\" → \"your teacher\" → *ilinniaqtanga* → \"teacher\" in *ilinniaqt*\n- So teacher root is *ilinniaqt*\n- saw → *takuj*\n- object: \"the boy\" → \"the boy\" → in sentence 2: \"the boy shot doctor\" → *iluaqhaiji* → so \"boy\" is *iluaqhaiji*\n- in which case, object: \"the boy\" → is marked with what?\n- In sentence 8: \"your doctor cured your boy\" → *aarqijanga* → *-janga* → possessive object\n- In sentence 2: \"the boy shot the doctor\" → *iluaqhaiji qukiqtanga* → *qukiqtanga* → *-tanga*\n- So \"the doctor\" → marked with *-tanga*\n\nSimilarly, \"the boy\" → should be marked as *-tanga*?\n\nBut no verb uses \"boy\" directly.\n\nBut sentence 2: \"the boy shot the doctor\" → *iluaqhaiji qukiqtanga* → \"doctor\" marked with *-tanga*\n\nSo \"the boy\" is not marked → subject?\n\nSo when object is marked → suffix like *-tanga*, *-jaatit*, *-anga*, *-janga*\n\nIn that case, \"saw the boy\" → verb *takuj* + object marking?\n\nBut in sentence 1: \"your dog saw you\" → *takujaatit* → *-aatit* → object \"you\"\n\nBut \"you\" is not possessive → may be personal object\n\nIn sentence 2: \"the boy shot the doctor\" → *iluaqhaiji qukiqtanga* → object is \"doctor\" → *qukiqtanga* → *tanga*\n\nSo object marked with *-tanga*?\n\nBut sentence 4: \"cured you\" → *aarqijaatit* → *-jaatit* → not *-tanga*\n\nInconsistency?\n\nPerhaps different verb roots have different suffixes.\n\nBut “saw” is the same verb.\n\nSentence 1: \"your dog saw you\" → *takujaatit* → *-aatit* → object \"you\"\n\nSentence 2: \"the boy shot the doctor\" → *qukiqtanga* → *-tanga* → object \"doctor\"\n\nSo for different verbs, object suffix varies.\n\nBut “saw” has *-aatit* with “you” → might be consistent?\n\nBut “you” is not possessive.\n\nBut “the doctor” in sentence 2 is not personal.\n\nSo could saw use *-aatit* for all personal objects?\n\nBut in sentence 4: “cured you” → *aarqijaatit* → *-jaatit*\n\nSo different verbs → different suffixes?\n\nBut “saw” is *takuj*, others are *qukiq*, *aarqi*, *iputuj*\n\nSo perhaps each verb has a standard object marker.\n\nBut sentence 1: *takujaatit* → \"you\"\n\nSentence 2: *qukiqtanga* → \"doctor\"\n\nSo for *takuj*, with object → *-aatit*? (only one example)\n\nBut in sentence 10: “dog hurt your teacher” → *aanniqtanga* → *-anga* (possessive)\n\nSo object marking depends on object type?\n\nFor personal object (you, me, etc.) → *-a*, *-it*, *-anga*, etc.\n\nBut in sentence 1: \"saw you\" → *takujaatit* → *-aatit*\n\nIn sentence 4: \"cured you\" → *aarqijaatit* → *-jaatit*\n\nSo two verbs → different object suffixes?\n\nBut both have object \"you\"\n\nUnless suffix varies by verb.\n\nPossible.\n\nBut for saw, object → *-aatit*\n\nThen for teacher saw boy → \"boy\" is not a personal pronoun — it's a noun → “the boy”\n\nWhat’s the marking for “the boy”?\n\nIn sentence 2: boy → subject, doctor → object → *qukiqtanga* → object marked with *-tanga*\n\nSo when object is a noun (specific person), use *-tanga*?\n\nBut in sentence 8: “your doctor cured your boy” → *aarqijanga* → *-janga*\n\nSo \"your boy\" → possession → *-janga*\n\nSimilarly, \"your teacher\" → in sentence 10 → *aanniqtanga* → *-anga*\n\nSo:\n- Possessive objects → suffix like *-anga*, *-janga*\n- Non-possessive, specific object → *-tanga*?\n\nIn sentence 2: “doctor” → object → *qukiqtanga* → *-tanga* → noun object\n\nIn sentence 4: “you” → object → *aarqijaatit* → *-jaatit* → personal object\n\nSo conservative pattern:\n- Personal pronouns → *-jaatit* or *-a*, *-utit*\n- Possessive → *-anga*, *-janga*\n- Specific nouns → *-tanga*\n\nSo for “the boy” → noun → so should be marked with *-tanga*?\n\nBut in sentence 8: “your boy” → “aarqijanga” → *-janga* → possessive\n\nSo in general, if object has possessive, use *-janga*, *-anga*; if it's a neutral noun, use *-tanga*?\n\nBut sentence 2: object = doctor → *qukiqtanga* → *-tanga*\n\nSentence 10: object = your teacher → *aanniqtanga* → *-anga*\n\nOh — in sentence 10: \"your teacher\" → possessive → *-anga*\n\nSentence 2: \"the doctor\" → non-possessive → *-tanga*\n\nSo object marking:\n- If object has possessive prefix (“your”, “your”) → use *-anga* or *-janga*\n- If object is just a noun (no possessive) → use *-tanga*\n\nSo “the boy” → object → no possessive → use *-tanga*\n\nSo verb: *takuj* + *-aatit*? But with \"the boy\"\n\nNo direct example of saw + noun object\n\nBut in sentence 1: “your dog saw you” → saw you → *takujaatit* → *-aatit*\n\n\"you\" is personal → so probably *-a* suffix variants\n\nHypothesis: object suffix based on object type\n\nPattern from examples:\n- Personal object (you, me, yourself) → *-a*, *-it*, *-utit*\n- Possessive object (your teacher, your boy) → *-anga*, *-janga*\n- Non-possessive noun object → *-tanga*\n\nSo", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11617.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "iid", + "sample_index": 2, + "output": "We are given a set of Inuktitut sentences with English translations. Our task is to infer the linguistic pattern (especially verb structure, possessive marking, and transitivity) to translate five new sentences into Inuktitut.\n\nStep 1: Identify verb morphology and meaning patterns.\n\nLook at the verb forms:\n\n- \"takujaatit\" → \"saw\" (1), uses suffix -jaa- + -tita (past tense, 3rd person)\n- \"iluaqhaiji\" → \"shotted\" (2), verb root \"iluaqha\" + -j (intransitive? transitive?)\n- \"aanniqtutit\" → \"hurt yourself\" (3), verb \"aanniqt\" + -utit (past, 3rd person)\n- \"aarqijaatit\" → \"cured you\" (4), \"aarqi\" + \"jaa\" + \"tutit\"\n- \"iputujait\" → \"speared\" (5), \"iputu\" + \"jait\"\n- \"qukiqtanga\" → \"shot\" (2), verb root \"qukiq\" + -tanga (passive or causative?)\n\nObserve that verbs often end in:\n- -jaa- → seen, observed\n- -tutit → hurt (e.g., aanniqtutit)\n- -jaatit → healed (aarqijaatit)\n- -jait → speared (iputujait)\n- -tanga → shot (qukiqtanga)\n\nNote the source and recipient marking:\n- Possessive \"your\" appears with \"iluaqhaijiup\" → \"your doctor\" (in 8), \"your boy\" → \"inuuhuktuit\"\n- \"your dog\" → \"qingmivit\" → subject, so in \"qingmiq iputujait\" → \"you speared the dog\", so \"qingmiq\" = dog, \"iputujait\" = speared\n\nIn sentence 3: \"Aanniqtutit\" → \"you hurt yourself\" → reflexive: no explicit object, but \"yourself\"\n\nIn sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → clear transitive verb with object\n\nSentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"qingmiq\" = dog, \"iputujait\" = speared\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → \"cured\" = aarqisijuq, object \"a doctor\" = iluaqhaijimik\n\nSo \"aarqisijuq\" = cured (with subject \"shaman\"), object = \"iluaqhaijimik\" = doctor\n\nThus, verb \"aarqijaatit\" → cured someone; \"aarqisijuq\" → cured (possibly causative, object marked)\n\nBut \"aarqijaatit\" is transitive: one person cured another.\n\nSimilarly, \"takujaatit\" → saw someone.\n\nSo transitive verbs have object marking: root + object marker (e.g., iluaqhaijimik = a doctor)\n\nNow look at the verb \"aanniqtutit\" = you hurt yourself → reflexive, self-object.\n\n\"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → \"iluaqhaijivit\" (your doctor), \"inuuhuktuit\" (your boy), \"aarqijanga\" = cured.\n\nSo action is transitive: agent → object\n\nNow, in sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → verb \"ilinniaqtitsijiit\" = hurt (root ilinniaqti) → hurts + object \"your teacher\" → aanniqtanga.\n\nSo the verb root is \"ilinniaqti\" → hurt, with object marker.\n\nSo pattern:\nVerb + object (marked with possessive prefix or suffix like -mik, -sijiit)\n\nNow for reflexive: \"you hurt yourself\" = \"aanniqtutit\" → no object, just verb.\n\nNow subject marking:\n- \"your dog\" → \"qingmivit\"\n- \"the doctor\" → \"iluaqhaiji\"\n- \"your doctor\" → \"iluaqhaijivit\"\n- \"your boy\" → \"inuuhuktuit\"\n- \"the shaman\" → \"angatkuq\"\n- \"the hunter\" → \"angunahukti\"\n\nSo, possessive prefixes:\n- qingmi- → dog\n- iluaqhai- → doctor\n- inuuhuk- → boy\n- angatkuq- → shaman\n- angunahuk- → hunter\n\nSo, general structure:\n[Possessive prefix] + [verb root with object marker] → transitive verb\n\nWhen object is \"you\", the marker is typically -it or -mik?\n\nCheck:\n- \"iluaqhaijimik\" = a doctor → object of \"cured\" → a doctor\n- \"aanniqtanga\" = your teacher → object of \"hurt\"\n\nSo object is marked with suffix like -mik, -sijiit, -it\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"nanurmik\" = a polar bear → object marked with -mik\n\nSo object is marked by a suffix: -mik, -sijiit, etc.\n\nNow, reflexive: \"aanniqtutit\" → \"you hurt yourself\" → no object suffix → verbal root + -utit\n\nNow, for translation:\n\n19. The shaman hurt you.\n\nWho? The shaman → \"angatkuq\"\n\nVerb: \"hurt\" → from \"aanniqt\" → aanniqtit (base) → with object \"you\"\n\n\"you\" = \"you\" → in previous sentences, \"you\" is marked as \"takujait\" or \"it\"?\n\nIn sentence 1: \"qingmivit takujaatit\" → \"your dog saw you\" → object \"you\"\n\nSo object is marked as \"you\" → not possessive, just \"you\" → used as object\n\nIn sentence 3: \"Aanniqtutit\" → \"you hurt yourself\" → reflexive\n\nSo \"you\" as object → must be marked.\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → object is \"your teacher\" → marked with possessive\n\nSimilarly, in sentence 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → object is \"you\" → marked with suffix?\n\nHere: \"aarqijaatit\" — \"you\" is not marked with a possessive? But \"aarqijaatit\" is derived from \"aarqijait\" — is \"you\" marked?\n\nWait: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → no possessive prefix on \"you\"\n\nBut the object is \"you\", so should be marked?\n\nCompare: \"iluaqhaijimik aarqisijuq\" → \"a doctor\" → object with -mik\n\nSo \"you\" as object → appears without possessive? Like \"you\" is a pronoun, not a noun.\n\nBut in \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → both possessive: \"your doctor\", \"your boy\"\n\nSo \"you\" as object? In \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → object is unpossessed \"you\"\n\nWhereas in \"the dog hurt your teacher\" → \"your teacher\" → possessive\n\nSo object is marked as:\n- when possessed → possessive + noun (e.g., your teacher)\n- when unpossessed → \"you\" or \"him\", etc., not marked with possessive\n\nSo \"hurt you\" → \"angatkuq aanniqtutit\" ???\n\nBut \"aanniqtutit\" is \"you hurt yourself\"\n\nIf \"hurt you\", it should be transitive → verb with object\n\nSo verb root \"aanniqt\" → \"aanniqtit\" → past tense → with object \"you\"\n\nSo: \"angatkuq aanniqtutit\" → \"the shaman hurt you\"?\n\nBut in sentence 3: \"Aanniqtutit\" → \"you hurt yourself\" — this is subject \"you\" + verb → reflexive\n\nSo how to mark object?\n\nIn sentence 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → transitive → agent + verb + object (you)\n\nSo the verb is \"aarqijaatit\" — root \"aarqi\" + \"jaat\" + \"it\" → cured you\n\nSimilarly, \"aanniqtutit\" = you hurt yourself → reflexive → no object\n\nSo \"aanniqt\" → hurt → with object → ends in -utit? — no, only reflexive ends in -utit.\n\nWait: \"aanniqtutit\" → root \"aanniqt\" → with -ut → past? But in \"aanniqtanga\" → \"your teacher\" → so -anga = without possession?\n\nWait — look at \"aanniqtanga\" → \"your teacher\" — object → attaches to end?\n\n\"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → verb is ilinniaqtitsijiit, object is aanniqtanga\n\nSo aanniqtanga = your teacher\n\nSimilarly, \"iluaqhaijimik\" = a doctor\n\nSo object is marked with pseudo-noun suffix: -mik, -sijiit, -anga\n\nSo \"you\" as object → must be a form of \"you\" → in sentence 4: \"you\" is not marked with possessive prefix, but is part of \"aarqijaatit\" — is \"you\" the object?\n\nPossibly: \"aarqijaatit\" → cured (you) → \"you\" is the patient → object\n\nSo object marker is attached to verb?\n\nLook: \"aarqijaatit\" → verb ending in -jaatit → \"you\"\n\nCompare: \"iputujait\" → \"speared\" → object not marked?\n\nIn sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → object is \"the dog\" → marked as \"qingmiq\"\n\nSo object marked as noun with prefix\n\nSimilarly, in sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"dog hurt your teacher\" → object \"your teacher\" with possessive\n\nSo pattern:\nTransitive verb = [agent] + [verb root + object marker] + [object]\n\nWhere:\n- agent = subject, attached with possessive if needed\n- verb root + -it / -sijiit etc. → for transitive action\n- object = either possessive noun or pronoun\n\nIn verb forms:\n- aanniqtutit → reflexive (you hurt yourself)\n- aanniqtanga → your teacher (object noun)\n- iluaqhaijimik → a doctor (object)\n- ilinniaqtitsijiit → hurt (with -sijiit)\n\nSo the verb root has a suffix indicating transitivity and object.\n\nNow for \"hurt you\" → agent + verb root + \"you\" suffix?\n\nIn sentence 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\"\n\nSo \"aarqijaatit\" → cured + you\n\nSo yes, the object is marked by suffix -jaatit?\n\n- \"jaat\" = you?\n\nIn aanniqtanga → teacher → -anga = teacher\n\nSo object suffixes:\n- -it → you?\n- -mik → a doctor\n- -sijiit → (in ilinniaqtitsijiit)\n- -anga → teacher\n\nSo likely, -it = you\n\nBut in sentence 4: \"aarqijaatit\" → cured you → -jaatit → so -jaat = you?\n\nSimilarly, in \"iluaqhaijiup aarqijaatit\" → object \"you\"\n\nAnd \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → has possessive + noun → \"your boy\"\n\nSo object \"your boy\" = inuuhuktuit → noun with possessive\n\nThus, when object is unpossessed \"you\", it is marked with suffix -it or -jaat?\n\nIn \"aarqijaatit\" → ends in -jaatit → likely -jaat = you\n\nThus, verb \"aanniqt\" → hurt → \"aanniqtit\" = hurt (reflexive)\n→ for object \"you\": \"aanniqtjait\"? → not found\n\nBut \"aanniqtanga\" = your teacher → -anga → teacher\n\nSo key: the object is marked with a suffix that shows the person, and the suffix types are:\n- -it → you?\n- -mik → a [person]\n- -anga → teacher\n- -sijiit → (possibly a person)\n\nIn sentence 10: \"ilinniaqtitsijiit\" → hurt → with -sijiit → so root \"ilinniaqti\" + -sijiit → hurt (someone)\n\n\"ilinniaqtitsijiit aanniqtanga\" → hurt your teacher → object aanniqtanga\n\nSo the verb form has object suffix (-sijiit?) but object is attached in noun.\n\nActually, looking at verb structure:\n\nIn sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → object \"the dog\" → \"qingmiq\" → noun, marked with prefix\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"iluaqhaiji\" = doctor, \"qukiqtanga\" = shot\n\nSo \"qukiqtanga\" → \"shot\" → root \"qukiq\" + -tanga → for object \"doctor\"\n\nSimilarly, \"iluaqhaijimik\" → doctor, with -mik → so object marked with -mik\n\nAnd \"qukiqtanga\" → shot → -tanga\n\nSo object marker varies per verb.\n\nNow for \"hurt\" → root \"aanniqt\"\n\n- \"aanniqtutit\" → you hurt yourself → reflexive\n- \"aanniqtanga\" → your teacher → object + -anga\n- \"iluaqhaijimik\" → a doctor → object + -mik\n\nSo object suffixes:\n- -mik → specific noun\n- -anga → teacher\n- -it → like you?\n\nBut in sentence 4: \"aarqijaatit\" → cured you → -jaatit\n\n\"aarqijaatit\" → object \"you\"\n\nSo for \"you\" → suffix -jaatit?\n\nBut \"jaatit\" is not a standard CVC pattern.\n\nPerhaps \"jaat\" = you\n\nBut \"takujaatit\" → saw you → -jaa- (see) + -jait?\n\ntakujaatit → root \"takuj\" + \"a\" + \"jait\"? → likely \"takuj\" + \"a\" + \"jait\" → \"saw you\"\n\ntakuj + a + jait → \"saw you\"\n\nSimilarly, aarqijaatit → \"cured you\" → aarqi + j + aatit?\n\nBut \"aarqijaatit\" → likely root \"aarqi\" + \"jaat\" + \"it\" → cured you\n\nSo \"jaat\" = you\n\nSimilarly, \"aanniqtutit\" → \"you hurt yourself\" → no object\n\n\"ilinniaqtitsijiit\" → hurt (root) + -sijiit → for object?\n\nIn 10: \"ilinniaqtitsijiit\" — formation: ilinniaqti + sijiit → hurt (something)\n\nAnd \"aanniqtanga\" — object\n\nSo the verb \"ilinniaqtitsijiit\" is transitive, with suffix -sijiit → used when object appears?\n\nBut object is \"aanniqtanga\"\n\nSo the verb form has a suffix that indicates direction or object, but object is then marked separately.\n\nNo — look at sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → object \"the dog\" is \"qingmiq\"\n\nSo object is noun phrase with prefix\n\nSimilarly, in sentence 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → object is \"you\", not a noun → treated as pronoun\n\nIn sentence 1: \"qingmivit takujaatit\" → \"your dog saw you\" → object \"you\"\n\nSo verb \"takujaatit\" — root \"takuj\" + \"a\" + \"jait\"? → \"saw you\"\n\nSo \"jait\" = you?\n\nSimilarly, \"aarqijaatit\" — \"cured you\" → \"jaatit\"\n\n\"ilinniaqtitsijiit\" — \"hurt\" → with -sijiit — not clearly object-based.\n\nBut in 10: \"ilinniaqtitsijiit aanniqtanga\" → hurt your teacher → verb + object\n\nIn 3: \"aanniqtutit\" → you hurt yourself → no object\n\nSo the only verb form with object \"you\" is \"aarqijaatit\" → cured you\n\n\"takujait\" → saw you? Not found — \"takujaatit\"\n\nSo likely, objects are marked by specific suffixes:\n\n- -it → you\n- -mik → a person (a doctor, etc.)\n- -anga → teacher\n- -sijiit → used to mark transitive action?\n\nBut in 5: \"iputujait\" → speared → no object suffix — object is \"the dog\"\n\nIn 5: \"Qingmiq iputujait\" → \"you speared the dog\" → object not marked with suffix, marked with noun\n\nSo general rule:\n- For transitive verbs with person/object, either:\n - object is a possessive noun → e.g., \"your teacher\" → \"aanniqt", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11988.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the verb patterns in the given Inuktitut examples.\n\nFrom the list:\n- \"Qingmivit takujaatit\" = Your dog saw you → \"saw\" is expressed with *takujaatit*, with past tense suffix *-vit*, and object-marking *-takujaatit*\n- \"Inuuhuktuup iluaqhaiji qukiqtanga\" = The boy shot the doctor → \"shot\" is *iluaqhaiji*, and \"the doctor\" is *qukiqtanga*\n- \"Aanniqtutit\" = You hurt yourself → verb *aanniqtutit*, suffix *-tutit* (past tense, reflexive)\n- \"Iluaqhaijiup aarqijaatit\" = The doctor cured you → verb *aarqijaatit*, *-jaatit* = past tense, object marked\n- \"Qingmiq iputujait\" = You speared the dog → *iputujait*, past tense\n- \"Angatkuq iluaqhaijimik aarqisijuq\" = The shaman cured a doctor → verb *aarqisijuq*, past tense, object marked\n- \"Nanuq qaijuq\" = The polar bear came → *qaijuq*, base verb\n- \"Iluaqhaijivit inuuhuktuit aarqijanga\" = Your doctor cured your boy → verb *aarqijanga*, past tense, object marked\n- \"Angunahuktiup amaruq iputujanga\" = The hunter speared the wolf → *iputujanga*, past tense, object marked\n- \"Qingmiup ilinniaqtitsijiit aanniqtanga\" = The dog hurt your teacher → *aanniqtanga*, past tense, object marked\n- \"Ukiakhaqtutit\" = You fell → *uqiakhaqtutit*, past tense, reflexive\n- \"Angunahukti nanurmik qukiqsijuq\" = The hunter shot a polar bear → *qukiqsijuq*, past tense\n\nStep 2: Identify consistent verb construction.\n\nAll verbs are in the past tense, with object marking via the suffix *-jaatit*, *-janga*, *-jait*, etc.\n\nNote:\n- Reflexive harm: “You hurt yourself” → *aanniqtutit*\n- Verb + object → often uses *-a* + object (e.g., *iluaqhaiji* = shot, *aarqijaatit* = cured you)\n- Possession or reference: \"your\" = *your-* (e.g., *your dog* = *qingmiup*)\n- Agents (doers): \"the shaman\" = *angatkuq*, \"the teacher\" = not directly present, but likely *ilinniaqtit* or *qinmiq*? Wait — look for pattern.\n\nInvestigate verb forms for common events:\n\nFrom (1): “Your dog saw you” → *qingmivit takujaatit* → \"saw\" = *takujaatit*, with agent *qingmivit* → agent + verb (past) + object (you)\n\nBut in (2): *Inuuhuktuup iluaqhaiji qukiqtanga* → agent (boy) + verb (shot) + object (doctor)\n\nIn (3): *Aanniqtutit* → you hurt yourself → reflexive, no object marked (itself)\n\nIn (4): *iluaqhaijiup aarqijaatit* → doctor cured you → verb *aarqijaatit*, so verb ends in *-jaatit*, object marked\n\nSo generic pattern:\n- Agent + verb (base verb) + object → verb is base form, object suffix as *-jaatit*, *-janga*, etc.\n- Reflexive form: verb with *-tutit* after past tense\n- \"You hurt yourself\" = *aanniqtutit* → verb root *aanniqt* + past *-tutit*\n\nSimilarly, \"the shaman healed a doctor\" = *angatkuq iluaqhaijimik aarqisijuq* → agent (shaman) + verb \"cured\" (aarqisijuq) + object (doctor)\n\nThus: verb root + past tense suffix + object marking\n\nNow, build the translations.\n\n19. The shaman hurt you → “hurt” → from example (3) “you hurt yourself” = *aanniqtutit* → root *aanniqt*, so “hurt” = *aanniqt* → past tense and object marked → *aanniqtutit*? But this is reflexive.\n\nBut in (6) \"the shaman cured a doctor\" → *angatkuq iluaqhaijimik aarqisijuq* → verb “cured” is *aarqisijuq*\n\nWait — “cure” is in (4) and (6): \"curer\" = *aarqijaatit* (cured you), *aarqisijuq* (cured a doctor)\n\nSo healer verbs: *aarqijaatit*, *aarqisijuq* → base forms likely *aarq* (cure)\n\nBut “hurt” is not cure — from (3): you hurt yourself → *aanniqtutit* → so root *aanniqt*\n\nSo “the shaman hurt you” → agent *angatkuq*, verb root *aanniqt*, past tense + object marking → likely *angatkuq aanniqtutit*\n\nBut “you hurt yourself” = *aanniqtutit* → used reflexive form *-tutit*\n\nWhen object is external → object marked? In (1) “your dog saw you” → *qingmivit takujaatit* → saw you = *takujaatit*\n\nSo: verb + object marking → *-jaatit*, *-janga*, etc.\n\nCheck: (1) → dog saw you → *takujaatit*\n\n(4) → doctor cured you → *aarqijaatit*\n\n(6) → shaman cured doctor → *aarqisijuq*\n\nSo pattern: verb root + past tense + object marking → object is marked with suffix *-jaatit*, *-janga*, or similar\n\nNow, “hurt” → from “you hurt yourself” → reflexive: *aanniqtutit*\n\nFor external object: likely *aanniqt* + past + object suffix → *aanniqt* → in (10): “the dog hurt your teacher” → *qingmiup ilinniaqtitsijiit aanniqtanga*\n\n→ “hurt your teacher” = *aanniqtanga*\n\nSo yes: verb root *aanniqt*, then addition of object marker → *-anga* (plausible from *-a* + object)\n\nSo “the shaman hurt you” → agent *angatkuq*, verb *aanniqt*, object *you* → *angatkuq aanniqtutit*?\n\nBut “you” is object → is it marked with *-tak* or *-tut*?\n\nFrom (1): “your dog saw you” → *qingmivit takujaatit*\n\n→ “you” → in object position → gets suffix *-takujait* → *takujaatit* — so object is marked with *-takujait*?\n\nWait — the verb is *takujait* → base *takuj*, object suffix?\n\nIn (3): “you hurt yourself” → *aanniqtutit* — reflexive → object is self\n\nIn (10): “the dog hurt your teacher” → *qingmiup ilinniaqtitsijiit aanniqtanga*\n\n→ \"your teacher\" = *ilinniaqtitsijiit* → therefore \"hurt\" is *aanniqtanga* → so object is marked as *aanniqtanga*\n\nSo: verb root + suffix meaning object → *-anga* for teacher?\n\nCould the object be marked with something like *-takujait*, *-janga*, etc.?\n\nFrom (4): *iluaqhaijiup aarqijaatit* → doctor cured you → *aarqijaatit*\n\n→ verb *aarqijaatit* → so base *aarqi*, object *you*\n\nIn (6): *angatkuq iluaqhaijimik aarqisijuq* → shaman cured a doctor → object *doctor* → *iluaqhaijimik*\n\nSo object marker: *-jimik*? — not consistent.\n\nWait — *iluaqhaijimik* → “a doctor” — so *iluaqhaiji* is “the doctor”, *-mik* = genitive?\n\nPossibility: object is in genitive form, marked by suffix *-mik*, *-ji*, etc.\n\nBut look: (1): \"your dog saw you\" → *qingmivit takujaatit* — “you” is object → *takujait* → not genitive\n\n(4): “doctor cured you” → *aarqijaatit* — “you” in object → *jaatit*\n\n(6): “shaman cured a doctor” → *aarqisijuq* — “a doctor” = *iluaqhaijimik*\n\n→ object is *iluaqhaijimik* → so object is marked with *-mik*?\n\nIn (8): “your doctor cured your boy” → *iluaqhaijivit inuuhuktuit aarqijanga* → object is *your boy* → *inuuhuktuit* → so *inuuhuktuit* = “your boy”\n\n→ base *inuuhuktuup* = “boy”, *-uit* → possessive?\n\nSimilarly, (9): “hunter speared the wolf” → *angunahuktiup amaruq iputujanga* → object = *amaruq* = “wolf” → not genitive, no suffix?\n\nBut in (12): “hunter shot a polar bear” → *angunahukti nanurmik qukiqsijuq* → “a polar bear” = *nanurmik* → *nanur* + *-mik*\n\nSo yes — object is marked with *-mik* when in accusative or possessed?\n\nBut in (1): “saw you” → no *-mik* → instead: *takujaatit*\n\nBut *takujait* ≠ *takujimik* — different\n\nPossibility: different verbs have different object marking.\n\nBut verb *takuj* → object marked with *-jaatit*?\n\nIn (4): *aarqijaatit* — “cured you” → *jaatit*\n\nIn (10): *aanniqtanga* — “hurt your teacher” → *anga*\n\nSo object marking varies per verb root.\n\nThus: the object is marked with a suffix specific to the verb, and the form depends on the verb itself.\n\nNow, for translation:\n\n19. The shaman hurt you → agent: *angatkuq*, verb: *aanniqt*, object: *you* → so must be *angatkuq aanniqtutit*?\n\nBut in (3): *aanniqtutit* = you hurt yourself → reflexive\n\nIn (10): *qingmiup ilinniaqtitsijiit aanniqtanga* = the dog hurt your teacher → object *your teacher* → *aanniqtanga*\n\nSo for external object, object is in form *aanniqtanga* → similar to *iluaqhaijimik* → genitive *-mik*\n\nThus, “you” as object → likely *aanniqtutit*? But *utit* is reflexive.\n\nIn (3): \"you hurt yourself\" = aanniqtutit → reflexive\n\nSo \"you\" as object → not reflexive → must be marked with a different suffix?\n\nBut in (10): hurt your teacher → object is *your teacher*, marked with *-tsijiit* (possessive) and *-anga*?\n\nActually: *ilinniaqtitsijiit aanniqtanga* → the form *aanniqtanga* suggests the verb + object suffix *-anga*\n\nSimilarly, in (4): *aarqijaatit* → object *you* → *jaatit*\n\nSo no consistent object suffix.\n\nWait — in (6): *angatkuq iluaqhaijimik aarqisijuq* → “cured a doctor” → object = *iluaqhaijimik* → *-mik*\n\nIn (8): “your doctor cured your boy” → *iluaqhaijivit inuuhuktuit aarqijanga* → object = *inuuhuktuit* = “your boy” → *-uit*\n\nSo object marking: possessive form — *-uit*, *-mik*, *-takujait*, etc.\n\nThus, object is expressed in a possessive or genitive form.\n\nSo for the verb “hurt”:\n\n- Example (3): “you hurt yourself” = *aanniqtutit* → reflexive, base verb + *-tutit*\n- Example (10): “the dog hurt your teacher” = *qingmiup ilinniaqtitsijiit aanniqtanga*\n → object = *ilinniaqtitsijiit* = “your teacher” → marked with possessive + genitive?\n\nBut *aanniqtanga* → could be verb *aanniqt* + *-anga* → not in corpus\n\nBut in (4): “doctor cured you” = *aarqijaatit* → object *you* = *jaatit*\n\nSo verbs seem to have internal object marking.\n\nConclusion: the verb root determines how object is marked.\n\nSo for “hurt”:\n- When external: use *aanniqt* + object suffix → in (10) is *aanniqtanga* → so likely *aanniqtanga* for “hurt you”\n\nBut in (10): full phrase: “the dog hurt your teacher” = *qingmiup ilinniaqtitsijiit aanniqtanga*\n\nSo verb pattern: agent + object (in possessive form) + verb + base + object suffix?\n\nActually, no — agent first, then verb, then object?\n\nIn (1): *qingmivit takujaatit* = “your dog saw you” → agent (dog) + verb (saw) + object (you)\n\nIn (10): *qingmiup ilinniaqtitsijiit aanniqtanga* → agent (dog) + object (your teacher) + verb (hurt)\n\nOrder is agent, object, verb?\n\nBut in (2): *Inuuhuktuup iluaqhaiji qukiqtanga* → boy shot doctor → agent, verb, object\n\nSo different?\n\nIn (2): agent → boy, then verb → shot, then object → doctor\n\nIn (10): agent — dog, then object — teacher, then verb — hurt → *aanniqtanga*\n\nBut in (1): *qingmivit takujaatit* → agent (dog), verb (saw), object (you)\n\nSo inconsistent?\n\nWait — in (10): “the dog hurt your teacher” → the dog is agent, “your teacher” is object → so object must be marked with possessive\n\nIn (1): “saw you” → object *you* — marked with *-takujait*\n\nIn (4): “cured you” → *aarqijaatit*\n\nSo object form is attached after the verb?\n\nThus, the structure is: agent + verb + object\n\nIn (1): *qingmivit takujaatit* → agent (your dog) + verb (saw) + object (you)\n\nIn (4): *iluaqhaijiup aarqijaatit* → doctor + verb (cured) + object (you)\n\nIn (10): *qingmiup ilinniaqtitsijiit aanniqtanga* → agent (dog), object (your teacher), verb (hurt)\n\nBut verb comes at end — so verb is *aanniqtanga* — this must be a combined verb-object form?\n\nBut that would be unusual.\n\nAlternatively, typo or structure?\n\nIn (10): “Qingmiup ilinniaqtitsijiit aanniqtanga” → “the dog hurt your teacher”\n\nBut in other cases, verb is directly after agent:\n\n(1): qingmivit takujaatit — dog saw you\n\n(2): Inuuhuktuup iluaqhaiji qukiqtanga — boy shot doctor\n\n(6): Angatkuq iluaqhaijimik aarqisijuq — shaman cured doctor\n\n(8): Iluaqhaijivit inuuhuktuit aarqijanga — your doctor cured your boy\n\nSo all have agent, then verb, then object?\n\nBut in (10): “Qingmiup ilinniaqtitsijiit aanniqtanga” — it seems like agent, object, verb?\n\nUnless it’s a typo.\n\nBut the original is: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" = \"The dog hurt your teacher\"\n\nPossibly the verb is *aanniqtanga*, meaning \"hurt you\" — so after agent, object is *ilinniaqtitsijiit* — so object marked.\n\nThen verb is *aanniqtanga* — which includes object?\n\nNo — *aanniqtanga* likely means \"hurt you\", not \"hurt your teacher\"\n\nBut it is used in the middle?\n\nMissed structure.\n\nLet’s re-analyze:\n\nIn (1): Qingmivit takujaatit → “your dog saw you” → agent (Qingmivit) + verb (takuj) → verb is *takuj* → object is *takujaatit* → so *-jaatit* suffix for object?\n\nBut in (10): Qingmiup ilinniaqtitsijiit aanniqtanga → if verb is *aanniqtanga*, then it may be the verb form with object included?\n\nBut in (4): aarqijaatit → doctor cured you — verb *aarqi* + *-jaatit*\n\nSimilarly, in (6): aarqisijuq — cured a doctor → *-sjujuq*?\n\nSo no — verb form includes object marking", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11820.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "iid", + "sample_index": 0, + "output": "Step 1: Identify the linguistic pattern in the given Nooni sentences.\n\nThe sentences consistently use a structure where time references are tied to specific days of the week (e.g., Bvumbon, Bvusɔw, Bvuzhi, etc.), and the time expressions are encoded in a specific way.\n\nLook at time markers:\n\n- \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → \"yesterday\" is linked to a day name via a temporal prefix.\n- \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"on X, verb\" structure.\n- \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"day after tomorrow\" is marked with \"fɔ̀ shě\" (meaning \"the day after tomorrow\").\n- \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"tomorrow\" is \"ntfǔː\", which seems to be a day-specific marker.\n- \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\" → \"day before yesterday\" is \"kefwé cí\".\n\nSo we can infer that:\n\n- \"yesterday\" = fɔgò cǐ\n- \"today\" = mɛ / me / wɔ̀\n- \"tomorrow\" = ntfǔː\n- \"the day after tomorrow\" = fɔ̀ shě\n- \"the day before yesterday\" = kefwé cí\n\nNow, verbs are tied to time using a structure like:\n- On X, [subject] [verb] [object]\n\nThe verb structure seems to encode a temporal quality: present/future/past, often marked by tone or particle.\n\nLook at verb usage:\n\n- \"I came to the market\" → \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → \"me + verb + object + day\"\n- \"he found the book\" → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → [subject] + [verb] + [object] + on [day]\n\nSo the pattern is:\n[subject] + [verb] + [object] + on [day] → for events in a specific day.\n\nNow, time expressions:\n\n- \"on Bvusɔw\" → appears as \"bvúsɔ̀w\"\n- \"the day after tomorrow\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → fɔ̀ shě (the day after tomorrow) + ntfǔː (tomorrow) → so \"fɔ̀ shě ntfǔː\" is \"day after tomorrow\"\n\nBut in (5): \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → so \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\", and \"is\" is implied in the structure.\n\nSimilarly, (8): \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"ntfǔː\" = tomorrow, \"nú\" = is.\n\nSo we observe:\n- \"tomorrow\" = ntfǔː\n- \"today\" = implicitly in the day being discussed\n- \"on X\" = used to refer to a specific day (e.g., \"on Bvusɔw\")\n\nBut note: time references are embedded in the sentence with time markers.\n\nNow, what about the verb forms?\n\n- \"came\" → ncí\n- \"found\" → tɔ̀\n- \"will steal\" → cɔ́ŋ\n- \"will help\" → fí\n- \"heard\" → tɔ̀ (as in 7: wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → \"you heard the thief\")\n\nSo verbs are often in present/future tense, and \"will\" is marked with a specific form like cɔ́ŋ or fí.\n\nNow look at (20): \"On Bvusɔw, I helped the man.\"\n\n- Subject: me\n- Verb: helped → same as \"help\" (fí) → in past?\n- Object: the man → dìɛ̀msɛ̌n\n\nIn sentence (12): \"I am about to help the man\" → \"me nú nfí dìɛ̀msɛ̌n\"\n\n→ \"me nú nfí dìɛ̀msɛ̌n\" = I am about to help the man\n\n\"nú\" = about to, \"nfí\" = help.\n\nSo \"help\" = fí, \"about to\" = nú.\n\nIn (14): \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\n→ \"we will steal\" → \"bèsèn nǔ géː cɔ́ŋ mutù\"\n\nSo \"will\" = cɔ́ŋ, \"steal\" = géː? Wait — earlier: \"you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"cɔ́ŋ\" = steal.\n\nSo \"cɔ́ŋ\" = steal.\n\nBut in (14): \"we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù\" → here, \"geː\" is used as \"will\"?\n\nWait — style inconsistency.\n\nLook again:\n\n(2): \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\n\"yúː\" → likely the form of \"you\" (sg), and \"cɔ́ŋ\" = steal.\n\n(14): \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\n\"bèsèn\" = we, \"nǔ\" = will? Or \"nǔ\" = we?\n\nBut \"nǔ\" is used in (2): \"wɔ̀ nǔ yúː\" → \"you\"\n\nIn (14): \"bèsèn nǔ géː cɔ́ŋ\" → \"we\" + \"will\" (geː?) → but \"geː\" is not the same.\n\nAlternatively, maybe \"geː\" is \"see\"?\n\nCheck (15): \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n\"bɔ́\" = they, \"nɔ̂ː\" = saw, \"yɛ᷅n me lé\" = me at the market.\n\nSo \"saw\" = nɔ̂ː.\n\nSimilarly, (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\nSo \"saw\" = nɔ̂ː.\n\nTherefore, \"saw\" = nɔ̂ː.\n\nThen in (14): \"we will steal\" → \"bèsèn nǔ géː cɔ́ŋ\"\n\n\"geː\" must be a verb meaning \"will\", but \"cɔ́ŋ\" is \"steal\".\n\nWait — (2): \"you will steal\" → \"yúː cɔ́ŋ\" → \"cɔ́ŋ\" = steal, verb.\n\nSo stealing verb is cɔ́ŋ.\n\nBut in (14): \"we will steal\" → \"bèsèn nǔ géː cɔ́ŋ\" → here \"geː\" appears as prefix?\n\nBut in (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\"\n\nSo \"cǐ\" = on, \"nɔ̂ː\" = saw.\n\nSo the verb \"saw\" is nɔ̂ː.\n\nIn (14): \"we will steal\" → must be \"will + steal\".\n\nBut in (2), \"will\" is not marked — it's just \"cɔ́ŋ\".\n\nBut in (14): \"bèsèn nǔ géː cɔ́ŋ\" → \"bèsèn\" = we, \"nǔ\" = ? , \"geː\" = will?\n\nAlternatively, \"nǔ\" = we?\n\nBut \"nǔ\" is used for \"you\" (sg) in (2): \"wɔ̀ nǔ yúː\" → \"you\".\n\nIn (14): \"bèsèn nǔ géː\" — \"bèsèn\" = we, \"nǔ\" = ? / could be \"will\"?\n\nBut this seems inconsistent.\n\nAnother possibility: the verb \"will\" is encoded in the tense via a particle or tone.\n\nInstead, consider the time reference.\n\nAll time references are of the form:\n\n- [day name] → e.g., bvúsɔ̀w, bvúmbòn, bvûŋka\n\nWhen the day is not named, the time is referenced via relative terms:\n\n- yesterday = fɔgò cǐ\n- today = wɔ̀ or me\n- tomorrow = ntfǔː\n- the day after tomorrow = fɔ̀ shě\n- the day before yesterday = kefwé cí\n\nIn the translations, the sentence specifies the day of reference.\n\nIn (c), the sentences are spoken on Bvumbon.\n\nSo we must refer to other days using relative terms or the day names.\n\nNow:\n\n20. On Bvusɔw, I helped the man.\n\n→ related to Bvusɔw → use \"on Bvusɔw\"\n\nSubject: I → me\n\nVerb: helped → in past → better capture: (12) \"I am about to help\" = \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo \"help\" = nfí\n\n\"about to\" = nú\n\nBut \"helped\" is past.\n\nIn (9): \"Today, I chose the book\" → \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\"\n\n\"chose\" = mbɛ̂ː\n\nSo verb \"choose\" = mbɛ̂ː\n\nIn (3): \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\n\"help me\" = fí me\n\nSo \"help\" = fí\n\nSo \"help\" = fí\n\nThen \"helped\" = past tense?\n\nBut in sentence (12): \"I am about to help\" = \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo \"nfí\" = help (future or about to)\n\nBut in (3): \"will help\" = \"fí\"\n\nSo \"fí\" = will help\n\nThen \"helped\" = past?\n\nIs there a past form?\n\n(1): \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\"\n\nSo past tense is implied.\n\nIn (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\"\n\n\"nɔ̂ː\" = saw → past.\n\nSo \"saw\" = nɔ̂ː\n\nSimilarly, in (2): \"you will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"cɔ́ŋ\" = steal → present/future\n\nSo the verb form doesn’t have a clear past tense.\n\nBut in (3): \"will help\" → \"fí\"\n\nSo \"fí\" = will help or help (future)\n\nIn (12): \"I am about to help\" → \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo \"nfí\" = help (present/future)\n\nSo possibly \"fí\" and \"nfí\" are different forms?\n\nWait — in (3): \"the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\n\"bóy\" = will? Or just \"the woman\"?\n\nNo, \"bóy\" = woman.\n\n\"will\" = not marked.\n\nIn (14): \"we will steal\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\n\"bèsèn\" = we, \"nǔ\" = ? , \"géː\" = will?\n\nBut \"cɔ́ŋ\" = steal.\n\nSo likely \"geː\" is \"will\".\n\nBut in (2): \"you will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" — no \"will\" particle.\n\nSo timing may be inferred from the day or tense marker.\n\nAlternative: the tense is given by the time clause.\n\n\"Yesterday\" = past, \"today\" = present, \"tomorrow\" = future.\n\nIn (5): \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → present tense.\n\nSo all events are in the present or future with reference to the day.\n\nNow for translation:\n\n20. On Bvusɔw, I helped the man.\n\n→ \"On Bvusɔw, I will help the man\" or past?\n\nBut \"helped\" → past.\n\nIs there a past tense verb?\n\nWe have:\n\n- saw = nɔ̂ː → past\n- came = ncí → past\n- found = tɔ̀ → past\n- will steal = cɔ́ŋ → future\n- will help = fí → future\n\nIn (12): \"I am about to help\" = \"me nú nfí dìɛ̀msɛ̌n\" → present fut.\n\nIn (3): \"will help\" = \"fí\"\n\nSo \"fí\" = future \"help\"\n\nSo \"helped\" = past?\n\nNo example of \"helped\" in past.\n\nBut in (15): \"They saw me just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"just now\" → so \"saw\" = nɔ̂ː, but with \"just now\" marked?\n\n\"just now\" is not marked in structure.\n\nBut in (7): \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"heard\" = tɔ̀, and \"a long time ago\" is implied.\n\nSo past tense is realized with verb + time reference.\n\nSo \"helped\" = past tense = \"fí\" with a past marker?\n\nBut no such marker.\n\nWait — in (3): \"will help\" = fí\n\nIn (12): \"about to help\" = nfí\n\nSo \"fí\" and \"nfí\" are distinct: one future, one about-to.\n\nBut \"helped\" is past.\n\nNo verb form matches \"helped\".\n\nBut perhaps the verb is \"help\" and the time reference indicates past.\n\nThe sentence is \"On Bvusɔw, I helped the man\" — past.\n\nSo perhaps the past form is not marked, and \"help\" is used in a past context.\n\nBut we only have past examples: \"came\", \"found\", \"saw\".\n\nIn (4): \"he found the book\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\n\n\"found\" = tɔ̀ nɔ̂ː\n\nSo \"tɔ̀ nɔ̂ː\" = past tense.\n\n\"helped\" — no example.\n\nIn (3): \"will help\" = fí\n\nSo perhaps \"help\" in past and future differs.\n\nBut in (12): \"I am about to help\" = \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo \"nfí\" = help.\n\nSo maybe there are multiple forms.\n\nBut for now, since no past form of \"help\" exists, and the only verb form used is \"fí\" for \"help\", possibly \"fí\" is used in various tenses, and \"on Bvusɔw\" implies past.\n\nBut still.\n\nAlternative: all time-relative events are tied to the day, and verbs are in default form.\n\nBut in (5): \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"is\" = nú.\n\nSo \"is\" = nú.\n\nSimilarly, \"will\" = cɔ́ŋ or géː?\n\nIn (2): \"you will steal\" → \"cɔ́ŋ\"\n\nIn (14): \"we will steal\" → \"geː cɔ́ŋ\"\n\nSo \"cɔ́ŋ\" = steal, \"geː\" = will?\n\nBut in (2), \"will\" is not marked.\n\nUnless tone or context indicates future.\n\nIn fact, (2): \"you will steal\" — refers to future, so \"cɔ́ŋ\" may be future.\n\nSimilarly, (3): \"will help\" → \"fí\"\n\nSo \"fí\" = future helping.\n\nSo \"helped\" = past → not in the data.\n\nBut in sentence (1): \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → \"nú\" = is, present.\n\nSo \"is\" = nú.\n\nFor \"helped\", we lack a past form.\n\nBut perhaps the pattern is: when time is given (like \"on Bvusɔw\"), the verb is in past or present.\n\nIn (3): \"On Bvuzhi, the woman will help me\" → \"fí\" — future.\n\nIn (12): \"I am about to help\" — present fut.\n\nSo probably, without a time reference, the verb is in present.\n\nBut here, time is referenced: \"on Bvusɔw\".\n\nSo likely past.\n\nBut no past help.\n\nWe must use the pattern from verb forms.\n\nFrom (3): \"will help\" = fí\n\nSo in (2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10365.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "iid", + "sample_index": 1, + "output": "We are translating into Nooni, a Beboid language with a complex system of tense, aspect, and temporal marking, particularly using calendar days (days of the week) as reference.\n\nWe are told the days are spoken on Bvumbon, so all translations must reflect that day as the reference point.\n\nGo through each sentence, extract temporal and grammatical patterns from the examples.\n\n---\n\n**Step 1: Identify temporal markers and their forms**\n\nFrom the examples:\n\n- \"Yesterday was Bvumbon\" → fɔgò cǐ nú bvúmbòn → \"yesterday\" is linked to \"Bvumbon\"\n- \"On Bvumbon, I came to the market\" → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn → \"On Bvumbon\" = fɔ̀wǎy bvúmbòn\n- \"On Bvusɔw, you will steal...\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\n- \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅ → \"day after tomorrow\" = fɔ̀ shě ntfǔː\n- \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"tomorrow\" = ntfǔː\n- \"The day before yesterday was Bvuŋka\" → kefwé cí nú bvûŋka → \"day before yesterday\" = kefwé cí\n- \"Today\" appears as \"wvù\" (e.g., \"Today, he killed\") → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\n- \"Just now\" appears in \"they saw me at the market just now\" → \"fɔ̀wǎy\" used for \"market\" → e.g., \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"saw me at the market just now\"\n\n→ Key temporal markers:\n- yesterday: fɔgò cǐ\n- today: wvù\n- tomorrow: ntfǔː\n- day before yesterday: kefwé cí\n- day after tomorrow: fɔ̀ shě ntfǔː\n- on X: fɔ̀wǎy X\n\n→ So, \"On Bvusɔw\" = fɔ̀wǎy bvúsɔ̀w\n\n---\n\n**Step 2: Group verb forms by aspect and tense**\n\n- Past: e.g., \"he found\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː → wvù (today) + verb + object\n- Future: e.g., \"I will choose\" → me nú mbóy ncáw mutù → \"on Bvutfu, I will choose\"\n- Present (imperfect or ongoing): \"I am about to help\" → me nú nfí dìɛ̀msɛ̌n → \"am about to help\"\n- \"Just now\" = fɔ̀wǎy (used in \"just now\" or with verbs indicating recent past)\n\nNote: \"just now\" often appears with verbs like \"saw\", \"heard\", \"killed\" with fɔ̀wǎy (same as market)\n\nIn sentence 15: \"They saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy → \"saw me at the market\" + fɔ̀wǎy (just now)\n\nSo: **\"just now\"** is marked by **fɔ̀wǎy** in the object or location, or as a temporal adverb.\n\nAlso: \"the day after tomorrow\" = fɔ̀ shě ntfǔː → \"fɔ̀\" (day after tomorrow?), \"shě\" (something like \"after\")\n\nWait: in sentence 5: \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅ → so “fɔ̀ shě” = the day after tomorrow\n\nThus:\n- fɔ̀ shě = day after tomorrow\n- kefwé cí = day before yesterday\n- ntfǔ = tomorrow\n- fɔgò cǐ = yesterday\n- wvù = today\n- fɔ̀wǎy = at the market / just now\n\n→ So “just now” is marked with **fɔ̀wǎy** when it modifies a verb (like saw, heard, killed)\n\nNow look at verb constructions.\n\n---\n\n**Step 3: Verb forms**\n\n- \"I came\" → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy → \"me\" (I) + ncí (came) + nɔ̂ː (to) + ntɔ᷅ (market) + fɔ̀wǎy (at market) — likely \"ncí\" is the verb\n- \"I will choose\" → me nú mbóy ncáw mutù → \"me nú\" (on Bvutfu) + \"mbóy\" (will choose) + mutù (car)\n- \"I am about to help\" → me nú nfí dìɛ̀msɛ̌n → \"me nú\" (on Bvutfu) + \"nfí\" (am about to) + dìɛ̀msɛ̌n (the man)\n\nSo:\n- \"will\" → mbóy (in \"will choose\")\n- \"am about to\" → nfí\n- \"heard\" → tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → \"heard\" = tɔ̀ (past) + nɔ̂ː (to) + yo᷅w (thief) + cɔ̌ŋ (the thief?) → maybe \"tɔ̀\" is \"heard\", \"yo᷅w\" = thief\n\nIn 7: \"You(sg) heard the thief a long time ago\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → \"heard\" = \"tɔ̀\", \"yo᷅w\" = thief\n\nSo \"heard\" = tɔ̀ (historical or past)\n\nThus, verb meanings:\n- to come → ncí\n- to choose → mbóy\n- to help → nfí\n- to steal → cɔ́ŋ\n- to see → yɛ᷅n\n- to kill → bɛ̂ː (used in \"he killed the woman\" = wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n)\n- to find → tɔ̀ (same as heard?) — \"he found the book\" = wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà → found = tɔ̀\n→ So \"tɔ̀\" = found / heard / saw / perceive?\n\nWait: in 15: \"They saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n\n\"yɛ᷅n\" = saw\n\nBut in 7: \"you heard the thief\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → \"tɔ̀\" = heard\n\nIn 4: \"he found the book\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà → \"tɔ̀\" = found\n\nSo \"tɔ̀\" = found / heard / saw?\n\nBut different verbs: \"yɛ᷅n\" = saw, \"tɔ̀\" = heard / found\n\n→ Possibly tone or context distinguishes them.\n\nBut in sentence 21: \"The thief stole the yam just now\" → must use a past form, but \"just now\" → use fɔ̀wǎy\n\nThe thief → yo᷅w, stole → cɔ́ŋ\n\nSo: \"yo᷅w cɔ́ŋ\" = thief stole\n\nThen with \"just now\" → likely attached to the verb or object.\n\nSentence 15: \"They saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n\nSo \"fɔ̀wǎy\" is added after the verb with location.\n\nSimilarly, in 21: \"just now\" should be added similarly.\n\nSo: \"the thief stole the yam just now\" = yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy\n\nBut check if \"fɔ̀wǎy\" is only for market. In 15 it's \"at the market\".\n\nIn 21, \"yam\" — is \"yam\" in a location?\n\n\"kèŋkfǔ\" = yam\n\nIn sentence 2: \"On Bvusɔw, you will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\n\n\"yam\" = kèŋkfǔ\n\nSo “stole the yam” → cɔ́ŋ kèŋkfǔ\n\nThen “just now” → add fɔ̀wǎy?\n\nBut in 21: \"The thief stole the yam just now\" → so likely: yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy\n\nBut is \"fɔ̀wǎy\" used only with \"market\"? Or can it be used for \"yam\"?\n\nIn utterance 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě ntfǔː\", not fɔ̀wǎy.\n\nIn 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\n\"yɛ᷅n wáy\" = saw the market\n\nSo \"saw the market\" → yɛ᷅n wáy\n\nSimilarly, \"saw me\" → yɛ᷅n me\n\nSo for \"saw the yam\"? Not directly.\n\nIn sentence 2: \"steal the yam\" = cɔ́ŋ kèŋkfǔ\n\nNo \"fɔ̀wǎy\" with yam.\n\nBut in 15: \"saw me at the market just now\" → \"fɔ̀wǎy\" used with \"market\"\n\nSo likely \"fɔ̀wǎy\" is used to mark “at the market” or “just now” in verbs of perception.\n\nBut is there a verb equivalent for “just now”?\n\nSentence 21: \"The thief stole the yam just now\" — likely “just now” = fɔ̀wǎy, attached to the verb.\n\nLook at sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\nNo fɔ̀wǎy — implies it's about a specific event, not necessarily “just now”.\n\nOnly when it's immediate past (like saw me just now) → includes fɔ̀wǎy.\n\nSo “just now” is marked by fɔ̀wǎy, attached to the perception or action.\n\nSo for stealing with \"just now\": yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy\n\n---\n\n**Step 4: Build translations**\n\nNow translate each requested sentence, spoken on Bvumbon.\n\nAll are presented on Bvumbon, so all are from the perspective of Bvumbon.\n\n---\n\n**20. On Bvusɔw, I helped the man.**\n\n- \"On Bvusɔw\" → fɔ̀wǎy bvúsɔ̀w\n- \"I helped\" → me nfí dìɛ̀msɛ̌n → \"me\" (I), \"nfí\" (am about to help), \"dìɛ̀msɛ̌n\" (the man)\n\n→ So → me nfí dìɛ̀msɛ̌n fɔ̀wǎy bvúsɔ̀w\n\nNote: in sentence 12: \"I am about to help the man\" → me nú nfí dìɛ̀msɛ̌n → \"on Bvutfu\"\n\nSo \"am about to\" = nfí, then object.\n\nHere, \"on Bvusɔw\" = fɔ̀wǎy bvúsɔ̀w\n\n→ me nfí dìɛ̀msɛ̌n fɔ̀wǎy bvúsɔ̀w\n\n→ c.1: me nfí dìɛ̀msɛ̌n fɔ̀wǎy bvúsɔ̀w\n\n---\n\n**21. The thief stole the yam just now.**\n\n- \"the thief\" → yo᷅w\n- \"stole\" → cɔ́ŋ\n- \"the yam\" → kèŋkfǔ\n- \"just now\" → fɔ̀wǎy\n\n→ yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy\n\n→ c.2: yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy\n\n---\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- \"On Bvuŋkaden\" → fɔ̀wǎy bvûŋka᷆ːde᷆n\n- \"I will hear\" → me mbóy nɔ̂ː yɛ᷅n → \"mbóy\" = will, \"nɔ̂ː\" = to, \"yɛ᷅n\" = hear\n- In 14: \"we will steal the car\" → bèsèn nǔ géː cɔ́ŋ mutù → \"géː\" = steal\n- In 9: \"I chose the book\" → me mbɛ̂ː nca᷅w ŋwà → \"mbɛ̂ː\" = chose, \"nca᷅w\" = book\n- So \"hear\" = yɛ᷅n\n- \"will\" = mbóy (used in \"will choose\", \"will steal\")\n\nSo: me mbóy nɔ̂ː yɛ᷅n mutù fɔ̀wǎy bvûŋka᷆ːde᷆n\n\n→ c.3: me mbóy nɔ̂ː yɛ᷅n mutù fɔ̀wǎy bvûŋka᷆ːde᷆n\n\n---\n\n**23. Today, the woman will kill the man.**\n\n- \"today\" → wvù\n- \"the woman\" → kwɔ᷆ːn\n- \"will kill\" → bɛ̂ː (used in \"he killed\", \"killed the woman\")\n- In 6: \"he killed the woman\" → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n → \"bɛ̂ː\" = killed\n- So \"will kill\" = mbóy bɛ̂ː\n- \"the man\" → dìɛ̀msɛ̌n\n\n→ kwɔ᷆ːn mbóy bɛ̂ː dìɛ̀msɛ̌n wvù\n\n→ c.4: kwɔ᷆ːn mbóy bɛ̂ː dìɛ̀msɛ̌n wvù\n\n---\n\n**24. Today, the man saw you(sg).**\n\n- \"today\" → wvù\n- \"the man\" → dìɛ̀msɛ̌n\n- \"saw\" → yɛ᷅n\n- \"you(sg)\" → nɔ̂ː (as in \"you to me\", or \"you in object form\"?)\n\nIn sentence 15: \"They saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n\n\"me\" = object\n\nIn sentence 20: \"I helped the man\" → me nfí dìɛ̀msɛ̌n\n\nSo \"you(sg)\" in object → likely \"nɔ̂ː\" as in \"to you\"?\n\nBut in \"you(sg) will steal\" → \"wɔ̀ nǔ yúː\" → \"wɔ̀\" = you, \"nǔ\" = you(sg), \"yúː\" = will steal\n\nSo \"you\" = nǔ\n\nObject of \"saw\" → likely \"nɔ̂ː\" (to you)\n\nIn absence of direct form, may use \"nɔ̂ː\" for \"you (object)\"\n\nIn sentence 15: \"saw me\" → yɛ᷅n me\n\nSo \"saw you\" → yɛ᷅n nɔ̂ː\n\n→ So: dìɛ̀msɛ̌n yɛ᷅n nɔ̂ː wvù\n\n→ c.5: dìɛ̀msɛ̌n yɛ᷅n nɔ̂ː wvù\n\n---\n\nFinal answers:\n\nc.1: me nfí dìɛ̀msɛ̌n fɔ̀wǎy bvúsɔ̀w \nc.2: yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy \nc.3: me mbóy nɔ̂ː yɛ᷅n mutù fɔ̀wǎy bvûŋka᷆ːde᷆n \nc.4: kwɔ᷆ːn mbóy bɛ̂ː dìɛ̀msɛ̌n wvù \nc.5: dìɛ̀msɛ̌n yɛ᷅n nɔ̂ː wvù\n\n\\boxed{c.1: me nfí dìɛ̀msɛ̌n fɔ̀wǎy bvúsɔ̀w; c.2: yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀wǎy; c.3: me mbóy nɔ̂ː yɛ᷅n mutù fɔ̀wǎy bvûŋka", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8794.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Identify the grammatical structure of the given examples.\n\nWe are given multiple sentences in Nooni with dates (Bvutfu, Bvusɔw, Bvuzhi, etc.) and their English translations. The date system seems to be cyclical and based on relative days.\n\nFrom the sentences:\n\n- Sentence 1: “Yesterday was Bvumbon” → indicates a reference to the day before the speaking day.\n- Sentence 5: “The day after tomorrow is Bvutfu” → indicates that Bvutfu occurs two days after the speaking day.\n- Sentence 8: “Tomorrow is Bvuŋkaden” → indicates a forward day.\n- Sentence 11: “The day before yesterday was Bvuŋka” → indicates two days before.\n\nSo, days are marked by reference to relative time from the current day (the speaking day). Specific days are used as labels.\n\nStep 2: Determine how time markers function.\n\nThe structure for expressing time:\n- “On X, Y” → used for events on a specific day (X)\n- “The day after tomorrow” → “ntfǔː nú” (from sentence 5)\n- “Tomorrow” → “ntfǔː nú” or “ntfǔː nú” in other forms\n- “Yesterday” → “fɔgò cǐ” (sentence 1)\n- “The day before yesterday” → “kefwé cí” (sentence 11)\n\nPattern of time markers:\n- “fɔgò cǐ” = yesterday\n- “ntfǔː nú” = tomorrow\n- “kefwé cí” = day before yesterday\n- “fɔ̀ shě” = day after tomorrow (sentence 5)\n- “me nú” = “on X, I will…” (future)\n- “wɔ̀ tɔ̀ nɔ̂ː” = “you (sg) heard” (past)\n\nThe time markers are often placed before the day name (e.g., “On Bvusɔw”), but they can also appear in relative form.\n\nStep 3: Identify verbs and their forms.\n\n1. “I came to the market” → “me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn” → “me ncí” = came to (ncí = to go? to come?)\n → \"me ncí nɔ̂ː [place]\" → “me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy” = came to the market\n\n2. “you(sg) will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “wɔ̀ nǔ yúː cɔ́ŋ” = you will steal\n\n3. “the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “kwɔ᷆ːn nǔ bóy fí me” = the woman will help me\n\nSo verb patterns:\n- Present/future actions: “will + verb” → “cɔ́ŋ” = steal, “fí” = help, “kèŋkfǔ” = yam (object)\n\nNote: “cɔ́ŋ” = steal; appears in 2 and 14.\n\nAlso, “yúː” = will → used in “wɔ̀ nǔ yúː cɔ́ŋ” → so “yúː” marks future tense.\n\n“fí” = help → “fí me” = help me\n\n“bèsèn” = will → in sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù” = today, we will steal the car.\n\nThus, future tense markers:\n- “yúː” in “you will steal”\n- “bèsèn” in “we will steal”\n- “me nú” in “on X, I will choose”\n\nSo the future is marked by:\n- “yúː” for singular (you)\n- “bèsèn” for plural (we)\n- “me nú” for “on X, I will”\n\nStep 4: Analyze past tense.\n\nSentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “wɔ̀ tɔ̀” = you heard (past), “yo᷅w” = thief, “cɔ̌ŋ” = heard (verb)\n\nSo “tɔ̀” = past tense of “hear” or “hear from”\n\nIn sentence 6: “he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “bɛ̂ː” = killed\n\nThus, “bɛ̂ː” = kill\n\nSo “bɛ̂ː” = kill (past), used in past tense.\n\nNow, for “just now” → sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = saw (past), “yɛ᷅n” = at, “me lé” = me, “fɔ̀wǎy” = market.\n\n“bɔ́” = see → past tense.\n\nSo the past tense markers:\n- “bɛ̂ː” = kill\n- “bɔ́” = see\n- “wɔ̀ tɔ̀” = heard\n\nNow, “just now” appears in:\n- 15: “just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → past, immediate\n\nSo “bɔ́” is present-tense past (just now)\n\nSimilarly, in 21: “The thief stole the yam just now” → must use “just now” expression.\n\nTherefore, for “just now” → future present (immediate past) = “bɔ́” (saw, heard) or “tɔ̀”?\n\nBut “wɔ̀ tɔ̀” = you heard a long time ago → not “just now”\n\nSentence 7: “You(sg) heard the thief a long time ago” → uses “tɔ̀” with time reference.\n\nSo “bɔ́” is used for just now (sentence 15), and “tɔ̀” for a long time ago.\n\nThus, for “just now” → use “bɔ́” as a verb (see, hear, etc.) in past form.\n\nStep 5: Identify object and encoding.\n\n- “the yam” = “kèŋkfǔ”\n- “the car” = “mutù”\n- “the woman” = “kwɔ᷆ːn”\n- “the man” = “dìɛ̀msɛ̌n”\n- “the book” = “bɛ̀n”\n\nWe deduce:\n- Nouns: ky familiar, bɛ̀n = book, mutù = car, kèŋkfǔ = yam, dìɛ̀msɛ̌n = man, kwɔ᷆ːn = woman\n\nStep 6: Apply to translation of (c)\n\nAll translations are to be spoken on Bvumbon.\n\nSo the reference day is Bvumbon.\n\nNow:\n\n20. On Bvusɔw, I helped the man.\n\n- “On Bvusɔw” → time marker: “me nú” with day name → “me nú bvúsɔw”\n- “I helped the man” → “me fí dìɛ̀msɛ̌n”\n→ So “me nú bvúsɔw me fí dìɛ̀msɛ̌n”\n\nBut is “me fí” in passive or active?\n\nIn sentence 3: “kwɔ᷆ːn nǔ bóy fí me” → woman helps me → “fí me” = help me\n→ so “fí” is transitive when followed by object.\n\nSo “me fí dìɛ̀msɛ̌n” → I help the man → correct.\n\nBut the sentence says “I helped” → past tense.\n\nSo tense?\n\n- “me nú” = on X, I will → future\n- But “helped” = past\n\nTherefore, need past form.\n\nIn sentence 1: “Yesterday was Bvumbon” → “fɔgò cǐ nú” → use of “fɔgò cǐ” for past time.\n\nBut in “I helped” — we need the past tense form of “help”.\n\nNo explicit past tense of “help” in data.\n\nBut in sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me” → present/future\n\nIn sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = saw (past)\n\nSo “bɔ́” = past tense for see.\n\nWe don’t have a direct “help” past form.\n\nBut in sentence 6: “he killed” → “bɛ̂ː” — past.\n\nIn sentence 7: “you heard” → “tɔ̀”\n\nSo likely, the past tense of “help” is missing, but in context, “helped” is to be interpreted as “helped” → which is likely a past tense verb.\n\nBut the structure for time is “on X” → future\n\nWe have “on Bvusɔw” — which is a specific day — so \"on Bvusɔw, I helped\" → must be past.\n\nHence, likely a different construction.\n\nLook at sentence 4: “On Bvuŋka, he found the book” → “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “tɔ̀” = past, verb “found”\n\nSo in time-specific sentences, if the time is a specific day, and the event is past, it uses a past tense verb.\n\nIn sentence 5: “The day after tomorrow is Bvutfu” → present\n\nSo only in future, we use “me nú” (on X, I will...)\n\nSo for past event on a day → use past tense.\n\nTherefore, “I helped the man” = “me fí dìɛ̀msɛ̌n” in past tense.\n\nBut is “fí” in past? In data, “fí” appears only in future: “the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me”\n\nNo past form.\n\nPossibility: the word “fí” is used only in future, and we need a different verb?\n\nNo — “fí” is used with “me” as “I help”.\n\nBut maybe in relative past, the verb structure is similar.\n\nAnother clue: sentence 15: “They saw me at the market just now” — uses “bɔ́” — which is a past tense verb.\n\nWe can infer that the past tense is marked by a verb form.\n\nSo for “helped” → likely the verb is “fí” with a past form or tense indicator.\n\nBut no data with “helped” in past.\n\nAlso, on Bvumbon — the speaking day.\n\nBvusɔw is not the speaking day — so “on Bvusɔw” — past or future?\n\nThe day system is relative.\n\nWe know from earlier:\n- 1: “yesterday was Bvumbon” — so on that day, Bvumbon was yesterday → so Bvumbon is the day before speaking day\n- So speaking day = Bvumbon → so Bvusɔw is some day before or after?\n\nFrom sentence 2: “On Bvusɔw, you will steal” → so Bvusɔw is a specific day → so when speaking on Bvumbon, Bvusɔw is in the past or future?\n\nWe need to know the sequence.\n\nFrom sentence 5: “The day after tomorrow is Bvutfu” → spoken on Bvusɔw → day after tomorrow = Bvutfu → so Bvutfu is two days after Bvusɔw.\n\nFrom sentence 4: spoken on Bvusɔw → “On Bvuŋka, he found the book” → so Bvuŋka is a day from Bvusɔw.\n\nFrom sentence 1: spoken on Bvutfu → “Yesterday was Bvumbon” → so yesterday was Bvumbon → so on Bvutfu, yesterday = Bvumbon → so Bvumbon is one day before Bvutfu.\n\nSo the order:\n- Bvutfu → yesterday: Bvumbon\n- So Bvumbon → one day before Bvutfu\n\nFrom sentence 5: day after tomorrow = Bvutfu → spoken on Bvusɔw → so from Bvusɔw, day after tomorrow = Bvutfu → so Bvutfu is two days after Bvusɔw.\n\nSo: Bvusɔw → Bvutfu in two days → so Bvusɔw is two days before Bvutfu.\n\nBut Bvumbon is one day before Bvutfu → so Bvusɔw is one day before Bvumbon.\n\nTherefore:\nBvusɔw → Bvumbon → Bvutfu → ...\n\nTimeline:\n- Bvusɔw → Bvumbon → Bvutfu → Bvuzhi → Bvuŋka → Bvuŋkaden?\n\nBut sentence 11: “The day before yesterday was Bvuŋka” → spoken on Bvukema\n\nSpoken on Bvukema → day before yesterday = Bvuŋka → so Bvuŋka is two days before Bvukema.\n\nSpoken on Bvusɔw → day after tomorrow = Bvutfu → so Bvutfu two days after.\n\nSpoken on Bvukema → tomorrow is Bvuŋkaden → so Bvuŋkaden one day after.\n\nSo order:\n- Bvusɔw → Bvumbon → Bvutfu → Bvuzhi → Bvuŋka → Bvuŋkaden → (cycle)\n\nBut Bvusɔw → Bvumbon → Bvutfu → then Bvuzhi → then Bvuŋka (two days after Bvukema?)\n\nSo the days are in a cycle.\n\nNow, for sentence 20: “On Bvusɔw, I helped the man.”\n\nSpoken on Bvumbon.\n\nWe now know:\n- Bvusɔw is one day before Bvumbon.\n\nSo “on Bvusɔw” → past day.\n\nSo the event happened in the past.\n\nWe must use a past tense verb.\n\nIn data:\n- Past tense for hear: “wɔ̀ tɔ̀” → “you heard”\n- Past tense for see: “bɔ́” → “they saw”\n- Past tense for kill: “bɛ̂ː” → “he killed”\n\nSo to express “I helped” in past → we need a past tense form.\n\nBut we don’t have “helped” directly.\n\nHowever, in sentence 3: “the woman will help me” → future.\n\nBut no past.\n\nUnless “fí” is used in past with different context.\n\nPossibility: in Nooni, past tense of \"help\" may be built from verb root.\n\nSince “fí” is used for help, and duplicated in future, it may be used in past with the same form in context.\n\nBut in example 15: “They saw me at the market just now” → “bɔ́” = saw → past.\n\nWe can infer that for “helped”, the verb is “fí” used with past tense marker, but marker not in data.\n\nAlternative: perhaps “fí” is only with future.\n\nBut in no example is “helped” used.\n\nWait — sentence 13: “On Bvutfu, the woman saw the market” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → uses “cǐ” (on), “nɔ̂ː” (the), “yɛ᷅n wáy” = saw the market.\n\nSo “cǐ nɔ̂ː” → “on X, the woman saw” — uses “cǐ” for “on” and “nɔ̂ː” for “the”.\n\nBut verb is “yɛ᷅n” — see.\n\nSo for “she saw” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n…”\n\nSo present/future tense verbs are used.\n\nFor past events, present tense is used in relative time.\n\nThus, in Nooni, time is marked by the verb or the day label.\n\nFor example:\n- “On X, I will…” → future\n- “On X, I saw…” → past\n\nBut “will” is not used in all contexts.\n\nIn sentence 13: “On Bvutfu, the woman saw the market” — “saw” — past.\n\nSo likely, verb tense is determined by context.\n\nSo “I helped” — likely “me fí dìɛ̀msɛ̌n” → in past form.\n\nBut no marker.\n\nPossibility: “fí” is used with a time marker like “cǐ” for “on X” and implies past.\n\nBut in sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me” → future.\n\nSo if “cǐ” is used with “fí”, it may be past or future?\n\nIn sentence 3 → future → so likely “fí” = present/future, not past.\n\nSo how to express past “helped”?\n\nNo direct data.\n\nBut sentence 21: “The thief stole the yam just now” → “just now” = immediate past → likely uses a past verb.\n\nWe have:\n- “cɔ́ŋ” = steal → used in “you will steal” → future\n- “cɔ̌ŋ” = heard → in past\n\nSo “cɔ́ŋ” is future, “cɔ̌ŋ” is past.\n\nSimilarly, “bɛ̂ː” = kill (past)\n\nSo verb roots differ for past and future.\n\nFor “stole” → “cɔ̌ŋ”\n\nFor “kill” → “bɛ̂ː”\n\nFor “see", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, 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Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "iid", + "sample_index": 3, + "output": "We are given several Nooni sentences spoken on different days of the Nooni week, with translations. We must infer the linguistic pattern—especially regarding time expressions and verb forms—to translate five new sentences, all spoken **on Bvumbon**.\n\n---\n\n### Step 1: Identify time expressions and their structures\n\nFrom the examples:\n\n- **\"On Bvusbon\"** (day of reference): \n - Sentence 1: “Yesterday was Bvumbon.” → *fɔgò cǐ nú bvúmbòn* \n - Sentence 3: “On Bvuzhi, the woman will help me.” → *kwɔ᷆ːn nǔ bóy fí me bvúzhí* \n → Structure: *On [day], [subject] [verb]*, with day as a noun phrase.\n\n- **\"The day after tomorrow\"**: \n - Sentence 5: *fɔ̀ shě ntfǔː nú bvútfu᷅* → “The day after tomorrow is Bvutfu.” \n → The phrase *ntfǔː nú* = “the day after tomorrow”\n\n- **\"Tomorrow\"**: \n - Sentence 8: *ntfǔː nú bvûŋka᷆ːde᷆n* → “Tomorrow is Bvuŋkaden” \n → *ntfǔː nú* = tomorrow\n\n- **\"The day before yesterday\"**: \n - Sentence 11: *kefwé cí nú bvûŋka* → “The day before yesterday was Bvuŋka” \n → *kefwé cí nú* = the day before yesterday\n\n- **\"Today\"**: \n - Sentence 6: *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n* → “Today, he killed the woman” \n → *wvù* = today\n\n- **\"Just now\"**: \n - Sentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “They saw me at the market just now” \n → *bɔ́* = just now? Or *bɔ́* is a temporal particle?\n\nWait: Sentence 15: \n“bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → \"They saw me at the market just now\" \n→ *bɔ́* appears to mark **just now**.\n\nAlso, Sentence 7: *wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ* → “You(sg) heard the thief a long time ago” → *tɔ̀* = long time ago?\n\nSo temporal markers:\n\n| Temporal expression | Marker |\n|---------------------|--------|\n| yesterday | fɔgò cǐ |\n| today | wvù |\n| tomorrow | ntfǔː nú |\n| the day after tomorrow | fɔ̀ shě ntfǔː nú |\n| the day before yesterday | kefwé cí nú |\n| just now | bɔ́ (from sentence 15) |\n| a long time ago | tɔ̀ (from sentence 7) |\n\nNow, analyze the verb forms and subject markers.\n\n---\n\n### Step 2: Verb forms\n\nWe see various verb forms:\n\n- \"I came to the market\" → *me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn* \n → *me* = I, *ncí* = came, *nɔ̂ː* = to, *ntɔ᷅* = market, *bvúmbòn* = on Bvumbon.\n\n- \"You(sg) will steal\" → *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* \n → *wɔ̀* = you(sg), *yúː* = will, *cɔ́ŋ* = steal, *kèŋkfǔ* = yam, *bvúsɔ̀w* = on Bvusɔw.\n\n- \"The woman will help me\" → *kwɔ᷆ːn nǔ bóy fí me bvúzhí* \n → *kwɔ᷆ːn* = the woman, *nǔ* = will, *bóy* = help, *me* = me, *bvúzhí* = on Bvuzhi.\n\n- \"He found the book\" → *wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː* \n → *wvù* = today, *tɔ̀* = found, *bɔ᷅ŋ* = book, *ŋwà* = the, *bvûŋka᷆ː* = on Bvuŋka.\n\n- \"I will choose the car\" → *me nú mbóy ncáw mutù bvútfu᷅* \n → *me* = I, *nú* = will, *mbóy* = choose, *ncáw* = car, *bvútfu᷅* = on Bvutfu.\n\n- \"I chose the book\" → *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n* \n → *me* = I, *mbɛ̂ː* = chose, *nca᷅w* = book, *ŋwà* = the, *ɛ̀bɛ̀n* = woman.\n\n- \"The man is about to see him\" → *dìɛ̀msɛ̌n nú yɛ́n wvù lě* \n → *dìɛ̀msɛ̌n* = man, *nú* = is about to, *yɛ́n* = see, *wvù* = him → presents \"is about to\" as *nú*\n\n- \"The woman saw the market just now\" → *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* \n → *kwɔ᷆ːn* = woman, *cǐ* = saw, *nɔ̂ː* = to, *yɛ᷅n* = market, *wáy* = the, *é* = at, *bvútfu᷅* = on Bvutfu.\n\n→ So: *cǐ* = saw → past tense for \"saw\"\n\n→ *nú* = future, \"will\"\n\n→ *bɔ́* = just now → in sentence 15\n\n→ *tɔ̀* = long time ago\n\n---\n\n### Step 3: Identify temporal markers\n\nWe now see that:\n\n- **\"yesterday\"** → *fɔgò cǐ* \n- **\"today\"** → *wvù* \n- **\"tomorrow\"** → *ntfǔː nú* \n- **\"the day after tomorrow\"** → *fɔ̀ shě ntfǔː nú* \n- **\"the day before yesterday\"** → *kefwé cí nú* \n- **\"just now\"** → *bɔ́* \n- **\"a long time ago\"** → *tɔ̀* \n\nSo temporal marker patterns:\n- Past and future time references are prefixed with specific temporal particles.\n- The day name is a noun (e.g., Bvutfu, Bvusɔw, Bvuŋkaden)\n- Verb form depends on tense: *cǐ* = past, *nú* = future, *bɔ́* = just now (present), *wvù* = present/today\n\n---\n\n### Step 4: Translate each required sentence (spoken on Bvumbon)\n\nWe are to translate:\n\n**20. On Bvusɔw, I helped the man.** \n→ \"On Bvusɔw, I helped the man\" \nWe know: \n- “On X” → *nú* + day name? From sentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí* → “On Bvuzhi, the woman will help me” → but “will” is *nǔ*. \nBut in sentence 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* → “On Bvusɔw, you will steal” → so “On X” structure is: [subject] + [verb] + [day] \n\nBut sentence 1: *fɔgò cǐ nú bvúmbòn* → \"yesterday was Bvumbo\" → so \"was\" is above, not verb. \nBut for speaker's action: we need verb forms.\n\nSentence 13: *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* → \"On Bvutfu, the woman saw the market\" → *cǐ* = saw → past tense.\n\nSo:\n- Past: *cǐ* \n- Future: *nǔ* or *nú*? \n In sentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí* → \"On Bvuzhi, the woman will help me\" → *nǔ* = will\n\nBut in sentence 5: *me nú mbóy ncáw mutù bvútfu᷅* → \"On Bvutfu, I will choose the car\" → *nú* = will\n\n→ So two options for future: *nú* vs *nǔ*?\n\nCheck tone and spelling:\n\n- *nú* = in sentence 5: *me nú mbóy ncáw mutù bvútfu᷅* → \"will choose\" \n- *nǔ* = in sentence 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* → \"will steal\" \n→ So both are used. Are they interchangeable?\n\nPossibly *nú* and *nǔ* both mean \"will\", with different tones?\n\nBut “help” is not in future yet.\n\nWe need: “On Bvusɔw, I helped the man.”\n\n→ So past tense: “I helped” = *me* + help verb + past marker?\n\nFind verb for “help” \nSentence 3: *bóy* = help \nSentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí* → “the woman will help me” → use of *nǔ* = future \nBut not past.\n\nWhere is past help?\n\nWe don’t have it directly.\n\nBut: “I helped” → likely uses *cǐ* for “saw”, so perhaps *cǐ* for “helped”?\n\nBut in sentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “They saw me at the market just now” → *bɔ́* = just now.\n\nCompare to: could *cǐ* = past?\n\nYes: in sentence 13: *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* → “On Bvutfu, the woman saw the market” → past verb.\n\nSo *cǐ* = past tense of see, saw\n\nLikely *cǐ* = past tense for help too?\n\nSo “I helped the man” = *me cǐ bóy dìɛ̀msɛ̌n* (since *dìɛ̀msɛ̌n* = man)\n\nBut what is the structure?\n\nFrom sentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí* → subject + verb + object + day\n\nBut here: subject = I → *me*, verb = helped → *cǐ bóy*, object = man → *dìɛ̀msɛ̌n*, day = Bvusɔw → *bvúsɔ̀w*\n\nSo: *me cǐ bóy dìɛ̀msɛ̌n nú bvúsɔ̀w*?\n\nBut is the day required to follow? In all cases, the day is at the end.\n\nSentence 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* → “you will steal yam on Bvusɔw” → day at end\n\nSentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí* → day at end\n\nSentence 1: *fɔgò cǐ nú bvúmbòn* → past, day at end\n\nSentence 5: *me nú mbóy ncáw mutù bvútfu᷅* → day at end\n\nSo format: [subject] [verb] [object] [day]\n\nSo for 20: *me cǐ bóy dìɛ̀msɛ̌n nú bvúsɔ̀w*\n\nNote: “helped” → *cǐ bóy* (past help)\n\n→ But is *bóy* used only in past? In sentence 3, it's used with *nǔ* (future) → so it can be used in both tenses.\n\nSo past is *cǐ bóy*, future is *nǔ bóy*\n\nSo ✅ 20. *me cǐ bóy dìɛ̀msɛ̌n nú bvúsɔ̀w*\n\n---\n\n**21. The thief stole the yam just now.**\n\n\"just now\" → from sentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “just now, they saw me at the market”\n\nSo *bɔ́* = just now\n\n\"the thief\" = *yo᷅kwɔ᷆ːn* → from sentence 6: *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n* → \"he killed the woman\"\n\n→ *yo᷅kwɔ᷆ːn* = thief\n\n\"stole\" = *cɔ́ŋ* → from sentence 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* → “you will steal the yam”\n\n→ *cɔ́ŋ* = steal\n\n\"the yam\" = *kèŋkfǔ*\n\n\"just now\" = *bɔ́*\n\nStructure: [subject] [verb] [object] + [temporal marker]\n\n→ In sentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → *bɔ́* + *nɔ̂ː* + [object] → so temporal marker at start?\n\nWait: *bɔ́* is at the beginning.\n\nSo likely: *bɔ́* + *yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ*\n\n→ So: *bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ*\n\nCheck if temporal marker must be first.\n\nYes — in sentence 15, *bɔ́* is at start.\n\nSo 21: *bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ*\n\n→ Yes.\n\n---\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n\"On Bvuŋkaden\" → day name at end?\n\nAs in all others: day at end.\n\n\"I will hear\" → *me* + future verb + *the car*\n\n\"hear\" → not in dictionary, but given: \"I will choose\" → *me nú mbóy ncáw*\n\n\"will\" → *nú* (sentence 5)\n\n\"hear\" → likely derived from \"see\" or \"hearing\" — no direct match.\n\nSentence 10: *dìɛ̀msɛ̌n nú yɛ́n wvù lě* → \"the man is about to see him\" → *nú* = is about to\n\n\"see\" = *yɛ́n*\n\nSo *yɛ́n* = see\n\nBut “hear” → could be a different verb?\n\nNo other verbs.\n\nPossibility: is \"hear\" a synonym or a variant?\n\nIn sentence 21: saw = *yɛ᷅n* → \"saw the market\"\n\nSo \"saw\" = *yɛ᷅n*\n\n\"hear\" → possibly not directly present.\n\nBut the sentence says \"hear the car\", so need a verb for hearing.\n\nNo example with \"hear\".\n\nBut in sentence 9: *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n* → chose the book\n\nSentence 5: *me nú mbóy ncáw* → will choose the car\n\nSo verb for \"choose\" = *mbóy*\n\n\"hear\" = not present.\n\nBut sentence 13: *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* → “saw the market”\n\nCould “hear” be “yɛ́n” or “yɛ᷅n”?\n\n\"yɛ᷅n\" = saw → so not hear.\n\nCould it be borrowed?\n\nAlternatively, may be a different verb.\n\nBut in absence of data, look at pattern.\n\nIn sentence 10: \"the man is about to see him\" → *dìɛ̀msɛ̌n nú yɛ́n wvù lě* → *nú* for \"is about to\"\n\nSo for \"will hear\", use *nú* + hear verb\n\nIs there any verb for \"hear\"?\n\nNo example given.\n\nBut look at sentence 15: “They saw me at the market just now” → *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy*\n\nSo *yɛ᷅n* = saw\n\nNo \"hear\".\n\nCould the verb for \"hear\" be missing?\n\nAlternatively, in some Beboid languages, \"hear\" might be from a root like *wɛ* or *yɛ*.\n\nBut no direct evidence.\n\nBut perhaps the verb is not standard.\n\nWait — **sentence 14**: *", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9581.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "iid", + "sample_index": 0, + "output": "Start by analyzing the given translations to identify patterns in Jaqaru.\n\nGiven:\n- aq”ipsa → the cave too\n- aq”na → in the cave\n- qucxap”a → through the lake\n- qucxst”psa → from our1+2 lake too\n- chushp”a → his corner\n- marka → the town\n- chushuntxi → is it in the corner?\n- markp”t”a → from his town\n- ishinhna → in my bed\n- ishma → your bed\n- p”ak”u → the pot\n- p”ak”unhpsa → my pot too\n- qaqat”a → from the cliff\n- yapsanpsa → in our1+2 field too\n\nPattern recognition:\n\n1. Possessive or shared reference:\n- \"our1+2\" = \"mine and yours\" → appears in:\n - qucxst”psa → from our1+2 lake too\n - yapsanpsa → in our1+2 field too\n → suggests \"our1+2\" is used with prepositions to form locative expressions.\n\n2. \"too\" is marked by suffix -psa:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n→ so, -psa = \"too\" (additive)\n\n3. Negation or questions:\n- chushuntxi → is it in the corner?\n- ishinhna → in my bed\n- markstxi → is it our1+2 town?\n→ appears that \"stxi\" = \"is it?\" (question form)\n\n4. Possessive forms:\n- chushp”a → his corner\n- marka → the town\n- markp”t”a → from his town\n- utamt”a → from your house\n→ possessive nouns:\n - his → chush- (corner)\n - your → ish- (bed), uta- (house)\n - our → mark- (town)\n\n5. In prepositional phrases:\n- in + [possessed noun] → in + [noun]\n- from + [possessed noun] → from + [noun]\n- is it + [noun] → stxi\n\nThus:\n- \"in\" = prefixed to noun\n- \"from\" = prefixed to noun\n- \"is it\" = stxi + noun\n\nNow solve each:\n\n4. our1+2 cliff → from known:\n- qaqat”a → from the cliff → base: qaqat → from cliff\n- we need \"our1+2\" cliff → so: from our1+2 cliff → qaqat”a with \"our1+2\" prefix\n\nPattern: qucxst”psa = from our1+2 lake → so \"our1+2\" + \"from\" + noun → [our1+2] + qaqat”a?\n\nBut qaqat”a is \"from the cliff\" → so the base is qaqat.\n\nFrom qucxst”psa = from our1+2 lake → qucx + st + psa = from our1+2 lake → so affixes:\n- qucx → from\n- st → lake\n- psa → too\n\nBut \"lake\" and \"cliff\" are different. The base form is likely:\n- qaqat”a → from the cliff\n\nSo from our1+2 cliff → would be: qaqat”a with \"our1+2\" attached? \nBut in qucxst”psa: \"qucx\" + \"st\" + \"psa\" → from our1+2 lake\n\nSo perhaps: “our1+2” is attached to the beginning of the prepositional phrase?\n\nBut \"qucx\" is from → so \"from\" is a prefix.\n\nTherefore, likely pattern:\n- [from] + [possessed noun] → prefix “from” → qucx- / qaqat-?\n\nBut qaqat”a is “from the cliff” → so qaqat is the noun stem for cliff.\n\n\"our1+2\" appears in:\n- qucxst”psa → from our1+2 lake → qucx + st + psa → so the possessive 'our1+2' is attached to the noun?\n\nBut \"st\" = lake, not \"our1+2\".\n\nWait — in qucxst”psa → from our1+2 lake too → so the “our1+2” is embedded in the word.\n\nSo: base form is \"qucx\" (from) + \"st\" (lake) + \"psa\" (too) → but \"our1+2\" is indicated by the context.\n\nBut look: chushp”a = his corner → chush- = corner, p”a = his?\n\nNo — chushp”a → his corner → so chush- = corner; p”a = his?\n\nBut ishinhna = in my bed → in + my + bed → so \"my\" is a possessive.\n\nSimilarly, ishma = your bed → your bed.\n\nSo:\n- chushp”a = his corner → chush- + p”a = corner + his\n- markp”t”a = from his town → mark- + p”t”a = town + his\n- markstxi = is it our1+2 town? → mark- + stxi → our1+2 + town?\n\nWait: markstxi → is it our1+2 town?\n\nBut marka = the town → so mark- = town.\n\nSo:\n- markstxi → is it our1+2 town? → stxi = is it?\n\nSo the possessive \"our1+2\" comes with the noun → mark + stxi → is it our1+2 town?\n\nBut in marka: mark + a → the town → so a = the?\n\nLikely:\n- The possessive is added to the noun after the noun or with a classifier.\n\nBut in chushp”a → his corner → chush + p”a → corner + his → so possessive suffix?\n\nBut p”a is not \"our1+2\".\n\nNow, \"our1+2\" appears only in:\n- qucxst”psa: from our1+2 lake too → so from (qucx) + (our1+2) + lake (st) + too (psa)?\n- yapsanpsa: in our1+2 field too → in (ya) + (our1+2) + field (san) + too (psa)?\n\nIn qucxst”psa: qucx + st + psa → so the \"our1+2\" must be implied in the stem or embedded?\n\nCompare:\n- qucxap”a → through the lake → qucx + ap”a → through the lake\n- qucxst”psa → from our1+2 lake too → qucx + st + psa → so \"lake\" is with \"st\", and \"our1+2\" is attached via a different form?\n\nWait: the only noun with \"our1+2\" is \"lake\" and \"field\".\n\nIn:\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nSo the pattern is:\n- from + our1+2 + [noun] + too → qucx + [our1+2] + st + psa\n- in + our1+2 + [noun] + too → ya + [our1+2] + san + psa\n\nSo the possessive \"our1+2\" is attached to the noun before the \"too\" marker.\n\nBut how is \"our1+2\" encoded?\n\nIn the words:\n- qucxst”psa → from our1+2 lake too → so when the verb is \"from\", the noun is \"lake\" with \"our1+2\"\n- yapsanpsa → in our1+2 field too → \"field\" with \"our1+2\"\n\nSo the possessive \"our1+2\" is prefixed to the noun stem?\n\nSo \"st\" = lake, \"san\" = field\n\nSo:\n- from + our1+2 + lake + too → qucx + (our1+2) + st + psa\n- in + our1+2 + field + too → ya + (our1+2) + san + psa\n\nThus, to form:\n4. our1+2 cliff → this means \"from our1+2 cliff\"? or \"the cliff (ours)\"?\n\n\"our1+2 cliff\" is a noun phrase: the cliff that belongs to us (both mine and yours)\n\nBut the question is \"our1+2 cliff\" — likely the noun \"cliff\", with possessive.\n\nLook at known:\n- qaqat”a → from the cliff → so \"cliff\" is qaqat\n\nSo \"our1+2 cliff\" → likely: qaqat with \"our1+2\" prefix?\n\nBut in the other cases, \"our1+2\" is attached to the noun.\n\nSo: \"our1+2 cliff\" = qaqat with \"our1+2\" → so use the pattern from qucxst”psa: from our1+2 lake → so the noun is quoted with our1+2\n\nSo \"our1+2 cliff\" → likely qaqat + possessive?\n\nBut no possessive marker in the data for \"cliff\" alone.\n\nBut in \"from the cliff\" = qaqat”a\n\nSimilarly, \"in our1+2 field\" = yapsanpsa\n\nSo \"in our1+2 field\" → ya + our1+2 + san + psa\n\nBut \"our1+2\" is attached to \"san\", field.\n\nSo pattern: [preposition] + [our1+2] + noun + [too] → for in and from.\n\nWe don’t have \"our1+2 cliff\" as a standalone — but the question is “our1+2 cliff”, not “from” or “in”.\n\nSo likely the noun phrase: our1+2 cliff → just the noun with possessive.\n\nBut we are missing the possessive form.\n\nWait — compare:\n- chushp”a → his corner → possessive = p”a\n- ishinhna → in my bed → \"my\" missing\n- marka → the town → no possessive\n- markp”t”a → from his town → possessive = p”t”a → his town\n\nBut \"our1+2\" is not marked like that.\n\nOnly \"our1+2\" appears with \"lake\" and \"field\" with \"too\".\n\nIn:\n- qucxst”psa → from our1+2 lake too → so it includes both \"from\" and \"our1+2\"\n- yapsanpsa → in our1+2 field too\n\nSo \"our1+2\" must be a suffix or infix.\n\nBut in both cases, it's attached to the noun directly before \"too\".\n\nSo, likely, \"our1+2\" is added to the noun stem before the final suffix.\n\nNow for:\n4. our1+2 cliff → the noun \"cliff\" is \"qaqat\"\n\nThus, \"our1+2 cliff\" = qaqat with possessive → so qaqat + our1+2?\n\nBut no such form is given.\n\nAlternatively, \"our1+2\" is encoded as a prefix with the noun.\n\nBut seen in: from our1+2 lake → qucxst”psa → so the form is qucx + st + psa → no prefix for \"our1+2\"?\n\nWait — perhaps the possessive is built into the noun.\n\nNo — \"chushp”a\" = his corner → chush + p”a → so \"p”a\" = his.\n\nSimilarly, \"utamt”a\" = from your house → uta + mt”a → your house?\n\nBut \"your\" is not directly seen.\n\n\"ishma\" = your bed → ish + ma → your bed\n\n\"markp”t”a\" = from his town → mark + p”t”a → his town\n\nSo possessive suffixes: p”a = his, p”t”a = his (town), ma = your (bed), mt”a = your (house)\n\nSo possessive markers are suffixes.\n\nNow, how is \"our1+2\" formed?\n\nOnly seen in with \"lake\" and \"field\" with \"too\".\n\nIn qucxst”psa → qucx (from) + st (lake) + psa (too) → but \"our1+2\" is missing?\n\nBut the translation says \"from our1+2 lake too\" → so \"our1+2\" must be embedded.\n\nPerhaps the \"our1+2\" is not a suffix, but a modifier added via a different pattern.\n\nLook at:\n- aq”na → in the cave\n- aq”ipsa → the cave too\n\nSo \"the cave\" = aq”na? → aq”ipsa is “the cave too”\n\nSo aq”ipsa = the cave too\n\nSo in the cave = aq”na\n\nSo \"the\" might be in aq”na, \"too\" in aq”ipsa.\n\nSo possibly, aq”na = in the cave, aq”ipsa = the cave (too)\n\nBut \"in the cave\" = aq”na\n\nSo in → aq\n\nThus:\n- in + cave → aq”na\n- in + cave too → aq”ipsa\n\nSimilarly:\n- in + field too → yapsanpsa → yapsanpsa → in our1+2 field too\n\nSo in our1+2 field → yapsan → yapsanpsa\n\nSo “in” + “our1+2” + “field” + “too”\n\nThus:\n- in + [our1+2] + [field] + too → ya + [our1+2] + san + psa\n\nSimilarly:\n- from + [our1+2] + [lake] + too → qucx + [our1+2] + st + psa\n\nBut no word shows “our1+2” as a suffix.\n\nThe only thing marking “our1+2” is the “too” suffix, but that's for “too”.\n\nSo perhaps “too” indicates “our1+2”?\n\nBut “in our1+2 field too” — “too” is at the end.\n\nSimilarly, “the cave too” — “too” at end.\n\nSo perhaps “too” = “our1+2”?\n\nNo — “too” means “also” or “also this one”.\n\nBut in “the cave too” = means “the cave (as well)”, not “our1+2”.\n\nBut in “in our1+2 field too”, “too” marks the additional element.\n\nSo likely, “our1+2” is a possessive, and it is added to the noun stem.\n\nBut how?\n\nIn:\n- chushp”a → his corner → chush + p”a\n- ishma → your bed → ish + ma\n- utamt”a → from your house → uta + mt”a\n- marka → the town → mark + a\n\nSo possessive suffixes: p”a (his), ma (your), mt”a (your house), p”t”a (his town)\n\nFor \"our1+2\", what suffix?\n\n“our1+2” must be a separate possessive.\n\nBut it doesn't have a suffix like p”a.\n\nBut it appears in:\n- from our1+2 lake → qucxst”psa\n- in our1+2 field → yapsanpsa\n\nSo “our1+2” is attached to the noun before “too”.\n\nSo perhaps the form is:\n- [preposition] + [our1+2] + noun + [too]\n\nBut no such suffix.\n\nThe only possibility is that “our1+2” is encoded as part of the stem.\n\nLook at the base of the nouns:\n- \"lake\" = st\n- \"field\" = san\n- \"cliff\" = qaqat\n\nWe have qucxst”psa = from our1+2 lake too → but no “our1+2” suffix.\n\nAlternatively, is it possible that “our1+2” is represented by the suffix “psa”?\n\nBut “psa” appears in:\n- aq”ipsa → the cave too\n- qucxst”psa → from our1+2 lake too\n- p”ak”unhpsa → my pot too\n- yapsanpsa → in our1+2 field too\n\nSo “psa” = “too”\n\nThus, “too” = -psa\n\nSo “our1+2” is not in the suffix.\n\nThen, in which words does “our1+2” appear?\n\nOnly in the translations.\n\nBut in the given, the only possessive form with “our1+2” is in:\n- from our1+2 lake too → so the word is qucxst”psa\n\nSo to form \"our1+2 cliff\", likely it is qaqat with possessive.\n\nBut what is the possessive for “our1+2”?\n\nOnly in the lake and field, and that is with the preposition.\n\nBut we don’t have a suffix for “our1+2”.\n\nAha: compare:\n- qucxst”psa → from our1+2 lake too\n- qaqat”a → from the cliff\n\nSo perhaps the possessive for “our1+2” is not a suffix, but a prefix to the noun stem?\n\nIn the word yapsanpsa: in our1+2 field too → already has “our1+2”\n\nSo likely, the pattern is:\n\n- [preposition] + [our1+2] + noun + too\n\nSo for 4. our1+2 cliff → we need the noun for cliff = qaqat\n\nBut \"our1+2 cliff\" is not a prepositional phrase — it's a noun phrase.\n\nSo perhaps \"our1+2 cliff\" = qaqat with \"our1+2\" attached.\n\nBut no such form.\n\nAlternatively, “our1+2” is built with a noun stem that includes it.\n\nBut there is no token like that.\n\nAnother idea: the position of \"our1+2\" is in the base noun.\n\nIn the lake, it's \"st\" — is that \"lake\"?\n\nBut \"st\" is not \"our1+2\".\n\nPerhaps \"our1+2\" is indicated by the presence of \"too\" and the context.\n\nBut we have to form the word.\n\nLet’s try for 5:", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11280.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "iid", + "sample_index": 1, + "output": "We are given a set of Jaqaru words and their English translations. We need to translate several phrases into Jaqaru, based on pattern recognition.\n\nFirst, identify patterns in the given data.\n\nGiven examples:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishma → your bed \n- utamt”a → from your house \n- utnha → my house \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too\n\nNow, analyze the patterns.\n\n1. The suffix -na means \"in\" (as in aq”na = in the cave)\n2. The suffix -psa means \"too\" (aq”ipsa = the cave too; p”ak”unhpsa = my pot too)\n3. The suffix -t”a means \"from\" (utamt”a = from your house; markp”t”a = from his town)\n4. The suffix -stxi means \"is it X?\" (chushuntxi = is it in the corner?; markstxi = is it our1+2 town?)\n5. \"our1+2\" appears in compounds like qucxst”psa (from our1+2 lake too), yapsanpsa (in our1+2 field too), and markstxi (is it our1+2 town?)\n6. Possessive prefixes:\n - his → chush-\n - my → ut- (in utnha = my house; utamt”a = from your house? Wait — utamt”a is from your house → so 'your' is prefixed to 'house', not 'my')\n - 'your' appears in ishma (your bed), utamt”a (from your house)\n → So 'your' prefix is 'um-'? But utamt”a has 'ut-' → maybe ut- = my, um- = your?\n\nLet’s test:\n\n- ishma → your bed → um + sha? But 'sha' not in database. 'isha' → 'is' + 'ha'? Not clear.\n\nBut note: ishma → your bed; utamt”a → from your house → uta? utamt”a = from your house.\n\nCompare:\n- utnha → my house → ut- + nha → utnha\n- utamt”a → from your house → ut- + amt”a → utamt”a → but \"your\" is implied\n\nWait: \"your\" is used in:\n- ishma → your bed\n- utamt”a → from your house\n\n\"my\" in:\n- utnha → my house\n- p”ak”u → the pot (no possessive)\n- p”ak”unhpsa → my pot too → p”ak”u + unhpsa → might be \"my pot too\"\n\n\"his\" → chushp”a → his corner\n\nSo possessive markers:\n- chush- → his\n- ut- → my (in utnha, utamt”a — wait, utamt”a is from your house → contradiction)\n\nWait — utamt”a = from your house → so prefix 'ut-' is not 'my'?\n\nBut utnha = my house.\n\nSo: ut- is attached to house → utnha → my house \nBut utamt”a → from your house → so ut- is not 'my' or 'your' here?\n\nWait — could \"your\" be a separate prefix?\n\nLook: ishma → your bed \n→ ish- → your? But ish is in ishma → ishna → in my bed? → ishinhna → in my bed.\n\nSo:\n- ishinhna → in my bed → ishi + nha → ish = my?\n- ishma → your bed → ish = your?\n\nBut ishinhna → in my bed → so ish + inhna → in my bed → so ish = my?\n\nBut ishma = your bed → why not ish + ma?\n\nPerhaps ish is \"my\", then ishma = your bed → must be a different prefix.\n\nAlternative: look at prefix changes.\n\nIn chushp”a → his corner → chush-\nIn chushuntxi → is it in the corner? → chush- + untxi → \"is it in the corner?\"\nIn marka → the town\nIn markp”t”a → from his town → mark + p”t”a → from his town → p”t”a = his town → so markp”t”a = from his town\nIn markstxi → is it our1+2 town? → so mark + stxi → is it our1+2 town?\n\nSo:\n- possessive marker:\n - chush- → his\n - mark- → the town (base), markp”t”a → from his town → p”t”a = his town → so p”t”a = his town\n - markstxi → is it our1+2 town? → so mark + stxi = is it X?\n\nSo it appears that:\n- stxi = is it in X?\n- t”a = from\n- na = in\n- psa = too\n- unp + un + a = perhaps form of 'too'\n\nNow, examine:\n\n4. our1+2 cliff → what is the word for cliff?\n\nWe have: qaqat”a → from the cliff\n\nSo \"from the cliff\" → qaqat”a\n\nThus, \"the cliff\" → qaqat”a → remove \"from\" → qqa\"? → likely qaqa?\n\nSo \"the cliff\" = qaqa\n\nTherefore, \"our1+2 cliff\" = our1+2 + cliff → must be some marker + qaqa\n\nWe have:\n- qucxst”psa → from our1+2 lake too → so our1+2 + lake → qucx? (lake) → qucx = lake\n- yapsanpsa → in our1+2 field too → our1+2 + field → yap + field\n\nSo in:\n- qucxst”psa → from our1+2 lake → prefix = qucx (lake) → so our1+2 is attached as a modifier → likely the structure is [possessive] + [noun]\n\nBut we see:\n- qaqat”a = from the cliff → so \"the cliff\" = qaqat”a → likely the base noun is qaqa → qaqat”a = from qaqa\n\nSo \"our1+2 cliff\" → our1+2 + cliff → likely → qaqap”a? → or with possessive marker?\n\nWe have no direct example of \"our1+2\" with a noun.\n\nIn:\n- qucxst”psa → from our1+2 lake too → possessive is attached to \"lake\"\n\nBut \"lake\" is qucx → so qucxst”psa = from our1+2 lake too → so the possessive is “our1+2” → appears in the main stem.\n\nSo: the pattern is:\n- To say \"our1+2 X\" = [X] with possessive added → in qucxst”psa → st”psa = from + too → so might be affix?\n\nWait: qucxst”psa = from our1+2 lake too\n\nBreak it: qucx → lake, st”psa → from our1+2 lake too?\n\nBut \"from\" is present — so st”psa = from + our1+2 lake too?\n\nWait — no: qucxst”psa = from our1+2 lake too → so the \"from\" is part of the word? But we already have qaqat”a → from the cliff → so \"from\" is a separate prefix?\n\nIn qaqat”a → from the cliff → so \"from\" is a prefix.\n\nIn qucxst”psa → from our1+2 lake too → again \"from\"?\n\nBut qucxst”psa → contains \"st”psa\" → where does “our1+2” go?\n\nPossibility: in Jaqaru, the possessive \"our1+2\" is attached as a suffix or infix.\n\nLook at:\n- qucxst”psa → from our1+2 lake too\n→ qucx = lake, st”psa = from + too?\n\nBut also: yapsanpsa → in our1+2 field too → yap = field, anpsa = in + too?\n\nCheck:\n- qucxap”a → through the lake → ap”a → through?\n- qaqat”a → from the cliff\n- qucxst”psa → from our1+2 lake too → so after \"lake\", we have \"st”psa\" → which might mean \"from + too\", but with \"our1+2\"\n\nWait — perhaps the structure is:\n- For “our1+2 + X” → the noun is modified by adding a suffix or prefix.\n\nBut observe:\n- markstxi → is it our1+2 town? → mark + stxi → is it our1+2 town?\n→ so “our1+2” is embedded in the question → clearly marked by “stxi”\n\nIn qucxst”psa → from our1+2 lake too → so again, “our1+2” is embedded in the structure.\n\nIn fact:\n- qaqat”a → from the cliff → no \"our1+2\"\n- qucxst”psa → from our1+2 lake too → has \"our1+2\"\n- yapsanpsa → in our1+2 field too → has \"our1+2\"\n\nSo when “our1+2” is present, it is attached via the stem.\n\nNow, the structure seems to be:\n- To form “our1+2 X”, we take the base noun X and add a suffix combining with the possessive?\n\nBut observe:\n- lake → qucx → qucxst”psa → from our1+2 lake too → so the \"st”psa\" must contain both \"from\" and \"too\" and \"our1+2\"?\nBut we have qaqat”a → from the cliff → so “from” is a prefix for the noun?\n\nThen in qucxst”psa → “from our1+2 lake too” → so “from” is prefix, “our1+2” is in the stem?\n\nBut qucxst”psa → does not have a prefix, just qucxst”psa.\n\nBut qaqat”a → from the cliff → has qaqat”a → might have a prefix?\n\nWait — is there a prefix for \"from\"?\n\nWe have:\n- qaqat”a → from the cliff\n- utamt”a → from your house\n- markp”t”a → from his town\n\nSo:\n- from → appears as prefix: q, u, m\n\nq → qaqat”a\nu → utamt”a\nm → markp”t”a\n\nSo the prefix \"from\" is:\n- q- → from the cliff\n- u- → from your house\n- m- → from his town\n\nSo \"from\" is a prefix.\n\nNow, \"our1+2\" is used in:\n- qucxst”psa → from our1+2 lake too → so the base is \"lake\" → qucx → and “our1+2” is part of the stem?\n\nBut no prefix? So how is “our1+2” marked?\n\nIn qucxst”psa → break into: qucx + st”psa → so st”psa = from our1+2 lake too?\n\nBut we already have that “from” is a prefix, so why is “from” in st”psa?\n\nPossibly, the stem “st”psa” means “from + too” → and “our1+2” is embedded?\n\nBut in markstxi → is it our1+2 town? → mark + stxi → so stxi = is it in X?\n\nSo stxi = is it in X?\n\nThen st”psa → from + too?\n\nBut we are missing the marker for “our1+2”.\n\nWait — in qucxst”psa → “from our1+2 lake too” → the “our1+2” appears because the base noun is modified with the possessive.\n\nThus, the pattern is: to say “our1+2 X”, the noun X is modified with “our1+2” via a suffix or infix.\n\nBut in markstxi → is it our1+2 town? → mark + stxi → so \"our1+2\" is part of the descriptive verb.\n\nSimilarly, in qucxst”psa — from our1+2 lake too → so “our1+2” is part of the stem \"st”psa\"?\n\nBut st”psa = from too? — doesn’t include “our1+2”.\n\nAlternative hypothesis:\n\nPossessive marker for “our1+2” is attached as a suffix.\n\nLook at:\n- aq”na → in the cave → aq → cave\n- aq”ipsa → the cave too → aq”ipsa → so “too” is suffix?\n\nSo:\n- too → -psa\n- in → -na\n- from → -t”a\n- is it in → -stxi\n\nSo:\n- aq”na → in cave\n- aq”ipsa → the cave too\n- aq”ipsa = aq + “ipsa” → “ipsa” = too?\n\nIn aq”ipsa → “ipsa” = too → so -ipsa = too?\n\nBut in p”ak”unhpsa → my pot too → p”ak”u + unhpsa → unhpsa = too?\n\nBut also yapsanpsa → in our1+2 field too → yap + sanpsa → sanpsa = in + too?\n\nBreak:\n- yaputxi → is it the field?\n- yapsanpsa → in our1+2 field too → so in + field + too?\n\nSo sanpsa = in + too?\n\nSimilarly:\n- markstxi → is it our1+2 town? → mark + stxi → is it in town?\n\nSo stxi = is it in?\n\nThus:\n- -stxi = is it in?\n- -na = in\n- -psa = too\n- -t”a = from\n\nAnd possessive:\n- For \"our1+2\" — it is a shared modifier → appears in:\n - qucxst”psa → from our1+2 lake too → we have:\n - \"from\" = prefix\n - \"our1+2\" = in the noun stem?\n - \"too\" = suffix?\n\nBut the word is qucxst”psa → so \"qucx\" + \"st”psa\" → perhaps \"st”psa\" = from + too?\n\nBut \"from\" is a prefix here? Earlier qaqat”a = from the cliff → so it might be that “from” is a prefix to the noun.\n\nSo in both:\n- qaqat”a → from the cliff → q → from + cliff\n- utamt”a → from your house → u → from + your house\n- markp”t”a → from his town → m → from + his town\n\nSo the prefix indicates \"from\", and the noun is the object.\n\nTherefore, “our1+2” is not a prefix — it is embedded in the noun base.\n\nBut where?\n\nLook at the translation:\n- qucxst”psa → from our1+2 lake too\n\nWe have:\n- qucx → lake\n- st”psa → from + too?\n\nBut \"from\" is a prefix in the other examples — so how is \"our1+2\" indicated?\n\nPerhaps in this case, \"from our1+2 lake too\" = [from] + [our1+2 lake] + [too]\n\nBut there is no prefix \"from\" here — no \"q\" or \"u\" or \"m\" prefix.\n\nSo is “from” a suffix or a stem?\n\nOnly in qaqat”a, utamt”a, markp”t”a is \"from\" marked — in qaqat”a, which is base — so likely prefix.\n\nBut qucxst”psa has no such prefix — so the “from” must be part of the suffix “st”psa.\n\nSo perhaps st”psa = from + too, and within that, “our1+2” is attached?\n\nBut how?\n\nNotice that in markstxi → is it our1+2 town? → mark + stxi → mark = the town, stxi = is it in?\n\nSo stxi = is it in?\n\nThen in qucxst”psa → from our1+2 lake too → “from” and “too” are in “st”psa?\n\nBut also “our1+2” is present.\n\nSo perhaps the structure is: [noun] + [possessive suffix] + [additional marker]\n\nBut we have no direct example.\n\nAnother idea: \"our1+2\" is indicated by the presence of the possessive in the stem, and it appears in all constructions with \"our1+2\".\n\nSince we need to translate:\n\n4. our1+2 cliff → so we have “cliff” = qaqat”a (from the cliff) → so “the cliff” = qaqat”a → remove “from” → qaqat”a → so base is qqa?\n\nBut qaqat”a = from the cliff → so “cliff” = qqa?\n\nBut qaqat”a → “q” + “qat”a → so likely qaqa = the cliff?\n\nThen “our1+2 cliff” = our1+2 + cliff = qqa + our1+2?\n\nBut in other cases:\n- qucx → lake → qucxst”psa = from our1+2 lake too → so for lake, with “our1+2”, it becomes qucxst”psa\n\nBut qucxst”psa is not the base word — it's a compound.\n\nCompare:\n- qucx → lake (base)\n- qucxst”psa → from our1+2 lake too\n\nSo “our1+2” is attached in the suffix.\n\nSimilarly:\n- yap → field → yaputxi = is it", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11346.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "iid", + "sample_index": 2, + "output": "We are given English translations and their corresponding Jaqaru forms. Our task is to translate specific sentences into Jaqaru, using the established patterns.\n\nStep 1: Identify known forms and patterns.\n\nFrom the table:\n\n- \"the cave\" → aq”ipsa \n- \"in the cave\" → aq”na \n- \"through the lake\" → qucxap”a \n- \"from our1+2 lake too\" → qucxst”psa \n- \"his corner\" → chushp”a \n- \"is it in the corner?\" → chushuntxi \n- \"the town\" → marka \n- \"from his town\" → markp”t”a \n- \"is it our1+2 town?\" → markstxi \n- \"your bed\" → ishma \n- \"my bed\" → ishinhna \n- \"the pot\" → p”ak”u \n- \"my pot too\" → p”ak”unhpsa \n- \"from the cliff\" → qaqat”a \n- \"in our1+2 field too\" → yapsanpsa \n- \"is it the field?\" → yaputxi \n\nWe note the following patterns:\n\n1. Possessive forms:\n - \"our1+2\" = mine and yours → used in \"our1+2 lake\", \"our1+2 town\", \"our1+2 field\"\n - \"your\" = ishma (bed), so \"your corner\" should be derived similarly.\n\n2. \"in X\" → base + \"na\" \n - e.g., in the cave = aq”na \n - in my bed = ishinhna \n - in your bed = ishma → but \"in your bed\" is not given directly; \"your bed\" is ishma.\n\n Wait: \"your bed\" = ishma \n So \"in your bed\" = ishma + na? Possibly not directly, but pattern in \"in the cave\" = aq”na.\n\n3. \"from X\" → base + \"t”a\" \n - from his town → markp”t”a \n - from the cliff → qaqat”a \n - from our1+2 lake → qucxst”psa \n → So \"from X\" = X + t”a\n\n4. \"is it in X?\" → X + untxi \n - in the corner → chushuntxi \n - is it our1+2 town? → markstxi \n → So: \"is it in X?\" = X + untxi\n\n5. \"too\" → suffix \"-psa\" or \"-hpsa\" \n - \"the cave too\" → aq”ipsa \n - \"from our1+2 lake too\" → qucxst”psa \n - \"my pot too\" → p”ak”unhpsa \n → \"too\" → suffix \"-psa\" (or -hpsa if possessive)\n\n6. \"our1+2\" = prefix applied to noun \n - from our1+2 lake = qucxst”psa → so \"our1+2 lake\" = qucxst (with suffix? or base + t”a? no) \n → Actually, \"from our1+2 lake\" = qucxst”psa → so \"our1+2 lake\" is qucxst → base: qucx (lake), + st” (our1+2?) then + t”a? \n But \"from our1+2 lake\" → qucxst”psa → so pattern: [base] + [possessive] + t”a + psa? \n Alternately, look at \"in our1+2 field too\" = yapsanpsa \n → \"field\" = yapu \n → \"in our1+2 field too\" → yapu + san + psa → appears to be “san” = our1+2 \n → \"in\" = -na \n So: in (our1+2) field = yapu + san + na → yapusana? → but it’s yapsanpsa → so maybe \"san\" is attached to \"yap\" → yapsan? \n\nWait: yapsanpsa → likely: yap (field) + san (our1+2) + psa (too) → and \"in\" is implicit? But the form is \"in our1+2 field too\" → so this suggests \"in\" is not marked separately.\n\nBut \"in the cave\" = aq”na \nSo \"in X\" = X + na\n\nThus, \"in our1+2 field\" should be: [our1+2 field] + na \n→ \"our1+2 field\" = yapu + san (our1+2) → yapsan \n→ so \"in our1+2 field\" = yapsan + na → yapsana \nBut given form is yapsanpsa — ends with psa, not na.\n\nWait — what if \"in our1+2 field too\" = \"in our1+2 field\" + \"too\" → so \"in X\" + \"too\"? \n→ So \"too\" = suffix -psa \n→ So \"in X\" = X + na \n→ \"in our1+2 field too\" = (our1+2 field) + na + psa → yapsan + na + psa → yapsanpsa → yes! \n\nTherefore: \n\"in X too\" = (X) + na + psa \n→ So \"in your corner too\" = (your corner) + na + psa \n\nBut first, what is \"your corner\"?\n\nWe have:\n- \"his corner\" → chushp”a \n- \"corner\" base = chush \n- \"your\" = ? From \"your bed\" = ishma → perhaps \"your\" = ish? \nBut \"his corner\" = chushp”a → \"his\" = p”? → chush + p”a = chushp”a → so the suffix \"p”a\" may mark the possessor.\n\nSimilarly, \"his town\" → markp”t”a → mark + p”t”a? \n\nPattern: possessive marker attached to noun. \n\"his\" → p”a, but \"p”a\" in chushp”a → so chush + p”a \n\"his town\" → markp”t”a → mark + p”t”a → so \"p”t”a\" may be \"his\"? \nBut for \"your\", if \"your bed\" = ishma, then \"your corner\" = ish + chush → ishchush? \n\nBut no such form is given. \n\nAlternatively, may be \"your\" → \"isha\" → \"ish\" + \"a\"? \n\nBut \"in your corner\" → we need to find this.\n\nLook at: \n\"from our1+2 lake\" → qucxst”psa \n\"our1+2\" = st? \nNote: qucxst”psa → qucx + st” + psa → but \"from\" is marked by t”a? \nBut qucxst”psa → ends with psa → so \"from our1+2 lake too\"? \nWait original: \"from our1+2 lake too\" → qucxst”psa → so it's \"from our1+2 lake\" + too → thus \"too\" = psa \n\nSo: \"from X too\" = (X) + t”a + psa \n\nSimilarly, \"in X too\" = (X) + na + psa \n\nNow, \"from our1+2 lake\" → qucxst”psa → qucx + st” + t”a + psa? \nBut no \"t”a\" from \"qucxst”psa\"? It ends with psa → possibly the \"t”a\" is implied in the base? \n\nWait: \"from the cliff\" = qaqat”a → this is \"from\" + cliff \nSo: from X = X + t”a \n\nSo from our1+2 lake = our1+2 lake + t”a → qucxst”psa = (qucx + st”) + t”a → but it ends with psa, not t”a. \n\nBut actually, \"qucxst”psa\" may be (qucx + st”) + t”a + psa → so \"from our1+2 lake too\" = (our1+2 lake) + t”a + psa → so the \"t”a\" is attached. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" = p”ak”u + unh → but \"my\" = unh? \n\nWe have: \n\"my house\" = utnha \n\"my pot\" = p”ak”u \n\"my pot too\" = p”ak”unhpsa → so \"too\" = psa → and \"my\" = unh → so \"my pot too\" = p”ak”u + unh + psa → p”ak”unhpsa → yes → so \"unh\" = my \n\nSimilarly, in \"our1+2 town?\" = markstxi → mark + st + txi → so \"our1+2\" = st \n\nSo across:\n\n- \"our1+2\" = st \n- \"my\" = unh \n- \"your\" = ? \n- \"his\" = ? \n\nFrom: \n\"his corner\" = chushp”a → chush + p”a → so \"his\" = p”a \n\"his town\" = markp”t”a → mark + p”t”a → if \"his\" = p”a, why p”t”a? \n\nWait: markp”t”a → if \"his\" = p”a, then markp”a should be \"his town\"? But it's marked as markp”t”a → so may be different. \n\nAlternatively, perhaps \"his\" = p”a → chush + p”a → chushp”a \n\"from his town\" = markp”t”a → mark + p”t”a → so \"p”t”a\" = from his town? \n\nBut \"from the cliff\" = qaqat”a → cliff + t”a → so \"from X\" = X + t”a \n→ So for \"from his town\" = (his town) + t”a → but his town = markp”a? → markp”t”a → so \"t”a\" is attached → so \"p”t”a\" = his town with \"from\" indicator? \n\nNot clear. \n\nBut we have \"from X\" = X + t”a \nSo \"from your corner\" = your corner + t”a \n\nNow, what is \"your corner\"? \nWe have \"your bed\" = ishma → ish + ma → or ish + a → likely \"ish\" = your \nSo \"your corner\" = ish + chush → ishchush? \n\nBut no such form. \n\nBut ish in \"your bed\" = ishma → so \"your\" = ish \n\nSo \"your corner\" = chush + ish → ishchush? \n\nBut we need \"in your corner\" = (your corner) + na = ishchush + na → ishchushna? \n\nSimilarly, \"in your corner too\" = (your corner) + na + psa = ishchush + na + psa → ishchushnapsa? \n\n\"from your corner too\" = (your corner) + t”a + psa → ishchush + t”a + psa → ishchush t”a psa → ishchush t”a psa \n\n\"from the cave\" → aq”na → no, that's \"in the cave\". \n\"from the cave\" → not directly given. \nWe have \"from the cliff\" = qaqat”a → so from X = X + t”a \nSo \"from the cave\" = aq” + t”a → aq”t”a \n\n\"from the cave\" → aq”t”a \n\nBut question 8: \"is it from the cave?\" → is it in (from the cave)? \nWe have: \"is it in X?\" → X + untxi \n\nSo \"is it in (from the cave)?\" → (from the cave) + untxi → aq”t”a + untxi → aq”t”auntxi? \n\nSimilarly, \"is it the house?\" → house = utnha → so \"is it the house?\" = utnha + untxi → utnhauntxi \n\nNow, back to the list:\n\n4. our1+2 cliff \n→ \"our1+2 cliff\" = cliff + st → qaq + st → qaqst? \nBut \"from the cliff\" = qaqat”a → so \"cliff\" = qaq → so \"our1+2 cliff\" = qaq + st → qaqst → but possibly with aspiration? \n\"cliff\" is qaq → so \"our1+2 cliff\" = qaqst → qaqst? \n\nBut check: \"our1+2 lake\" = qucxst → with \"st\" → so yes, pattern: base + st \n\nSo: our1+2 cliff = qaqst \n\n5. in your corner \n= (your corner) + na \n= (ish + chush) + na → ishchushna \n\n6. in your corner too \n= (your corner) + na + psa → ishchushnapsa \n\n7. from your corner too \n= (your corner) + t”a + psa → ishchush + t”a + psa → ishchush t”a psa \n\n8. is it from the cave? \n= (from the cave) + untxi \n= (aq” + t”a) + untxi → aq”t”auntxi \n\n9. is it the house? \n= (the house) + untxi → utnha + untxi → utnhauntxi \n\nNow verify with known forms:\n\n- \"from the cliff\" = qaqat”a → so cliff base = qaq → cliff + t”a = qaqat”a → matches \n- \"our1+2 lake\" = qucxst → qcxst → yes \n- \"our1+2 field\" = yapsan → yapu + san → yes \n- \"my house\" = utnha → so house = utnha → so \"is it the house?\" = utnha + untxi → yes \n\n\"his corner\" = chushp”a → chush + p”a → so for \"your corner\" = ish + chush → ishchush → but ish is your, so natural extension.\n\nNo parallel form for \"in your corner\" → but logically consistent.\n\nThus:\n\nb.1 / 4.: our1+2 cliff → qaqst \nb.2 / 5.: in your corner → ishchushna \nb.3 / 6.: in your corner too → ishchushnapsa \nb.4 / 7.: from your corner too → ishchush t”a psa \nb.5 / 8.: is it from the cave? → aq”t”auntxi \nb.6 / 9.: is it the house? → utnhauntxi\n\nFinal check: \n- \"too\" → suffix -psa → used in aq”ipsa (too), p”ak”unhpsa (too), yapsanpsa (too) → correct \n- \"in X\" → X + na → e.g., in the cave = aq”na → correct \n- \"from X\" → X + t”a → e.g., from the cliff = qaqat”a → correct \n- \"is it in X?\" → X + untxi → e.g., is it in the corner? = chushuntxi → correct \n- \"our1+2\" = st → established from qucxst (our1+2 lake) \n- \"your\" = ish (from ishma) \n- \"his\" = p”a → chushp”a \n\nAll consistent.\n\n\\boxed{b.1: qaqst; b.2: ishchushna; b.3: ishchushnapsa; b.4: ishchush t”a psa; b.5: aq”t”auntxi; b.6: utnhauntxi}", + "generated_tokens": 3652, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: qaqst; b.2: ishchushna; b.3: ishchushnapsa; b.4: ishchush t”a psa; b.5: aq”t”auntxi; b.6: utnhauntxi", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9102.0, + "ioling_final_answer_chars": 105.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the pattern in the given examples.\n\nWe are given translations in Jaqaru and their English equivalents.\n\nLook at the words:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too\n\nObservation: The possessive markers and locative constructions follow a pattern involving:\n\n- possession: our1+2, my, your, his \n- locative: in, from, is it, too \n\nPattern 1: Possession is encoded in the word root, with suffixes indicating possession.\n\nPattern 2: The particle “too” is marked by suffix -hpsa or -npsa depending on context.\n\nLook at: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\n→ “too” is marked by -hpsa or -npsa. \nNote: aq”ipsa has “too”, but no suffix. \nBut p”ak”unhpsa has “my pot too” → “unhpsa” likely derived from base “p”ak”u” + “unhpsa” \nSimilarly, qucxst”psa → “our1+2 lake too” → “qucxap”a” base → “qucxst”psa” → stem + “st” (from “through”) → “st” may be part of “from”?\n\nWait: qucxst”psa → “from our1+2 lake too” → base: “qucxap”a” → “through the lake” \nBut “qucxst”psa” has “st” → perhaps “st” = from, “psa” = too?\n\nCheck:\n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too\n\nSo “st” vs “ap” → perhaps “st” = from?\n\nSimilarly:\n- chushp”a → his corner \n- markp”t”a → from his town → “p”t”a” = from his town \n- chushuntxi → is it in the corner? → “untxi” = is it?\n\nSo possible structure:\n- Base word + locative marker + possession marker + optional “too” suffix\n\nLocative markers:\n- in → “na” (ishinhna → in my bed) \n- from → “t” (markp”t”a → from his town) \n- through → “ap” (qucxap”a → through the lake)\n\nBut “in” appears in: ishinhna → in my bed, markstxi → is it our1+2 town? → “stxi” = is it?\n\nWait — “is it” is a question form with “t” or “ntxi”?\n\nLook at:\n- chushuntxi → is it in the corner? \n→ chushp”a → his corner → + untxi → is it?\n\nSo “untxi” = is it?\n\nSimilarly:\n- markstxi → is it our1+2 town? → “mark” + “stxi” → is it our1+2 town?\n\nSo “stxi” = is it?\n\nTherefore, the question form is “noun + stxi” → is it [noun]?\n\nSo “is it in the corner?” = chushp”a + untxi → untxi? \nBut untxi → “unt” = in? Or “un” = in?\n\nishinhna → in my bed → “ishin” + “hna” → “hna” = in? \nishma → your bed → “ish” + “ma”?\n\nWait: ishinhna → in my bed → “ishin” + “hna” → “hna” = in?\n\nchushuntxi → is it in the corner? → “chush” (his corner) + “untxi” → “untxi” = is it in?\n\nTherefore, “untxi” = is it in?\n\nBut ishinhna → “ishin” + “hna” = in my bed → “hna” = in?\n\nThen “untxi” → perhaps “un” + “t” + “xi” → “un” = in?\n\nYes! “un” may be the in-prefix.\n\nSo:\n- in → “na” or “un”? \nishinhna → “ishin” + “hna” → “hna” → in? \nBut chushuntxi → “chush” + “untxi” → “un” + “t” + “xi” → in + it?\n\nPossibly “un” = in?\n\nBut “na” is also in “aq”na → in the cave.\n\nSo “na” = in?\n\nThen how to reconcile?\n\nIn aq”na → in the cave \nIn ishinhna → in my bed \nChushuntxi → is it in the corner?\n\nSo “na” appears as “in” in noun phrases.\n\nBut in chushuntxi → “untxi” — may “t” be from “from”?\n\nWait — chushuntxi → is it in the corner? → “is it” + “in”?\n\nSo “unt” → in? → “un” + “t” → in?\n\nPossibly “unt” = in?\n\nBut “na” also means in (aq”na).\n\nSo maybe “na” and “unt” both mean in?\n\nBut in different forms?\n\nCheck: aq”na → in the cave \nishinhna → in my bed → “ishin” + “hna” → “hna”?\n\nWait — “hna” and “na” — is “hna” = in?\n\nPossibly a variant?\n\nBut “chushuntxi” → “chush” + “untxi” → “untxi” = is it in?\n\nSo “unt” → in?\n\nYes! Therefore, “unt” = in?\n\nBut “na” also appears in “aq”na → in the cave.\n\nCould both be forms? Unlikely.\n\nAlternative: “na” is in, “unt” is is it in?\n\nBut “untxi” = is it in → so “unt” = in?\n\nThen both \"na\" and \"unt\" can be in?\n\nBut “na” is used in aq”na → in the cave → so \"na\" is in.\n\nSo perhaps “na” = in (at a noun), and “unt” = in (in questions)?\n\nNot consistent.\n\nBetter: the question form has “stxi” = is it?\n\nLook at:\n- chushuntxi → is it in the corner → “chush” + “untxi” → “untxi” = is it in → so “unt” = in?\n- markstxi → is it our1+2 town? → “mark” + “stxi” → “stxi” = is it?\n\nSo “stxi” = is it?\n\nSimilarly, “chushuntxi” → “chush” + “unt” + “txi” → “unt” = in?\n\nBut “stxi” = is it → “untxi” = is it in?\n\nSo “unt” = in?\n\nBut “na” = in?\n\nSo both “na” and “unt” mean “in”?\n\nPossibly “na” is a suffix, “unt” is a formation.\n\nWait — look at “yaputxi” → is it the field? → “yap” + “utxi” → “utxi” = is it?\n\nYes — “utxi” = is it?\n\nSimilarly: \n- markstxi → is it our1+2 town? → “stxi” = is it \n- chushuntxi → is it in the corner? → “untxi” = is it in → “unt” = in \n- yaputxi → is it the field? → “utxi” = is it \n\nSo “stxi” and “utxi” both = is it\n\n→ Therefore, “stxi” = is it \n→ Questions: “[noun] + stxi” = is it [noun]? \nWith locative: “[noun] + unt + stxi” = is it in [noun]?\n\nBut “unt” may not be necessary.\n\nActually:\n\n- markstxi → is it our1+2 town? → “mark” + “stxi” → is it our1+2 town \n→ so “stxi” = is it \n- yaputxi → is it the field? → “yap” + “utxi” → “utxi” = is it \n→ so “utxi” = is it \n→ “stxi” and “utxi” both mean “is it”?\n\nYes — so “stxi” and “utxi” are both “is it”.\n\nBut “stxi” is used in markstxi, chushuntxi → with “unt” before?\n\nchushuntxi → chush + unt + txi → “unt” = in?\n\nSo “unt” = in?\n\nBut “na” → in the cave → “aq”na → “na” = in?\n\nSo perhaps “na” is the locative for “in”?\n\nThen: in = na \nin = unt?\n\nConflict?\n\nUnless “unt” is not in.\n\nCheck: “chushuntxi” → is it in the corner? \nBut “chush” → his corner → so is it in his corner?\n\nSo “unt” = in?\n\nSimilarly, ishinhna → in my bed → “ishin” + “hna” → “hna” = in?\n\nSo “hna” = in?\n\nThen multiple forms?\n\nPossibility: in is marked by “na” or “hna” or “unt”?\n\nBut in “qucxst”psa → from our1+2 lake too → “st” = from?\n\nqucxap”a → through the lake → “ap” → through? \nqucxst”psa → from our1+2 lake too → “st” → from?\n\nSimilarly, markp”t”a → from his town → “pt”a → “t” = from?\n\nSo “t” = from?\n\nAnd “ap” = through?\n\nSo:\n- in → ? \n- from → “t” \n- through → “ap”\n\nNow, “too” appears in:\n- aq”ipsa → the cave too → no suffix \n- p”ak”unhpsa → my pot too → “unhpsa” → “hpsa” \n- qucxst”psa → from our1+2 lake too → “st” + “psa” → “psa” \n- yapsanpsa → in our1+2 field too → “anpsa” → “npsa”\n\nSo “psa” or “npsa” = too?\n\n“hpsa”, “psa”, “npsa” → all include “psa”?\n\nThen “too” suffix = -hpsa or -npsa?\n\nIn p”ak”unhpsa → “un” (my) + “hpsa” (too) → “hpsa” \nIn qucxst”psa → “st” (from) + “psa” → “psa” \nIn yapsanpsa → “an” (our1+2) + “npsa” → “npsa”\n\nSo the “too” is marked by “hpsa”, “npsa”, or “psa” depending on context?\n\nPossibly, the suffix is always “-psa”, and the possessive part brings the prefix.\n\nNow, back to question.\n\n4. our1+2 cliff → our1+2 + cliff → “aq” is cliff?\n\nFrom given: qaqat”a → from the cliff → “qaqat”a → from the cliff\n\nSo base word for cliff → “qaqat”a → without “from”?\n\nBut “from the cliff” → qaqat”a\n\nSo the cliff is qaqat”a → “qaqat”a = from the cliff\n\nSo the cliff itself must be “qaqat”a (with “t” suffix meaning from)?\n\nNo — “qaqat”a” → from the cliff → so the root is “qaqata” → cliff?\n\nBut the word is “qaqat”a” — with “t” and “a”?\n\nPerhaps the noun is “qaqat” (cliff), and with “a” = marker?\n\nBut in “aq”na → in the cave → “aq” + “na” → so “aq” = cave?\n\nSimilarly, “chushp”a → his corner → “chush” = corner?\n\nSo:\n- cave → aq \n- corner → chush \n- town → mark \n- field → yap \n- house → utam \n- bed → ish \n\nSo:\n- cliff → qaqat → probably qaqat is cliff?\n\nBut qaqat”a” = from the cliff → so “qaqat” = cliff?\n\nYes — “qaqat”a = from the cliff → so base = qaqat\n\nTherefore, cliff = qaqat\n\nNow, 4. our1+2 cliff → “our1+2” + cliff → “our1+2 qaqat”\n\nIn other examples: \n- qucxst”psa → from our1+2 lake too → “our1+2” + lake + from + too \n- yapsanpsa → in our1+2 field too → “our1+2” + field + in + too\n\nSo “our1+2” is marked by “an” or “ust” or something?\n\nIn qucxst”psa → “qucx” (lake) + “st” (from) + “psa” (too) \n“qucx” = lake?\n\nSimilarly: “yapsanpsa” → “yap” + “s” + “anpsa” → “yap” = field → “an” = our1+2?\n\nYes — “yapsanpsa” → in our1+2 field → “an” in “npsa”\n\nSo “an” = our1+2\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi”\n\nSo “our1+2” is represented by “an” in possessive phrases.\n\nSo 4. our1+2 cliff → “an” + “qaqat” → but missing suffix?\n\nIn “yapsanpsa” → “yap” + “an” + “npsa” → field + our1+2 + too\n\nBut for “our1+2 cliff” → no “too”?\n\nSo just “an” + “qaqat”\n\nBut is “qaqat” the base?\n\nqaqat”a” → from the cliff → so “qaqat” with “a” = from?\n\nSo “qaqat” = cliff?\n\nSo “an qaqat” → our1+2 cliff?\n\nYes → but what about aspiration?\n\nIn “aq”ipsa → “aq” → cave → “a” may be aspirated?\n\nIn “aq”ipsa → “aq” — “a” with “q”?\n\nBut “qaqat”a — “qaqat”a → “q” “a” “q” “a” “t” “a”?\n\nThe mark ” indicates aspiration.\n\nIn “aq”ipsa — “a” has a mark → aq” → a with aspiration?\n\nSimilarly, “chushp”a → chushp”a → “p” has aspiration?\n\nIn “markp”t”a” → p”t”a → “p” and “t” have aspiration?\n\nSo when a consonant is followed by a vowel, it may be aspirated?\n\nBut in “qaqat”a → “qaqat”a → “q” → consonant → “a” → vowel → so “q” is aspirated?\n\nSo “qaqat”a” — q a q a t a — all consonants?\n\nBut written as “qaqat”a” → so “q” in first position?\n\nPossibly “qa” = aspirated q?\n\nSo “an qaqat” → our1+2 cliff?\n\nBut is it “an qaqat” or “an qaqata”?\n\nIn the given: qaqat”a” → so the word ends with “a” and has aspiration.\n\nSo probably “qaqat”a = from the cliff → so “qaqat” + a\n\nSo the form is “an qaqat”a” → but that would be “from the cliff” with “our1+2”?\n\nNo — “an” is possessive, not locative.\n\nSo “an qaqat” — do we need the “a”?\n\nIn “aq”na → aq”na → aq”na = in the cave → so “a” has aspiration, and “na” = in\n\nSo “qaqat”a” → from the cliff → so “qaqat” with “a” = from?\n\nSo the form is “qaqat”a” = from the cliff\n\nTherefore, “cliff” = qaqat\n\nSo “our1+2 cliff” = “an” + “qaqat”\n\nBut do we need a final “a”? Probably not — since in “qucxst”psa” — “st” + “psa” → no “a”\n\nSimilarly, “markstxi” → “mark” + “stxi” → no “a”\n\nSo “an qaqat” → our1+2 cliff?\n\nBut in “yapsanpsa” → “yap” + “an” + “npsa” → so “an” between “yap” and “npsa”\n\nSo “an” is embedded.\n\nSo “our1+2 cliff” → “an qaqat” → but should it have an “a”?\n\nIn “qaqat”a” — only when “from the cliff”\n\nSo probably “an qaqat” — without final a\n\nThus, 4 →", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10438.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "iid", + "sample_index": 0, + "output": "Step 1: Identify the grammatical patterns in the given sentences.\n\nLook at sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (possessive, agent) \n- \"takujaatit\" = saw you (verb + object) \nPattern: Agent (possessive) + verb (past tense) + object (possessive)\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (agent) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (verb) \nVerb is not marked with object; uses a different marking pattern.\n\nCompare sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"Iluaqhaijiup\" = the doctor (agent) \n- \"aarqijaatit\" = cured you (verb + object) \n→ Agent + verb + object\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"Qingmiq\" = you (agent) \n- \"iputujait\" = speared the dog (verb + object) \n→ Agent + verb (with object)\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman (agent) \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured (verb) \n→ Agent + object + verb? But verb is marked as past.\n\nWait: the verb comes after the object.\n\nCheck: sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n→ Agent + object + verb \nBut sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" → agent + verb + object \nContradiction?\n\nBut in 1: \"takujaatit\" — \"saw you\" — object is \"you\", not \"dog\" (wait: \"your dog saw you\" → \"dog\" is agent, \"you\" is object) \nSo verb is attached to object (object + verb)?\n\nIn 1: \"Qingmivit takujaatit\" → agent + verb (with object) \nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → agent + object + verb \nSo different patterns?\n\nBut in sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" → agent + verb + object \n→ Object is \"you\", verb is \"cured\", object is attached to verb.\n\nIn sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" → agent + object + verb \nVerb comes last.\n\nWait, verb is \"aarqisijuq\" — \"cured\", which is past tense.\n\nIn 1: \"takujaatit\" — \"saw\", past tense with object — but object is \"you\", attached to verb?\n\n\"Qingmivit takujaatit\" — if takujaatit is \"saw you\", then \"you\" is object, attached to verb.\n\nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" — \"The boy shot the doctor\" → agent, object, verb → verb comes last.\n\nIn 4: \"Iluaqhaijiup aarqijaatit\" — agent + verb + object → \"the doctor cured you\" → verb then object.\n\nIn 5: \"Qingmiq iputujait\" — you speared the dog → agent + verb + object\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ agent: \"Qingmiup\" — the dog \n→ \"ilinniaqtitsijiit\" = your teacher \n→ \"aanniqtanga\" = hurt \n→ so agent + object + verb → verb last\n\nBut in 1: agent + verb + object → verb in middle?\n\nWait: in 1: \"Qingmivit takujaatit\" → your dog saw you → verb \"takujaatit\" includes \"you\" as object?\n\nYes — in Inuktitut, verb is inflected for object. So \"takujat\" + \"it\" = \"saw you\".\n\nSo the verb suffix includes the object.\n\nSimilarly, \"iputujait\" = \"speared you\"? But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → agent \"you\", verb \"iputujait\" = \"speared the dog\"\n\nSo verb includes object.\n\nIn 2: \"qukiqtanga\" = \"shot\" — no object marking? But object is \"the doctor\" — incorporated in noun phrase?\n\n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — noun phrase + noun + verb\n\nBut if verb doesn't mark object, then object is separate.\n\nCompare sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" — agent + verb + object → verb has object suffix\n\nSo inconsistent?\n\nBut sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n→ agent: \"Angunahukti\" \n→ \"nanurmik\" = a polar bear \n→ \"qukiqsijuq\" = shot \n→ agent + object + verb\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ agent: \"Angunahuktiup\" \n→ \"amaruq\" = the wolf \n→ \"iputujanga\" = speared \n→ agent + object + verb\n\nSentence 3: \"Aanniqtutit\" → \"You hurt yourself\" \n→ \"aanniqtutit\" = \"you hurt yourself\" — includes reflexive.\n\nSo verb includes reflexive object.\n\nSentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb includes object (yourself)? \"yourself\" implied.\n\nSo verbs inflect for object — especially in transitive verbs.\n\nNow look at the inflections:\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"takujat\" — saw \n→ \"it\" — object \"you\" \n→ so verb has suffix for object\n\nIn sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" \n→ \"iputujait\" — speared the dog \n→ so verb has object suffix\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" \n→ \"aanniqtanga\" — hurt \n→ object is \"your teacher\" → comes after verb?\n\nNo: only structure: agent + object + verb → not consistent.\n\nWait: in 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n\"ilinniaqtitsijiit\" = your teacher (object) \n\"aanniqtanga\" = hurt (verb) \n→ verb comes last\n\nBut in 1: \"takujaatit\" — contains object\n\nSo what is the pattern?\n\nPerhaps the verb is inflected for object, and the object appears as a noun phrase that is attached to the verb via a suffix or in an unmarked position.\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"iluaqhaijimik\" = a doctor (object) \n→ \"aarqisijuq\" = cured \n→ verb comes last\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n→ verb last\n\nWhereas sentence 1: \"takujaatit\" — verb has object suffix\n\nSo contradiction?\n\nBut look at verb forms:\n\n\"takujat\" → see (to) \n\"qukiqtanga\" → shoot \n\"aarqisijuq\" → cure \n\"iputujait\" → spear \n\"aanniqtanga\" → hurt \n\"qukiqsijuq\" → shot\n\nSo verb roots are consistent.\n\nThe object type affects the position or form.\n\nLooking at sentences with unmarked object:\n\nIn 2: Inuuhuktuup iluaqhaiji qukiqtanga → \"the boy shot the doctor\" \n→ agent + object + verb → object after agent, verb at end\n\nIn 4: Iluaqhaijiup aarqijaatit → \"doctor cured you\" → agent + verb + object → verb + object\n\nIn 5: Qingmiq iputujait → \"you speared the dog\" → agent + verb + object\n\nIn 6: Angatkuq iluaqhaijimik aarqisijuq → \"shaman cured a doctor\" → agent + object + verb\n\nIn 9: Angunahuktiup amaruq iputujanga → \"hunter speared the wolf\" → agent + object + verb\n\nIn 10: Qingmiup ilinniaqtitsijiit aanniqtanga → \"dog hurt your teacher\" → agent + object + verb\n\nIn 12: Angunahukti nanurmik qukiqsijuq → \"hunter shot polar bear\" → agent + object + verb\n\nIn 1: Qingmivit takujaatit → \"your dog saw you\" → agent + verb + object\n\nSo why is 1 different?\n\nIn 1: \"your dog\" is agent → possessive \n\"takujat\" with suffix \"it\" → \"saw you\"\n\nSo verb has object suffix.\n\nBut in others, object appears as a noun phrase after agent and before verb.\n\nPerhaps the pattern depends on whether the object is a pronoun or a noun phrase.\n\nIn 1: object is \"you\" — pronoun → verb carries suffix \"it\"\n\nIn 2: object is \"the doctor\" → noun → appears as noun phrase before verb\n\nIn 4: object is \"you\" → pronoun → verb with suffix \"aarqijaatit\" → \"cured you\"\n\nIn 5: object is \"the dog\" → noun → verb with object suffix? \"iputujait\" — speared the dog — seems to have object included.\n\nWait — \"iputujait\" — does it include object?\n\nIn 5: \"Qingmiq iputujait\" → \"you speared the dog\" — yes, \"iputujait\" includes \"the dog\"\n\nIn 1: \"takujaatit\" — includes \"you\"\n\nIn 4: \"aarqijaatit\" — includes \"you\"\n\nIn 6: \"aarqisijuq\" — \"cured\" — no object — but object is \"a doctor\" in \"iluaqhaijimik\" — so object as noun phrase\n\nIn 2: \"qukiqtanga\" — \"shot\" — no object marking — but object \"doctor\" is in noun phrase\n\nSo conclusion: \nWhen the object is a pronoun (you, yourself, etc.), the verb inflects to include the object (e.g., \"saw you\", \"cured you\") \nWhen the object is a noun phrase (the doctor, the dog, etc.), it appears before the verb in the sentence as a separate noun phrase.\n\nIn sentences:\n\n- 1: object = you (pronoun) → verb contains \"you\" → \"takujaatit\"\n- 4: object = you → \"aarqijaatit\"\n- 5: object = dog (noun) → \"iputujait\" includes \"the dog\" → so verb contains object\n- 6: object = doctor (noun) → \"iluaqhaijimik\" before \"aarqisijuq\" → object noun phrase\n- 2: object = doctor → \"iluaqhaiji\" before \"qukiqtanga\" → object noun phrase\n- 9: object = wolf → \"amaruq\" before \"iputujanga\" → noun phrase\n- 10: object = teacher → \"ilinniaqtitsijiit\" before \"aanniqtanga\" → noun phrase\n- 12: object = polar bear → \"nanurmik\" before \"qukiqsijuq\" → noun phrase\n\nBut in 5: \"Qingmiq iputujait\" — \"you speared the dog\" — dog is a noun, but verb includes it?\n\nYes — \"iputujait\" includes object — so inflected verb with object.\n\nSimilarly, in 1: \"takujaatit\" — includes object\n\nSo the verb can either:\n- Inflect with object (pronoun or noun) — then object is embedded in verb\n- Or object is a separate noun phrase before the verb\n\nNow classify based on object:\n\n- Pronoun object → verb inflected (e.g., \"saw you\", \"cured you\", \"hurt yourself\") → verbal form includes object\n- Noun object → appears as separate noun phrase before verb → verb is unmarked\n\nNow look at the target sentences:\n\n13. Amaruup angatkuit takujanga \n\"amaruup\" = a hunter? Or \"the hunter\"? \n\"angatkuit\" = came? \n\"inuktitut\" — \"angatkuq\" = the shaman → \"angatkuit\" = past tense of \"come\"? \n\"takujanga\" = saw? \n\"takujanga\" = saw (past) \nObject of \"saw\" is missing\n\nStructure: Agent + verb (with object?) or agent + object + verb?\n\n\"amaruup\" → likely \"the hunter\" or \"a hunter\" \n\"angatkuit\" → past of \"angatkuq\" = \"came\" \n\"takujanga\" → saw (past)\n\nSo \"the hunter came and saw...\" — but \"saw\" has object?\n\nNo object — so object missing? \nBut in previous sentences, if object is missing, it must be implied.\n\nBut in 3: \"Aanniqtutit\" → \"you hurt yourself\" — reflexive\n\nIn 11: \"Ukiakhaqtutit\" → \"you fell\" — no object, but reflexive\n\nSo perhaps when no object, it's reflexive or self-reference.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — agent + verb (came) + verb (saw) → two verbs?\n\n\"angatkuit\" = came \n\"takujanga\" = saw\n\nBut what about object?\n\nNo object indicated.\n\nPerhaps \"takujanga\" has object implied? Like \"saw you\"?\n\nBut earlier, when object is pronoun, verb includes it.\n\nBut here, \"saw\" needs object.\n\nPossibly, \"takujanga\" has a missing object — so it's \"saw you\" or \"saw someone\".\n\nBut no pronoun.\n\nMaybe \"amaruup\" is agent, then \"angatkuit\" (he came), then \"takujanga\" (saw) → with implied object.\n\nBut in previous examples, \"saw\" includes object.\n\nIn 1 and 4 and 5, \"saw you\", \"cured you\", \"speared the dog\" — so if object is missing, it may be implied by context.\n\nBut here, in 13, \"takujanga\" — no object.\n\nIn sentence 1: \"Qingmivit takujaatit\" → saw you\n\nSo \"takujanga\" would be saw (without object) — but must have object.\n\nUnless the object is in the agent — no.\n\nPerhaps \"amaruup\" includes a pronoun? Unlikely.\n\nAlternatively, is \"angatkuit takujanga\" a compound verb?\n\nIn Inuktitut, compounds can happen.\n\nBut from the data:\n\nSentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → agent + verb — no object\n\nSentence 11: \"Ukiakhaqtutit\" → \"you fell\" — agent + verb — no object\n\nSo yes — when no object, it's either reflexive or no object action (come, fall, see with implied object?)\n\nBut in 13: \"Amaruup angatkuit takujanga\"\n\nBreak down:\n\n- \"amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (past)\n\nLikely: \"The hunter came and saw [someone]\" — but who?\n\nMissing object.\n\nBut in the pattern, verbs like \"saw\" include object when object is pronoun.\n\nIf no object, perhaps it's a mistake — but likely, the object is missing, so we infer it must be with object.\n\nBut in which form?\n\nLook at sentence 1: \"your dog saw you\" — object is \"you\"\n\nIn sentence 4: \"the doctor cured you\" — object is \"you\"\n\nIn sentence 1: \"Qingmivit takujaatit\" — saw you\n\nIn 13: \"amaruup angatkuit takujanga\" — perhaps \"the hunter came and saw you\"?\n\nThat would make sense — like \"came and saw you\" idiom.\n\nIn sentence 2: \"the boy shot the doctor\" — clear object\n\nIn 12: \"the hunter shot a polar bear\" — clear\n\nSo in 13: hunter came and saw you?\n\nYes — plausible.\n\nAlso, other sentences with objects:\n\n14. Nanuit inuuhukturmik aanniqsijuq \n\"nanuit\" = the boy? \n\"inuuhukturmik\" = a boy (object)? \n\"aanniqsijuq\" = hurt (verb) \n→ agent + object + verb → \"the boy hurt a boy\"\n\n→ \"aanniqsijuq\" = hurt — verb\n\nSo \"Nanuit\" = the boy (agent) \n\"inuuhukturmik\" = a boy (object) \n\"aanniqsijuq", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12388.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Identify the core structure of the given sentences to detect patterns in verb usage and object marking.\n\nLooking at sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog saw (active voice, saw as a verb) \n- \"takujanga\" = you (object) \n\nNote: The verb is in the past tense with a subject and object marked.\n\nSentence 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga.\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (subject) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot \n\n\"qukiqtanga\" corresponds to \"shot\" — a transitive verb.\n\nSentence 3: \n\"Aanniqtutit.\" → \"You hurt yourself.\" \n- Reflexive verb \"aanniqtutit\" = you hurt yourself \n- No explicit object; self-referential.\n\nSentence 4: \n\"Iluaqhaijiup aarqijaatit.\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor (subject) \n- \"aarqijaatit\" = cured you (verb with object)\n\nSentence 5: \n\"Qingmiq iputujait.\" → \"You speared the dog.\" \n- \"iputujait\" = speared (verb), meaning to pierce or spear \n- \"Qingmiq\" = the dog (object)\n\nSentence 6: \n\"Angatkuq iluaqhaijimik aarqisijuq.\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman (subject) \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured\n\nSentence 7: \n\"Nanuq qaijuq.\" → \"The polar bear came.\" \n- \"qaijuq\" = came (intransitive verb)\n\nSentence 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga.\" → \"Your doctor cured your boy.\" \n- \"iluaqhaijivit\" = your doctor (subject) \n- \"inuuhuktuit\" = your boy (object) \n- \"aarqijanga\" = cured \n\nSentence 9: \n\"Angunahuktiup amaruq iputujanga.\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter \n- \"amaruq\" = the wolf (object) \n- \"iputujanga\" = speared (past tense)\n\nSentence 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga.\" → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog (subject) \n- \"ilinniaqtitsijiit\" = your teacher (object) \n- \"aanniqtanga\" = hurt \n\nSentence 11: \n\"Ukiakhaqtutit.\" → \"You fell.\" \n- \"you fell\" — intransitive\n\nSentence 12: \n\"Angunahukti nanurmik qukiqsijuq.\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter \n- \"nanurmik\" = a polar bear \n- \"qukiqsijuq\" = shot \n\nNow examine the verb morphology: \nThe verbs often have a common stem, with suffixes indicating tense, voice, and object.\n\nActive verbs: \n- takujaatit → saw \n- qukiqtanga → shot \n- aanniqtutit → hurt (reflexive) \n- aarqijaatit → cured \n- iputujait → speared \n- aarqisijuq → cured \n- qaijuq → came \n- aarqijanga → cured \n- iputujanga → speared \n- aanniqtanga → hurt \n- qukiqsijuq → shot \n\nObservation: The verb root appears to be the action (e.g., see, shoot, hurt, cure, spear). \nEach transitive verb is marked with object suffixes.\n\nKey pattern: \n- In all cases, the verb is in past tense, and object is marked with suffix depending on the gender or type of noun.\n\nNow, look at affix patterns:\n\n1. When an object is present, it is marked by a suffix or pronoun. \nFor example, in:\n- \"Qingmivit takujaatit\" → your dog saw you \n- \"Qingmiq iputujait\" → you speared the dog \n\nHere, \"Qingmi*q\" is object of \"iputujait\". \nYet in sentence 5, \"Qingmiq\" is subject? \nNo: \"Qingmiq iputujait\" → \"You speared the dog\" → so \"you\" is subject, \"dog\" is object.\n\nThus, \"Qingmiq\" is the object being speared.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"your dog\" is subject, \"you\" is object.\n\nSo auxiliary structure: \n- Subject marker (e.g., \"your\") + verb (past, transitive) + object marker?\n\nNow look at sentence 13: \"Amaruup angatkuit takujanga.\"\n\nLooking at this: \n\"Amaruup\" → likely \"the hunter\" or \"a hunter\" (similar to \"Angunahuktiup\" in sentence 9) \n\"angatkuit\" → verb? \n\"takujanga\" → you?\n\nCompare to sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" → verb = \"iputujanga\" = speared\n\nSentence 13: \"Amaruup angatkuit takujanga\" → \"Amaruup\" likely = the hunter \n\"angatkuit\" → what is this?\n\nCompare to: \n- \"angatkuq\" in sentence 6 = \"the shaman\" — so \"angat-\" is likely a noun prefix \n- \"angatkuit\" → might be a verb form\n\nWait: \"angatkuq\" → shaman (noun) \nBut \"angatkuq\" ends in \"-kuq\" — perhaps a noun ending.\n\nBut in sentence 13: \"angatkuit\" — ends in \"-uit\" → could be past tense of a verb?\n\nPossibility: common verb root is -takuj- for \"see\", -qukiq- for \"shoot\", -iputuj- for \"spear\", -aarq- for \"cure\", -aanniqt- for \"hurt\".\n\nIn sentence 1: \"takujaatit\" → saw you \nIn sentence 2: \"qukiqtanga\" → shot \nIn sentence 4: \"aarqijaatit\" → cured \nIn sentence 5: \"iputujait\" → speared \nIn sentence 10: \"aanniqtanga\" → hurt\n\nSo the verb suffix indicates object and tense.\n\nPattern: \n- A verb stem + object prefix or suffix = transitive verb. \n- The object is marked with a suffix. \n- The subject is marked with a possessive or determiner.\n\nNow, for sentence 13: \"Amaruup angatkuit takujanga\"\n\n\"Amaruup\" → similar to \"amaruq\" in sentence 9 → \"the wolf\" \nBut \"amaruq\" is a noun → \"amaruup\" could be \"a hunter\"? — no.\n\n\"Angunahukti\" = hunter \n\"Amaruq\" = wolf \n\"Amaruup\" might be \"a hunter\"?\n\nNo: \"angunahukti\" = hunter \nSo \"Amaruup\" might be a noun: \"a hunter\", but no known word \"amaruup\" as a subject.\n\nWait: in sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf \nSo \"Angunahuktiup\" = hunter (subject) \n\"amaruq\" = wolf (object)\n\nNow sentence 13: \"Amaruup angatkuit takujanga\"\n\n\"Amaruup\" → could be a noun? \nBut likely it's \"a hunter\" — but the root is \"angat\" → what is \"angat\"?\n\nIn sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor\n\n\"angatkuq\" = the shaman \nSo \"angatkuq\" = shaman → indicates noun root \"angat-\" \n\nSo \"angatkuit\" → could be a verb form of \"angat\" → could be \"came\"? \nBut \"qaijuq\" = came — so \"angatkuit\" is not clearly a verb.\n\nAlternative: is \"angatkuit\" a verb derived from \"angat\"?\n\nWait — perhaps all verbs are marked with a suffix indicating the object.\n\nIn sentence 1: \"Qingmivit takujaatit\" → dog saw you → \"takujanga\" → you \n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → \"qukiqtanga\" \n\nSo verb endings: \n- takujanga → saw you \n- qukiqtanga → shot doctor \n- aarqijaatit → cured you \n- iputujait → speared dog \n- aarqisijuq → cured doctor \n- aanniqtanga → hurt teacher \n\nSo pattern: \n- [Subject] [Object] [Verb] with object suffix\n\nBut verb stem is consistent: \n- takuj- = see \n- qukiq- = shoot \n- aarq- = cure \n- iputuj- = spear \n- aanniqt- = hurt \n\nNow sentence 13: \"Amaruup angatkuit takujanga\"\n\n\"Amaruup\" → likely \"the hunter\" or \"a hunter\" — but in sentence 9, \"Angunahukti\" = hunter → so \"Amaruup\" must be \"a hunter\"? But \"amaru\" not matching.\n\nWait — perhaps \"Amaruup\" = \"a hunter\" — but in sentence 9: \"Angunahuktiup amaruq iputujanga\" → the hunter speared the wolf\n\nSo \"Angunahuktiup\" is subject → so word order: subject + object + verb?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → subject (dog) + verb (saw) + object (you) — wait, no: \"takujanga\" = you → it is the object.\n\nSo structure: subject + verb + object?\n\nBut in sentence 1: \"Qingmivit takujaatit\" — \"takujanga\" is at end → object.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" — object \"iluaqhaiji\" is before verb?\n\nWait: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → subject (boy) → object (doctor) → verb (shot)\n\nSo object is before verb.\n\nSimilarly: \nSentence 4: \"Iluaqhaijiup aarqijaatit\" → object (doctor) → verb (cured) \nSentence 5: \"Qingmiq iputujait\" → \"Qingmiq\" = dog? → object? But \"you speared the dog\" → subject \"you\", not \"dog\"\n\nContradiction.\n\nSentence 5: \"Qingmiq iputujait\" → translated \"You speared the dog\"\n\nSo if \"Qingmiq\" is the object, then subject must be \"you\".\n\nBut in sentence, it is \"Qingmiq iputujait\" — does it mean \"the dog speared you\"?\n\nBut translation says \"you speared the dog\".\n\nSo \"Qingmiq\" = dog — object? But in that case, subject is \"you\", so the verb must be in form with subject \"you\".\n\nThe structure must be: [subject] [verb] [object]\n\nIn sentence 5: \"You speared the dog\" → subject + verb + object → \"you\" is subject, \"dog\" is object.\n\nBut \"Qingmiq\" is not \"you\". \"Qingmiq\" = the dog.\n\nSo if \"Qingmiq\" is the object, it must be after verb?\n\nBut in sentence 5: only two elements — \"Qingmiq iputujait\" → likely \"you\" is implied (subject), \"the dog\" is object.\n\nSo the verb \"iputujait\" = speared.\n\nStem: \"iputuj\" + suffix → -ait → past tense?\n\nSimilarly, \"takujanga\" in sentence 1: \"your dog saw you\" → verb = \"takujanga\" → saw you\n\nSo in that case, object is marked \"you\".\n\nNow sentence 13: \"Amaruup angatkuit takujanga\"\n\nBreak into parts: \nAmaruup — likely a noun, e.g., a hunter \nangatkuit — a verb form? \ntakujanga — saw you?\n\nSo \"angatkuit\" → perhaps a verb stem meaning \"see\" or \"saw\"?\n\nBut \"takujanga\" is clearly \"saw you\"\n\nSo is \"angatkuit\" a verb meaning \"saw\"?\n\nBut no verb \"angat\" for \"see\".\n\nWait — in sentence 1, \"takuj\" = saw \nCould all verbs be derived from common stems?\n\nNote: \n- \"takuj\" = see \n- \"qukiq\" = shoot \n- \"iputuj\" = spear \n- \"aarq\" = cure \n- \"aanniqt\" = hurt \n- \"qaij\" = come \n\nSo each verb has a root stem.\n\nIn sentence 13: \"angatkuit\" — if \"angat\" is from \"angat\" (shaman), doesn't match.\n\nAlternative pattern: Object marking.\n\nLook at object suffixes:\n\n- takujanga → you \n- qukiqtanga → doctor \n- aarqijaatit → you (in sentence 4) \n- iputujait → dog \n- aanniqsijuq → doctor (sentence 14) \n- aarqisijuq → doctor (sentence 6)\n\nSo object is marked with a suffix in the verb.\n\nThe verb form includes a suffix indicating who is being seen, cured, etc.\n\nIn sentence 13: \"Amaruup angatkuit takujanga\" \ntakujanga = saw you → so object = you\n\nSo \"angatkuit\" must be a verb meaning \"saw\"\n\nBut \"takuj\" is \"see\", not \"angat\"\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured doctor → verb = \"aarqisijuq\"\n\nIn sentence 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → verb = \"aarqijanga\"\n\nSo verb stem is in \"aarq\" = cure\n\nSimilarly, \"takuj\" = see\n\nSo no \"angat\" verb like \"see\"\n\nWait — could \"angatkuit\" be \"came\"?\n\n\"qaijuq\" = came\n\nIs there a verb \"angat\" for \"come\"?\n\nNo — \"qaijuq\" = came \n\"nanuq qaijuq\" = polar bear came\n\n\"angat\" not used for movement.\n\nConclusion: \"angatkuit\" may be a typo or misreading.\n\nWait — look at sentence 13: \"Amaruup angatkuit takujanga\"\n\nCompare to sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf\n\nSo structure: [subject] + [object] + [verb] → but verb is at end.\n\nIn sentence 9: subject + object + verb\n\nIn sentence 1: \"Qingmivit takujaatit\" → subject (your dog) + verb (saw) + object (you) — but object is not marked after verb.\n\n\"takujanga\" — at end.\n\nIn sentence 1: \"takujanga\" = you → object\n\nSo verb + object at end.\n\nIn sentence 9: \"iputujanga\" = speared → at end.\n\nSo all transitive verbs have object suffix at end.\n\nSo verb = [stem] + [suffix]\n\n- takujanga → saw you \n- qukiqtanga → shot doctor \n- aarqijaatit → cured you \n- aarqisijuq → cured doctor \n- iputujait → speared dog \n- aanniqtanga → hurt teacher\n\nSo the object is integrated into the verb.\n\nNow in sentence 13: \"Amaruup angatkuit takujanga\"\n\n\"angatkuit\" = verb? \n\"takujanga\" = saw you\n\nBut \"takujanga\" is already the verb form — cannot be object and verb.\n\nUnless \"angatkuit\" is the subject.\n\nSo \"Amaruup angatkuit takujanga\" = [subject] [verb] [object]?\n\nBut \"angatkuit\" is not a known verb.\n\nAlternative: \"angatkuit\" = a noun → \"the shaman\" or \"a hunter\"?\n\nBut in sentence 6: \"Angatkuq\" = the shaman\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear\n\n\"Angunahukti\" = hunter\n\n\"angatkuit\" — could it be a typo of \"angunahukti\"?\n\nUnlikely.\n\nPerhaps the verb is \"takujanga\" = saw, and \"Amaruup angatkuit\" is the subject.\n\nBut \"Amaruup\" is likely a subject, like \"a hunter\"\n\n\"angatkuit\" might be a possessive or marked noun.\n\nWait — look at sentence 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n\"nanuit\" = the boy? \n\"inuuhukturmik\" = a boy's boy? \n\"aanniqsijuq\" = hurt (verb)\n\n\"aanniqsijuq\" = hurt\n\nSo \"Nanuit", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11908.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Analyze the given sentences to identify consistent patterns in Inuktitut grammar, especially in verb structures and nominalization.\n\nLook at sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n→ \"Qingmivit\" = \"your dog saw\" (verb with subject + object) \n→ \"takujanga\" = \"saw\" (base verb) → likely \"takuj\" = to see, \"a\" = object marker? \n\nBut in sentence 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"Qingmiq\" = \"you speared\" → \"iputuj\" = to spear \n\nIn sentence 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n→ \"inuuhuktuup\" = \"the boy shot\" (subject), \"qukiqtanga\" = \"shot\" (verb), \"iluaqhaiji\" = doctor → \"qukiqtanga\" = past verb \"shot\" \n\nCompare with sentence 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" → \"cured\" (past tense) \n\nSo verbs are in a past tense form, often with a suffix indicating tense or aspect.\n\nStep 2: Identify markers for possession and subject.\n\nSentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = \"you hurt yourself\" → \"aanniqt\" = hurt, \"ut\" = past suffix, \"self\" implied \n\nSentence 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" → \"you fell\", \"ut\" = past tense marker \n\nSentence 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"nanuq\" = polar bear, \"qaijuq\" = came (past tense verb)\n\nStep 3: Identify object and subject markers.\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"takuj\" = saw, \"a\" = object? → \"takujaatit\" = saw you → \"a\" = object marker → \"takujaat\" = saw + object → \"takujanga\" = saw → \"takujanga\" = saw (past) → \"takuj\" + \"a\" → object\n\nNote in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared (past) \n\nSo verb form: root + suffix to indicate past tense, and object.\n\nStep 4: Identify any regularity in participles or nominalizations.\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"ilinniaqtitsijiit\" = \"hurt\", \"aanniqtanga\" = hurt → \"ilinniaqt\" = hurt → \"ilinniaqtitsijiit\" = past tense + object? \n\"ilinniaqtitsijiit\" → possibly \"ilinniaqt\" + \"sijiit\" → past, object? \nCompare: sentence 10: \"the dog hurt your teacher\" → object is \"your teacher\" → \"sijiit\" likely object marker \n\nBut in 3: \"You hurt yourself\" → \"aanniqtutit\" → \"aanniqt\" = hurt, \"ut\" = past → no object marker?\n\nWait: sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → object is \"your teacher\" → marked with \"sijiit\"?\n\nPossibly suffix \"sijiit\" marks object.\n\nNow look at sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\nThis has \"ilinniaqtitsiji\" → likely the stem of \"ilinniaqt\" (hurt), \"siji\" = object → so \"ilinniaqtitsiji\" = hurt (subject) + object → then \"qukiqtait\" = (to shoot) → but verb?\n\nWait — \"qukiqtait\" likely = \"shot\", with suffix \"ait\" = past tense?\n\nCompare to sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n\"qukiqtanga\" = past tense of \"qukiqt\" = to shoot → \"anga\" = past? → \"qukiqtanga\" = shot\n\nSimilarly, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared (past)\n\nSo verb suffix = \"ait\" or \"anga\" = past tense.\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → subject = \"the dog\", verb = \"hurt\", object = \"your teacher\", past = \"itsijiit\"?\n\nNo — \"ilinniaqtitsijiit\" → contains \"itsijiit\" → may be past tense of \"ilinniaqt\" + object suffix.\n\nSo likely: verb root + object suffix + past tense suffix.\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"takujaatit\" = saw + object (you), so \"takuj\" + \"a\" + \"it\" = past tense?\n\nBut “takujanga” = saw? “a” is object marker?\n\nIn sentence 16: \"Ilinniaqtitsiji qukiqtait\" → \"the dog shot the teacher\"? \n\nPossibly: \"ilinniaqtitsiji\" = the dog hurt (subject) + object marker (siji) → so \"ilinniaqtitsiji\" = the dog hurt [someone] → then \"qukiqtait\" = past tense of \"to shoot\"?\n\nBut \"qukiqtait\" = shot? → yes, based on sentence 2.\n\nSo \"ilinniaqtitsiji\" = \"the dog hurt\" (someone), \"qukiqtait\" = \"shot\" → so full sentence is \"the dog hurt (and) shot\" → doesn't make sense.\n\nAlternatively, \"ilinniaqtitsiji\" = the dog's past action (hurt), and \"qukiqtait\" = shot — plural?\n\nBut sentence 16 says: \"Ilinniaqtitsiji qukiqtait\" → likely \"the dog (hurt) the teacher\" → but why \"qukiqtait\"?\n\nWait — look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → object is \"your teacher\" → \"aanniqtanga\" = hurt\n\nSo the verb \"ilinniaqtitsijiit\" = hurt → object is \"aanniqtanga\"? But that's a noun.\n\nNo — \"ilinniaqtitsijiit\" = hurt (past), \"aanniqtanga\" = your teacher → object?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\"\n\nSo verb + object → \"ilinniaqtitsijiit\" = verb, \"aanniqtanga\" = object? → \"aanniqt\" is root, \"anga\" = past?\n\nThen in sentence 16: \"Ilinniaqtitsiji qukiqtait\" — no object?\n\nPossibly missing an object.\n\nBut in the sentence, it's just \"Ilinniaqtitsiji qukiqtait\" — only two elements.\n\nUnless \"qukiqtait\" is a verb and \"ilinniaqtitsiji\" is the subject.\n\n\"ilinniaqtitsiji\" — possible noun phrase: \"the dog\" + \"hurt\" → but \"ilinniaqtitsiji\" = the dog hurt? → and \"qukiqtait\" = shot?\n\nSo \"the dog hurt and shot\"?\n\nBut that doesn't fit.\n\nAlternatively, perhaps the verb is \"qukiqtait\" = shot, and \"ilinniaqtitsiji\" is object?\n\nBut \"ilinniaqtitsiji\" = hurt → not a noun.\n\nAnother pattern: look at sentence 18: \"Angunahuktimik aarqisijutit\"\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"angunahuktiup\" = hunter speared (past), \"amaruq\" = wolf, \"iputujanga\" = speared (past)\n\nSo verb: \"angunahuktiup\" = speared (past)\n\nRoot: \"angunahuk\" = to spear\n\nSo past tense suffix: \"-it\" or \"-up\"?\n\nSentence 9: \"angunahuktiup\" → verb past → \"up\" suffix?\n\nSentence 14: \"Nanuit inuuhukturmik aanniqsijuq\" → \"Your boy was cured by a doctor\"?\n\nRoot: \"inuuhuk\" = to shoot → \"inuuhukturmik\" = boy was shot? → \"turmik\" = past?\n\nCompare to sentence 2: \"inuuhuktuup\" → \"the boy shot\" → \"tuup\" = past?\n\nNo consistency.\n\nWait — look at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy\"\n\n\"iluaqhaijivit\" = your doctor cured? → \"aarqijanga\" → cured (past)\n\n\"iluaqhaijivit\" = doctor cured (past) → \"vit\" = past? \n\"v\" = past? → similar to \"takujanga\", \"iputujait\"\n\nSo verb stems: \n- takuj (see) → takujaatit \n- iputuj (spear) → iputujait \n- aarq (cure) → aarqijaatit \n- inuuhuk (shoot) → inuuhuktuup \n- ilinniaqt (hurt) → ilinniaqtitsijiit → likely \"ilinniaqt\" + suffix\n\nSo many verbs end in \"it\" or \"ait\" or \"anga\" — past tense.\n\nNow look at object markers:\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"takujat\" = saw? \"a\" = object? → \"takujat\" = saw someone → \"a\" = object.\n\nIn sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" → verb = speared (past) → object = \"the dog\" → not marked?\n\nBut in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → object = \"amaruq\" → \"amaruq\" = wolf → not marked?\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → object = \"aanniqtanga\" → marked?\n\nNo object marker in the noun.\n\nBut in sentence 1, object is marked with \"a\" → \"takujatit\" → \"a\" before?\n\n\"takujatit\" → \"a\" or \"at\"? → possibly \"a\" = object.\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" is object → marked with \"a\"?\n\nYes — \"takuj\" + \"a\" → saw someone → \"a\" = object marker.\n\nIn sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → \"aarqijaatit\" → \"a\" + \"arqijaatit\"? → \"a\" = object?\n\nYes — object marker \"a\" (or \"at\") used.\n\nIn sentence 13: \"Amaruup angatkuit takujanga\"\n\n\"Amaruup\" → \"the hunter\"? → compare with sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"angunahuktiup\" = the hunter speared the wolf.\n\nSo \"angunahuk\" → to spear → \"angunahuktiup\" = past tense.\n\nSimilarly, \"angatkuit\" → \"to come\"? → \"angatkuq\" = came → in sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\"\n\n\"qaijuq\" = came (past)\n\nSo \"angatkuit\" = came? → past tense → \"tuit\" = past?\n\n\"tuit\" = past?\n\nIn sentence 7: \"qaijuq\" = came → no suffix like \"tuit\"\n\nBut in sentence 13: \"Amaruup angatkuit takujanga\" → \"the hunter came saw?\"\n\n\"takujanga\" = saw?\n\nSo \"the hunter came and saw\"?\n\nBut is that right?\n\nNow: \"angatkuit\" → likely past form of \"angatkuq\" = came → \"tuit\" vs \"kuq\" → \"tuit\" = past?\n\nSimilarly, in sentence 18: \"Angunahuktimik aarqisijutit\" → \"the hunter cured a doctor\"\n\n\"angunahuktimik\" → \"the hunter cured\" → \"timik\" = past?\n\nIn sentence 2: \"inuuhuktuup\" → \"the boy shot\" → \"tuup\" = past\n\nSo past suffix varies.\n\nBut notice: in most verbs, when the verb is in past, a suffix is added, and the object is marked with \"a\" or \"at\".\n\nNow look at sentence 13: \"Amaruup angatkuit takujanga\"\n\n- \"Amaruup\" = the hunter? → similar to \"Angunahuktiup\" → \"up\" = past?\n- \"angatkuit\" = came? → verb \"angatkuq\" = came → \"tuit\" = past?\n- \"takujanga\" = saw → verb?\n\nSo \"the hunter came and saw\"?\n\nBut \"came\" and \"saw\" — could be sequential.\n\nBut is it \"came and saw\"?\n\nAlternatively, could \"angatkuit\" be \"came\", and \"takujanga\" be \"saw someone\"?\n\nYes — \"takujanga\" = saw (past) → object implied?\n\nBut no object marker — so possibly object missing?\n\nBut in previous verbs, object is marked with \"a\" or \"at\".\n\nCompare to sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object = \"you\" → \"a\" + \"you\"? → \"takujaatit\" → \"a\" before object?\n\n\"takujatit\" → \"a\" is part of it?\n\nIn sentence 1: \"takujaatit\" → likely \"takuj\" + \"a\" + \"at\"? → \"a\" object marker.\n\nBut in sentence 13: \"takujanga\" → \"takuj\" + \"anga\"? → no \"a\"?\n\n\"anga\" = past? — in sentence 2, \"qukiqtanga\" = shot → past tense.\n\nSo \"takujanga\" = saw (past) — verb.\n\nBut object not marked?\n\nSo is the object missing?\n\nLook at sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\n\"Ilinniaqtitsiji\" → likely subject? — \"the dog hurt\" + object marker \"siji\"?\n\nBut \"siji\" is a suffix — perhaps object marker?\n\nIn sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\"\n\nSo \"ilinniaqtitsijiit\" = hurt (verb) → \"itsijiit\" → past + object?\n\n\"itsiji\" = object?\n\nIn sentence 16: \"ilinniaqtitsiji\" → missing \"it\"? → perhaps object not present?\n\n\"qukiqtait\" = shot → past tense verb.\n\nSo \"the dog (hurt) and shot\"? — no object.\n\nBut that seems odd.\n\nSentence 17: \"Qaijutit\" → \"you fell\" → from sentence 11: \"Ukiakhaqtutit\" = \"you fell\"\n\nSo \"qaijutit\" → likely past tense of \"qaij\" = to fall → \"ut\" = past?\n\nSo \"qaijutit\" = you fell.\n\nSentence 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured the wolf\"?\n\n\"angunahuktiit\" = the hunter cured? → past tense of \"angunahuk\" = to spear → but cured?\n\nWait — \"aarq\" = cure → so \"aarqijuq\" = cured?\n\n\"anga\" = past?\n\nBut \"angunahuktiit\" = hunter cured? → not matching.\n\nContradiction.\n\nWait: \"angunahuk\" = to spear, not to cure.\n\nCurative verbs: \"aarq\" = cure.\n\nSo \"angunahuk\" = to spear.\n\nSo \"angunahuktiit\" = hunter speared?\n\nBut sentence 18: \"Angunahuktimik aarqisijutit\" → \"the hunter cured a doctor\"\n\nSo \"aarqisijutit\" = cured (past) → \"sij\" = object?\n\nAnd \"angunahuktimik\" = the hunter (subject) — past?\n\nSo \"timik\" = past?\n\nThen sentence 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured the wolf\"?\n\n\"aarqijuq\" = cured?\n\nBut \"a\" = object marker?\n\n\"ijuq\" = cured? — \"a\" before \"arq\"?\n\nIn sentence 8: \"inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object = \"your boy\" → marked?\n\n\"aarqijanga\" — \"a\" + \"arqijanga\" → object?\n\nSo object marked with \"a\"?\n\nSimilarly, in sentence 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured [someone]\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11451.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify patterns in the given Inuktitut sentences and their English translations.\n\nFrom sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n→ \"Qingmi-\" (dog), \"v\" (past tense), \"takujaatit\" = \"saw you\" \nNote: \"Qingmivit\" = \"your dog saw\" → possessive + verb stem + object.\n\nSentence 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"Qingmiq\" (dog), \"iputujait\" = \"speared\" → same root, different verb.\n\nSentence 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"Angunahuktiup\" = \"the hunter\", \"amaruq\" = \"wolf\", \"iputujanga\" = \"was speared\" → passive?\n\nSentence 12: \n\"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"Angunahukti\" (hunter), \"nanurmik\" (a polar bear), \"qukiqsijuq\" = \"was shot\" → passive.\n\nSo, we see:\n- \"iputujait\" = active form (to spear)\n- \"iputujanga\" = passive form (was speared)\n- \"qukiqtanga\" = \"was shot\"\n- \"aarqijaatit\" = \"cured you\"\n- \"aarqijanga\" = \"was cured\"\n- \"aanniqtanga\" = \"hurt yourself\"\n- \"aanniqtanga\" appears with \"you\" in both active and passive?\n\nLooking at sentence 3: \n\"Aanniqtutit\" → \"You hurt yourself.\" → active, self-harm.\n\nSentence 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" → active.\n\nSentence 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" → active (cured doctor), but \"aarqisijuq\" = \"cured\" → passive? \"aarqisijuq\" may be passive.\n\nWait — in sentence 4, \"aarqijaatit\" = \"cured you\" → active.\n\nSentence 6: \"aarqisijuq\" = \"cured\" → but object is \"a doctor\", not \"you\". So likely passive or nominalized.\n\nBut sentence 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\"\n\n→ \"iluaqhaijivit\" = \"your doctor\", \"inuuhuktuit\" = \"your boy\", \"aarqijanga\" = \"was cured\" → passive?\n\nNo — \"cured your boy\" → active? But \"aarqijanga\" = \"was cured\"? That’s inconsistent.\n\nWait: likely morphological pattern.\n\nLet’s extract verb stems and object markers.\n\nCommon verbs:\n\n- Takuj- → to see\n- Iputu- → to spear\n- Aarqi- → to cure\n- Aanni- → to hurt\n- Qukiq- → to shoot\n- Iluaqhai- → doctor\n- Angat- → shaman\n- Anguna- → hunter\n- Qingmi- → dog\n- Nanuq- → polar bear\n- Inuu- → boy\n- Aaru- → may be \"to\" or object\n- Qaiju- → fall?\n\nSentence 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"Ukiakhaq\" → \"fall\", \"tutit\" → past, \"you\"?\n\nSo \"Ukiakhaqtutit\" = \"you fell.\"\n\nNow look at sentence 17: \"Qaijutit\" → likely \"you fell\" → same pattern?\n\n\"Qaijutit\" — possibly \"qaiju\" stem + \"tutit\" → past tense, 1st person.\n\nCompare with sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — Ukiakhaq → fall.\n\nSo \"Qaijutit\" → implies \"you fell\" (same verb, same tense, possibly just a different root).\n\nSo verb patterns:\n\n1. Verb root + possessive prefix + suffix for object or context → agent > patient\n\nNow analyze sentence 13: \n\"Amaruup angatkuit takujanga.\"\n\nBreak it down:\n\n- \"Amaruup\" → likely \"a wolf\" (amaruq = wolf; up = genitive or possessive? Or object marker?)\n\nBut in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → amaruq = wolf, directly object.\n\nSo here \"amaruup\" — may be \"the wolf\" or \"a wolf\"?\n\n\"Angatkuit\" → likely \"saw\", from \"takuj\" (see), \"angat-\" may be a suffix?\n\nWait — sentence 1: \"Qingmivit takujaatit\" → dog saw you.\n\n\"takuj\" = see; \"aata\" = object? \"takujaa\" = saw?\n\n\"takujaatit\" = \"saw you\" → possessive \"you\" marked?\n\nBut in 13: \"angatkuit takujanga\" → \"saw\"?\n\n\"takujanga\" → likely passive \"was seen\"?\n\nBut in sentence 6: \"aarqisijuq\" = cured → passive.\n\nSo \"takujanga\" → passive form of \"to see\".\n\nIn sentence 1: \"Qingmivit takujaatit\" → active: dog (subject) saw (you — object)\n\nSo \"takujanga\" → passive: \"was seen\"\n\nSimilarly:\n\n- iputujait → active: speared\n- iputujanga → passive: was speared\n- aarqijaatit → active: cured you\n- aarqijanga → passive: was cured\n- aanniqtanga → active: hurt (you)\n- aanniqtutit → hurt yourself (in 3)\n\nThus: \nAll verbs have active and passive forms. Passive has suffix -anga, active has -ait, -at, etc.\n\nNow, in 13: \"Amaruup angatkuit takujanga\" → \"Amaruup\" = the wolf? Or \"a wolf\"?\n\nBut in sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf → \"amaruq\" = wolf → object.\n\nIn 13: \"amaruup\" → likely object: \"the wolf\"\n\n\"angatkuit\" → \"saw\"? angat- = shaman? In sentence 6: \"angatkuq\" = shaman (agent)\n\nSo \"angat\" = shaman?\n\nIn sentence 13: \"angatkuit\" → shaman saw?\n\n\"takujanga\" → was seen?\n\nSo is this: \"the shaman saw the wolf\" → but in passive, \"the wolf was seen by the shaman\"?\n\nBut structure: \"Amaruup angatkuit takujanga\" → object + agent + passive verb?\n\nBut that doesn't fit standard order.\n\nWait — Inuktitut often has agent + patient, or patient + agent?\n\nCompare to sentence 1: \"Qingmivit takujaatit\" → dog (agent) saw you (object).\n\nSo → agent + verb + object\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter (agent) + wolf (object) + passive verb → \"the hunter speared the wolf\" → active.\n\nBut \"iputujanga\" = \"was speared\" → so it's passive.\n\nSo: when verb has -anga suffix, it's passive → patient acted upon.\n\nSo in 13: \"amaruup angatkuit takujanga\"?\n\n\"angatkuit\" → if \"angat\" = shaman, then \"angatkuit\" = shaman saw?\n\nBut \"takujanga\" → was seen.\n\nSo shaman saw the wolf → active.\n\nBut \"takujanga\" = was seen → passive.\n\nSo only one passive form per verb.\n\nSo: if \"takujanga\" is passive, then \"the wolf was seen by the shaman\".\n\nBut word order: \"amaruup angatkuit takujanga\"\n\n→ wolf + shaman + saw (passive)\n\n→ likely: \"the wolf was seen by the shaman\"\n\nSimilarly:\n\n14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\nBreak down:\n\n- \"Nanuit\" → polar bear (nanuq = polar bear, \"nit\" = 1st person?) → no.\n\nWait — sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\"\n\nSo \"nanuq\" = polar bear → agent\n\n\"nanuit\" → may be \"the polar bear\" or possessive?\n\n\"nanuit\" → could be \"the polar bear\" with possessive or noun?\n\nBut \"inuuhukturmik\" → inuuhuktuit = boy, \"mik\" = plural or possessive?\n\n\"inuuhukti\" = hunter? In sentence 2: \"inuuhuktuit\" = boy? Wait.\n\nSentence 2: \"inuuhuktuit\" → \"the boy\" → inuuhukti = boy?\n\nIn sentence 9: \"Angunahukti\" = hunter\n\nSo \"inuuhukti\" = boy?\n\nThen \"inuuhukturmik\" = \"your boy\" (mik = possessive)\n\n\"aanniqsijuq\" → likely passive form of \"to hurt\"\n\n\"anniq\" = hurt? From \"aanniqtanga\" → hurt\n\n\"aanniqsijuq\" → \"was hurt\"\n\nSo \"inuuhukturmik aanniqsijuq\" → \"your boy was hurt\"\n\n\"nanuit\" → \"the polar bear\"?\n\nSo: \"The polar bear hurt your boy\" → but verb is passive?\n\nNo — \"aanniqsijuq\" = was hurt → passive.\n\nSo agent → polar bear, patient → your boy → \"your boy was hurt by the polar bear\"\n\nThus: \"The polar bear hurt your boy\" is active, but here it's passive.\n\nSo \"nanuit inuuhukturmik aanniqsijuq\" → \"The polar bear hurt your boy\" — but verb is passive → so must be \"your boy was hurt by the polar bear\"\n\nSo translation: \"Your boy was hurt by the polar bear\"\n\nSimilarly in 15: \"Angunahuktiit aarqijuq\"\n\n\"angunahuktiit\" → hunter (agent), past tense, \"it\" may mark object?\n\n\"aarqijuq\" → \"was cured\"\n\nSo → \"the hunter was cured\"?\n\nBut \"aarqijuq\" → passive, \"was cured\"\n\nBut hunter is agent, curing someone?\n\nNo — hunter is being cured?\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → active\n\nSo \"aarqisijuq\" → cured (active) or was cured (passive)?\n\nHere: \"aarqijuq\" — likely passive.\n\nSo \"Angunahuktiit aarqijuq\" → \"the hunter was cured\"\n\nBut is that plausible?\n\nSentence 15: \"Angunahuktiit aarqijuq\" → likely \"The hunter was cured\"\n\n16: \"Ilinniaqtitsiji qukiqtait\"\n\n\"Ilinniaqtitsiji\" → likely \"your teacher\" or \"teacher\" with possessive?\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\"\n\n→ \"ilinniaqtitsijiit\" = \"your teacher\"\n\nSo \"ilinniaqtitsiji\" → \"your teacher\"\n\n\"qukiqtait\" → active form of \"to shoot\"? \"qukiq\" = to shoot\n\n\"qukiqtait\" → active?\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\"\n\n\"qukiqsijuq\" → passive → \"was shot\"\n\nSo active → qukiq + -tait → \"shot\"\n\nSo \"qukiqtait\" → shot\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\n→ but who? Object missing?\n\nStructure: subject + verb → \"Your teacher shot\"\n\nBut missing object? In context, likely omitted.\n\nBut all sentences have full meaning.\n\nPossibly: \"your teacher shot\" → implied object?\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher\n\n→ agent: dog, patient: your teacher\n\nSo object is \"your teacher\"\n\nSo here: \"ilinniaqtitsiji\" = your teacher, \"qukiqtait\" = shot → so \"your teacher shot\"\n\nBut shot what? Unspecified.\n\nBut likely implied — perhaps \"your teacher shot someone\"?\n\nBut no object.\n\nAlternatively, maybe \"your teacher shot\" as in \"your teacher shot [someone]\" — but still incomplete.\n\nWait — sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\nNo object.\n\nCompare to sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n\"qukiqtanga\" → passive → \"was shot\"\n\nSo in 2, \"qukiqtanga\" = passive\n\nIn 16: \"qukiqtait\" → active\n\nSo \"your teacher shot\" → subject + active verb\n\nBut without object, it may be incomplete — but probably meant to be an action.\n\nPossibly: \"Your teacher shot\" → as in \"your teacher shot someone\" — implied.\n\nBut in context, likely it's a verb, so the translation is \"Your teacher shot\".\n\n17: \"Qaijutit\" → from earlier, \"you fell\" — same as sentence 11: \"Ukiakhaqtutit\" → you fell.\n\nSo \"Qaijutit\" = \"you fell\"\n\n18: \"Angunahuktimik aarqisijutit\"\n\n\"angunahuktimik\" → hunter (agent), \"mik\" = possessive or plural?\n\n\"inuuhukti\" = boy? \"mik\" → \"your boy\"?\n\n\"aarqisijutit\" → passive form of \"cured\"?\n\n\"aarqisijuq\" → passive → \"was cured\"\n\n\"aarqisijutit\" → with suffix -utit → may be past?\n\nSo \"was cured\"\n\nThus: \"the hunter was cured\"\n\nBut again, passive form.\n\nSo \"Angunahuktimik aarqisijutit\" → \"the hunter was cured\"\n\nBut earlier 15: \"Angunahuktiit aarqijuq\" → also \"the hunter was cured\"\n\nSo both 15 and 18 seem to be \"the hunter was cured\"\n\nBut 15: \"Angunahuktiit aarqijuq\" → \"the hunter was cured\"\n\n18: \"Angunahuktimik aarqisijutit\" → \"the hunter was cured\"\n\nBut different verb — \"aarqijuq\" vs \"aarqisijutit\"?\n\n\"aarqisijutit\" → likely \"was cured\" → same as \"aarqijanga\"?\n\nPossibly different possessive.\n\n\"mik\" = possessive (your) vs \"it\" = no possessive?\n\nSo 15: \"the hunter was cured\"\n\n18: \"your hunter was cured\"?\n\nBut \"angunahuktimik\" → \"your hunter\"?\n\n\"angunahukti\" = hunter → \"mik\" = your → \"your hunter\"\n\nSo \"your hunter was cured\"\n\nIn 15: \"angunahuktiit\" — does \"it\" mark possessive?\n\n\"angunahuktiit\" → likely \"the hunter\" → no possessive\n\nSo 15: \"The hunter was cured\"\n\n18: \"Your hunter was cured\"\n\nNow back to 13: \"Amaruup angatkuit takujanga\"\n\n\"amaruup\" = wolf (object)\n\n\"angatkuit\" = shaman (agent) + saw?\n\n\"takujanga\" = passive → \"was seen\"\n\nSo: \"the wolf was seen by the shaman\"\n\nBut is \"angatkuit\" = shaman saw? Yes — with passive.\n\nSo translation: \"The wolf was seen by the shaman\"\n\n14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n\"nanuit\" = polar bear (agent)\n\n\"inuuhukturmik\" = your boy (patient)\n\n\"aanniqsijuq\" = was hurt\n\nSo: \"Your boy was hurt by the polar bear\"\n\n15: \"Angunahuktiit aarqijuq\" → \"The hunter was cured\"\n\n16: \"Ilinniaqtitsiji qukiqtait\" → \"Your teacher shot\" → but needs object?\n\nIn sentence 10: \"the dog hurt your teacher\" → agent: dog, patient: teacher\n\nSo object is patient.\n\nIn this sentence, \"ilinniaqtitsiji\" = your teacher, \"qukiqtait\" = shot → so subject is teacher, verb active.\n\nSo \"your teacher shot\" — likely meaning \"your teacher shot [someone]\" — but implied.\n\nBut no object, so likely just \"Your teacher shot\".\n\nBut is that acceptable? In the pattern, agents are often followed by object.\n\nPerhaps the object is missing, but grammatically, it's an incomplete clause.\n\nBut in the context, perhaps it's equivalent to \"your teacher shot the dog\" or something.\n\nBut no clue.\n\nWait — compare sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot polar bear\n\n→ agent (hunter), object (polar bear), passive verb.\n\nSo here, \"ilinniaqtitsiji\" = object → \"your teacher\" → so \"your teacher shot [someone]\" → but no object.\n\nSo probably, it's a mistake or missing object.\n\nBut perhaps it's simply \"Your teacher shot\" — as a verb phrase.\n\nBut in the list, it's likely to mean \"Your teacher shot someone\" (unspecified).\n\nBut in standard translations, they may", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12125.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "iid", + "sample_index": 0, + "output": "We are given several equations in Nahuatl and Arammba, and our goal is to determine how to write the numbers 42 and 494 in Nahuatl.\n\nFirst, note that the problem is about deriving a pattern in Nahuatl number expressions, likely based on additive or multiplicative structures.\n\nWe examine the equations to find patterns of formation.\n\n---\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nThis looks like: (A × A) = B \n\"mahtlactli-on-cë\" seems to be a multiplicative unit or a \"times\" operator. \n\"mahtlactli\" is likely a number (perhaps 1 or a unit), so (1 × 1) = something. \nBut more likely, \"mahtlactli\" is a base unit (like 1), and \"on-cë\" is a structure (e.g. \"times\" or \"of\") — perhaps indicating multiplication.\n\nBut equation (1): \nA × A = result \nThe result is mäcuïl-pöhualli-om-mahtlactli\n\nWe compare to other equations.\n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n\nHere, multiplication is being applied to two terms (cem-pöhualli and öme), and we get öm-pöhualli.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n\nAddition: sum of two terms gives another.\n\nEquation (4): \nmäcuïlli + öme = chicöme \n\nAddition again.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\nMultiplication leads to a long compound.\n\nEquation (6): \nmäcuïlli × ëyi = caxtölli \n\nAnother multiplication.\n\nEquation (7): \nngámbi + ngámbi = ngámbi × yànparo \n\nIn Arammba: two same things added equal to their product with yànparo. This suggests that the operation is associative, and there's a relationship between addition and multiplication.\n\nFrom (7): a + a = a × b → implies that b is such that 2a = a × b → b = 2 → so yànparo = 2?\n\nSo in Arammba, \"yànparo\" = 2?\n\nAlso (8): ngámbi + asàr = tambaroy — addition of two units gives a compound.\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 + x) = 2 × fete? \nWait: \"tàxwo\" seems to be a modifier or operator — perhaps \"täxwo\" means \"of\" or \"multiplied by\", or associates decomposition.\n\nBut (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ suggests that \"täxwo\" may associate multiplication by a unit.\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (a × a) = (fete) × a → implies fete = 1, and multiplication is commutative? \nOr possibly: a² = fete × a → a = fete → so fete = a? \nBut then fete = yenówe? Not consistent.\n\nAlternatively, “täxwo” may be a distributive operator.\n\nBut let’s look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nAnd (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n\nWe now suspect that \"cen\" may be a unit (like 1), and the expressions represent compositions that correspond to number operations.\n\nLet’s try to find a mapping.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2a = a × yànparo → yànparo = 2\n\nSo in Arammba, yànparo = 2.\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nWe interpret: (a × a) = (fete × a) → so a = fete → so fete = a → fete = yenówe?\n\nSo fete = yenówe.\n\nFrom (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba \nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe → so yenówe = nimbo + 2\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → if fete = yenówe, then this becomes: \nyenówe × (yenówe) = yenówe × yenówe → identity → consistent.\n\nFrom (11): nimbo × yenówe = tarumba\n\nBut from (12): yenówe = nimbo + 2 → so we can substitute:\n\nnimbo × (nimbo + 2) = tarumba\n\nSo tarumba = nimbo² + 2×nimbo\n\nNow look at (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nWe see that the expression on left is a compound, and on right is \"yànparo tarumba\" → 2 × tarumba\n\nAlso from (15): cen-tzontli = tarumba tambaroy fete asàr \n→ 1 = tarumba × tambaroy × fete × asàr? But that would make 1 = large number → contradiction.\n\nWait — perhaps \"cen\" stands for 1? \"tzontli\" is part of a base?\n\nAlternatively, in Nahuatl, \"cen\" may be a unit (1), and expressions like \"cen-tzontli\" may represent composite values.\n\nLooking back: in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nIn (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nFrom (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nPossibly, \"mahtlactli\" = 1, \"öme\" = 2? Or other values.\n\nTry to map the structure.\n\nNotice that in (4): mäcuïlli + öme = chicöme \nSo opening to additive.\n\nIn (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nThis may be (1 × ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (ëyi) × (ëyi) = something → so ëyi × ëyi = result\n\nSimilarly, (6): mäcuïlli × ëyi = caxtölli → so 1 × ëyi = caxtölli → so caxtölli = ëyi?\n\nSo ëyi = caxtölli\n\nFrom (5): ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui → so (caxtölli)² = cem-pöhualli-on-caxtölli-on-nähui\n\nSo the square of a number is represented as a compound with \"cem-pöhualli\" at front, then caxtölli (the number), then \"on-nähui\"\n\nSo square = cem-pöhualli-on-caxtölli-on-nähui\n\nThus, for any x, x² = cem-pöhualli-on-x-on-nähui?\n\nBut only for x = ëyi = caxtölli\n\nSo in this case, x = ëyi, x² = cem-pöhualli-on-x-on-nähui\n\nSo this seems to be a pattern: square of a number = cem-pöhualli-on-number-on-nähui\n\nSimilarly, look at (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (a) × (a) = mäcuïl-pöhualli-om-a → if a = mahtlactli\n\nSo palindromic structure: square = mäcuïl-pöhualli-om-a → where a is the base\n\nBut here it is: \"mäcuïl-pöhualli-om-mahtlactli\"\n\nSo square = mäcuïl-pöhualli-om-base\n\nIn (6), square = cem-pöhualli-on-base-on-nähui\n\nDifferent pattern? One uses “on”, the other “om”?\n\nPerhaps different base?\n\nBut note: in (1), base is mahtlactli — prefix × a = mäcuïl-pöhualli-om-mahtlactli\n\nIn (5): base is ëyi = caxtölli → (caxtölli)² = cem-pöhualli-on-caxtölli-on-nähui\n\nSo two different patterns? Or same?\n\nBut in (5), the square is represented as: cem-pöhualli-on-base-on-nähui\n\nIn (1): square of mahtlactli is: mäcuïl-pöhualli-om-mahtlactli — similar but different.\n\nBut “om” vs “on” — perhaps just different phrasings.\n\nBut now look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\n\"yë-tzontli\" may be a number, and the rest follows the pattern: i.e., the whole thing is a number.\n\nWe also have (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nNow, yànparo = 2 (from Arammba (7))\n\nSo right-hand side: 2 × tarumba\n\nLeft-hand side: cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nWhat does \"cen-tzontli\" mean? May be 1 × tzontli?\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo 1 = tarumba × tambaroy × fete × asàr → which would imply that the product is 1 → so the units are reciprocals.\n\nBut in (14): the left is 1 × tzontli on (cem-pöhualli-om-mahtlactli-om-öme)\n\nThis looks like tzontli × (c...om...om...)\n\nNow, from (2): cem-pöhualli × öme = öm-pöhualli\n\nSo cem-pöhualli × öme = öm-pöhualli\n\nSo maybe öme = 2, and cem-pöhualli × 2 = öm-pöhualli\n\nIf öme = 2, then (c) × 2 = d → d = 2c\n\nSo the structure might represent multiplication.\n\nBut more insight: from (14): left = right \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba = 2 × tarumba\n\nSo left-hand side = 2 × tarumba\n\nNow, what is the structure of the left?\n\nIt is: tzontli × (something involving cem-pöhualli, mahtlactli, öme)\n\nFrom the pattern, we see that multiplication is being represented with specific prefixes.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli → so a × b = c\n\nIn (4): mäcuïlli + öme = chicöme → a + b = c\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf \"cen-tzontli\" is 1, then 1 = tarumba × tambaroy × fete × asàr → therefore the product is 1.\n\nBut that implies that tarumba, tambaroy, fete, asàr are units that multiply to 1 → meaning they are reciprocals.\n\nFrom (11): nimbo × fete = tarumba\n\nFrom (8): ngámbi + asàr = tambaroy\n\nBut in Arammba, yànparo = 2\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo → nimbo + 2 = yenówe\n\nSo yenówe = nimbo + 2\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → so (yenówe)² = fete × yenówe → so yenówe = fete → so fete = yenówe\n\nFrom (11): nimbo × fete = tarumba → so nimbo × yenówe = tarumba\n\nBut yenówe = nimbo + 2 → so tarumba = nimbo × (nimbo + 2)\n\nSo tarumba = n(n+2) = n² + 2n\n\nThus, tarumba = n² + 2n\n\nNow, from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAnd \"cen\" = 1 → so 1 = tarumba × tambaroy × fete × asàr\n\nBut fete = yenówe = nimbo + 2 → and tarumba = nimbo × (nimbo + 2)\n\nSo 1 = [nimbo × (nimbo + 2)] × tambaroy × (nimbo + 2) × asàr\n\n→ 1 = nimbo × (nimbo + 2)² × tambaroy × asàr\n\nThis is very strange unless values are fractions.\n\nBut perhaps \"cen-tzontli\" is not 1.\n\nAlternatively, maybe \"cen\" is not 1 — perhaps it is a base value.\n\nAnother idea: the structure \"A-on-B\" may mean addition (A + B)\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo left: (A on B) + (C on D) = (E on F)\n\nSo sum of two compounds gives a new compound.\n\nIn (3): yë-pöhualli-on-chicöme is a unit, plus (mahtlactli on nähui), equals (näuh-pöhualli-on-cë)\n\nSo possibly addition is \"on\"\n\nIn (4): mäcuïlli + öme = chicöme → addition\n\nSo likely \"on\" and \"+\" are equivalent.\n\nNow, in (1): \"mahtlactli-on-cë × mahtlactli\" = mäcuïl-pöhualli-om-mahtlactli\n\nSo if \"on\" is addition, this is \"a on b\" × c = d\n\nBut \"a on b\" is a compound.\n\nPerhaps the entire expression is based on multiplication involving compound numbers.\n\nBack to (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe suspect “ndamno” is a number.\n\nSimilarly, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe have yànparo = 2\n\nSo right-hand side: 2 × tarumba\n\nLeft-hand side: cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nThis may represent: cen-tzontli × (cem-pöhualli × mahtlactli) × öme? Or nested.\n\nAlso, from (2): cem-pöhualli × öme = öm-pöhualli\n\nSo the product cem-pöhualli × öme is öm-pöhualli\n\nSo in (14), we have cen-tzontli-on-(something that equals öm-pöhualli) → so cen-tzontli-on-öm-pöhualli = 2 × tarumba\n\nBut \"on\" may be addition.\n\nSo cen-tzontli + öm-pöhualli = 2 × tarumba\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAgain, if \"on\" means addition, then cen-tzontli is a compound, but (15) says cen-tzontli equals a product of four units.\n\nThis suggests that units may be additive on the left, multiplicative on the right.\n\nPerhaps the key is to find the value of the expression in numbers.\n\nFrom (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe know from (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxt", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10720.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "iid", + "sample_index": 1, + "output": "We are given a series of equations from Nahuatl and Arammba, and we are to deduce the linguistic pattern to write out \"42\" and \"494\" in Nahuatl.\n\nWe start by analyzing the equations to find how numbers are constructed.\n\n---\n\n**Step 1: Look for multiplicative patterns**\n\nIn Nahuatl, we have:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nNote: \"on\" appears to be a composition operator, possibly meaning \"plus\" or \"combined with\".\n\nBut also, expressions like \"A × B\" suggest multiplication. Some equations reflect multiplication or addition, and products are built from compound forms.\n\nLet’s test (1): \nmahtlactli-on-cë × mahtlactli → mäcuïl-pöhualli-om-mahtlactli \n\nWe may need to interpret components. Let's denote elements as units.\n\nTry to assign values or decode possible meanings.\n\n---\n\n**Step 2: Identify possible number values**\n\nWe suspect that certain compound expressions represent numbers.\n\nFrom (4): mäcuïlli + öme = chicöme\n\nFrom (6): mäcuïlli × ëyi = caxtölli\n\nFrom (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n(6) suggests mäcuïlli × ëyi = caxtölli → likely multiplication.\n\nSo mäcuïlli × ëyi = caxtölli → if ëyi = 1, then mäcuïlli = caxtölli → may not hold.\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n“mahtlactli” may represent a base number. Let’s suppose:\n\nLet’s denote:\n\n- mahtlactli = 20 \n- cem-pöhualli = 1? (from (2): cem-pöhualli × öme = öm-pöhualli) \n- öme = 1?\n\n(2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 1, then cem-pöhualli × 1 = öm-pöhualli → so cem-pöhualli = öm-pöhualli?\n\nUnlikely unless they are equal. But in (13), we get a long expression that yields \"ndamno\".\n\nAlso, (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nNow, notice:\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut from (8): ngámbi + asàr = tambaroy → suggests addition\n\nSimilarly, in Arammba:\n\n(7): ngámbi + ngámbi = ngámbi × yànparo → suggests ngámbi = 1, yànparo = 2? \nAlso, (8): ngámbi + asàr = tambaroy → so if ngámbi = 1, then asàr = tambaroy - 1?\n\nBut in (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ maybe “tàxwo” is a marker (like “times” or “and”)? \nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ seems like “×” or multiplication with addition?\n\nPossibly the “tàxwo” means “multiplied by” or “times”, or it's a marker.\n\nBut (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → suggests that “yenówe” × “yenówe” = “fete yenówe”?\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nNow, look at (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nCompare value: \nSuppose cen-tzontli = base number? \nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut from (11): nimbo × fete = tarumba → tarumba = nimbo × fete\n\nAlso, in Arammba: (11) nimbo × fete = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo\n\nSuppose that “yànparo” = 1, “tàxwo” = “multiplied by”, then:\n\n(12): nimbo + yànparo = yenówe → nimbo + 1 = yenówe \n(10): yenówe × yenówe = fete yenówe → yenówe² = fete yenówe → implies fete = yenówe\n\nSo from (10): (yenówe)² = fete × yenówe → so fete = yenówe\n\nThen from (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\nFrom (12): nimbo + 1 = yenówe → so nimbo = yenówe - 1\n\nSubstitute: \ntarumba = (yenówe - 1) × yenówe = yenówe² - yenówe\n\nBut from (10), fete = yenówe, and yenówe² = fete × yenówe → holds.\n\nSo tarumba = yenówe² - yenówe\n\nNow (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut tambaroy = ngámbi + asàr → from (8)\n\nSuppose ngámbi = 1 → then tambaroy = 1 + asàr\n\nThus, cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut this seems messy.\n\nAlternatively, maybe the compounds mean multiplication.\n\nGo back to the original equations.\n\nIn Nahuatl:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nIf “on” means “plus”, then:\n\nmahtlactli + cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nBut that doesn’t match.\n\nAlternatively, \"on\" may mean \"times\" or \"multiplied by\".\n\n(1) mahtlactli-on-cë × mahtlactli → maybe (mahtlactli × cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nNo clear equality.\n\nBetter approach:\n\nLook at the map from Arammba to Nahuatl in (13)-(16):\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nNow, in Arammba, (14) has yànparo tarumba, which is a compound.\n\nIn Nahuatl, (14) is cen-tzontli-on-... = yànparo tarumba\n\nBut in Arammba, yànparo and tarumba appear as separate units, so perhaps the compound in Nahuatl represents a number.\n\nSo: cen-tzontli-on-... = yànparo tarumba → suggests that “yànparo tarumba” is a value derived from cen-tzontli and other elements.\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli is expressed as sum: tarumba + tambaroy + fete + asàr?\n\nBut in (15) of Nahuatl: cen-tzontli = tarumba tambaroy fete asàr → likely addition.\n\nNow from Arammba (11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo = yenówe\n\nAnd (10): yenówe × yenówe = fete yenówe → so yenówe² = fete × yenówe → fete = yenówe\n\nThus fete = yenówe\n\nThen (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo = yenówe → nimbo = yenówe - yànparo\n\nPlug in: \ntarumba = (yenówe - yànparo) × yenówe = yenówe² - yànparo × yenówe\n\nBut from (10): (yenówe)² = fete yenówe → and fete = yenówe, so consistent.\n\nNow we have tarumba = yenówe² - yànparo yenówe\n\nSo tarumba = yenówe(yenówe - yànparo)\n\nNow what if we assume in Arammba, yànparo = 1?\n\nThen nimbo = yenówe - 1 \ntarumba = yenówe (yenówe - 1)\n\nSo (14) in Arammba: yànparo tarumba = 1 × tarumba = tarumba = yenówe(yenówe - 1)\n\nSo values: \n- yànparo = 1 \n- tarumba = n(n-1) → a product of two numbers\n\nIn Nahuatl, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom earlier, yànparo tarumba = (from Arammba) = tarumba = n(n-1)\n\nBut in Arammba, (7): ngámbi + ngámbi = ngámbi × yànparo → so if yànparo = 1, then 2×ngámbi = ngámbi × 1 → 2ng = ng → ng = 0 → contradiction.\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2ng = ng × yànparo → 2ng = ng × yànparo → ng(2 - yànparo) = 0 → so either ng = 0 or yànparo = 2\n\nThus yànparo = 2\n\nThen from (7): 2ng = ng × 2 → holds for any ng.\n\nSo yànparo = 2\n\nNow (8): ngámbi + asàr = tambaroy\n\n(12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe → nimbo = yenówe - 2\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → so yenówe × yenówe = fete × yenówe → fete = yenówe\n\n(11): nimbo × fete = tarumba → (yenówe - 2) × yenówe = tarumba\n\nSo tarumba = yenówe(yenówe - 2)\n\nWe now have:\n\n- tarumba = n(n - 2) → where n = yenówe\n\nSo in Arammba, tarumba = n(n-2)\n\nNow in (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis appears to be additive: cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut fete = yenówe = n\n\ntarumba = n(n-2)\n\ntambaroy = ngámbi + asàr\n\nasàr is unknown\n\nBut can we get values?\n\nWe are to write “42” and “494” in Nahuatl.\n\nSo we must find the base linguistic structure.\n\nFrom (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may represent a specific number.\n\n(14) has cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba = 2 × [n(n-2)]\n\nBut from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut this seems too many variables.\n\nAlternative idea: look at Nahuatl equations and try to find what numbers correspond.\n\nLook at (4): mäcuïlli + öme = chicöme\n\n(6): mäcuïlli × ëyi = caxtölli\n\nSo mäcuïlli × ëyi = caxtölli\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nBut mahtlactli-om-ëyi × ëyi = (mahtlactli × ëyi) + (ëyi × ëyi)? No.\n\nPerhaps “om” means “times”, and “on” means “plus”.\n\nTry to assign:\n\nLet’s suppose that:\n\n- mahtlactli = 20 \n- öme = 1 \n- cem = 1 \n- cem-pöhualli = 1 \nBut (2): cem-pöhualli × öme = öm-pöhualli → so if both 1, then 1×1 = 1 → holds.\n\nNow (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nAssume on = plus, so (mahtlactli + cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nIf mahtlactli = 20, then left side: (20 + cë) × 20 = 400 + 20cë\n\nRight side: mäcuïl-pöhualli-om-mahtlactli → possibly mäcuïl-pöhualli is a compound like 1×pöhualli.\n\nBut we don’t know.\n\nLook at (4): mäcuïlli + öme = chicöme → could mean 1 + 1 = 2 \n(6): mäcuïlli × ëyi = caxtölli → so 1 × x = caxtölli → caxtölli = x\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli-om-ëyi = mahtlactli × ëyi → so (20 × x) × x = 20x²\n\nRight side: cem-pöhualli-on-caxtölli-on-nähui = 1 × caxtölli × nähui = x × nähui\n\nSo: 20x² = x × nähui → 20x = nähui → so nähui = 20x\n\nBut from (6): caxtölli = x\n\nSo if x = 1, then nähui = 20\n\nIf x = 2, nähui = 40\n\nBut we have no base yet.\n\nNow (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSuppose that “on” means “plus”, then:\n\nyë-tzontli + näuh-pöhualli + caxtölli + cë = ndamno\n\nBut we don't know values.\n\nAlternatively, the “on” might mean “times” or “mult.”.\n\nBut no clear pattern.\n\nBack to numbers.\n\nFrom Arammba, we have:\n\n- tarumba = n(n - 2) with n = yenówe \n- yànparo = 2\n\nSo possible values:\n\nIf n = 3 → tarumba = 3(1) = 3 \nn = 4 → 4×2 = 8 \nn = 5 → 5×3 = 15 \nn = 6 → 24 \nn = 7 → 35 \nn = 8 → 48 \nn = 9 → 63 \nn = 10 → 80 \nn = 11 → 99 \nn = 12 → 120 \nn = 13 → 143 \n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9767.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "iid", + "sample_index": 2, + "output": "We are to translate the numbers **42** and **494** into Nahuatl, based on the given linguistic patterns from the examples.\n\n---\n\nStep 1: Identify the arithmetic operations and their structural patterns.\n\nLook at the equations:\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\nAlso, the compound equations:\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nStep 2: Identify structural arithmetic.\n\nNotice that in Nahuatl, some operations follow compound structural rules, and the multiplication is often represented via a base structure with suffixes.\n\nLook at (1): `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\n- Left: A × A → Right: mäcuïl-pöhualli-om-mahtlactli \n- This suggests a multiplication rule involving a component “mahtlactli” and a “pöhualli”-related structure.\n\nAlso (2): `cem-pöhualli × öme = öm-pöhualli` \n→ cem-pöhualli × öme → öm-pöhualli → very simplified, perhaps one component duplicates.\n\nEquation (4): `mäcuïlli + öme = chicöme` \n→ Addition of two components makes a third. Could be a unit of measurement or a number structure.\n\nEquation (6): `mäcuïlli × ëyi = caxtölli` \n→ Multiplication: mäcuïlli × ëyi = caxtölli\n\nBut (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nThis suggests patterns involving compound terms with multiplication and stacking.\n\n---\n\nStep 3: Observe equation (13): \n\n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe observe:\n\n- The left side is composed of a chain: yë-tzontli-on-... \n- It is being reduced to a single word: ndamno\n\nCould this represent a number?\n\nNote that “tzontli” may be a unit. In Nahuatl, “tzontli” means “unit” or “cake”, and “pöhualli” is “20”, and “mahtlactli” is “1” or “unit”.\n\nWait — “pöhualli” is likely a base unit (20), and “mahtlactli” is 1.\n\nFrom equation (1):\n\n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n\nBreak down:\n\n- `mahtlactli` = 1 \n- So 1 × 1 = ? → gives mäcuïl-pöhualli-om-mahtlactli \n\nBut that would mean 1 × 1 = a larger structure.\n\nWait — maybe multiplication is not just the product but a concatenation?\n\nAnother thought: in Nahuatl number systems, numbers are built via 20s and 1s.\n\nIn the expression:\n\n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\n- “tzontli” may be 1 \n- “pöhualli” = 20 \n- “caxtölli” may be related to multiplication\n\nLook at (6): `mäcuïlli × ëyi = caxtölli` → so caxtölli is mäcuïlli × ëyi\n\n(5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nLeft is (mahtlactli-om-ëyi) × ëyi → result is cem-pöhualli-on-caxtölli-on-nähui\n\nBut since mahtlactli = 1, mahtlactli-om-ëyi may be a unit × something.\n\nLet’s suppose:\n\n- “ëyi” = 2 \n- “öme” = 3 \n- “pöhualli” = 20 \n- “mahtlactli” = 1 \n- “mäcuïlli” = 4? (since 4 × 2 = 8, and caxtölli might be 8?)\n\nLet’s test known values.\n\nTry to assign values:\n\nSuppose:\n\n- ëyi = 2 \n- öme = 3 \n- mahtlactli = 1 \n- pöhualli = 20 \n- mäcuïlli = 4 \n- caxtölli = mäcuïlli × ëyi = 4 × 2 = 8 \n\nThen (4): mäcuïlli + öme = 4 + 3 = 7 → chicöme → so maybe chicöme = 7\n\n(1): mahtlactli-on-cë × mahtlactli = 1 × 1 = ?\n\n→ gives mäcuïl-pöhualli-om-mahtlactli\n\nmäcuïl-pöhualli → 4 + 20 = 24? Or 4 × 20 = 80?\n\n\"mahtlactli-on-cë\" may be 10 or 1?\n\nIn some systems, \"cë\" might be 10.\n\nWait — in Nahuatl, “cë” may represent “10”.\n\nLet’s test that.\n\nSuppose:\n\n- cë = 10 \n- ëyi = 2 \n- öme = 3 \n- pöhualli = 20 \n- mahtlactli = 1 \n- mäcuïlli = 4 \n\nThen (1): mahtlactli-on-cë × mahtlactli = (10) × 1 = 10 → but output is mäcuïl-pöhualli-om-mahtlactli\n\nmäcuïl-pöhualli → 4 × 20 = 80?\n\nBut input is 1 × 10 = 10 → not matching.\n\nAlternatively, (1): (10) × 1 = 10 → result is mäcuïl-pöhualli-om-mahtlactli → 4×20 = 80 → doesn’t match.\n\nAlternate idea: multiplication produces a compound number with a base and a multiplier.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSuppose:\n\n- tzontli = 1 \n- pöhualli = 20 \n- caxtölli = 8 (from 4×2) \n- cë = 10 \n\nSo: 1-on-20-on-8-on-10 = ?\n\nStructure: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\n“on” is likely a connector.\n\nSo order: tzontli (1) → 20 → 8 → 10?\n\nBut this seems like a compound like a × 20 + b × 10 + c?\n\nBut no canonical order.\n\nWait — look at (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe have:\n\n(11) nimbo × fete = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n(8) ngámbi + asàr = tambaroy \n(15) cen-tzontli = tarumba tambaroy fete asàr\n\nSo perhaps:\n\n- cen-tzontli = 100? \nBecause “cen” often means 100 in Nahuatl number systems.\n\nYes — “cen” = 100 (in Maya/Nahuatl systems)\n\nSo cen-tzontli = 100 units of tzontli → likely 100\n\nThen: cen-tzontli = tarumba tambaroy fete asàr\n\nBreak down right side:\n\n- tarumba = nimbo × fete (from 11) \n- tambaroy = ngámbi + asàr \n- fete = fete\n\nWe don’t have values.\n\nBut suppose:\n\n- fete = 2 \n- asàr = 5 \n- then tambaroy = ngámbi + 5 → but not known\n\nBut from (8): ngámbi + asàr = tambaroy → and (7): ngámbi + ngámbi = ngámbi × yànparo\n\nEven more: (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThis may suggest that \"tãxwo\" means \"of\" or \"reduced to\", and when added, it reduces.\n\nFor instance, yànparo tàxwo + fete asàr tàxwo → yànparo fete → suggests that “tãxwo” drops out.\n\nThis suggests that possession or multiplication is reversed.\n\nBut back to (13):\n\nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe suspect this means 1, 20, 8, 10 → compound.\n\nIf “tzontli” = 1 \n“pöhualli” = 20 \n“caxtölli” = 8 \n“cë” = 10 \n\nThen what is the value?\n\nCould be structured as:\n\n(1 × 20) + (8 × 10) → 20 + 80 = 100\n\nThen equals \"ndamno\" → which may be 100.\n\nBut in (15): cen-tzontli = 100 → and it equals tarumba tambaroy fete asàr → which is a compound.\n\nSo both expressions represent 100.\n\nSo likely: 100 is represented by cen-tzontli\n\nThus, \"ndamno\" = 100\n\nNow (13): the expression equals 100.\n\nSo the expression `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë` = 100\n\nWe break it into components:\n\n- yë- = perhaps 1? \n- tzontli = 1 \n- näuh-pöhualli = 20? \n- caxtölli = 8? \n- cë = 10\n\nSo is it structured as a compound number?\n\nIf it is a number like:\n\na × 20 + b × 10\n\nBut “on” may mean \"plus\" or \"combined with\".\n\nBut order: tzontli (1) → pöhualli (20) → caxtölli (8) → cë (10)\n\nSo: 1 on 20 on 8 on 10 → perhaps: 1×20, 8×10 → 20 + 80 = 100\n\nYes.\n\nAlternatively: (1×20) + (8×10) = 100\n\nSo base units: 20 (pöhualli), 10 (cë), and multipliers.\n\nNow, to get 42 and 494.\n\n42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14 → 480 + 14 = 494\n\nOr 494 = 24×20 + 14 = (494 / 20) = 24.7 → 24×20 = 480 → remainder 14 → 14 = 1×10 + 4\n\nSo 24×20 + 1×10 + 4 → 480 + 10 + 4 = 494\n\nBut 4 is not a base.\n\nWe have to build a number using the structure seen in equations.\n\nFrom (13): Multiple components combined with “on” → the value is 100.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\ncen-tzontli = 100 \ncem-pöhualli = ? \nmahtlactli = 1 \nöme = 3 \n\nSo: 100 + (cem-pöhualli) × (1) × (3) ??\n\nBut expression: cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\n\"on\" may mean sum, \"om\" may mean multiplication.\n\n\"om\" is used in (1): mahtlactli-on-cë × mahtlactli → suggests \"om\" is part of multiplication.\n\nIn (1): mahtlactli-om-ëyi × ëyi → so “om” links components in multiplication.\n\nSo \"A-om-B\" might be A × B\n\nIn (5): mahtlactli-om-ëyi × ëyi → (1 × 2) × 2 = 4 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nBut we already had cem-pöhualli × öme = öm-pöhualli (equation 2)\n\nSo cem-pöhualli × 3 = öm-pöhualli → suggests cem-pöhualli = 1 → 1×3 = 3 → öm-pöhualli = 3 → so öm-pöhualli = 3\n\nWait — that would be strange.\n\nc-em-pöhualli × öme = öm-pöhualli\n\nIf öme = 3, then cem-pöhualli × 3 = öm-pöhualli\n\nSo unless 1×3 = 3, then cem-pöhualli = 1\n\nThus: cem-pöhualli = 1\n\nThen in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nStructure:\n\n- cen-tzontli = 100 \n- cem-pöhualli = 1 \n- om-mahtlactli = 1 \n- om-öme = 3\n\nSo this expression: 100 + (1) × (1) × (3) → but “on” and “om” may mean different operations.\n\nThe expression: cen-tzontli-on- (cem-pöhualli-om-mahtlactli-om-öme)\n\nSo “cem-pöhualli-om-mahtlactli” = 1 × 1 = 1? Then × öme = 3?\n\nSo the whole thing: 100 + 3 = 103?\n\nBut result is yànparo tarumba\n\nFrom (11): nimbo × fete = tarumba\n\nWe don't know values.\n\nBut (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nSo perhaps yànparo = 20?\n\nAnd fete = 2 → then nimbo × 2 = tarumba → could be 4?\n\nNot clear.\n\nWe need to find a way to build 42 and 494.\n\nFrom (13): builder for 100 → yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nSo:\n\n- tzontli = 1 \n- pöhualli = 20 \n- caxtölli = 8 \n- cë = 10\n\nSo value: 1×20 + 8×10 = 20 + 80 = 100 → correct.\n\nSo general rule:\n\nA number is built from units: \n- 1 (tzontli) \n- 20 (pöhualli) \n- 10 (cë) \n- 8 (caxtölli)\n\nBut 8 is not a base.\n\nBut 8 = mäcuïlli × ëyi → and mäcuïlli = 4, ëyi = 2\n\nSo caxtölli = 4×2 = 8\n\nSo 8 = 4 × 2\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9505.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "iid", + "sample_index": 3, + "output": "We are given a series of equations in Nahuatl and Arammba, and we are to deduce the linguistic pattern to write out the numbers 42 and 494 in Nahuatl.\n\nWe focus on the Nahuatl equations, since the target is to write in Nahuatl.\n\n---\n\nFirst, examine the equations and extract possible numerical patterns.\n\nEquation (1): \n**mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli**\n\nLet’s try to interpret this.\n\nNote that:\n- \"mahtlactli\" likely means \"1\", as it appears in multiplication and may be a base unit.\n- \"cë\" might be a suffix or marker for \"on\", like \"on\" in compound numbers, possibly indicating a decimal or positional marker.\n- Left: mahtlactli-on-cë × mahtlactli → (x × 1) = result.\n- Right: mäcuïl-pöhualli-om-mahtlactli\n\nBut note that \"pöhualli\" is a known Nahuatl word for \"20\". For example, \"pöhualli\" often refers to the 20-day cycle.\n\nAlso, in Nahuatl, numbers are often built using 20 as a base.\n\nNow, equation (4): \n**mäcuïlli + öme = chicöme**\n\nIf \"öme\" is \"1\", then \"mäcuïlli + 1 = chicöme\".\n\nIf we suppose \"mäcuïlli\" is 19, then 19 + 1 = 20 → \"chicöme\" = 20.\n\nSimilarly, \"öme\" = 1.\n\nThus: \nmäcuïlli = 19 \nöme = 1 \nchicöme = 20\n\nNow equation (2): \n**cem-pöhualli × öme = öm-pöhualli**\n\nIf \"pöhualli\" = 20, and \"öme\" = 1, then:\n\ncem-pöhualli × 1 = öm-pöhualli\n\nSo: (20 × something) × 1 = something.\n\nBut left side: cem-pöhualli → likely \"1 × pöhualli\" → 20?\n\nBut then right side is \"öm-pöhualli\" — perhaps \"öm\" is a different form.\n\nWait — \"cem-pöhualli\" might be \"1 × pöhualli\" → 20?\n\nBut if 20 × 1 = 20, then 20 × 1 = 20 → so right side is \"öm-pöhualli\", which may be equivalent to \"cem-pöhualli\".\n\nDoesn't help directly.\n\nBut equation (3): \n**yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë**\n\nBreak down:\n\n- \"yë-pöhualli-on-chicöme\" = yë × 20 + 20? Not clear.\n\nBut \"pöhualli\" = 20, \"chicöme\" = 20 → so \"yë-pöhualli-on-chicöme\" may be \"yë × 20 + 20\"?\n\nBut yë could be 1 → 1×20 + 20 = 40.\n\n\"mahtlactli-on-nähui\" = 1 × ? \n\nNähui? Possibly another unit.\n\nRight side: näuh-pöhualli-on-cë\n\n\"näuh\" might be a marker.\n\nNow equation (5): \n**mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui**\n\nLeft: (mahtlactli-om-ëyi) × ëyi = ?\n\n\"mahtlactli-om-ëyi\" → 1 × ëyi → ëyi?\n\nSo: ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nIf ëyi = 7? Then 7×7 = 49.\n\nRight side: cem-pöhualli-on-caxtölli-on-nähui → contains \"cem-pöhualli\" = 1×20 = 20?\n\nBut 20 + ? = 49? → 49 − 20 = 29 → doesn't match.\n\nBut look at equation (6): \n**mäcuïlli × ëyi = caxtölli**\n\nWe have: \nmäcuïlli = 19 (from earlier: 19 + 1 = 20) \nSo: 19 × ëyi = caxtölli\n\nSo caxtölli = 19 × ëyi\n\nNow from equation (5): \n(ëyi) × (ëyi) = cem-pöhualli-on-caxtölli-on-nähui\n\nLet’s suppose the right-hand side is cem-pöhualli (20) + caxtölli?\n\nSo: \nëyi² = 20 + caxtölli\n\nBut caxtölli = 19 × ëyi → \nëyi² = 20 + 19×ëyi \nëyi² − 19×ëyi − 20 = 0\n\nSolve quadratic: \nëyi = [19 ± √(361 + 80)] / 2 = [19 ± √441]/2 = [19 ± 21]/2 \n→ (19+21)/2 = 40/2 = 20 \n→ (19−21)/2 = −2/2 = −1 (discard)\n\nSo ëyi = 20\n\nThen caxtölli = 19 × 20 = 380\n\nAnd ëyi² = 400 \nRight side: 20 + 380 = 400 → matches.\n\nSo ëyi = 20 → but \"ëyi\" is used in multiplication like \"× ëyi\", so if ëyi = 20, that would make sense.\n\nBut earlier we thought \"öme\" = 1, \"mäcuïlli\" = 19 → 19 + 1 = 20 → \"chicöme\" = 20.\n\nNow if ëyi = 20, and \"pöhualli\" = 20, so ëyi = pöhualli?\n\nSo \"ëyi\" = 20.\n\nTherefore, base units:\n\n- 1 = mahtlactli \n- 20 = pöhualli = ëyi\n\nNow check equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nLeft: (1) × (1) = 1 → so just 1?\n\nRight: mäcuïl-pöhualli-om-mahtlactli → mäcuïl? 14? 1×20 + 1 = 21?\n\nWait — does \"mäcuïl\" mean 14?\n\nNote: 14 is \"mäcuïl\" — known in Nahuatl.\n\nSo mäcuïl-pöhualli → 14 × 20 + 1? No — mäcuïl-pöhualli = 14×20 = 280?\n\nBut left is 1 × 1 = 1.\n\nDoesn't match.\n\nAlternative: \"mahtlactli-on-cë\" → perhaps means \"cë\" is a multiplier?\n\nMaybe \"on\" means \"times\" — so \"mahtlactli-on-cë\" = 1 × cë?\n\nThen (1 × cë) × 1 = mäcuïl-pöhualli-om-mahtlactli\n\nSo cë × 1 = mäcuïl-pöhualli-om-mahtlactli\n\nSo cë = mäcuïl-pöhualli-om-mahtlactli\n\nIs this 14×20 + 1?\n\nYes — 280 + 1 = 281?\n\nBut 1×cë = 281 → cë = 281? Unlikely.\n\nAlternate idea: perhaps \"on\" is \"plus\"?\n\nThen mahtlactli-on-cë = 1 + cë?\n\nAh! That fits better.\n\nSo \"A-on-B\" = A + B\n\nThen equation (1): (mahtlactli-on-cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSo (1 + cë) × 1 = 1 + cë → so must equal mäcuïl-pöhualli-om-mahtlactli\n\nTherefore: 1 + cë = mäcuïl-pöhualli-om-mahtlactli\n\nNow, mäcuïl = 14, pöhualli = 20 → so 14×20 = 280 → then +1 → 281\n\nSo 1 + cë = 281 → cë = 280\n\nSo cë = 280? → cë = 14 × 20\n\nSo \"cë\" = 14 × 20\n\nBut wait — cë is a unit, not a number. But if we can assign numerical values, then:\n\nmahtlactli = 1 \npöhualli = 20 \nmäcuïl = 14\n\nSo 14 × 20 = 280\n\nThen cë = 280\n\nNow other equations.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nInterpret \"A-on-B\" as A + B\n\n→ yë-pöhualli + chicöme + 1 + nähui = näuh-pöhualli + cë\n\nWe have:\n- pöhualli = 20\n- chicöme = 20\n- nähui = ? \n- näuh-pöhualli = ? \n- cë = 280\n\nSo: yë × 20 + 20 + 1 + nähui = näuh × 20 + 280\n\nLeft: 20yë + 21 + nähui \nRight: 20näuh + 280\n\nSo: 20yë + nähui + 21 = 20näuh + 280 \n→ 20yë + nähui = 20näuh + 259\n\nNow we have no direct value.\n\nBut look at equation (13) and (14) — they are given as compound expressions.\n\nWe are to write 42 and 494.\n\nWe can build these via known components.\n\nRecall from earlier:\n- 1 = mahtlactli\n- 20 = pöhualli\n- 14 = mäcuïl\n- 1 = öme\n\nWe can build numbers using base 20.\n\nLet’s first try to write 42.\n\n42 = 2×20 + 2\n\nSo: 2×20 + 2 = 42\n\nWe would expect: (2 × pöhualli) + 2\n\nBut in Nahuatl, what is the form?\n\nWe can use \"yë\" = 2? If \"yë\" = 2.\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli\n\ncem-pöhualli → 1 × 20 = 20 \n× 1 → 20 → öm-pöhualli → possibly 1×20?\n\nSo 20 × 1 = 20 → consistent.\n\nBut no indication of 2.\n\nEquation (8): ngámbi + asàr = tambaroy — in Arammba, not Nahuatl.\n\nBack to Nahuatl.\n\nEquation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe previously solved and got ëyi = 20\n\nNow equation (6): mäcuïlli × ëyi = caxtölli → 19 × 20 = 380 → caxtölli = 380\n\nEquation (4): mäcuïlli + öme = chicöme → 19 + 1 = 20 → 20 → consistent.\n\nSo numbers:\n- 1 = mahtlactli\n- 20 = pöhualli = ëyi\n- 19 = mäcuïlli\n- 20 = chicöme\n\nNow build 42:\n\n42 = 2×20 + 2 = 40 + 2\n\nSo: 2×pöhualli + 2\n\nIn Nahuatl, likely: \"yë-pöhualli + 2\"\n\nWe have to find what means 2.\n\nLook at equation (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem-pöhualli = 1×pöhualli = 20 → 20×1 = 20 → no.\n\nBut what about (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe can work backward.\n\nBut we need to find a way to write 42.\n\nNote that 42 = 2×20 + 2\n\nWe have no \"2\" directly, but perhaps \"yë\" is 2?\n\nTry to find \"yë\" in context.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n→ [yë×20 + 20] + [1 + nähui] = [näuh×20 + 280]\n\nSo: 20yë + 20 + 1 + nähui = 20näuh + 280 \n→ 20yë + nähui + 21 = 20näuh + 280 \n→ 20yë + nähui = 20näuh + 259\n\nNow equation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe also have equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAnd equation (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nWe may not need all.\n\nBut we are to write 42 and 494.\n\nTry to write 42.\n\nWhat is 42 in base 20?\n\n42 ÷ 20 = 2 remainder 2\n\nSo: 2×20 + 2 → we need to represent 2.\n\nIn Nahuatl, typically, numbers are expressed as:\n\n[high digit] × 20 + [low digit]\n\nSo for 42: (2 × pöhualli) + 2\n\nSo: yë-pöhualli + yë → if yë = 2?\n\nBut yë-pöhualli = 2×20 = 40 → then +2 → 42\n\nSo expression: yë-pöhualli + yë\n\nBut in the compound, if \"+\" is used, likely written as \"yë-pöhualli-on-yë\"?\n\nBut the equations use \"on\" as a linking operator.\n\nBut equation (3): yë-pöhualli-on-chicöme + ... → so \"A-on-B\" = A + B?\n\nSo \"yë-pöhualli-on-yë\" = yë×20 + yë\n\nSo number: (yë × 20) + yë = yë×21\n\nWe want this to be 42 → yë = 2\n\nSo if yë = 2, then 2×21 = 42 → correct.\n\nSo yë = 2 is consistent.\n\nNow, does any equation confirm this?\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem-pöhualli = 2×20 = 40? Then 40×1 = 40 → which would be \"öm-pöhualli\"? But not clear.\n\nBut no indication.\n\nEquation (5): ëyi = 20 → not 2.\n\nBut perhaps yë is a different number.\n\nWait — in equation (3), \"yë-pöhualli-on-chicöme\" → yë×20 + 20\n\nIf yë = 1 → 40 → then + 1 + nähui = 41 + nähui\n\nRight: 20näuh + 280\n\nSet equal: 41 + nähui = 20näuh + 280 → nähui = 20näuh + 239\n\nFor small nähui, not possible.\n\nIf yë = 2 → 40 + 20 = 60 → 60 + 1 + nähui = 61 + nähui = 20näuh + 280 → nähui = 20näuh + 219\n\nStill large.\n\nBut no contradiction.\n\nWe may not need to resolve all.\n\nWe have:\n\n- 20 = pöhualli\n- 1 = mahtlactli\n- 14 = mäcuïl\n- 19 = mäcuïlli\n\nNow write 42 = 2×20 + 2\n\nIf we accept yë = 2, then", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8784.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "iid", + "sample_index": 0, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe are to derive the pattern step-by-step using the given equations.\n\n---\n\nStart with the equations in Nahuatl and Arammba, focusing on how numbers are formed.\n\nIn Nahuatl, we see constructions involving:\n- \"on\" = addition?\n- \"×\" = multiplication?\n- \"om\" = perhaps a possessive or a combining element?\n- \"cë\", \"öme\", \"ëyi\", \"pöhualli\", \"mahtlactli\", etc., are components.\n\nBut the real target is to interpret how numbers are built, especially in the context of multiplicative and additive expressions.\n\nLet’s examine the examples in detail.\n\n---\n\nLook at (1):\n\nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nThis appears to be:\nA × B = C\n\nBut note that “mahtlactli-on-cë” may represent (A + cë), and that the product is a compound.\n\nBut other examples suggest addition and multiplication.\n\nTry (2):\n\ncem-pöhualli × öme = öm-pöhualli\n\nThis suggests: X × Y = Z\n\nBut the left side is a product, the right side is simpler.\n\n(3):\n\nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nAddition? Left is two compounds, right is a compound.\n\n(4):\n\nmäcuïlli + öme = chicöme\n\nAddition.\n\n(5):\n\nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSo (A × B) = C\n\n(6):\n\nmäcuïlli × ëyi = caxtölli\n\nMultiplication.\n\nNow look at the last set of equations (13–16), which relate to the numbers:\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nHere, \"cen-tzontli\" appears to represent a number.\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut from (11): nimbo × fete = tarumba\n\n(8): ngámbi + asàr = tambaroy\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nThe key is to find the arithmetical pattern.\n\nLet’s try to interpret the base units.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nThis is strange: A + A = A × B → suggests A × B = A + A → so A × B = 2A → B = 2\n\nSo we infer: yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy\n\nSo A + B = C\n\nFrom (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nLet’s assume \"tàxwo\" means \"times\" or \"multiplied by\".\n\nSo: yànparo × (fete asàr) = yànparo fete\n\n\"asàr\" and \"fete\" may be components.\n\nBut from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nSo: X × (X tàxwo) = fete X tàxwo\n\nNow, compare to (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nLet’s suppose “fete” and “asàr” are components of “tambaroy”.\n\nFrom (8): ngámbi + asàr = tambaroy\n\nFrom (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo we are building numbers from components.\n\nNow (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo \"cen-\" is a number prefix.\n\nThe key might be that “cen-” is the number 1.\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAnd in (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThis suggests that “cen-” is a base number.\n\nLet’s find what \"cen-tzontli\" corresponds to.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThe structure is: cen-tzontli + compound = yànparo tarumba\n\nBut yànparo = 2 (from (7))\n\nSo: cen-tzontli + X = 2 × tarumba\n\n(11): nimbo × fete = tarumba\n\n(8): ngámbi + asàr = tambaroy\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have:\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo → implies yànparo = 2\n\nBecause if A + A = A × B → 2A = A × B → B = 2\n\nThus, yànparo = 2\n\nNow (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nLet X = yenówe\n\nThen: X × (X tàxwo) = fete X tàxwo\n\nSuppose \"X tàxwo\" means X × 2? Or \"X times\"?\n\nSimilarly, (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nyànparo = 2 → yànparo tàxwo = 2 × something?\n\nBut perhaps tàxwo means \"times\" or \"multiplied by\", and can be used in multiplication.\n\nNote (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nAssume \"fete asàr\" is a unit, and \"tàxwo\" applies to the entire expression?\n\nBut perhaps each term has a multiplier \"tāxwo\".\n\nAlternatively, this might be addition with units.\n\nBut the multiplication equations are more revealing.\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nSuppose X × (X) = fete X — no, right side is \"fete X\"\n\nBut left is X × X.\n\nUnless \"X tàxwo\" means X × 2 → then X × (2X) = 2X²\n\nRight: fete X — so 2X² = fete X → 2X = fete\n\nMaybe not.\n\nTry assigning values.\n\nSuppose that the language has a base unit.\n\nLook at (7): ngámbi + ngámbi = ngámbi × yànparo\n\n→ implies 2 ngámbi = ngámbi × yànparo → yànparo = 2\n\nSo yànparo = 2\n\nNow (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nAssume \"tāxwo\" means multiplication by 2? (from yànparo = 2)\n\nThen yànparo tàxwo = 2 × yànparo = 4?\n\nThat might be too strong.\n\nSuppose \"A tàxwo\" means A × yànparo, or A × 2.\n\nThen:\n\n(12): nimbo + (yànparo × 2) = yenówe × 2 → nimbo + 4 = 2 × yenówe\n\n(10): yenówe × (yenówe × 2) = fete × yenówe × 2\n\nSo: yenówe × (2 yenówe) = fete × (2 yenówe)\n\n→ 2 (yenówe)^2 = 2 yenówe × fete → (yenówe)^2 = yenówe × fete → yenówe = fete\n\nThus, fete = yenówe\n\nThen from (12): nimbo + 4 = 2 × yenówe\n\nSo nimbo + 4 = 2 fete\n\nNow from (11): nimbo × fete = tarumba\n\nSubstitute: (2fete - 4) × fete = tarumba → 2fete² - 4fete = tarumba\n\nNow (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut from (8): ngámbi + asàr = tambaroy\n\nWe don’t have a value for ngámbi.\n\nPerhaps “cen-tzontli” is a number, say N.\n\nWe are to find 43 and 569.\n\nLook at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nBut in Nahuatl, \"tzontli\" may be a unit, and \"on\" may mean addition.\n\nSimilarly, \"pöhualli\" may be a unit.\n\nEarlier in (1), we had mahtlactli × mahtlactli-on-cë = mäcuïl-pöhualli-om-mahtlactli\n\nBut (4): mäcuïlli + öme = chicöme → addition\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nThis implies multiplicative structure.\n\nBut the last equations are most relevant.\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis suggests the number \"cen-tzontli\" is composed of tarumba, tambaroy, fete, asàr — which may be units.\n\nBut (8): ngámbi + asàr = tambaroy\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe found fete = yenówe\n\nAnd yànparo = 2\n\nSo (12): nimbo + 4 = 2 × fete → nimbo = 2fete - 4\n\nThen tarumba = nimbo × fete = (2fete - 4) × fete = 2fete² - 4fete\n\nNow in (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut tambaroy = ngámbi + asàr\n\nWe don’t know ngámbi or asàr.\n\nBut perhaps “cen-tzontli” is a simple number, like 1.\n\nBut we have (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo cen-xiquipilli is a number, possibly another.\n\nAlso, in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSo: cen-tzontli + (compound) = 2 × tarumba\n\nBut from above, tarumba = 2fete² - 4fete\n\nSo right side = 2 × (2fete² - 4fete) = 4fete² - 8fete\n\nLeft side: cen-tzontli + X = 4fete² - 8fete\n\nIf cen-tzontli is a number, say C, then C + X = 4fete² - 8fete\n\nWe still don’t know X.\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf that is an addition, then cen-tzontli = (tarumba) + (tambaroy) + (fete) + (asàr)\n\nBut tambaroy = ngámbi + asàr\n\nSo = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr\n\nThis is messy.\n\nAnother possibility: the compound \"cen-tzontli\" represents a number, and the base unit is 1.\n\nIn many such olympiad problems, the structure is based on multiplication and addition of units, where numbers are defined recursively.\n\nLook at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n\"on\" likely means addition.\n\nSo yë-tzontli + näuh-pöhualli + caxtölli + cë = ndamno\n\nBut in Nahuatl, \"mahtlactli\" might be 1, \"pöhualli\" might be 20, etc.\n\nIn Classical Nahuatl, there are base units:\n\n- 1 = mahtlactli\n- 20 = pöhualli\n- 400 = cem-pöhualli (or something)\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nmahtlactli-on-cë → mahtlactli + cë → possibly (1 + 1) = 2?\n\n1 × 2 = 2?\n\nBut left = 1 × (1 + cë)\n\nRight = mäcuïl-pöhualli-om-mahtlactli\n\n\"mäcuïl\" might be 10?\n\n\"pöhualli\" is 20?\n\nSo mäcuïl-pöhualli = 10×20 = 200? Or 10+20?\n\nBut it has \"om-mahtlactli\" → so component.\n\nNot clear.\n\nBut from (4): mäcuïlli + öme = chicöme\n\nmäcuïlli = 10?\n\nöme = 1?\n\nchicöme = 11?\n\nThen (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nyë-pöhualli-on-chicöme = yë + 20 + 11 = ?\n\nmahtlactli-on-nähui = 1 + nähui\n\nright = näuh-pöhualli-on-cë = 20 + cë\n\nNot clear.\n\nBut look at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n\"tzontli\" may be 1 or 20.\n\nIn Nahuatl, \"tzontli\" often means 1.\n\n\"pöhualli\" = 20\n\n\"caxtölli\" = 100?\n\n\"cë\" = 1\n\nSo \"yë\" may be 2.\n\nSo yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = 2 + 20 + 100 + 1 = 123?\n\nThen ndamno = 123?\n\nBut we are to find 43 and 569 in Arammba.\n\nFrom the Arammba equations, perhaps \"cen-\" is 1, and we can find the value of \"tzontli\" or other units.\n\nGo back to (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf cen-tzontli = 1, then 1 = tarumba + tambaroy + fete + asàr → impossible unless values are less than 1.\n\nSo not additive.\n\nPossibility: \"cen-tzontli\" is a compound that equals a number, and the components are units with values.\n\nFrom (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nAlso, (14): cen-tzontli-on-... = yànparo tarumba\n\nSo \"cen-tzontli\" may represent a number, and the \"on\" part is addition.\n\nBut in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSo cen-tzontli + compound = 2 × tarumba\n\nBut from earlier, tarumba = 2fete² - 4fete\n\nAnd if we assume that fete is a unit with value, say f, then tarumba = 2f² - 4f\n\nThen the right side is 2(2f² - 4f) = 4f² - 8f\n\nLeft side: C + D = 4f² - 8f, where C = cen-tzontli\n\nBut we also have from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSo C = (2f² - 4f) + tambaroy + f + asàr\n\nToo many unknowns.\n\nAnother idea: perhaps \"cen-\" is 1, and \"tzontli\" is a value.\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nAssume the units:\n\n- yë = 2\n-", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10149.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "iid", + "sample_index": 1, + "output": "We are given several equations in Nahuatl and Arammba, and we are to derive how to express the numbers 43 and 569 in Arammba.\n\nWe are to solve (c): Write out in Arammba: 43; 569.\n\nLet’s proceed step by step using the provided equations.\n\n---\n\nFirst, analyze the equations to detect number patterns.\n\n### Step 1: Look for multiplication or addition patterns.\n\n#### Nahuatl equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ This looks like: A × A = B \nNote: \"mahtlactli-on-cë\" may be a noun, \"×\" is multiplication.\n\nBut observe: \n(4) mäcuïlli + öme = chicöme \n→ Addition of two units gives a composite.\n\n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nThese suggest multiplication patterns.\n\nAlso: \n(2) cem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × öme = öm-pöhualli → perhaps öme = 1, cem-pöhualli × 1 = öm-pöhualli \nBut cem and öm look similar — maybe a pattern of multiplication by 1?\n\n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ addition.\n\nNow, equations (13) and (14) link structured forms.\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo \n\nNote: In (15): cen-tzontli = tarumba tambaroy fete asàr \nThis suggests that \"cen-tzontli\" is a unit that equals a sum of components — possibly representing a number.\n\nSimilarly, (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThe key might be that \"cen-\" is a numeral base.\n\nIn many indigenous numeral systems, \"cen\" represents 100, and \"tzontli\" or \"xiquipilli\" could be 10 or 1.\n\nLook at (15): cen-tzontli = tarumba tambaroy fete asàr\n\nFrom equation (8): ngámbi + asàr = tambaroy \n→ so asàr is part of tambaroy.\n\nThus, tambaroy = ngámbi + asàr \nSo tarumba tambaroy fete asàr = tarumba + (ngámbi + asàr) + fete → total of several terms.\n\nBut (15) says cen-tzontli = tarumba tambaroy fete asàr \nSo if \"cen-tzontli\" represents a compound number, perhaps this is 100 × 10 = 1000?\n\nAlternatively, in some systems, \"cent\" = 100, \"tzontli\" = 10 → 100 × 10 = 1000.\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo \nIf xiquipilli = 1 → then cen-xiquipilli = 100\n\nBut in (16): it equals a sum of components.\n\nFrom (11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nSo long-term, the structure may encode numbers via combinations.\n\nNow, in Arammba, we have:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ ngámbi × yànparo = 2 × ngámbi \nSo yànparo = 2 → doubling structure.\n\nIn (8): ngámbi + asàr = tambaroy \n→ likely 1 + 1 = 2 → so ngámbi = 1, asàr = 1?\n\nBut if ngámbi = 1, then from (7): 1 + 1 = 1 × 2 → 2 = 2 → consistent.\n\nSo ngámbi = 1, yànparo = 2.\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ This may mean: (2) + (fete) = 2 fete → suggests fete is additive identity? Or fete = 1?\n\nPossibly \"tàxwo\" is a marker meaning \"times\" or \"in multiplication\".\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ If \"yenówe tàxwo\" is a unit, and yenówe × (yenówe tàxwo) = fete yenówe tàxwo \nThis suggests: (x) × (x) = fete x \n→ x² = fete × x → implies x = fete \nSo fete = x → fete = yenówe \n→ So fete = yenówe\n\n(11) nimbo × fete = tarumba → so nimbo × yenówe = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe (since yànparo tàxwo = 2) → so yenówe = nimbo + 2\n\nBut from above, fete = yenówe → so fete = nimbo + 2\n\nThen from (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba\n\nLet’s suppose nimbo is a number. Let x = nimbo.\n\nThen x × (x + 2) = tarumba\n\nAlso from (12): x + 2 = yenówe\n\n(15): cen-tzontli = tarumba tambaroy fete asàr \nWe already see tambaroy = ngámbi + asàr = 1 + 1 = 2 \nasàr = 1 → fete = 1? But above fete = yenówe = x+2 → conflict?\n\nWait. In (8): ngámbi + asàr = tambaroy\n\nAssume ngámbi = 1 → then 1 + asàr = tambaroy\n\nIf that equals 2, then asàr = 1.\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nWe deduced fete = yenówe\n\nSo fete = yenówe\n\nNow (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \nyànparo tàxwo = 2 → so nimbo + 2 = yenówe → so fete = yenówe → fete = nimbo + 2\n\nThen tarumba = nimbo × (nimbo + 2)\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\n= [nimbo(nimbo+2)] + [1+1] + [nimbo+2] + 1 \n= n(n+2) + 2 + (n+2) + 1 = n² + 2n + 2 + n + 2 + 1 = n² + 3n + 5\n\nBut cen-tzontli is a single unit. If it is a number, and likely 100 × 10 = 1000, or 100 × something?\n\nIn many Nahuatl systems, numbers are built on base 20.\n\nBut Arammba shows a different pattern.\n\nNow look at (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nxiquipilli in Nahuatl is often 1 → so cen-xiquipilli = 100 × 1 = 100\n\nSimilarly, in (16), it is expressed as a sum: weremeke + tarumba + nimbo + yànparo\n\nSo the decomposition may be that 100 = weremeke + tarumba + nimbo + yànparo\n\nLet’s suppose that the components represent values.\n\nWe already have: yànparo = 2\n\nSuppose that the components are numbers.\n\nLet’s try to assign values.\n\nSuppose that:\n\n- ngámbi = 1 \n- yànparo = 2 \n- asàr = 1 \n- fete = yenówe = nimbo + 2 \n- tarumba = nimbo × (nimbo + 2)\n\nAnd from (16): cen-xiquipilli = 100 = weremeke + tarumba + nimbo + yànparo\n\nThat is: \nweremeke + [nimbo(nimbo+2)] + nimbo + 2 = 100 \n→ weremeke + n(n+2) + n + 2 = 100 \n→ weremeke + n² + 2n + n + 2 = 100 \n→ weremeke + n² + 3n + 2 = 100 \n→ weremeke = 98 - n² - 3n\n\nweremeke must be positive → n² + 3n < 98\n\nTry small n:\n\nn = 1 → weremeke = 98 - 1 - 3 = 94 \nn = 2 → 98 - 4 - 6 = 88 \nn = 3 → 98 - 9 - 9 = 80 \nn = 4 → 98 - 16 - 12 = 69 \nn = 5 → 98 - 25 - 15 = 58 \nn = 6 → 98 - 36 - 18 = 44 \nn = 7 → 98 - 49 - 21 = 28 \nn = 8 → 98 - 64 - 24 = 8 \nn = 9 → 98 - 81 - 27 = -10 → invalid\n\nSo valid for n ≤ 8\n\nWe need more constraints.\n\nNow go to (13) and (14)\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nLook at (14): cen-tzontli-on-... = yànparo tarumba\n\nyànparo = 2, tarumba = n(n+2)\n\nSo the entire right-hand side is 2 + n(n+2)\n\nBut left-hand side: cen-tzontli-on-... which may represent a number.\n\nIn Nahuatl, \"cen\" may be 100, \"tzontli\" = 10 → 1000?\n\nAlso, cem-pöhualli-om-mahtlactli-om-öme → from (2): cem × öme = öm-pöhualli — perhaps cem = 1, öme = 1 → 1 × 1 = 1\n\nSo perhaps the compound is 100 × 10 = 1000? (cen-tzontli = 1000)\n\nThen the equation is: 1000 = 2 + n(n+2)\n\n→ n(n+2) = 998\n\nTry integers: \nn² + 2n - 998 = 0 → discriminant = 4 + 3992 = 3996 → not square → no integer n\n\nNot possible.\n\nAlternative: maybe \"cen-tzontli\" is not 1000, but 100.\n\nSuppose cen-tzontli = 100\n\nThen centzontli-on-... = 100 → equals yànparo tarumba = 2 + n(n+2)\n\nSo 100 = 2 + n(n+2) → n(n+2) = 98\n\nn² + 2n - 98 = 0 \ndiscriminant = 4 + 392 = 396 → not square → not integer\n\nTry n=6: 6×8=48 \nn=7: 7×9=63 \nn=8: 8×10=80 \nn=9: 9×11=99 → too big → 99 > 98 → no solution.\n\nNo match.\n\nTry (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nFrom earlier: \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli\n\nSuppose mäcuïlli = 1 → then 1 × ëyi = caxtölli → caxtölli = ëyi\n\nThen (5) → mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n→ (A) × (ëyi) = B\n\nBut hard to parse.\n\nGo back to the Arammba equations with multiplication.\n\n(7) ngámbi + ngámbi = ngámbi × yànparo → 1+1 = 1×2 → 2=2 → consistent.\n\n(8) ngámbi + asàr = tambaroy → 1+1=2 → so asàr = 1\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ 2 + fete = 2 fete → implies fete = 2\n\nSo fete = 2\n\nBut earlier (10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ yenówe × (yenówe) = fete × (yenówe) → so yenówe² = fete × yenówe → if yenówe ≠ 0 → yenówe = fete\n\nSo fete = yenówe\n\nThus yenówe = 2\n\nNow from (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = 2 → so nimbo = 0 → not possible.\n\nContradiction!\n\nTherefore, our assumption must be wrong.\n\nWhat if \"tàxwo\" is not a multiplier, but a kind of unit or \"branch\"?\n\nConsider (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nPerhaps it means: (yànparo) times (tàxwo) + (fete) times (asàr) = yànparo times fete\n\nSo (2) × t + (f) × 1 = 2 × f → 2t + f = 2f → 2t = f\n\nSo f = 2t\n\n(10) yenówe × (yenówe tàxwo) = fete (yenówe tàxwo)\n\nSo (x) × (x t) = f × (x t) → x² t = f x t → if x t ≠ 0 → x = f\n\nSo f = x → f = yenówe\n\nTherefore f = x = yenówe\n\nFrom above, f = 2t → so yenówe = 2t\n\n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2t = (2t) t = 2t²\n\nSo nimbo = 2t² - 2t = 2t(t - 1)\n\n(11) nimbo × fete = tarumba → nimbo × f = tarumba \nBut f = 2t, so tarumba = nimbo × 2t = 2t × 2t(t-1) = 4t²(t-1)\n\nNow go to (15): cen-tzontli = tarumba + tambaroy + fete + asàr \ntambaroy = ngámbi + asàr = 1 + 1 = 2 \nfete = 2t \nasàr = 1 \ntarumba = 4t²(t-1) \nSo cen-tzontli = 4t²(t-1) + 2 + 2t + 1 = 4t³ - 4t² + 2t + 3\n\nFrom (16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo\n\nyànparo = 2\n\nWe assume cen-xiquipilli = 100\n\nSo:\n\n100 = weremeke + 4t²(t-1) + 2t(t-1) + 2 \n= weremeke + 4t³ - 4t² + 2t² - 2t + 2 \n= weremeke + 4t³ - 2t² - 2t + 2 \n\nSo weremeke = 100 - (4t³ - 2t²", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9215.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "iid", + "sample_index": 2, + "output": "We are given two linguistic systems: Nahuatl and Arammba, with equations showing operations and their results. We are to decode the meaning of the numbers **43** and **569** in Arammba, based on the patterns in the given equations.\n\n---\n\nStep 1: Identify possible number representations.\n\nWe look for equations involving numeric results or combinations that might represent numerical values.\n\nIn the Nahuatl equations, the forms often involve compound elements, and operations like addition, multiplication, or mixing of terms with affixes.\n\nBut our goal is to **translate 43 and 569 into Arammba**.\n\nWe are told that (13) and (14) and (15) and (16) show a mapping between Nahuatl and Arammba, likely involving structural parallels.\n\nThus, we look for patterns in the equations that could represent arithmetic or number construction.\n\n---\n\nStep 2: Examine the Nahuatl equations for numeric patterns.\n\nLook at equation (1): \n**mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli**\n\nThis resembles multiplication: A × B = C \nPossibly \"mahtlactli\" = 1, or a unit; \"on-cë\" may be a modifier.\n\nBut see equation (3): \n**yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë**\n\nThis is addition.\n\nEquation (4): **mäcuïlli + öme = chicöme**\n\nLikely, 1 + 1 = 2 (with a compound form).\n\nEquation (5): **mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui**\n\nAgain, multiplication.\n\nBut most importantly:\n\nEquation (13): \n**yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno**\n\nNote: The left-hand side is a compound noun. The right is \"ndamno\".\n\nEquation (14): \n**cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba**\n\nEquation (15): \n**cen-tzontli = tarumba tambaroy fete asàr**\n\nEquation (16): \n**cen-xiquipilli = weremeke tarumba nimbo yànparo**\n\nNow focus on (15): \n**cen-tzontli = tarumba tambaroy fete asàr**\n\n→ This suggests that \"cen-tzontli\" is a number, and its value is expressed in terms of components.\n\nSimilarly, (14): \n**cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba**\n\n\"cen-tzontli\" is likely a base number (perhaps 1), and the rest are derived.\n\nBut equation (15) says \"cen-tzontli = tarumba tambaroy fete asàr\"\n\n→ So 1 = tarumba + tambaroy + fete + asàr? That can’t be — quantities can’t be additive.\n\nWait: perhaps \"cen-tzontli\" is a number, and the right-hand side is a decomposition.\n\nBut (15) gives **cen-tzontli = tarumba tambaroy fete asàr**\n\nSo, likely, **cen-tzontli** is a single unit meaning 1, and equals the compound form of tarumba + tambaroy + fete + asàr — but that would be a sum.\n\nAlternatively, perhaps \"cen-tzontli\" is 1, and appears in expressions for numbers.\n\nSimilarly, (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo \"cen-xiquipilli\" is equal to a compound of weremeke, tarumba, nimbo, yànparo.\n\nNow, which of these are likely number units?\n\nFrom (8): ngámbi + asàr = tambaroy \nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nFrom (11): nimbo × fete = tarumba \nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nIn Arammba:\n\nLet’s look at (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × ngámbi = ngámbi × yànparo → so 2 = yànparo? \nThis suggests multiplicative identity.\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \nSo: 2 × a = a × b → implies 2 = b? \nThus, **yànparo = 2**\n\nAlternatively, if yànparo is a unit, then multiplication by yànparo might mean multiplication by 2.\n\nSimilarly, (8): ngámbi + asàr = tambaroy \n→ ngámbi + asàr = tambaroy\n\nBut from (7): ngámbi + ngámbi = ngámbi × yànparo \nIf ngámbi = 1, then 1 + 1 = 1 × yànparo → 2 = yànparo → so yànparo = 2\n\nSo in Arammba, **yànparo = 2**\n\nNow consider (12): nimbo + yànparo tàxwo = yenówe tàxwo \n\"tàxwo\" may indicate \"plus\", like a summation operator.\n\nSo: nimbo + (yànparo) tàxwo = yenówe tàxwo\n\nThat is: nimbo + (2) = yenówe\n\nSo if \"yànparo\" = 2, then **yenówe = nimbo + 2**\n\nEquation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo: (yenówe) × (yenówe) = fete yenówe\n\nSo: (a) × (a) = fete a → implies that \"a²\" = fete a\n\nSo multiplying a number by itself gives \"fete a\"\n\nThus, the square of a number is expressed as \"fete a\"\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → so (yenówe)² = fete yenówe\n\nNow from (12): nimbo + 2 = yenówe → so yenówe = nimbo + 2\n\nThen, (nimbo + 2)² = fete (nimbo + 2)\n\nNow equation (11): nimbo × fete = tarumba \nSo nimbo × fete = tarumba\n\nBut fete is likely a derived form related to square.\n\nBut tarumba may be a compound.\n\nNow go to (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = tarumba + tambaroy + fete + asàr?\n\nBut earlier, tambaroy = ngámbi + asàr\n\nSo perhaps we can write:\n\nLet’s try to assign values.\n\nAssume:\n\n- ngámbi = 1 \nThen (7): 1 + 1 = 1 × yànparo → 2 = yànparo → yànparo = 2 \n→ So \"yànparo\" means 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy\n\nWe don’t know asàr.\n\nBut now (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe\n\n(10): yenówe × yenówe = fete yenówe → (nimbo + 2)² = fete (nimbo + 2)\n\n(11): nimbo × fete = tarumba → nimbo × [(nimbo + 2)²] = tarumba\n\nNow from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nLet’s suppose that “cen-tzontli” represents a value, say 1.\n\nSo if cen-tzontli = 1, then:\n\n1 = tarumba + tambaroy + fete + asàr\n\nBut tarumba is a large product: nimbo × (nimbo+2)² → very large\n\nfete is (nimbo+2)² → also large\n\ntambaroy = 1 + asàr → possibly small\n\nasàr → unknown\n\nSo sum is large → contradiction.\n\nTherefore, the equation (15) is not giving a sum of values — it’s a **header or structural decoding**.\n\nAlternative idea: perhaps the compound on the left side represents a number, and the right side is its name.\n\nSo in (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nThis is a number = \"ndamno\"\n\nSimilarly, (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nHere, a compound = yànparo tarumba\n\nWe know from earlier that yànparo = 2\n\nSo the right-hand side is \"2 tarumba\"\n\nThus, the compound on the left is equal to “2 × tarumba”\n\nSimilarly, (15): cen-tzontli = tarumba tambaroy fete asàr → so “cen-tzontli” = tarumba + tambaroy + fete + asàr\n\nAnd (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo “cen-xiquipilli” = weremeke + tarumba + nimbo + yànparo\n\nBut “cen” might be a base — like 1.\n\nSo suppose:\n\n- cen-tzontli = 1 → (15) → 1 = tarumba + tambaroy + fete + asàr \nBut as above, products are large → contradiction.\n\nInstead, maybe “cen” is not 1, or the full expression is not a sum.\n\nAnother idea: perhaps \"cen\" is a base, and the structure represents multiplication.\n\nFor example, in (14):\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThe “on” and “om” may indicate operations.\n\n“on” might mean “plus”, “om” might mean “times”.\n\nIn Nahuatl, “on” is used in addition, “om” in multiplication.\n\nSo in (1), “mahtlactli-on-cë × mahtlactli” → addition then multiplication?\n\nBut the equation is written as A-on-B × C = D\n\nThis is ambiguous.\n\nBut in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ A-on-B + C-on-D = E-on-F → suggests “on” is addition.\n\nSimilarly, “om” is multiplication.\n\nSo in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nBreak it down: \ncen-tzontli-on-cem-pöhualli = A \nom-mahtlactli = B \nom-öme = C\n\nSo: (cen-tzontli-on-cem-pöhualli) × (mahtlactli) × (öme) = yànparo tarumba\n\nBut we don’t know meanings.\n\nBut we know from earlier that yànparo = 2\n\nSo this whole product = 2 × tarumba\n\nSimilarly, in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis seems to be a single number = \"ndamno\"\n\nIn the target, we need to write 43 and 569 in Arammba.\n\nSo likely, numbers are expressed by combining base units.\n\nWe need to find how numbers are constructed.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × 1 = 1 × 2 → consistent if yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ 1 + asàr = tambaroy → so tambaroy = 1 + asàr\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (yànparo) = yenówe → nimbo + 2 = yenówe\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (nimbo + 2) × (nimbo + 2) = fete (nimbo + 2)\n\nSo square of a number = fete (that number)\n\nFrom (11): nimbo × fete = tarumba \n→ nimbo × (nimbo+2)² = tarumba\n\nNow go to (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf this means that “cen-tzontli” is equal to the sum of those compounds, and we know values, then:\n\nLet’s suppose that:\n\n- asàr = 1 \nThen from (8): tambaroy = 1 + 1 = 2 \nfete = (nimbo + 2)² \ntarumba = nimbo × (nimbo + 2)² \nThen cen-tzontli = tarumba + tambaroy + fete + asàr\n\n= nimbo × (nimbo+2)² + 2 + (nimbo+2)² + 1 \n= (nimbo+2)² (nimbo + 1) + 3\n\nNow we also have equation (16): \ncen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo it's a sum of weremeke + tarumba + nimbo + yànparo\n\nBut we don’t know weremeke.\n\nBut note: all of this applies to the number systems.\n\nPerhaps the number representations are based on units:\n\n- 1 = ngámbi \n- 2 = yànparo \n- square of a number = fete (number) \n- product of nimbo and fete = tarumba\n\nWe are to write 43 and 569 in Arammba.\n\nSo we need a way to express arbitrary numbers.\n\nWe know:\n\n- ngámbi = 1 \n- yànparo = 2 \n- if a number is x, then x² = fete x \n- so x² can be written as fete x\n\nAlso, from (12): nimbo + 2 = yenówe → so yenówe = nimbo + 2\n\nLet’s suppose that nimbo represents 1 → then yenówe = 3\n\nThen: \nfete = 3² = 9 \ntarumba = 1 × 9 = 9 \ntambaroy = 1 + asàr → if asàr = 1 → tambaroy = 2 \nasàr = 1\n\nThen (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 9 + 2 + 9 + 1 = 21\n\nSo if “cen-tzontli” = 21\n\nBut if instead cen-tzontli is 1, it doesn’t work.\n\nBut perhaps “cen-tzontli” is not a number, it’s a unit.\n\nWait — in (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nIf we assume that values are additive, and the right-hand side is the expression for the number, then:\n\nLet’s set:\n\n- nimbo = 1 \nThen yànparo = 2 \nyenówe = 3 \nfete = 3² = 9 \ntarumba = 1 × 9 = 9 \nasàr = 1 \ntambaroy = 1 + 1 = 2\n\nNow (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 9 + 2 + 9 + 1 = 21\n\nSo \"cen-tzontli\" = 21\n\nSimilarly, (16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo = weremeke + 9 + 1 + 2 = weremeke + 12\n\nSo if \"cen-xiquipilli\" = some value, it's weremeke + 12\n\nBut we don’t know weremeke.\n\nNow (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis might be a specific number.\n\nWe don’t know what \"ndamno\" is.\n\nSimilarly, (14): a compound = yànparo tarumba → which is 2 × 9 = 18\n\nSo the left side is 18\n\nBut its components are not clear.\n\nWe need to find a way to build any number.\n\nPossibility: the language uses a base system where:\n\n- 1 = ngámbi \n- 2 = yànparo \n- 3 = yenówe → since yenówe = nimbo + 2 = 1 + 2 = 3 \n- 4 = ? \n- 5 = ? \n- etc.\n\nSquare of x = fete x \nSo 3² = fete 3 = 9\n\nThen 4² = fete 4\n\nBut how to get 4?\n\n4 = 2 + 2 = yànparo + yànparo\n\nSo 4 = yànparo + yànparo\n\nSimilarly, 5 = yànparo + ngámbi + ngámbi = 2 + 1", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10937.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "iid", + "sample_index": 3, + "output": "We are given several equations in Nahuatl and Arammba, and we are to determine how to write the numbers **43** and **569** in Arammba.\n\nWe are instructed to use the examples to infer linguistic patterns, especially focusing on how numbers are formed in Arammba.\n\n---\n\n### Step 1: Analyze the given equations to identify number patterns.\n\nWe have:\n\n#### Nahuatl equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo \n\n#### Arammba equations:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n(8) ngámbi + asàr = tambaroy \n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n(11) nimbo × fete = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n\n---\n\nWe now try to understand what the linguistic pattern is.\n\n---\n\n### Step 2: Identify base number units.\n\nIn Arammba:\n\n- **ngámbi** appears in (7): ngámbi + ngámbi = ngámbi × yànparo \n → This suggests ngámbi might be 1? But it's repeated on both sides.\n\n- (8): ngámbi + asàr = tambaroy \n If ngámbi = 1, asàr = 1? Then tambaroy = 2? \n But (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n This resembles addition: (a + b) = a fete if b is “asàr tàxwo”?\n\nAlso, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ Multiplication: product = fete of (yenówe) with (yenówe tàxwo)? \nThis suggests that “×” is marked with “tāxwo” and the result is a noun phrase with “fete”.\n\nNote: in (11): nimbo × fete = tarumba \n→ Again, multiplication with “fete” gives “tarumba”\n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ Addition: nimbo + yànparo tàxwo = yenówe tàxwo\n\nAlso, (15): cen-tzontli = tarumba tambaroy fete asàr \n→ This is a number expression built from “tarumba”, “tambaroy”, “fete asàr”\n\nBut (15) has: cen-tzontli = tarumba tambaroy fete asàr\n\nWe might interpret “cen-tzontli” as a number.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe don’t have full mapping, but we can notice that the Nahuatl equations use compounds of units.\n\nA key idea: the Arammba system may use **addition** and **multiplication** with specific markers.\n\nLet’s look at the **Arabic numerals**:\n\nWe are to write **43** and **569** in Arammba.\n\nWe need a way to decompose numbers into base components.\n\nPossibility: Arammba uses a **positional system** or **additive components**.\n\nLook at (8): ngámbi + asàr = tambaroy \n→ So if ngámbi = 1, asàr = 2, then tambaroy = 3? \nBut that would make tambaroy = 3.\n\nBut (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ This is addition, with “tāxwo” meaning “times” or “for”? \n\"yànparo tàxwo\" might mean \"yànparo times something\"\n\nBut also, the pattern in (9): (A + B) = A fete \nThat may mean that “fete” is a marker for addition, and “tāxwo” is a multiplier?\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ So if we interpret “×” as “tāxwo” and result is “fete × the term”, then this is multiplication where result is marked with “fete”.\n\nSimilarly, in (11): nimbo × fete = tarumba\n\nSo the “×” operation is written with “tāxwo” or some modifier.\n\nSo likely:\n\n- “a × b” = “a tāxwo b” or “a tāxwo b” = “fete a tāxwo b”\n\nBut (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ So multiplication of yenówe and yenówe tàxwo gives “fete yenówe tàxwo” — so the “tāxwo” is attached to the second term.\n\nPossibility: “tāxwo” is a multiplier, and “fete” is the result marker.\n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ Addition: nimbo + (yànparo tāxwo) = yenówe tāxwo\n\nSo “tāxwo” may be a marking for a multiplication or unit.\n\nNow look at (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis is likely a value assigned to a compound.\n\nWe don’t know the value yet, but perhaps we can find analogs.\n\nCompare with equation (13):\n\nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may be a representation of a number.\n\nBut we don’t have equivalents directly.\n\nNow, look at equations involving combinations.\n\nWe are to find 43 and 569 in Arammba.\n\nWe need to find how numbers are built.\n\nTry to extract base values.\n\nFrom (8): ngámbi + asàr = tambaroy \nIf \"tambaroy\" is a unit, and this is addition, then:\n\nLet ngámbi = 1 → asàr = ? → tambaroy = ?\n\nBut from (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 1 + 1 = 1 × yànparo \n→ 2 = 1 × yànparo ⇒ yànparo = 2\n\nSo yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ 1 + asàr = tambaroy \n→ tambaroy = 1 + asàr\n\nBut we don’t know asàr.\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (2 × something) = yenówe × something\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ so (a × b) = fete a b\n\nSo multiplication gives a term with “fete” and the item.\n\nIn (11): nimbo × fete = tarumba \nSo nimbo × fete = tarumba\n\nNow, we don’t know fete value.\n\nBut suppose that “fete” is the multiplier unit.\n\nThen “a × fete” means a times fete.\n\nBut (11) says nimbo × fete = tarumba → so tarumba = nimbo × fete\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (2 × tāxwo) = yenówe × tāxwo\n\nNow, it's very likely that:\n\n- “tāxwo” is a multiplier, and “fete” might be another multiplier.\n\nLet us suppose that:\n\n- yànparo = 2 \n- ngámbi = 1 \n- ngámbi + asàr = tambaroy → 1 + asàr = tambaroy\n\nAlso, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ 2×tāxwo + fete×asàr tāxwo = 2 fete\n\nSo (2 × tāxwo) + (fete × asàr tāxwo) = 2 fete\n\nIf this is addition, and right-hand side is 2 fete, then the left-hand side must sum to that.\n\nLet us suppose that multiplication is commutative and that “fete” is a unit multiplier.\n\nNow, try to find the value of “fete”.\n\nIn (11): nimbo × fete = tarumba \n→ tarumba = nimbo × fete\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli is composed of tarumba, tambaroy, fete asàr — perhaps additive?\n\nSo it may be that **cen-tzontli** is a large number, and it's built as a sum of:\n\n- tarumba = nimbo × fete \n- tambaroy = 1 + asàr \n- fete asàr\n\nSo cen-tzontli = (nimbo × fete) + (1 + asàr) + (fete × asàr)\n\nBut this is confusing without values.\n\nNow, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis suggests cen-tzontli is multiplied or added to other terms?\n\nBut it's not clear.\n\nWait — the structure is similar to Nahuatl.\n\nIn Nahuatl, (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nThe structure has A-on-B × A = C\n\nWe may be missing a parallel.\n\nBut in Arammba, (7): ngámbi + ngámbi = ngámbi × yànparo \nSo addition of ngámbi with itself gives multiplication with yànparo.\n\nBut earlier: if ngámbi = 1 → 1 + 1 = 1 × yànparo → 2 = yànparo → yànparo = 2\n\nConfirmed.\n\nFrom (8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy\n\nNow, (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 × tāxwo) + (fete × asàr tāxwo) = 2 fete\n\nLeft side is addition of two terms.\n\nBut what if we suppose that “tāxwo” is the same as “fete”? Or that it's a multiplier?\n\nSuppose that “fete” is a unit, and “tāxwo” is another.\n\nBut we can try to find the most plausible base value.\n\nWe have:\n\n- yànparo = 2 \n- ngámbi = 1 \n- tambaroy = 1 + asàr \n- (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ so (a × a tāxwo) = fete a tāxwo \n→ i.e., a² × tāxwo = fete a tāxwo \n\nIf tāxwo is a base multiplier, then perhaps a × tāxwo means a × 2?\n\nWait — if tāxwo = 2, then a × tāxwo = 2a\n\nSo (a × a tāxwo) = a × (a × 2) = 2a²\n\nRight-hand side: fete a tāxwo = fete a × 2\n\nSo 2a² = fete × 2a → a = fete\n\nSo fete = a\n\nSo fete = the number itself?\n\nSo e.g., if a = 1, then yenówe × yenówe tàxwo = fete × 1 tāxwo → 2(1)² = 2 → fete × 2 = 2 → fete = 1\n\nSo fete = 1\n\nSimilarly, if a = 2 → 2(4) = 8; fete × 4 = 8 → fete = 2\n\nYes! So fete = a\n\nSo the value of “fete” is the number of yenówe.\n\nSo “fete” is a tagging, not a base value.\n\nThus, “yenówe” is a number, and “fete” is a type of multiplication element.\n\nBut we need to know how numbers are expressed.\n\nNow go to (11): nimbo × fete = tarumba\n\nWe don’t know nimbo or tarumba.\n\nBut (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nyànparo = 2 → yànparo tàxwo = 2 × tāxwo\n\nSuppose tāxwo = 2 → then yànparo tàxwo = 4\n\nThen (12): nimbo + 4 = yenówe × 2\n\nNow, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nWith tāxwo = 2 → (yenówe × 2yenówe) = fete (yenówe × 2)\n\nSo (2y²) = fete (2y) → y = fete\n\nSo again, fete = y\n\nSo we can’t get absolute values.\n\nBut go to (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe interpret this as: cen-tzontli = tarumba + tambaroy + (fete × asàr)\n\nBecause it's a sum of elements.\n\nFrom (11): tarumba = nimbo × fete\n\nFrom (8): tambaroy = 1 + asàr\n\nSo cen-tzontli = (nimbo × fete) + (1 + asàr) + (fete × asàr)\n\nNow, suppose that fete = 1 (from earlier derivation when a=1)\n\nThen tarumba = nimbo × 1 = nimbo\n\ntambaroy = 1 + asàr\n\nfete × asàr = 1 × asàr = asàr\n\nSo cen-tzontli = nimbo + 1 + asàr + asàr = nimbo + 1 + 2asàr\n\nBut from (12): nimbo + 4 = yenówe × 2\n\nAnd from (10) with y=1: 1×2 = 2 = fete 1×2 → fete = 1 → ok\n\nSo suppose that \"yenówe\" is a base number.\n\nTry to see if we can find a value.\n\nBut we need to find 43 and 569.\n\nNotice the equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAnd from (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis may mean that cen-tzontli is being multiplied or used in a compound.\n\nAlternatively, perhaps the expression \"centzontli\" is a number word.\n\nIn many systems, \"cent\" means 100.\n\nIn Nahuatl, \"tzontli\" may mean \"ten\", or something.\n\nBut in Arammba, \"cen-tzontli\" may mean 100.\n\nAlso, (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo cen-xiquipilli is a number.\n\nWe may assume that:\n\n- \"cen-tzontli\" = 100 \n- \"cen-xiquipilli\" = 100 × something\n\nIn (15), cen-tzontli = tarumba tambaroy fete asàr\n\nSo 100 = tarumba + tambaroy + fete × asàr\n\nNow from (11): tarumba = nimbo × fete\n\nSo 100 = (nimbo × fete) + (1 + asàr) + (fete × asàr)\n\n= nimbo × fete + 1 + asàr + fete × asàr\n\nThis is one equation.\n\nFrom (12): nimbo + 4 = 2 × yenówe → yenówe = (nimbo + 4)/2\n\nFrom (10): when we plug in, we get consistency if fete = yenówe.\n\nFrom (10): y × y t", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10438.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "iid", + "sample_index": 0, + "output": "Step 1: Analyze the given sentences to identify patterns in Kunuz Nubian structure.\n\nLook at sentence 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"kanarri\" → buy) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n\nSo, the verb is \"kanarriːcciːg\" (buy), followed by the object \"kamiːg\", and a prepositional phrase \"jaːnticcirsu\" (for the neighbours).\n\nSentence 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = am buying \n- \"ajaːnirri\" = the necklaces \n\nHere, the present tense of \"buy\" is \"beyyeːcciːg\", and object is \"ajaːnirri\".\n\nSentence 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"kadeːcciːg\" = stole (past of \"kadeː\" → steal) \n- \"maːgtirsu\" = for the young man \n\nSo, the verb is \"kadeːcciːg\", object \"maːgtirsu\" is the indirect object (for whom?).\n\nIn sentence 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress \n\nSo verb is \"kadeːg\" (repair), object is \"allesu\" (the dress).\n\nSentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men \n- \"darbadki\" = will give \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" is missing — but from other cases, we can infer direction.\n\nWait — only \"biticcirra\" is object, then no prepositional phrase. But in sentence 3, it says \"to the dogs\" is implied.\n\nCheck sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = the owner? \n\"argi\" = give \n\"kamgi\" = the camels \n\"deːccirsa\" = to the thief?\n\n\"deːccirsa\" likely means \"to the thief\" (cf. sentence 7: \"tirt iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" → \"tirsa\" = to the thief)\n\nTherefore, suffixes like \"-irra\", \"-bki\", \"-tirsu\", \"-tirsa\" indicate direction (\"to\").\n\nStep: Identify the verb roots.\n\nFrom sentence 1: \"kanarriːcciːg\" → buy → \"kanarri\" root + past tense suffix \nSentence 5: \"beyyeːcciːg\" → present tense of \"buy\"\n\nSo:\n- \"kanarri\" root → buy → past: -cciːg, present: -beyyeːcciːg\n\nSentence 4: \"kadeːcciːg\" → steal → \"kadeː\" root → past: -cciːg \nSentence 2: \"kadeːg\" → repair → past tense of \"kadeː\"\n\nSo verb roots:\n- buy → kanarri\n- steal → kadeː\n- repair → kadeː \nBut \"kadeː\" has both steal and repair? Possibly different meanings; maybe tense or context differentiates.\n\nSentence 3: \"darbadki\" → will give \nSentence 7: \"magaski\" → gave (past) → \"magas\" = give → past: -ski \nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n\"magaski\" = gave (past of \"magas\" → give)\n\nSo:\n- \"magas\" → give\n- \"magaski\" → past tense of give\n- \"darbadki\" → future of give (will give)\n\nSimilarly:\n- \"kanarri\" → buy → past: -cciːg\n- \"beyyeːciːg\" → present buy\n\nNow, object markers:\n- \"kamiːg\" → the camels → in 1, 8, 7\n- \"allesu\" → the dress → in 2\n- \"biticcirra\" → the chicken → in 3\n- \"maːgtirsu\" → for the young man → in 4\n- \"maːgtirsu\" = for the young man → \"maːgti\" + \"rsu\" = to, for? (cf. sentence 7: \"eldeːnsu\" → the doors)\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"aygi\" = for me → \"for\" is \"aygi\" → so \"aygi\" = for (indirect object)\n\nSo:\n- \"aygi\" = for (indirect object)\n- \"maːgtirsu\" = for the young man (to the young man)\n\nIn sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" → probably \"the owner\" \n\"argi\" → give \n\"kamgi\" → the camels (object) \n\"deːccirsa\" → to the thief?\n\nAs in sentence 7: \"tirsa\" = to the thief → so \"deːccirsa\" = to the thief\n\nSo structure is: [Subject] [Verb] [Object] [To-recipient]\n\nNow, back to sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" → past of \"magas\" → give → so \"magasi\" = gave \n\"argi\" = give — but why \"argi\" and not \"magasi\"?\n\nWait — \"magasi\" = past of \"magas\" = gave \nBut in sentence 7, \"magaski\" = gave — so same root? \n\"magas\" → give \n\"magaski\" → past tense \n\"magasi\" → also past tense? Possibly orthographic variant? \n\nIn sentence 7: \"magaski\" → gave \nSentence 11: \"magasi\" → same root? Could be medial vowel change.\n\nBut in sentence 3: \"darbadki\" → will give → future \nSo \"argi\" → present or future? In sentence 14: \"tirti argi kamgi deːccirsa\" → \"the owner gives the camels to the thief\"\n\n\"argi\" must be the verb → so it's present or other tense?\n\nBut in sentence 14 it's not \"tirsa\", it's \"deːccirsa\" → so it's not past?\n\nWait — sentence 8: \"iːdi magaski kamiːg tirsa\" → past: \"gave\" → \"magaski\"\n\nSo \"argi\" → may be present of \"give\"?\n\nBut in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give\"\n\nSo \"darbadki\" = future → so future = \"darbadki\", present = \"argi\"? Possibly.\n\nBut in sentence 14: \"tirti argi kamgi deːccirsa\" → present?\n\nSentence 14: \"tirti argi kamgi deːccirsa\" → \"The owner gives the camels to the thief.\"\n\nAlso, sentence 13: \"hanu tirtiːg elirsu\" → \"I will strike the donkey\" or \"I am striking\"?\n\nLook at sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" \n\"hanuːg\" = strike → \"hanu\" = strike, \"hanuːg\" = will strike? Possibly \"hanuːg\" = future of strike\n\nSo \"hanuːg\" = future → strike\n\nSentence 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike? \"tirtiːg\" = to the owner? → \"elirsu\" = the doors?\n\nBut \"tirtiːg\" → \"to the owner\"? But in sentence 6: \"eldeːnsu\" = the doors\n\nPossibly: \"tirtiːg\" = to the owner? Or \"tirt\" = owner?\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\"\n\n→ \"aygi\" = for me → indirect object\n\nThus, in verb phrase: \n[Subject] + [verb] + [direct object] + [prepositional phrase to recipient]\n\nNow, identify patterns:\n\n- Verb roots with tense suffixes:\n - buy: kanarri → past: -cciːg, present: -beyyeːciːg\n - steal: kadeː → past: -cciːg\n - repair: kadeː → past: -g (without suffix?) → kadeːg\n - give: magas → past: -ski (magaski), future: -darbaki (darbadki), present: -argi?\n\nBut sentence 14: \"tirti argi kamgi deːccirsa\" — clearly \"argi\" is the verb, and it's not past (no -ski), so likely present.\n\nSentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" — past of \"magas\" → so \"gave\"\n\n\"argi\" — present? Inconsistent?\n\nWait — could \"argi\" be a different verb?\n\nNo — \"magasi\" likely = gave, as \"magas\" is root.\n\nSo \"magasi\" = past tense of give → \"gave\"\n\n\"argi\" = present tense of give → \"gives\"\n\nThen \"argi\" and \"magasi\" are both verbs? How can both be in one sentence?\n\nThe sentence is \"magasi argi ajomirra\" — two verbs?\n\nPossibly a typo or structure error?\n\nWait — perhaps this is a compound subject or verb?\n\nBut \"magasi\" + \"argi\" = \"he gave and gives\"? That's odd.\n\nAlternatively, maybe \"magasi\" is a typo or a noun?\n\n\"ajomirra\" → what is this?\n\nLook for similar word in translations.\n\nSentence 3: \"biticcirra\" → the chicken \nSentence 5: \"ajaːnirri\" → the necklaces \nSentence 6: \"eldeːnsu\" → the doors \nSentence 9: \"bijaːndi\" → strike the donkey — in sentence 15: \"ay darbadki bijaːndi\" → \"I will give the chicken to the donkey\"?\n\nNo — \"bijaːndi\" in sentence 9: \"I will strike the donkey\"\n\nSo \"bijaːndi\" = strike the donkey → verb is \"hanuːg\" = strike\n\nSo \"bijaːndi\" = strike (with object)\n\nThus, \"ajomirra\" → may be \"the donkey\"?\n\nBecause \"bijaːndi\" = strike the donkey → suggests \"ajomirra\" = the donkey?\n\nIn sentence 3: \"biticcirra\" = chicken \nSentence 5: \"ajaːnirri\" = necklaces \nSo object nouns:\n\n- nekkle → \"ajaːnirri\"\n- chicken → \"biticcirra\"\n- dress → \"allesu\"\n- camels → \"kamiːg\"\n- dogs → \"tirsa\" (in sentence 7: \"tirsa\" = to the thief)\n\nSo for \"ajomirra\", if it's a noun, likely \"the donkey\"\n\nSimilarly, in sentence 15: \"ay darbadki bijaːndi\" → \"I will give the chicken to the donkey\" → because \"bijaːndi\" = to the donkey?\n\nBut sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → so \"bijaːndi\" = strike the donkey\n\nBut in sentence 15: \"ay darbadki bijaːndi\" — may be \"I will give the chicken to the donkey\"?\n\nBut \"bijaːndi\" appears in two contexts.\n\nWait — is \"bijaːndi\" used only once?\n\nSentence 9: \"ay hanuːg bijomri\" → \"will strike the donkey\" \nSentence 15: \"ay darbadki bijaːndi\" → \"will give the chicken to the donkey\"?\n\nBut \"bijaːndi\" and \"bijaːndi\" — spelled similarly?\n\n\"bijaːndi\" vs. \"bijaːndi\" — in both?\n\nSentence 9: \"bijaːndi\" — \"will strike the donkey\" \nSentence 15: \"bijaːndi\" — \"I will give the chicken to the donkey\"? That would require \"bijaːndi\" to mean \"to the donkey\".\n\nBut \"bijaːndi\" cannot both mean \"strike\" and \"to the donkey\".\n\nIn sentence 9: \"hanuːg bijomri\" → \"will strike the donkey\" → likely \"biji\" + \"omri\" = strike the donkey\n\nSentence 15: \"ay darbadki bijaːndi\" — if \"bijaːndi\" = to the donkey, then it's a prepositional phrase.\n\nBut no \"to the donkey\" appears earlier.\n\nIn sentence 7: \"tirsa\" = to the thief \nIn sentence 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = to the owner? \"elirsu\" = the doors?\n\nSo \"tirtiːg\" = to the owner?\n\nSimilarly, \"maːgtirsu\" = for the young man → \"maːgti\" + \"rsu\" → \"to/for the young man\"\n\nSo \"rsu\" = to or for?\n\n\"tirsa\" = to the thief → \"tir\" + \"sa\" → to the thief\n\nThus, suffix \"-rsu\" = to (recipient)\n\n\"maːgtirsu\" = for the young man → \"to/for the young man\"\n\nSo uses of the recipient suffix:\n- \"tirsa\" = to the thief \n- \"maːgtirsu\" = for the young man \n- \"elirsu\" = the doors (object? or to the doors?) — sentence 13: \"hanu tirtiːg elirsu\" → \"I will strike the doors\"? or \"to the doors\"?\n\nSentence 13: \"hanu tirtiːg elirsu\" → \"I will strike the doors\"? or \"to the doors\"?\n\nBut sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijaːndi\" is not in 13.\n\nIn 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = to the owner, \"elirsu\" = the doors?\n\nSo \"tirtiːg\" = to the owner → similar to \"maːgtirsu\" → \"to the young man\"\n\nSo \"tirtiːg\" → to the owner\n\nSimilarly, in sentence 14: \"deːccirsa\" → to the thief\n\nNow, back to sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = past tense of \"give\" → gave \n\"argi\" = present tense of \"give\" → gives \n\"ajomirra\" = ? → could be \"the donkey\"\n\n\"argi\" and \"magasi\" — unlikely both verbs in a simple phrase.\n\nBut perhaps \"magasi\" is incorrect.\n\nCheck sentence 7: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\"\n\n\"magaski\" = past of give\n\nSentence 11: \"magasi\" → same root — could it be a variant?\n\nIn English: perhaps \"magasi\" = \"he gave\" → past\n\n\"argi\" = \"gives\" → present\n\nSo the full phrase: \"He gave and gives the donkey\" — very odd.\n\nAlternatively, is \"argi\" a noun? Unlikely.\n\nPerhaps it's a verb of transfer: \"give\" (present), and \"magasi\" is subject?\n\nBut no subject.\n\nPossibly a typo — or \"magasi\" is subject?\n\n\"magasi\" could be a noun?\n\nBut in other sentences, \"magasi\" does not appear.\n\nSentence 11: \"magasi argi ajomirra\"\n\nCompare sentence 3: \"jahali waliːg darbadki biticcirra\" — subject \"jahali waliːg\" → young men, verb \"darbadki\" → will give, object \"biticcirra\"\n\nSo structure: [subject] [verb] [object]\n\nSimilarly, sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → subject \"wal\", verb \"aygi\" (for), object \"eldeːnsu\"\n\nBut verb is \"baːbiːg\" → found\n\nSo verb + object + prepositional phrase\n\nNow, in sentence 11: perhaps \"magasi\" is the subject — \"he gave\"?\n\nThen \"argi\" is a redundant verb?\n\nUnlikely.\n\nMaybe \"argi\" is a verb and \"magasi\" is a noun or verb ending.\n\nWait — in sentence 14: \"tirti argi kamgi deːccirsa\" → \"the owner gives the camels to the thief\"\n\n\"argi\" = give → present tense\n\nIn sentence ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11332.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Identify core verb patterns and thematic roles in the given sentences.\n\nLook at the verb stems and their objects:\n\n- \"kanarriːcciːg\" → \"bought\" (in 1), \"kanarriːg\" → \"bought\" (in 12) → likely means \"buy\" with object.\n- \"kadeːg\" → \"repaired\" (in 2), \"kadeːcciːg\" → \"stole\" (in 4) → different meaning, but related verb form.\n- \"biticcirra\" → \"give\" (in 3), \"tirsa\" → \"give to\" (in 8), \"tirsa\" appears in \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\".\n- \"waliːg\" → \"young men\" (in 3), \"magas\" → \"thief\" (in 7), \"hanu\" → \"strike\" (in 9).\n- \"beyyeːcciːg\" → \"buy\" (in 5, 10), \"baːbiːg\" → \"found\" (in 6), \"darbadki\" → \"give\" (in 3,15).\n- \"maːgtirsu\" → \"the dresses\" (in 4), \"eldeːnsu\" → \"the doors\" (in 6), \"tirsa\" → \"give to\".\n\nPattern: The verb structure often includes a subject + verb + object + indirect recipient.\n\nStep 2: Identify syntactic structure of verb forms.\n\nNotice that verbs often appear in a pattern:\n\n- [Subject] [Verb] [Object] [For/To/for whom?]\n\nExamples:\n\n- 1: ar kanarriːcciːg kamiːg jaːnticcirsu → we bought the camels for the neighbours → \"kanarriːcciːg kamiːg\" = bought the camels, \"jaːnticcirsu\" = for the neighbours.\n- 2: tirt kadeːg allesu → the owner repaired the dress.\n- 3: jahali waliːg darbadki biticcirra → the young men will give the chicken to the dogs → \"darbadki\" = give, \"biticcirra\" = to the dogs.\n- 4: man jahalgi kadeːcciːg maːgtirsu → he stole the dresses → \"kadeːcciːg\" = stole.\n- 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces → \"beyyeːcciːg\" = buy, \"ajaːnirri\" = the necklaces.\n- 6: wal aygi baːbiːg eldeːnsu → the dog found the doors for me → \"baːbiːg\" = found, \"eldeːnsu\" = doors, \"for me\" not explicit but implied.\n- 7: magas ikki waliːg ticcirsu → the thief gave you the dogs → \"ticcirsu\" = gave to you.\n- 8: iːdi magaski kamiːg tirsa → the men gave the camels to the thief → \"magaski\" = the camels, \"tirsa\" = to the thief.\n- 9: ay hanuːg bijomri → I will strike the donkey → \"hanuːg\" = strike, \"bijomri\" = the donkey.\n- 10: sarkaːyi aygi beyyeːcciːg adeːnda → the cowards are giving me the necklaces → \"aygi beyyeːcciːg\" = are giving, \"adeːnda\" = to me.\n\nKey: The verb stem is often followed by an object, and then a purpose/recipient marker (for X), often as a separate element.\n\nLook at verb + object + [to/for] recipient.\n\nNow examine new sentences:\n\n11. magasi argi ajomirra.\n\n\"magasi\" → likely related to \"magas\" (thief), so \"magasi\" = the thief? (in 7: \"magas\" → thief)\n\"argi\" → likely \"give\" (in 3: \"darbadki\" = give, \"argi\" appears in 14)\n\"ajomirra\" → likely \"the donkey\" (like \"bijomri\")\n\nIn 9: \"hanuːg bijomri\" → \"I will strike the donkey\"\n\nSo \"bijomri\" = donkey → \"ajomirra\" = the donkey?\n\nThus: \"magasi argi ajomirra\" → the thief gives the donkey?\n\nBut \"argi\" = give? In 3: \"darbadki biticcirra\" → give to dogs → \"darbadki\" = give.\n\nBut \"argi\" is not in 3. Where is \"argi\"?\n\nCheck for similar forms:\n\nIn 7: \"magas ikki waliːg ticcirsu\" → gave to you (pl.)\n\nIn 14: \"tirti argi kamgi deːccirsa\" → probably \"the owner gives the camels to the thief\"?\n\n\"tirti\" = owner? (2: \"tirt kadeːg allesu\")\n\n\"kamgi\" = the camels? (1: \"kanarriːcciːg kamiːg\" → bought camels → \"kamiːg\" = camels)\n\n\"deːccirsa\" → perhaps \"to the thief\"? Like \"tirsa\" → \"to the thief\"?\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → gave the camels to the thief → \"tirsa\" = to the thief.\n\nSo \"tirsa\" = to the thief.\n\nThus, deːccirsa → to the thief?\n\nSimilarly, in 12: ay kanarriːg baːbki alletirsi.\n\n\"ay\" = I\n\n\"kanarriːg\" = buy (from 5: \"ay beyyeːcciːg\" → buying)\n\n\"baːbki\" → like \"baːbiːg\" = found (in 6)\n\n\"alletirsi\" → possibly \"for me\"?\n\nIn 6: wal aygi baːbiːg eldeːnsu → the dog found the doors for me → \"for me\"\n\nSo \"alletirsi\" → for me?\n\nIn 13: hanu tirtiːg elirsu.\n\n\"hanu\" → strike (9: \"hanuːg bijomri\")\n\n\"tirtiːg\" → likely \"tirt\" (repair) + \"iːg\" = for?\n\n\"elirsu\" → ? el = ? ir → perhaps \"the doors\"?\n\n\"eldeːnsu\" = doors (6)\n\nSo \"elirsu\" → doors?\n\nThus: \"hanu tirtiːg elirsu\" → strike the doors? Or \"strike the doors for whom\"?\n\n\"tirtiːg\" = repair for?\n\nIn 2: \"tirt kadeːg allesu\" → repaired the dress → no for.\n\nBut 13: hanu tirtiːg elirsu → may be \"I will strike the doors\" or \"I will strike the doors for someone\"?\n\nBut no recipient.\n\nAlternatively, is the form a pattern: [Subject] [Verb] [Object] [for recipient]?\n\nSo for 11: magasi argi ajomirra\n\n\"magasi\" = thief\n\n\"argi\" = give?\n\nBut no known \"give\" form with \"argi\".\n\nWait: in 3: \"darbadki biticcirra\" → give to the dogs\n\n\"biticcirra\" = to the dogs\n\nBut \"argi\" not there.\n\nUnless \"argi\" = give?\n\nIn 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" = owner? (tirt in 2 → repaired)\n\n\"kamgi\" = camels\n\n\"deːccirsa\" → to the thief?\n\nBecause \"tirsa\" = to the thief → deːccirsa = to the thief?\n\nIn 8: iːdi magaski kamiːg tirsa → gave to the thief → \"tirsa\"\n\nSo deːccirsa → to the thief?\n\nThen 14: tirti argi kamgi deːccirsa → the owner gives the camels to the thief.\n\n\"argi\" = gives?\n\nBut \"argi\" not in base form.\n\nCompare: in 3: \"darbadki\" = give → verb.\n\nSo \"argi\" might be a variant of \"give\"?\n\nOr perhaps is \"argi\" = \"give\"?\n\nLook at 11: magasi argi ajomirra\n\n\"magasi\" = thief\n\n\"argi\" = give?\n\n\"ajomirra\" = donkey?\n\nThen: the thief gives the donkey?\n\nBut in 9: \"ay hanuːg bijomri\" → I will strike the donkey → no give.\n\nSo \"argi\" might be \"give\".\n\nSimilarly, 12: ay kanarriːg baːbki alletirsi\n\n\"ay\" = I\n\n\"kanarriːg\" = buy\n\n\"baːbki\" → ? in 6: \"baːbiːg\" = found → \"baːbki\" = found?\n\n\"alletirsi\" → for me?\n\nSo: I am buying the found things for me? Doesn't make sense.\n\n\"baːbki\" — could be related to \"baːbiːg\", perhaps \"found\", but \"for me\"?\n\nBut what is \"baːbki\"? Perhaps a noun?\n\nAlternatively, could \"baːbki\" be the object?\n\nBut \"kanarriːg\" is buy — so \"buy X\" → what is X?\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → \"ajānirri\" = the necklaces.\n\nSo object = noun.\n\nIn 12: \"ay kanarriːg baːbki\" → I am buying the found?\n\n\"baːbki\" → not a known noun.\n\nUnless \"baːbki\" = the doors? But \"eldeːnsu\" = doors.\n\n\"elirsu\" = doors? In 13.\n\nPossibly \"elirsu\" = doors.\n\nThen 12: \"ay kanarriːg baːbki alletirsi\" → I am buying the found for me?\n\nBut \"the found\" is odd.\n\nAlternatively, \"baːbki\" = found → object → \"buying the found\" → grammatically odd.\n\nPerhaps \"baːbki\" is the recipient?\n\nBut verbs don't take object + recipient that way.\n\nWait — look at 10: sarkaːyi aygi beyyeːcciːg adeːnda → the cowards are giving me the necklaces → \"adeːnda\" = to me.\n\n\"aygi\" = are giving.\n\nIn 6: wal aygi baːbiːg eldeːnsu → dog found the doors for me.\n\n\"for me\" = alletirsi / adeːnda.\n\nSo \"alletirsi\" and \"adeːnda\" are both \"for me\".\n\nSimilarly, \"tirsa\" = \"to the thief\", \"deːccirsa\" = to the thief?\n\nSo \"deːccirsa\" = to the thief.\n\nIn 14: \"tirti argi kamgi deːccirsa\" → owner gives camels to thief.\n\nIn 13: \"hanu tirtiːg elirsu\" → strike the doors?\n\n\"tirtiːg\" = repair for?\n\n\"tirt\" = repair, so \"tirtiːg\" = for repair?\n\nLike \"to repair for\"?\n\nBut no recipient.\n\n\"hanu\" = strike → \"hanu tirtiːg elirsu\" → strike the doors for whom?\n\nMost likely: \"I will strike the doors\" — without a recipient, or perhaps with \"for me\" missing.\n\nBut \"tirtiːg\" might be \"repair\" with \"for\"?\n\nBut \"hanu\" is strike.\n\nSo this is not consistent.\n\nBack to 11: magasi argi ajomirra\n\n\"magasi\" = thief\n\n\"argi\" = give?\n\n\"ajomirra\" = the donkey?\n\n→ the thief gives the donkey?\n\nBut in 9: \"I will strike the donkey\" — donkey is object of strike.\n\nSo \"ajomirra\" = the donkey.\n\nSo likely: the thief gives the donkey.\n\nBut is \"argi\" = give?\n\nCheck if \"argi\" appears with \"to\".\n\nNo, but in other sentences, \"biticcirra\" = to the dogs.\n\nSo possible that \"argi\" is \"give\", and the object is the donkey.\n\nSo translation: the thief gives the donkey.\n\nNow 12: ay kanarriːg baːbki alletirsi\n\n\"ay\" = I\n\n\"kanarriːg\" = buy (as in 5)\n\n\"baːbki\" = ? possibly \"the found things\"? or \"the doors\"?\n\nBut no noun.\n\n\"allegtirsi\" = \"for me\"? same as \"adeːnda\"\n\nIn 6: wal aygi baːbiːg eldeːnsu → found the doors for me\n\nSo \"aygi\" = found, \"for me\"\n\n\"allegtirsi\" → for me?\n\nSo \"ay kanarriːg baːbki alletirsi\" → I am buying the found (for me)? → \"buying the found\" makes little sense.\n\nBut \"baːbki\" — compare to \"baːbiːg\" → found.\n\nPossibly \"baːbki\" = the found — i.e., something that was found?\n\nBut no standard noun form.\n\nAlternatively, could \"baːbki\" be the recipient?\n\nBut \"kanarriːg\" = buy — not a transitive verb that gives to.\n\nUnless \"buy\" takes a recipient?\n\nIn 1: ar kanarriːcciːg kamiːg jaːnticcirsu → bought camels for the neighbours → \"for the neighbours\"\n\nSo \"jaːnticcirsu\" = for the neighbours.\n\nSimilarly, in 10: sarkaːyi aygi beyyeːcciːg adeːnda → giving me the necklaces → \"adeːnda\" = to me.\n\nSo pattern: verb + object + for X\n\nIn 12: ay kanarriːg baːbki alletirsi → I am buying the found for me?\n\nBut \"baːbki\" = object of buying → the found?\n\nBut what is \"the found\"? Not clear.\n\n\"baːbki\" might be a noun meaning \"what was found\" — like \"the found thing\".\n\nBut in 6: wal aygi baːbiːg eldeːnsu → dog found the doors → \"eldeːnsu\" = doors.\n\nSo \"baːbiːg\" = found → verb.\n\n\"baːbki\" → perhaps a noun form of \"found\"?\n\nPossible.\n\nSo \"I am buying the found thing (the found doors?) for me\"?\n\nBut \"the found\" is vague.\n\nAlternatively, is \"baːbki\" = \"the doors\"?\n\nBut \"eldeːnsu\" = doors → so \"elirsu\" = doors?\n\nIn 13: hanu tirtiːg elirsu → strike the doors?\n\n\"tirtiːg\" = for repair? → \"repair the doors\"?\n\nBut \"hanu\" = strike — not repair.\n\n\"tirt\" = repair → so \"tirtiːg\" = repair for?\n\nThus \"hanu tirtiːg elirsu\" → strike the doors for repair?\n\nDoesn't make sense.\n\n\"hanu\" = strike → \"I will strike the doors\" → simple action.\n\n\"tirtiːg\" may be \"for the repair\" or \"to repair\"?\n\nBut \"tirt\" alone is repair → \"tirtiːg\" = repair for whom?\n\nLikely \"I will strike the doors\" — no recipient.\n\nBut then why \"tirtiːg\"?\n\nIn 2: \"tirt kadeːg allesu\" → repaired the dress — no for.\n\nIn 8: \"tirsa\" = to the thief.\n\nSo \"tirtiːg\" may be \"to repair for\"?\n\nBut with \"hanu\", no.\n\nPerhaps the \"iːg\" suffix indicates \"for\".\n\nSo \"tirtiːg\" = repair for? → for someone?\n\nBut \"hanu\" = strike — conflict.\n\nUnlikely.\n\nBetter to see pattern of verb-object-recipient.\n\nList all with recipient:\n\n1: kanarriːcciːg kamiːg jaːnticcirsu → for neighbours → jaːnticcirsu = for neighbours\n\n2: kadeːg allesu → no recipient\n\n3: darbadki biticcirra → to dogs → biticcirra = to dogs\n\n4: kadeːcciːg maːgtirsu → no recipient (stole)\n\n5: beyyeːcciːg ajaːnirri → no recipient\n\n6: baːbiːg eldeːnsu → for me → implied\n\n7: ticcirsu → to you\n\n8: tirsa → to thief\n\n9: bijomri → donkey — object\n\n10: adeːnda → to me\n\nSo forms with recipient: jaːnticcirsu, biticcirra, eldeːnsu, ticcirsu, tirsa, adeːnda\n\nEach has a structure: verb + object + recipient particle.\n\nParticles: jaːnticcirsu, biticcirra, alletirsi, deːccirsa, adeːnda\n\nNow look at shared roots:\n\n- jaːnticcirsu → for neighbours\n- biticcirra → to the dogs\n- eldeːnsu → doors\n- deːccirsa → to the thief?\n- alletirsi → for me?\n- adeːnda → to me?\n\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → dog found doors for me → \"eldeːnsu\" = doors\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me the necklaces → \"adeːnda\" = to me\n\nSo \"ade", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11000.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Identify recurring patterns in the given examples.\n\nLook at the verb structures and their meanings.\n\nSentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu → \"We bought the camels for the neighbours.\" \n\"kanarriːcciːg\" = bought (past), \"kamiːg\" = the camels, \"jaːnticcirsu\" = for the neighbours.\n\nSentence 2: tirt kadeːg allesu → \"The owner repaired the dress.\" \n\"tirt\" = repaired, \"kadeːg\" = the dress.\n\nSentence 3: jahali waliːg darbadki biticcirra → \"The young men will give the chicken to the dogs.\" \n\"jahali\" = the young men, \"waliːg\" = will, \"darbadki\" = the chicken, \"biticcirra\" = to the dogs.\n\nSentence 4: man jahalgi kadeːcciːg maːgtirsu → \"He stole the dresses for the young man.\" \n\"man\" = he, \"jahalgi\" = the dresses, \"maːgtirsu\" = for the young man.\n\nSentence 5: ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces.\" \n\"ay\" = I, \"beyyeːcciːg\" = buying, \"ajaːnirri\" = the necklaces.\n\nSentence 6: wal aygi baːbiːg eldeːnsu → \"The dog found the doors for me.\" \n\"wal\" = the dog, \"aygi\" = found, \"baːbiːg\" = the doors, \"eldeːnsu\" = for me.\n\nSentence 7: magas ikki waliːg ticcirsu → \"The thief gave you (pl.) the dogs.\" \n\"magas\" = the thief, \"ikki waliːg\" = you (pl.), \"ticcirsu\" = gave.\n\nSentence 8: iːdi magaski kamiːg tirsa → \"The men gave the camels to the thief.\" \n\"iːdi\" = the men, \"magaski\" = the camels, \"t irsa\" = to the thief.\n\nSentence 9: ay hanuːg bijomri → \"I will strike the donkey.\" \n\"ay\" = I, \"hanuːg\" = will, \"bijomri\" = strike the donkey.\n\nSentence 10: sarkaːyi aygi beyyeːcciːg adeːnda → \"The cowards are giving me the necklaces.\" \n\"sarkaːyi\" = the cowards, \"aygi\" = are giving, \"beyyeːcciːg\" = the necklaces, \"adeːnda\" = to me.\n\nStep 2: Identify verb forms and their use.\n\nCommon verb roots:\n- kanarriːc- → buy (past active)\n- tirt- → repair (past active)\n- darbad- → give (with object)\n- kadeː- → dress, especially repair or give\n- beyyeːc- → buy\n- baːbi- → find\n- maga- → thief/give\n- hanu- → strike, will\n- bijo- → strike\n\nNotice: \n\"bijeːc\" appears in \"beyyeːcciːg\" = buying \n\"bijo\" in \"bijomri\" = strike\n\n\"tirt\" = repair, also appears in \"tirtiːg\" → possibly future or passive?\n\nIn sentence 4: \"kadeːcciːg maːgtirsu\" = stole the dresses for the young man → \"kadeːcciːg\" = stole (past)\n\nIn sentence 10: \"aygi beyyeːcciːg adeːnda\" = are giving → \"aygi\" = are giving\n\nNow look at the target sentences:\n\nSentence 11: magasi argi ajomirra \n\"magasi\" = likely \"the thief\" (like \"magas\" in sentence 7) \n\"argi\" = possibly \"will\" or \"give\" (similar to \"waliːg\" or \"hanuːg\") \n\"ajomirra\" = likely \"strike\" or \"strike the donkey\" → similar to \"bijomri\"\n\n\"argi\" is not directly present. Compare:\n\n- \"waliːg\" → future (will)\n- \"hanuːg\" → future (will strike)\n\n\"argi\" might be the future form of \"give\"? Unlikely.\n\nBut \"tirti\" appears in sentence 14: \"tirti argi kamgi deːccirsa\" — here \"tirti\" is likely future of \"tirt\" (repair).\n\nSo stem identification:\n\n- \"tirti\" = will repair\n- \"kanarriːg\" = buy (past)\n- \"hanu\" = strike (present/future)\n- \"argi\" = possibly \"will strike\" or \"give\"?\n\nBut in sentence 11: \"magasi argi ajomirra\"\n\nCompare to sentence 9: \"ay hanuːg bijomri\" = I will strike the donkey \n\"hanuːg\" = will strike\n\nSo \"hanu\" = strike \n\"hanuːg\" = will strike\n\n\"argi\" — appears in 11 and 14.\n\nSentence 14: \"tirti argi kamgi deːccirsa\" → \"will repair the camels for the dogs\"?\n\n\"tirti\" = will repair \n\"argi\" = ? \n\"kamgi\" = the camels? \"kamgi\" vs \"kamiːg\" — sounds like same root\n\n\"deːccirsa\" = to the dogs? \"jaːnticcirsu\" = for the neighbours → \"deːccirsa\" = for the dogs?\n\nSound like \"deːccir\" → to the dogs.\n\nSo \"tirti argi kamgi deːccirsa\" = will repair the camels to the dogs?\n\nBut \"argi\" here is not clear.\n\nAnother possibility: \"argi\" = give?\n\nLook at sentence 3: \"waliːg darbadki biticcirra\" — \"waliːg\" = will, \"darbadki\" = the chicken, \"biticcirra\" = to the dogs.\n\nSo \"darbadki\" = the chicken (object), \"biticcirra\" = to the dogs.\n\n\"biticcirra\" = to the dogs \n\"deːccirsa\" = to the dogs?\n\nYes — similar.\n\nIn sentence 14: \"tirti argi kamgi deːccirsa\" — could \"argi\" = give?\n\nSo \"tirti\" = will repair, \"argi\" = give, \"kamgi\" = the camels, \"deːccirsa\" = to the dogs.\n\nBut \"tirti\" = will repair, not give.\n\nSo if \"argi\" means \"give\", and \"kanarriːg\" = buy, could \"argi\" = give?\n\nThen sentence 11: \"magasi argi ajomirra\" = the thief will give the donkey?\n\nBut \"ajomirra\" — similar to \"bijomri\" = strike.\n\nCould \"ajomirra\" = strike?\n\nSo \"argi\" = give, \"ajomirra\" = strike?\n\nDoesn't fit.\n\nWait — in sentence 9: \"ay hanuːg bijomri\" → will strike.\n\nSo \"hanu\" + suffix = will strike.\n\nSo is \"argi\" future of \"give\"?\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give\"\n\nSo \"waliːg\" = will\n\nTherefore, \"argi\" may be \"give\"\n\nTherefore:\n\n\"tirti\" = will repair \n\"argi\" = give \n\"kamgi\" = the camels \n\"deːccirsa\" = to the dogs\n\nSo sentence 14: \"will repair, give, the camels, to the dogs\" — sounds odd.\n\nNo object is given.\n\n\"tirti argi kamgi deːccirsa\" — maybe \"will give the camels to the dogs\" → repair is not present?\n\nBut \"tirti\" = will repair.\n\nInconsistent.\n\nAlternative: \"tirti\" = will repair, \"argi\" = will (auxiliary), \"kamgi\" = the camels, \"deːccirsa\" = to the dogs.\n\nBut \"tirti argi\" = will repair will? No.\n\nNot making sense.\n\nAlternate: look at sentence 8: \"iːdi magaski kamiːg tirsa\" → men gave camels to thief.\n\n\"tirsa\" = to the thief.\n\nSo \"tirsa\" = to?\n\n\"deːccirsa\" = to the dogs?\n\nYes — likely same pattern.\n\n\"argi\" — not in past, but in future.\n\nSentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" → the thief (like magas)\n\n\"argi\" → future of \"give\"?\n\n\"ajomirra\" → strike?\n\nBut \"bijomri\" = strike → \"bijomri\"\n\n\"ajomirra\" — same root? Seems like a variant.\n\nPossibly \"argi\" = give, \"ajomirra\" = give the donkey?\n\nBut \"ajomirra\" — no \"the\" or object.\n\nUnless it's \"give the donkey\" → missing object.\n\nBut in original sentence 9: \"ay hanuːg bijomri\" → I will strike the donkey → \"bijomri\" = strike the donkey\n\nSo \"bijomri\" = strike the donkey\n\n\"ajomirra\" = strike the donkey?\n\nYes — likely same.\n\nSo \"argi\" is not \"give\".\n\nBack to sentence 3: \"waliːg\" = will, \"darbadki\" = the chicken, \"biticcirra\" = to the dogs\n\nSo \"waliːg\" = will\n\nIn sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" might be \"will\"\n\n\"ajomirra\" = strike the donkey\n\nSo \"the thief will strike the donkey\"\n\nMakes sense.\n\nCompare: sentence 9: \"ay hanuːg bijomri\" = I will strike the donkey\n\n\"hanuːg\" = will strike\n\nSo \"hanu\" + suffix = will strike\n\nBut in \"argi\", no \"hanu\", so perhaps \"argi\" is not \"will\".\n\nBut \"argi\" appears in 11, 12, 13, 14, 15.\n\nSentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = buy (past) \n\"baːbki\" = the doors? (from \"baːbiːg\" = doors in sentence 6) \n\"alletirsi\" — \"alletir\" likely \"to\" or \"for\"?\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → dog found the doors for me → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for\n\n\"alletirsi\" — could be \"for the thief\"?\n\n\"al\" + \"letir\" — \"al\" = the, \"letir\" = to? or for?\n\n\"al\" might be part of \"al-letir\" = for?\n\nCompare with \"jaːnticcirsu\" = for the neighbours\n\nSo \"alletirsi\" = for the thief?\n\n\"al\" = the, \"letir\" = to?\n\nBut \"jaːnticcirsu\" has \"jaːnti\" = neighbours → \"jaːnti\" = neighbours, \"cirsu\" = for?\n\nSo maybe \"letir\" = to (like \"deːccir\") or \"for\"?\n\n\"deːccirsa\" = to the dogs → \"deːccir\" = to\n\n\"alletirsi\" — \"al\" could be \"the\", \"letir\" = to?\n\nBut \"letir\" not found.\n\nAlternate: \"alletir\" = for?\n\nIn sentence 6: \"eldeːnsu\" = for me\n\nNo \"letir\" there.\n\nBut sentence 8: \"iːdi magaski kamiːg tirsa\" → gave to thief → \"tirsa\" = to\n\nSo \"tirsa\" = to\n\n\"deːccirsa\" = to the dogs\n\nSo \"tirsa\" and \"deːccirsa\" both mean \"to\" + noun\n\nSo \"alletirsi\" might be \"to the [someone]\"\n\n\"al\" = the, \"letir\" = to?\n\nBut no such form.\n\nPerhaps \"alletirsi\" = for the neighbours?\n\nNot clear.\n\nBack to sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = will strike \n\"tirtiːg\" = will repair \n\"elirsu\" = to the owner? or for?\n\n\"elirsu\" = to the owner?\n\n\"tirtiːg\" = will repair → \"tirt\" = repair\n\n\"tirtiːg\" = will repair\n\n\"hanu\" = will strike\n\nBut \"hanu\" and \"tirtiːg\" together? \"will strike, will repair\"?\n\nUnlikely.\n\nPossibly \"hanu\" + \"tirtiːg\" = will strike the repair?\n\nNo.\n\nPossibility: \"hanu\" = will strike, \"tirtiːg\" = the repair?\n\n\"elirsu\" = to the owner?\n\nSo \"will strike the repair to the owner\"? Doesn't make sense.\n\nAnother idea: maybe \"tirtiːg\" is the object of \"hanu\"?\n\n\"hanu tirtiːg elirsu\" = I will strike the repair for the owner?\n\nBut \"repair\" is an abstract thing.\n\nUnlikely.\n\nAlternative: perhaps \"tirti\" = give or give to?\n\nBut in sentence 3, \"darbadki\" = the chicken, \"biticcirra\" = to the dogs.\n\nIn sentence 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" = will repair \n\"argi\" = ? \n\"kamgi\" = the camels \n\"deːccirsa\" = to the dogs\n\nStill awkward.\n\nWait — sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → he stole the dresses for the young man.\n\n\"maːgtirsu\" = for the young man.\n\nSo \"maːgtirsu\" = for the young man.\n\nIn sentence 2: \"tirt kadeːg allesu\" → repaired the dress.\n\nSo \"kadeːg\" = the dress.\n\nIn sentence 1: \"kanarriːcciːg kamiːg jaːnticcirsu\" → bought the camels for the neighbours → \"jaːnticcirsu\" = for the neighbours.\n\nPattern: [subject] [verb] [object] [for-preposition] [recipient]\n\nSo structure: S V O for P\n\nNow look at sentence 15: \"ay darbadki bijaːndi\"\n\n\"ay\" = I \n\"darbadki\" = the chicken \n\"bijaːndi\" → likely \"strike\" or \"strike the donkey\"?\n\n\"bijaːndi\" → similar to \"bijomri\"\n\n\"bijomri\" = strike the donkey\n\nSo \"bijaːndi\" = strike the donkey?\n\nYes — likely.\n\nSo sentence 15: \"I will give the chicken to the donkey\"? But no.\n\n\"darbadki\" = the chicken \n\"bijaːndi\" = strike?\n\nSo \"I will strike the chicken\" — possible?\n\nBut in sentence 3: \"will give the chicken to the dogs\"\n\nSo \"darbadki\" = the chicken\n\n\"bijaːndi\" = strike the chicken?\n\nBut \"bijaːndi\" → could be \"strike\" with object.\n\nBut in sentence 3, \"biticcirra\" = to the dogs → \"to\" is separate.\n\nSo \"bijaːndi\" might be \"strike the chicken\"\n\nBut why is \"bijaːndi\" used instead of \"bijomri\"?\n\nOnly difference is \"om\" vs \"an\" — \"om\" = donkey, \"an\" = chicken?\n\n\"bijomri\" = strike donkey \n\"bijaːndi\" = strike chicken?\n\nYes — likely.\n\nSo \"bijaːndi\" = strike the chicken\n\nThus, sentence 15: \"I will strike the chicken\"\n\nNow back to sentence 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" = will repair \n\"argi\" = ? \n\"kamgi\" = the camels \n\"deːccirsa\" = to the dogs\n\nIf \"argi\" = \"give\", then \"will repair, give the camels to the dogs\" — redundant.\n\nIf \"argi\" = \"will\", then \"will repair the camels to the dogs\"?\n\nStill doesn't make sense.\n\nWait — what does \"tirti\" mean?\n\nSentence 2: \"tirt\" = repair \nSentence 8: \"tirsa\" = to (the thief)\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" = men gave camels to thief → \"tirsa\" = to\n\nIn sentence 3: \"biticcirra\" = to the dogs\n\nSo \"deːccirsa\" = to the dogs\n\n\"tirsa\" = to the receiver\n\nSo \"tirti\" = future of repair\n\nBut is there a future of \"give\"?\n\nLook at sentence 3: \"waliːg\" = will\n\nBut no \"give\" future.\n\nWait — sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = buy \n\"baːbki\" = the doors \n\"alletirsi\" = for the thief?\n\n\"eldeːnsu\" = for me\n\nSo \"alletirsi\" likely means \"for the thief\"\n\n\"al\" = the, \"letir\" = for?\n\n\"letir\" not in other forms.\n\n\"jaːnticcirsu\" = for the neighbours → \"jaːnti\" = neighbours, \"cirsu", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11148.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "iid", + "sample_index": 3, + "output": "We are given a set of Kunuz Nubian sentences and their English translations. The task is to translate five new sentences (11–15) into English by identifying and applying the linguistic patterns from the given examples.\n\nStep 1: Extract verb–object–beneficiary structure.\n\nLook at sentence 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \nStructure: [subject] + [verb] + [object] + [for + beneficiary] → \"bought X for Y\"\n\nSentence 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n\"repaired\" is a verb, no beneficiary directly in the sentence.\n\nSentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \nStructure: [subject] + [will give] + [object] + [to + recipient]\n\nSentence 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n\"stole X for Y\" — same pattern as sentence 1: verb + object + for + beneficiary\n\nSentence 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"I am buying X\" — base verb with object\n\nSentence 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"found X for me\" — again, verb + object + for + beneficiary\n\nSentence 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n\"gave you the dogs\" → verb + to + recipient (you)\n\nSentence 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n\"gave X to Y\" — verb + object + to + recipient\n\nSentence 9: \n\"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n\"strike X\" — actor + verb + object\n\nSentence 10: \n\"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n\"are giving me X\" — passive-like structure: verb + me + object → \"are giving X to me\"\n\nNow, the key patterns:\n\n- \"for\" is used when the beneficiary is a recipient of the object (e.g., \"bought X for Y\" or \"stole X for Y\").\n- \"to\" is used when the recipient is direct, e.g., \"give X to Y\"\n- The verb \"give\", \"buy\", \"steal\", \"repair\", \"find\", \"strike\" are all transitive with object and a recipient (sometimes \"to\", sometimes \"for\")\n\nBut notice: in sentences 1, 4, 6, 10:\n- \"for\" is used with the beneficiary\n- In 3, 7, 8: \"to\" is used\n\nPattern: The preposition depends on the verb and whether \"for\" or \"to\" is intended. But cross-check:\n\n- \"bought for\" → \"for the neighbours\"\n- \"stole for\" → \"for the young man\"\n- \"found for me\" → \"found the doors for me\"\n- \"gave to\" → \"gave you the dogs\" → \"to the thief\"\n- \"giving me\" → \"are giving me the necklaces\" → \"to me\" (implied)\n\nSo primarily, the preposition is \"for\" when the beneficiary is direct (like \"we bought for the neighbours\"), and \"to\" when the recipient is direct.\n\nBut in sentence 10: \"giving me the necklaces\" → \"to me\"\n\nNow analyze the new sentences:\n\n11. magasi argi ajomirra.\n\nBreak it down:\n- \"magasi\" → likely \"the men\" or \"they\"\n- \"argi\" → likely \"will strike\"\n- \"ajomirra\" → root of \"strike\" or \"attack\"? Compare to sentence 9: \"hanuːg bijomri\" → \"I will strike the donkey\"\nSo \"bijomri\" = strike, \"ajomirra\" = \"the donkey\"?\n\n\"hanuːg bijomri\" → \"I will strike the donkey\"\nSo \"bijomri\" is \"strike\", and object is \"donkey\"\n\n\"argi\" = \"will strike\" (future tense of strike)\n\n\"magasi\" = \"they\" / \"the men\"\n\nThus: \"The men will strike the donkey.\"\n\n12. ay kanarriːg baːbki alletirsi.\n\n\"ay\" = \"I\"\n\"kanarriːg\" = \"will buy\" (from sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\", so present continuous; but \"kanarriːg\" likely future)\n\"baːbki\" = possibly \"the doors\" → compare to sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → \"baːbiːg\" = doors → \"baːbki\" is likely the same\n\"alletirsi\" → similar to \"eldeːnsu\" → \"the doors\" or \"the doors for me\"?\n\nSentence 6: \"found the doors for me\" → \"eldeːnsu\" = doors\n\n\"alletirsi\" = \"for me\"?\n\nCompare to sentence 10: \"adeːnda\" = \"me\"\n\nSo likely: \"I will buy the doors for me.\"\n\n13. hanu tirtiːg elirsu.\n\n\"hanu\" = \"I\" (from sentence 9: \"ay hanuːg bijomri\" → \"I will strike\")\n\"tirtiːg\" = \"will repair\" → from sentence 2: \"tirt kadeːg allesu\" → \"repaired\", so \"tirt\" = repair\nSo \"hanu tirtiːg\" → \"I will repair\"\n\"elirsu\" → likely \"the dress\" → sentence 2: \"kadeːg\" = dress → \"elirsu\" = dress?\n\nIn sentence 2: \"tirt kadeːg allesu\" → \"repaired the dress\" → so kadeːg = dress, elirsu = dress?\n\nPossibly \"elirsu\" = dress\n\nThus: \"I will repair the dress.\"\n\n14. tirti argi kamgi deːccirsa.\n\n\"tirti\" → future of repair → \"will repair\"\n\"argi\" → will strike\n\"kamgi\" → \"the camels\" → sentence 1: \"kanarriːcciːg kamiːg\" → \"bought the camels\" → \"kamiːg\" = camels → \"kamgi\" = camels?\n\"deːccirsa\" → \"to the men\" or \"for the men\"?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"tirsa\" = to the thief\n\n\"deːccirsa\" → likely \"to the men\" or \"to the men\"?\n\n\"deːccir\" → possibly \"to the men\"?\n\nCompare to sentence 3: \"darbadki biticcirra\" → \"give the chicken to the dogs\" → \"biticcirra\" = to the dogs\n\n\"deːccirsa\" → \"to the men\"\n\nSo \"tirti argi kamgi deːccirsa\" = \"will repair the camels to the men\"?\n\nBut \"repair the camels to the men\" is strange.\n\nWait — the verb \"argi\" means \"to strike\", not \"to repair\"\n\nSo the sentence is: \"tirti argi kamgi deːccirsa\" → \"will repair\" + \"will strike\" + \"the camels\" + \"to the men\"?\n\nThis cannot be — one verb, not two.\n\nMistake.\n\nPossibly \"tirti argi\" is a single verb? But no — \"tirti\" = repair, \"argi\" = strike — two verbs.\n\nUnless \"argi\" is not \"strike\" here.\n\nWait — \"argi\" appears in sentence 11: \"magasi argi ajomirra\" → \"the men will strike the donkey\"\n\nSo \"argi\" = strike\n\nBut in sentence 14: \"tirti argi\" — two verbs together?\n\nThat would mean \"will repair\" and \"will strike\"?\n\nBut sentence structure: subject + verb1 + verb2 + object + recipient?\n\nNo standard such construction.\n\nAlternative: is \"tirti argi\" a compound verb?\n\nNo — in sentence 8: \"magas ikki waliːg ticcirsu\" — \"gave\", not multiple verbs.\n\nAlternatively, perhaps the verb is \"tirt\" (repair) and \"argi\" is a different part.\n\n\"tirti\" — future of repair — so \"will repair\"\n\n\"argi\" — future form of \"strike\"\n\n\"kamgi\" — object: camels?\n\n\"deːccirsa\" — recipient?\n\nSo \"will repair the camels to the men\" or \"will strike the camels to the men\"?\n\nBut \"repair the camels to the men\" is odd — repair usually not to people.\n\n\"strike the camels to the men\"? No — strike is on an object, not \"to\" someone.\n\nBut sentence 3: \"give the chicken to the dogs\" → \"to\" the recipient\n\nSentence 14: \"tirti argi kamgi deːccirsa\" — maybe a typo or misreading.\n\nPossibly it's \"tirti kamgi argi deːccirsa\" — but no such order.\n\nLook at the original:\n\n14. tirti argi kamgi deːccirsa.\n\nAlternative parsing: \"tirti\" = future of repair → \"will repair\"\n\"kamgi\" = object — camels\n\"argi\" = ? Not strike here.\n\n\"argi\" only appears in strike context.\n\n\"deːccirsa\" = \"to the men\"?\n\nIs there a verb meaning \"repair\" and a separate object?\n\nSentence 2: \"tirt kadeːg allesu\" → \"repaired the dress\"\n\nSo likely: \"tirti\" = will repair\n\n\"argi\" — maybe misplaced?\n\nWait — in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\"\n\nIn sentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\"\n\n\"darbadki\" = give\n\n\"tirti\" = repair\n\nSo \"tirti\" is repair — not give.\n\nSo in sentence 14: \"tirti argi kamgi deːccirsa\" — perhaps \"tirti\" and \"argi\" are two verbs?\n\nBut that would require two actions: repair and strike on camels.\n\nBut the grammar doesn't support two verbs unless linked.\n\nAlternative: \"tirti\" = will repair → object is \"kamgi\" → \"the camels\" → \"to the men\"\n\nBut \"repair the camels to the men\" is not natural.\n\nIn sentence 6: \"found the doors for me\" — \"for me\"\n\nIn sentence 10: \"giving me the necklaces\" → \"to me\"\n\nSo preposition is \"to\" for direct recipient.\n\nBut \"repair\" is not typically used with \"to\".\n\nLook at sentence 1: \"bought the camels for the neighbours\" — \"for\"\n\nSentence 4: \"stole the dresses for the young man\" — \"for\"\n\nSentence 6: \"found the doors for me\" — \"for\"\n\nSentence 3: \"give the chicken to the dogs\" — \"to\"\n\nSentence 8: \"gave the camels to the thief\" — \"to\"\n\nSo pattern:\n\n- If preposition is \"for\", it's the intended recipient of the object\n- If \"to\", it's direct recipient\n\nNow in sentence 14: \"tirti argi kamgi deːccirsa\"\n\n\"deːccirsa\" → likely \"to the men\" or \"for the men\"?\n\nCompare to \"tirsa\" in sentence 8: \"tirsa\" → to the thief\n\nSo \"deːccirsa\" likely means \"to the men\"\n\nBut why both \"tirti\" and \"argi\"?\n\nWait — is \"argi\" a typo for \"tirsa\"? Or is \"tirti\" the verb?\n\nPerhaps \"tirt\" means \"repair\", \"argi\" means \"give\"?\n\nNo — \"argi\" only appears with \"strike\" in context.\n\nAnother possibility: \"argi\" is actually \"tirsa\" misread?\n\nNo — different sounds.\n\nAlternative: in sentence 14, \"tirti\" = will repair, \"kamgi\" = the camels, \"deːccirsa\" = to the men → \"will repair the camels to the men\" — but this is awkward.\n\nBut in Kunuz Nubian, verbs are often transitive, and prepositions like \"to\" or \"for\" specify the recipient.\n\nBut \"repair\" the camels to the men? → doesn't make sense.\n\nAlternatively, \"tirt\" = repair, \"argi\" = not acting, but \"kamgi\" = object, \"deːccirsa\" = for the men?\n\nSo \"will repair the camels for the men\"?\n\nStill unusual.\n\nWait — in sentence 1: \"bought the camels for the neighbours\" — buy for Y\n\nSentence 4: \"stole the dresses for the young man\" — stole for Y\n\nSentence 6: \"found the doors for me\" — for Y\n\nSo when the recipient is a beneficiary, \"for\" is used.\n\nIn sentence 3: \"give to the dogs\" — \"to\" used\n\nSo context determines preposition.\n\nFor \"repair\", is there a pattern?\n\nOnly one such sentence: sentence 2 — \"repaired the dress\" — no preposition.\n\nSo no indicator.\n\nBut in sentence 14: \"tirti argi kamgi deːccirsa\" — two verbs?\n\nNo — perhaps it's a misreading.\n\nLook again: is it possible that \"tirti\" is the verb, and \"argi\" is modifying?\n\nNo.\n\nAnother idea: in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\"\n\n\"darbadki\" = give\n\nIn sentence 8: \"gave to the thief\"\n\nIn sentence 14: \"tirti argi kamgi deːccirsa\" — perhaps \"argi\" is \"give\"?\n\nBut \"argi\" is in \"strike\" context.\n\n\"argi\" in 11: \"will strike\"\n\nOnly in strike context.\n\nSo must be strike.\n\nThus, sentence 14: \"will repair\" + \"will strike\" + the camels + to the men?\n\nBut that would be two verbs.\n\nUnless the sentence is misparsed.\n\nPerhaps it's \"tirti kamgi argi deːccirsa\" — \"will repair the camels\" and \"will strike the men\"?\n\n\"argi deːccirsa\" — \"will strike the men\"?\n\n\"deːccirsa\" = to the men?\n\n\"argi\" = strike → \"will strike the men\" — makes sense.\n\n\"tirti kamgi\" = \"will repair the camels\"?\n\nSo two verbs.\n\nBut the sentence is written as: \"tirti argi kamgi deːccirsa\" — which is ambiguous.\n\nBut in standard word order, subject + verb + object + preposition.\n\nSo perhaps \"tirti\" is subject? No — \"tirti\" is future of \"tirt\" (repair)\n\n\"argi\" — verb\n\n\"tirti argi\" — two verbs?\n\nOnly if both are verbs.\n\nBut the few examples show one verb per sentence.\n\nSo likely, one of them is a mistake.\n\nAlternatively, \"tirti\" = will give, but \"tirt\" = repair, not give.\n\nGive is \"darbadki\", not \"tirt\".\n\nSo no.\n\nAnother possibility: \"kamgi\" is not object — maybe it's \"for the camels\"?\n\nBut \"kamgi\" is a noun.\n\n\"deːccirsa\" = \"to the men\"\n\nBack to sentence 14: maybe it's \"will repair the camels to the men\" — but unusual.\n\nOr \"will give the camels to the men\" — but \"give\" is not present.\n\n\"argi\" is not give.\n\nConclusion: likely a parsing error — perhaps it's meant to be \"tirti kamgi deːccirsa\" — \"will repair the camels to the men\"\n\nBut this is awkward.\n\nAlternatively, \"tirti argi\" = a single verb?\n\nUnlikely.\n\nNew idea: in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\"\n\n\"aygi beyyeːcciːg\" → \"are giving\"\n\nSimilarly, in sentence 14: is it possible \"tirti argi\" is \"interact\" or something?\n\nNo.\n\nPerhaps \"tirti\" is future of \"tirt\" (repair), object \"kamgi\", and \"argi\" is a mistake for \"tirsa\"?\n\n\"tirsa\" = \"to the thief\"\n\nBut \"deːccirsa\" matches \"to the men\" → \"deːccir\" = men?\n\nIn sentence 3: \"biticcirra\" = to the dogs\n\nSo \"deːccirsa\" = to the men\n\nSo if verb is \"tirti\" (repair), then \"will repair the camels to the men\"\n\nStill odd.\n\nBut no alternative verb.\n\nCheck sentence 15.\n\n15. ay darbadki bijaːndi.\n\n\"ay\" = I\n\"darbadki\" = \"will give\" → from sentence 3: \"will give the chicken to the dogs\"\n\"bijaːndi\" = \"the donkey\"?\n\n\"bijaːndi\" — \"donkey\"? In sentence 9: \"hanuːg bijomri\" — \"strike the donkey\"\n\n\"bijaːndi\" —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12354.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "iid", + "sample_index": 0, + "output": "We are given several examples of Kunuz Nubian sentences and their English translations. We need to translate five new sentences into Kunuz Nubian by identifying patterns in the given examples.\n\n---\n\n**Step 1: Identify core patterns in the examples**\n\nLook at the structure of given sentences:\n\n- Sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → We bought the camels for the neighbours. \n → \"buy + object + for + recipient\"\n\n- Sentence 2: \"tirt kadeːg allesu\" → The owner repaired the dress. \n → \"repair + object\"\n\n- Sentence 3: \"jahali waliːg darbadki biticcirra\" → The young men will give the chicken to the dogs. \n → \"will give + object + to + recipient\"\n\n- Sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → He stole the dresses for the young man. \n → \"steal + object + for + recipient\"\n\n- Sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces. \n → \"I am buying + object\"\n\n- Sentence 6: \"wal aygi baːbiːg eldeːnsu\" → The dog found the doors for me. \n → \"found + object + for + me\"\n\n- Sentence 7: \"magas ikki waliːg ticcirsu\" → The thief gave you (pl.) the dogs. \n → \"gave + you (pl.) + object\"\n\n- Sentence 8: \"iːdi magaski kamiːg tirsa\" → The men gave the camels to the thief. \n → \"gave + object + to + recipient\"\n\n- Sentence 9: \"ay hanuːg bijomri\" → I will strike the donkey. \n → \"will strike + object\"\n\n- Sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → The cowards are giving me the necklaces. \n → \"are giving + me + object\"\n\n---\n\n**Common structures:**\n\n- **Giving**: verb + object + to/for + recipient \n - \"give\" or \"give to\" → \"ticcirsu\" (e.g., \"gave the dogs to the thief\")\n - \"give for\" → \"for + recipient\" (e.g., \"bought for the neighbours\", \"stole for the young man\")\n\n- **Buying**: \"ay beyyeːcciːg\" → \"I am buying\" \n - \"buy + object\"\n\n- **Stealing**: \"man + steal + object + for + recipient\" \n - e.g., \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\"\n\n- **Present/future tense markers**: \n - \"ay\" = I, present (e.g., \"I am buying\") \n - \"will\" = future (e.g., \"I will strike\") \n - \"are giving\" = present active (e.g., \"sarkaːyi aygi beyyeːcciːg adeːnda\")\n\n- **\"For\" is used in giving, stealing, or supplying** \n- **\"To\" is used in direct giving (\"gave to\")** \n- \"us\" is likely \"iːdi\" or \"iːdi\" in plural, or \"gaa\" or \"waliːg\" in context \n- \"the owner\" appears as \"tirt\" \n- \"the young man\" = \"jahali\" \n- \"the dog\" = \"wal\" \n- \"the chickens\" = \"biticcirra\" or \"darbadki\" \n- \"the neighbours\" = \"kamiːg\" \n- \"the thief\" = \"magas\" \n- \"the owners\" = \"iːdi\" (in sentence 19) \n- \"the coward\" = \"sarkaːyi\" \n\n---\n\nNow translate the five sentences:\n\n---\n\n**16. The neighbours are giving the necklace to the owner.**\n\n- \"The neighbours\" → \"kamiːg\" \n- \"are giving\" → \"iːdi\" or \"iːdi\" as in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" \n- \"the necklace\" → \"beyyeːcciːg\" (from sentence 5: \"I am buying the necklaces\") \n- \"to the owner\" → \"tirt\" (from sentence 2: \"the owner repaired\") \n- Structure: \"kamiːg iːdi beyyeːcciːg tirt\" → but \"to\" is needed.\n\nLook at 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"iːdi + object + to + recipient\"\n\nSo: **kamiːg iːdi beyyeːcciːg tirt**\n\nBut in 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"are giving + me + object\"\n\nSo present form of \"giving\" = \"iːdi\" or \"aygi\" for \"are giving\" (with \"aygi\" meaning \"are giving\")\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"aygi\" = \"are giving\"\n\nSo \"are giving\" = \"aygi\"\n\nIn sentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give\" → \"waliːg\"\n\nSentence 16 is present: \"are giving\"\n\nSo: \"kamiːg aygi beyyeːcciːg tirt\"\n\n\"the neighbours are giving the necklace to the owner\"\n\nYes → \"kamiːg aygi beyyeːcciːg tirt\"\n\n---\n\n**17. The young man bought the dog for us.**\n\n- \"The young man\" = \"jahali\" \n- \"bought\" = \"kadeːg\" or \"kanarriːcciːg\"? \n From sentence 1: \"ar kanarriːcciːg kamiːg\" → \"we bought\" → \"buy\" verb is \"kanarriːcciːg\" \n But in sentence 4: \"man jahalgi kadeːcciːg\" → \"he stole\" → \"kadeːcciːg\" → stealing \n Wait — \"bought\"?\n\nSentence 1: \"ar kanarriːcciːg kamiːg\" → \"we bought the camels\" → \"kanarriːcciːg\" = buy?\n\nBut sentence 4: \"man jahalgi kadeːcciːg\" → \"stole\" — so \"kadeːcciːg\" = steal?\n\nPossibility: \"buy\" = \"kanarriːcciːg\", \"steal\" = \"kadeːcciːg\"\n\nSo \"bought\" = \"kanarriːcciːg\"\n\n\"For us\" → in sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\"\n\nSo \"for me\" → \"eldeːnsu\" (me)\n\nSo \"for us\" → possibly \"eldeːnsu\" with plural?\n\nIn 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole for the young man\" → \"for + recipient\"\n\nSo in 17: \"the young man bought the dog for us\" → \"jahali kanarriːcciːg wal eldeːnsu\"\n\nBut \"us\" likely = \"eldeːnsu\" (we) → so \"for us\" = \"eldeːnsu\"\n\nYes — \"eldeːnsu\" = for me (in 6), for us in context?\n\nIn 17, \"for us\" → same structure.\n\nSo: **jahali kanarriːcciːg wal eldeːnsu**\n\nWait — in sentence 6: \"wal aygi baːbiːg eldeːnsu\" → the dog found the doors for me → \"eldeːnsu\" = for me\n\nSo \"for us\" = \"eldeːnsu\" (presumably the plural form?)\n\nIn Kunuz Nubian, \"me\" = \"eldeːnsu\", so \"us\" = \"eldeːnsu\" (shared pronoun? or implied)\n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"adeːnda\" = me\n\nSo likely \"adeːnda\" = me → so \"for us\" = \"eldeːnsu\"?\n\nBut no plural form explicitly given — however, \"for us\" is a plural recipient.\n\nIn sentence 4: \"for the young man\" — \"maːgtirsu\"\n\nSo \"for us\" → likely \"eldeːnsu\"\n\nSo: \"jahali kanarriːcciːg wal eldeːnsu\"\n\nBut in 1: \"ar kanarriːcciːg kamiːg\" → \"we bought the camels\" → \"kanarriːcciːg\" is not in past tense?\n\nBut we can use present or past?\n\n\"bought\" → past tense of \"buy\"\n\nIn sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\" → present\n\nSo \"bought\" = past — but in the database, no explicit past of \"buy\"\n\nBut in sentence 1: \"ar kanarriːcciːg kamiːg\" → \"we bought\" → so past form of buying is \"kanarriːcciːg\"\n\nSo yes, \"kanarriːcciːg\" = bought\n\nSo: **jahali kanarriːcciːg wal eldeːnsu**\n\n---\n\n**18. We will steal him.**\n\n- \"We\" → \"ar\" (from 1: \"ar kanarriːcciːg kamiːg\") \n- \"will\" → from sentence 3: \"jahali waliːg darbadki biticcirra\" → \"will give\" → \"waliːg\" \n- \"steal\" → from sentence 4: \"man jahalgi kadeːcciːg\" → \"he stole\" → \"kadeːcciːg\" \n- \"him\" → \"iːdi\"? or \"magas\"? \n \"them\" → \"ikki\", \"him\" → \"iːdi\"? or \"aːdi\"? \n In sentence 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\" → \"ikki\" = you pl. \n No \"him\" explicitly. \n But in sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"the donkey\" → object \n So \"him\" = object? \n In sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole for the young man\" → \"maːgtirsu\" = young man \n So \"him\" = \"iːdi\"? Not clear.\n\nPossibility: \"him\" = \"iːdi\"\n\nIn 17: \"for us\" → no, so no object marked.\n\nBut \"we will steal him\" → \"ar waliːg kadeːcciːg iːdi\"\n\nIs \"iːdi\" used for \"him\"?\n\nIn sentence 7: \"the thief gave you the dogs\" → \"ikki\" = you pl.\n\nWe have no masculine pronoun, but \"him\" = object.\n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"me\"\n\nSo object of giving? \"the necklaces\"\n\nSo perhaps objects are marked directly.\n\nSo \"steal him\" = \"kadeːcciːg iːdi\"\n\n\"we will steal him\" = \"ar waliːg kadeːcciːg iːdi\"\n\nYes — consistent with tense and verb forms.\n\nSo: **ar waliːg kadeːcciːg iːdi**\n\n---\n\n**19. The owners struck the thieves.**\n\n- \"The owners\" = \"iːdi\" (from sentence 7: \"the thief gave you\" → \"iːdi\" = men) \n- \"struck\" → in sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = strike \n- \"the thieves\" = \"magas\" (from sentence 7: \"the thief\") → plural? → \"magas\" can be plural or singular \n In sentence 19: \"the owners struck the thieves\" → \"magas\" may mean \"the thieves\" \n In sentence 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" → \"magas\" = thief → singular \n But \"thieves\" → plural → use \"magas\" as plural? Maybe \"ikkii\" or \"magas\"?\n\nIn sentence 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" → \"magas\" = the thief (singular)\n\nSimilarly, in sentence 4: \"he stole... for the young man\" → \"maːgtirsu\" = young man\n\nSo \"thieves\" = \"magas\" as a plural noun — accepted.\n\nSo: \"iːdi hanuːg magas\"\n\nBut \"struck\" — from \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\n\"hanuːg\" = strike\n\nSo present tense? The sentence is not future.\n\nNo tense marker — so present or simple.\n\nIn sentence 3: \"will give\" — future\n\nSentence 9: \"will strike\" — future\n\nSentence 8: \"gave\" — past\n\nSo in 19: \"the owners struck\" → past tense?\n\nBut \"struck\" is not marked in examples.\n\nAvailable verbs:\n\n- \"hanuːg\" = strike (future in 9) \n- \"kadeːcciːg\" = steal (past or present) \n- \"kanarriːcciːg\" = buy (past)\n\nBut no present past.\n\nIn sentence 3: \"will give\" → future\n\nNo past tense for \"strike\"\n\nPossibility: \"hanuːg\" is used in present and future?\n\nIn sentence 9: \"will strike\" → \"ay hanuːg bijomri\"\n\nSo \"hanuːg\" = strike, with future in \"ay\" + \"hanuːg\"\n\nSo \"striking\" = \"hanuːg\" with present or past?\n\nNo data.\n\nBut in sentence 10: \"aygi beyyeːcciːg\" → \"are giving\"\n\nSo \"aygi\" = present\n\nSo \"struck\" likely = past, but not in examples?\n\nWait — in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → past tense?\n\nBut \"gave\" is expressed in \"tirsa\"\n\nSimilarly, \"repair\" = \"tirt\" in sentence 2\n\nSo likely:\n\n- \"gave\" = \"tirsa\" \n- \"buy\" = \"kanarriːcciːg\" \n- \"steal\" = \"kadeːcciːg\"\n\nWe have \"strike\" = \"hanuːg\"\n\nIn sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\nSo \"hanuːg\" = strike (future)\n\nBut in a simple past, perhaps no marker.\n\nBut is there a past form?\n\nNo given.\n\nBut sentence 19 is not future — it's a simple statement: \"struck\"\n\nSo likely present or past.\n\nBut in the absence of a clear past tense form, and since no past form is given, perhaps \"hanuːg\" can be used in past with subject.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\" → \"tirt\" = past of repair?\n\nSo verbs have past forms.\n\nCould \"hanuːg\" be used in past?\n\nWe don't have it.\n\nBut note: in sentence 3: \"jahali waliːg darbadki biticcirra\" → future — \"waliːg\"\n\nSo \"will\" = \"waliːg\"\n\nSo present = without marker?\n\nIn 10: \"are giving\" → \"aygi\"\n\nSo \"are\" = \"aygi\"\n\nSo for past tense of strike, not given.\n\nBut sentence 19: \"The owners struck the thieves\" → likely simple past.\n\nCan we use \"hanuːg\" without \"will\"?\n\nIn sentence 9: \"ay hanuːg bijomri\" → present future\n\nBut if \"hanuːg\" is used without tense marker, it might be present.\n\nBut in examples, only future has \"will\" marker.\n\nSo in absence of \"will\" or \"are\", \"hanuːg\" may be used in present.\n\nBut the sentence says \"struck\" — past.\n\nWe must assume that past tense is used with no explicit marker.\n\nCompare with sentence 8: \"iːdi magaski kamiːg tirsa\" → \"gave\" (past)\n\nSimilarly, in sentence 2: \"tirt kadeːg allesu\" → \"repaired\"\n\nSo verbs have past forms:\n\n- buy → \"kanarriːcciːg\" (past) = sentence 1 \n- give → \"tirsa\" (past) = sentence 8 \n- steal → \"kadeːcciːg\" (past) = sentence 4 \n- strike → not directly given\n\nOnly \"strike\" has no past form.\n\nBut sentence 9: \"ay hanuːg bijomri\" → future\n\nSo \"hanuːg\" = strike, future\n\nNo past form.\n\nBut in 19, it's not future — it's a past statement.\n\nWe have no example of past \"strike\".\n\nSo perhaps \"hanuːg\" is used", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11345.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "iid", + "sample_index": 1, + "output": "Start by identifying the grammatical patterns in the given examples.\n\nLook at sentence 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \nStructure: [Subject] [object] [prepositional phrase] → \"We bought X for Y.\" \n\"for the neighbours\" is \"jaːnticcirsu\", which is a \"for\" construction with \"neighbours\".\n\nSentence 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n\"repaired\" is \"tirt\", \"dress\" is \"kadeːg\". No \"for\" here.\n\nSentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n\"will give\" is marked with future tense. \"give X to Y\" = \"waliːg darbadki biticcirra\" → [subject] [verb] [object] [to recipient].\n\nSentence 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n\"stole X for Y\" → \"kadeːcciːg maːgtirsu\" → \"dresses\" + \"for the young man\".\n\nSentence 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"buying\" = beyyeːcciːg, \"necklaces\" = ajaːnirri.\n\nSentence 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"found X for me\" = \"baːbiːg eldeːnsu\" → \"doors\" + \"for me\".\n\nSentence 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n\"given to you\" → \"waliːg ticcirsu\".\n\nSentence 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n\"give X to Y\" = magaski kamiːg tirsa → \"gave camels to thief\".\n\nSentence 9: \n\"ay hanuːg bijomri\" → \"I will strike the donkey.\" \nFuture verb “will strike” = hanuːg, object bijomri.\n\nSentence 10: \n\"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n\"are giving me\" = aygi beyyeːcciːg → \"giving\" + \"to me\".\n\nNow focus on key patterns:\n\n- Giving: verb + object + to recipient\n- For: often expressed with \"for X\" = \"to X\" where X is a person/group\n- \"for us\" = \"for [us]\" → equivalent of \"to us\" in some cases? But look:\n - Sentence 1: \"bought the camels for the neighbours\" → \"jaːnticcirsu\" → \"to the neighbours\"\n - Sentence 6: \"The dog found the doors for me\" → \"eldeːnsu\" → \"for me\" → \"to me\"?\n - But in 10: \"giving me the necklaces\" → \"to me\"\n\nThus, \"for\" seems to be interpreted as \"to\" in recipients, but subject is often the agent.\n\nNow go through each translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\n\"are giving\" → present tense of giving → should use a future or continuous structure?\n\nLook at sentence 10: \"The cowards are giving me the necklaces\" → \"sarkaːyi aygi beyyeːcciːg adeːnda\"\n\n\"are giving\" = aygi beyyeːcciːg (same as 5: beyyeːcciːg, but with aygi → making it \"are giving\")\n\nSo: [subject] aygi beyyeːcciːg [object] [to recipient]\n\nBut note: \"neighbours\" → from (1), \"jaːnticcirsu\" → \"the neighbours\"\n\n\"necklace\" → from (5), \"beyyeːcciːg\" → necklaces\n\n\"to the owner\" → \"tirt\" (owner), \"to\" → likely \"tirsa\" (from sentence 8), or \"to the owner\" = ?\n\nIn (8): \"The men gave the camels to the thief\" → \"iːdi magaski kamiːg tirsa\"\n\n→ \"gave X to Y\" = \"magaski kamiːg tirsa\"\n\nSo \"to the owner\" = \"tirsa\" + owner → \"tirsa tirt\"?\n\nBut in (6): \"dog found the doors for me\" → \"eldeːnsu\" — “for me” → different.\n\nDoes \"to\" always mean \"for\"? Not quite. In (1): \"bought for the neighbours\" → \"jaːnticcirsu\"\n\nIn (3): \"give the chicken to the dogs\" → \"darbadki biticcirra\" → \"to dogs\"\n\nSo \"to X\" is used, and \"for X\" is same?\n\nCompare:\n- Sentence 1: \"bought X for Y\" → \"jaːnticcirsu\"\n- Sentence 3: \"give X to Y\" → \"darbadki biticcirra\"\n\nSo “for” and “to” seem equivalent in structure.\n\nHence, “give X to Y” = verb + object + to Y\n\nIn (16): \"neighbours are giving the necklace to the owner\"\n\n→ Subject: \"neighbours\" → “jaːnticcirsu” in sentence 1 → so “jaːnticcirsu” is the noun for neighbours\n\n→ giving → “aygi beyyeːcciːg” (from 10: \"are giving\")\n\n→ object: “necklace” → “beyyeːcciːg” (necklaces)\n\n→ to the owner → “tirt” → so “tirsa tirt”?\n\nBut from (8): “gave the camels to the thief” → “magaski kamiːg tirsa” → object + to Y\n\nSo: [subject] [verb] [object] [to Y]\n\nSo 16: \"jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt\"? — no, duplicate.\n\n\"the necklace\" → one necklace, singular.\n\n\"beyyeːcciːg\" is necklaces (plural). In (5): \"I am buying the necklaces\" → plural.\n\nBut (1): \"the camels\" — plural.\n\nIn (3): \"the chicken\" → singular.\n\nSo could \"necklace\" be singular?\n\nCompare: \"the necklace\" → would require singular form.\n\nNo singular form for \"necks\" is given. But in (5), \"beyyeːcciːg\" is used for necklaces, plural.\n\nBut in (1) “camels” — plural.\n\nIn (4): “dresses” — plural.\n\nIn (6): “doors” — plural.\n\nSo probably, the base form is plural; singulars may be implied or not marked.\n\nBut (16) says \"the necklace\", singular.\n\nHowever, in the source examples, all objects are plural.\n\nAssume that \"necklace\" is used as plural; perhaps the grammar does not mark number.\n\nBut in (9): \"strike the donkey\" — singular.\n\nSo both singular and plural exist.\n\nThus, in (16): \"the necklace\" → must use singular form.\n\nBut no singular form given.\n\nWait — is \"beyyeːcciːg\" only for plural?\n\nYes, in (5): \"necklaces\", not \"necklace\".\n\nSo likely, base noun form is plural; singular is not marked.\n\nThus, assume \"necklace\" = beyyeːcciːg (used as unmarked plural).\n\nSo object: beyyeːcciːg\n\n\"to the owner\" = as in (8): \"to the thief\" = \"tirsa tirt\"\n\nSo \"tirsa tirt\"\n\n\"are giving\" = aygi beyyeːcciːg\n\n\"subject: neighbours\" → \"jaːnticcirsu\"\n\nSo full: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt?\n\nBut that has “beyyeːcciːg” twice — error.\n\nObject is “the necklace” → one noun.\n\nSo object = beyyeːcciːg → \"necklace\" (plural reassigned)\n\nBut perhaps \"necklace\" is semantically singular, but grammatically plural.\n\nAlternatively, maybe the noun is used in plural with structure.\n\nBut in sentence 3: “the chicken” → singular, and \"darbadki biticcirra\" → “the chicken to the dogs”\n\nSo singular should work.\n\nBut only plural forms are provided.\n\nSo likely, the lexicon does not have singular, or it is implied.\n\nThus, for consistency, use \"beyyeːcciːg\" for \"the necklace\" — even if plural.\n\nSo sentence 16: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt?\n\nNo — two beyyeːcciːg.\n\nOnly one object.\n\nNeed: [subject] [verb] [object] [to recipient]\n\nSo: jaːnticcirsu aygi beyyeːcciːg [beyyeːcciːg] tirsa tirt? → duplicate.\n\nMistake.\n\nObject is “necklace”, so only one.\n\nBut “beyyeːcciːg” is the word for necklaces (plural). Is there a singular?\n\nNot shown.\n\nPossibility: the structure uses \"beyyeːcciːg\" for singular or plural.\n\nIn (5): “I am buying the necklaces” — so plural.\n\nBut in (1): “bought the camels” — plural.\n\nIn (4): “stole the dresses” — plural.\n\nSo all have plural nouns.\n\nThus, “necklace” is probably treated as plural.\n\nSo we must use “beyyeːcciːg” for the object, even if it means \"necklaces\".\n\nBut the sentence says \"the necklace\", singular.\n\nBut in absence of singular, use plural form with pragmatic understanding.\n\nThus, final: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt → no, redundant.\n\nWait — syntax: subject + verb + object + to recipient\n\n\"give X to Y\" → so perhaps: [subject] [verb] [object] [to recipient]\n\n“to recipient” = “tirsa [Y]”\n\nSo: jaːnticcirsu aygi beyyeːcciːg [beyyeːcciːg] tirsa tirt? — again, double.\n\nUnless “beyyeːcciːg” is used once.\n\nMaybe the object is “the necklace”, and “beyyeːcciːg” is the noun, so only once.\n\nSo: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt → still two.\n\nWait — perhaps the word is just “beyyeːcciːg” for necklaces, and in context, it is used for \"the necklace\".\n\nSo object = beyyeːcciːg\n\nSo sentence: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt? — no.\n\nNo — only one object noun.\n\nSo: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt — impossible.\n\nMistake: “beyyeːcciːg” is the noun. It should appear once.\n\nSo: jaːnticcirsu aygi beyyeːcciːg [beyyeːcciːg] tirsa tirt? — no.\n\nI think there is a typo in construction.\n\nPerhaps the object construction is simple.\n\nIn (3): “jahali waliːg darbadki biticcirra” → \"the young men will give the chicken to the dogs\" — \"waliːg\" = subject, \"darbadki\" = the chicken, \"biticcirra\" = to the dogs.\n\nSo: [subject] [verb] [object] [to recipient]\n\nSo here: \"jahali\" → subject, \"waliːg\" → verb (give), \"darbadki\" → object (chicken), \"biticcirra\" → to dogs.\n\nSo similar.\n\nFor 16: subject = \"neighbours\" → \"jaːnticcirsu\"\n\nverb = \"are giving\" → \"aygi beyyeːcciːg\"\n\nobject = \"necklace\" → \"beyyeːcciːg\" (singular or plural)\n\nrecipient = \"owner\" → \"tirt\"\n\nto owner = \"tirsa tirt\"\n\nSo: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt → but again, two instances.\n\nBut in (3): \"waliːg darbadki biticcirra\" — only one “darbadki”\n\nIn (3), “chicken” → “darbadki”\n\nSimilarly, “dog” → not a noun in the list.\n\nIn (10): “giving me the necklaces” → “adeːnda” = me, “beyyeːcciːg” = necklace\n\nSo object = beyyeːcciːg\n\nSo in 16: object = beyyeːcciːg\n\nSo full: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt — still duplicate.\n\nUnless “beyyeːcciːg” is used once.\n\nSo perhaps the object is just “beyyeːcciːg” — representing \"the necklace\", plural or singular.\n\nThus: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt → confusion.\n\nWait — in (3): “the chicken” → “darbadki”\n\nSo \"chicken\" = \"darbadki\"\n\nSo \"necklace\" = \"beyyeːcciːg\"\n\nThus, object = beyyeːcciːg\n\nSo sentence: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt → two beyyeːcciːg.\n\nNo.\n\nI think the structure is:\n\nSubject + verb + object + to recipient\n\nSo: jaːnticcirsu + aygi beyyeːcciːg + beyyeːcciːg + tirsa tirt\n\nBut then object is duplicated.\n\nUnless “beyyeːcciːg” is both verb and object? No.\n\n\"aygi beyyeːcciːg\" — “aygi” = are, “beyyeːcciːg” = buying/giving?\n\nIn (5): “ay beyyeːcciːg” — “I am buying”\n\nIn (10): “sarkaːyi aygi beyyeːcciːg” — “the cowards are giving”\n\nSo “aygi” is auxiliary showing present tense.\n\n“beyyeːcciːg” is the verb \"to buy/give\".\n\nBut in (10), \"giving\" is “aygi beyyeːcciːg” — so “beyyeːcciːg” is the verb.\n\nTherefore, in 16: verb is “aygi beyyeːcciːg”\n\nObject is “necklace” → as in (5), “beyyeːcciːg” — but that’s the verb.\n\nNo — in (5), “beyyeːcciːg” is object (necklaces)\n\nSo “necklace” is “beyyeːcciːg”\n\nSo object = beyyeːcciːg\n\nThen: subject: jaːnticcirsu\n\nverb: aygi beyyeːcciːg\n\nobject: beyyeːcciːg\n\nrecipient: tirsa tirt\n\nSo: jaːnticcirsu aygi beyyeːcciːg beyyeːcciːg tirsa tirt\n\nBut this has two “beyyeːcciːg” — error.\n\nUnless the noun for \"necklace\" is different.\n\nIn (5): \"I am buying the necklaces\" → object is “ajānirri”?\n\nNo — sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\nSo “beyyeːcciːg” = verb (buying), “ajānirri” = necklaces.\n\nAh! Key point!\n\nIn (5): \"ay beyyeːcciːg ajaːnirri\" → \"beyyeːcciːg\" = verb, \"ajānirri\" = necklaces.\n\nSimilarly, \"neighbour\" in (1): \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"kanarriːcciːg\" = bought, \"kamiːg\" = camels, \"jaːnticcirsu\" = for neighbours.\n\nSo nouns:\n- camels = kamiːg\n- dress = kadeːg\n- chicken = darbadki\n- dresses = kadeːcciːg\n- doors = eldeːnsu\n- dogs = ticcirsu\n- donkey = bijomri\n- necklaces = ajaːnirri\n- neighbours = jaːnticcirsu\n- owner = tirt\n- young men = jahali\n- thief = magas\n- coward = sarkaːyi\n- dog = baːbiːg\n\nThus, \"necklace\" = ajaːnirri\n\nSo in (5): \"beyyeːcciːg\" = verb \"buying\", \"ajaːnirri\" = necklaces.\n\nSo object of \"giving\" is not \"beyyeːcciːg\", but \"ajaːnirri\"\n\nTherefore, for sentence 16: \"neighbours are giving the necklace to the owner\"\n\nSubject: jaːnticcirsu\n\nVerb: aygi beyyeːcciːg (are giving)\n\nObject: ajaːnirri (necklace)\n\nRecipient: tirt (owner) → \"tirsa", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11404.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "iid", + "sample_index": 2, + "output": "First, examine the given examples to identify consistent patterns in Kunuz Nubian syntax and verb structure.\n\nFrom examples:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu → \"We bought the camels for the neighbours.\" \n → \"buy (subject) + object + for (beneficiary)\" \n Structure: [subject] [verb] [object] [for] [beneficiary]\n\n2. tirt kadeːg allesu → \"The owner repaired the dress.\" \n → [subject] [verb] [object] \n No \"for\" here; verb is transitive, object direct.\n\n3. jahali waliːg darbadki biticcirra → \"The young men will give the chicken to the dogs.\" \n → [subject] [will] [verb] [object] [to] [recipient] \n \"to\" indicates direction of giving.\n\n4. man jahalgi kadeːcciːg maːgtirsu → \"He stole the dresses for the young man.\" \n → [subject] [verb] [object] [for] [beneficiary] \n Again, \"for\" indicates beneficiary.\n\n5. ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces.\" \n → [subject] [be] [verb] [object] \n Present continuous: \"be + verb\" for ongoing action.\n\n6. wal aygi baːbiːg eldeːnsu → \"The dog found the doors for me.\" \n → [subject] [verb] [object] [for] [beneficiary] \n \"for me\" = for the speaker.\n\n7. magas ikki waliːg ticcirsu → \"The thief gave you (pl.) the dogs.\" \n → [subject] [verb] [you (pl)] [the dogs] \n \"you (pl)\" = direct recipient.\n\n8. iːdi magaski kamiːg tirsa → \"The men gave the camels to the thief.\" \n → [subject] [verb] [object] [to] [recipient] \n \"to\" = recipient, not beneficiary.\n\n9. ay hanuːg bijomri → \"I will strike the donkey.\" \n → [subject] [will] [verb] [object] \n Future tense: \"will + verb\"\n\n10. sarkaːyi aygi beyyeːcciːg adeːnda → \"The cowards are giving me the necklaces.\" \n → [subject] [are + verb] [object] [to] [beneficiary?] → \"giving me\" → \"to me\" \n \"me\" = recipient of the giving.\n\nNow, identify the two constructions:\n\n- Giving: [subject] [verb] [object] [to/for] [recipient/beneficiary]\n - \"to\" marks recipient (receiver)\n - \"for\" marks beneficiary (someone who gains benefit)\n\n- Buying: [subject] [verb] [object] [for] [beneficiary]\n\nFrom (1), (4), (6): \"for\" = beneficiary \nFrom (3), (8): \"to\" = recipient\n\nSo:\n- \"give X to Y\" → X is object, Y is recipient\n- \"give X for Y\" → Y is beneficiary\n\nNow, address each translation:\n\n16. \"The neighbours are giving the necklace to the owner.\" \n → Subject: The neighbours \n → Verb: are giving → \"iːdi magaski\" (are giving) \n → Object: the necklace → \"beyyeːcciːg\" \n → To: the owner → \"tirt\" \n Structure: [subject] [are giving] [necklace] [to] [owner] \n From example (10): \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"aygi\" = \"are giving\", \"adeːnda\" = \"me\" \n So \"iːdi\" = \"are\" (they are), \"magaski\" = \"giving\", \"beyyeːcciːg\" = \"necklace\", \"tirt\" = \"owner\" \n → \"iːdi magaski beyyeːcciːg tirt\"\n\n17. \"The young man bought the dog for us.\" \n → Subject: The young man → \"jahali\" \n → Verb: bought → \"kadeːg\" or \"kadeːcciːg\"? \n Example (1): \"ar kanarriːcciːg kamiːg\" → \"we bought the camels\" → \"kanarriːcciːg\" = bought \n Example (4): \"man jahalgi kadeːcciːg\" → \"he stole the dresses\" → \"jahalgi\" = stole → so \"kadeːcciːg\" = stole \n \"kadeːg\" = repair? \"tirt kadeːg\" → repair \n So \"kadeːg\" = repair, \"kadeːcciːg\" = steal? Not likely \n But (1): \"kanarriːcciːg\" = bought \n (4): \"kadeːcciːg\" = stole \n So \"buy\" = \"kanarriːcciːg\"\n\nThus, \"The young man bought the dog\" = \"jahali kanarriːcciːg darbadki\" \nThen \"for us\" = \"for us\" → \"for\" + \"us\" \nWho is \"us\"? From (6): \"for me\" → \"maːgtirsu\" → \"for me\" \nSo \"for us\" → \"for waliːg\" \n\"us\" = waliːg \nThus: \"jahali kanarriːcciːg darbadki for waliːg\" \n→ \"jahali kanarriːcciːg darbadki waliːg\"\n\n18. \"We will steal him.\" \n → \"We\" = \"ar\" \n → \"will\" = \"aya\" or \"jay\"? Example (9): \"ay hanuːg\" → \"I will strike\" → \"ay\" = I, \"hanuːg\" = strike \n Future: \"will\" likely marked by \"ay\" or \"ji\"? But in (9): \"ay\" = I, \"hanuːg\" = strike → \"ay\" + verb \n (3): \"jahali waliːg...\" → \"will\" is implicit \n So future = \"ay\" or added prefix? \n Example (9): \"I will strike\" → \"ay hanuːg\" → \"ay\" = first person, future? \n But no explicit \"will\" marker. Future is often derived from auxiliary. \n Look at (3): \"jahali waliːg...\" → present future \n So future = \"will\" = waliːg prefix? \n In (3): \"jahali waliːg\" → \"the young men will give\" \n So \"waliːg\" marks future tense. \n Therefore, \"we will steal him\" → \n → \"ar waliːg kadeːcciːg\" → \"we will steal\" \n Object: \"him\" → male personal pronoun? \n What is \"him\"? Dunno. Example (4): \"for the young man\" → \"maːgtirsu\" \n \"him\" = \"magas\" (the thief)? In (7): \"magas\" = thief \n But no \"him\" explicitly. \n In (10): \"adeːnda\" = me; \"beyyeːcciːg\" = necklaces \n So pronouns: \n - me = adeːnda \n - you (pl) = waliːg \n - us = waliːg \n - him = ? \n Example (7): \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl) the dogs\" → no \"him\" \n Example (9): \"ay hanuːg bijomri\" → \"I will strike the donkey\" \n So \"the donkey\" = object \n \"him\" = likely a masculine singular pronoun → possibly \"maːgtirsu\" = young man? \n But \"maːgtirsu\" = \"for the young man\" \n From (4): \"kadeːcciːg maːgtirsu\" → \"stole for the young man\" \n So \"maːgtirsu\" = young man \n In (18): \"steal him\" → \"him\" = a person \n No direct pronoun, so likely \"magas\" = thief → \"steal the thief\"? \n But \"him\" likely refers to a person. \n No such pronoun in the examples. \n But look at (3): \"will give the chicken to the dogs\" → \"to dogs\" \n So \"him\" = possibly \"magas\" → \"the thief\" \n But we need to find a pronoun. \n In (1): \"for the neighbours\" → \"kamiːg\" = neighbours \n (2): \"the owner\" → \"tirt\" \n (5): \"buy the necklaces\" → \"beyyeːcciːg\" \n So possible pronouns: \n - me = adeːnda \n - you (pl) = waliːg \n - us = waliːg \n - him = ? \n\n In (19): \"the owners struck the thieves\" → \"the owners\" and \"the thieves\" → nouns \n So \"him\" is likely a person in a role. \n In absence of a direct pronoun, perhaps \"magas\" = thief \n So \"we will steal him\" → \"ar waliːg kadeːcciːg magas\" \n \"waliːg\" = will; \"kadeːcciːg\" = steal; \"magas\" = thief (him) \n\n So: \"ar waliːg kadeːcciːg magas\"\n\n19. \"The owners struck the thieves.\" \n → Subject: owners → \"tirt\" (owner) → plural? \"tir\" or \"tir iːdi\"? \n (2): \"tirt kadeːg\" → owner repaired \n So \"tirt\" = owner, singular \n \"owners\" = plural → likely \"tirsi\" or \"tir iːdi\"? \n Example (8): \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" \n \"iːdi\" = the men (plural) → so \"iːdi\" = plural subject \n \"owners\" → plural → so \"iːdi\" \n Verb: \"struck\" → (9): \"hanuːg bijomri\" → \"strike\" → \"hanuːg\" \n \"struck\" = \"hanuːg\" \n Object: \"the thieves\" → \"magas\" → \"the thieves\" \n So: \"iːdi hanuːg magas\" \n → \"the owners struck the thieves\"\n\n20. \"The dogs found the chickens for the coward.\" \n → Subject: dogs → \"dardar\" or \"dal\"? (7): \"magas\" = thief, (3): \"jahali\" = young men \n No \"dogs\" directly. \n (6): \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" \n So \"wal\" = dog \n \"found\" = \"baːbiːg\" \n \"the chickens\" = \"biticcirra\" (in 3: \"give the chicken to the dogs\") \n \"for the coward\" = \"for sarkaːyi\" (from 10) \n → \"wal baːbiːg biticcirra for sarkaːyi\" \n → \"wal baːbiːg biticcirra sarkaːyi\" → with \"for\" → \"for sarkaːyi\"\n\nSo now compile:\n\n16. The neighbours are giving the necklace to the owner. \n→ \"iːdi magaski beyyeːcciːg tirt\"\n\n17. The young man bought the dog for us. \n→ \"jahali kanarriːcciːg darbadki waliːg\"\n\n18. We will steal him. \n→ \"ar waliːg kadeːcciːg magas\"\n\n19. The owners struck the thieves. \n→ \"iːdi hanuːg magas\"\n\n20. The dogs found the chickens for the coward. \n→ \"wal baːbiːg biticcirra sarkaːyi\"\n\nVerify with original patterns:\n\n- Giving: [subject] [are giving] [object] [to] [recipient] → (16): matches \n- Buying: [subject] [buy] [object] [for] [us] → (17): yes \n- Future: [we] [will] [steal] → (18): yes \n- Striking: [owners] [struck] [theives] → (19): yes \n- Found: [dog] [found] [chickens] [for] [coward] → (20): yes\n\nAll patterns align.\n\nFinal translations:\n\nb.1 / 16.: iːdi magaski beyyeːcciːg tirt \nb.2 / 17.: jahali kanarriːcciːg darbadki waliːg \nb.3 / 18.: ar waliːg kadeːcciːg magas \nb.4 / 19.: iːdi hanuːg magas \nb.5 / 20.: wal baːbiːg biticcirra sarkaːyi\n\n\\boxed{b.1: iːdi magaski beyyeːcciːg tirt; b.2: jahali kanarriːcciːg darbadki waliːg; b.3: ar waliːg kadeːcciːg magas; b.4: iːdi hanuːg magas; b.5: wal baːbiːg biticcirra sarkaːyi}", + "generated_tokens": 3178, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: iːdi magaski beyyeːcciːg tirt; b.2: jahali kanarriːcciːg darbadki waliːg; b.3: ar waliːg kadeːcciːg magas; b.4: iːdi hanuːg magas; b.5: wal baːbiːg biticcirra sarkaːyi", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 8483.0, + "ioling_final_answer_chars": 172.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the grammatical structure of the given examples to detect patterns in Kunuz Nubian.\n\nLook at example 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \nStructure: [Subject] + [verb] + [object] + [for + recipient] \n\"ar\" = we; \"kanarriːcciːg\" = bought; \"kamiːg\" = the camels; \"jaːnticcirsu\" = for the neighbours.\n\nExample 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n\"tirt\" = owner; \"kadeːg\" = repaired; \"allesiːsu\" = the dress.\n\nExample 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men; \"waliːg\" = will; \"darbadki\" = give; \"biticcirra\" = the chicken; \"to the dogs\" → implied by structure.\n\nExample 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n\"man\" = he; \"jahalgi\" = stole; \"kadeːcciːg\" = the dresses; \"maːgtirsu\" = for the young man.\n\nExample 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"ay\" = I; \"beyyeːcciːg\" = am buying; \"ajaːnirri\" = the necklaces.\n\nExample 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = dog; \"aygi\" = found; \"baːbiːg\" = the doors; \"eldeːnsu\" = for me.\n\nExample 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n\"magas\" = thief; \"ikki\" = gave; \"waliːg\" = you (pl.); \"ticcirsu\" = the dogs.\n\nExample 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n\"iːdi\" = men; \"magaski\" = to the thief; \"kamiːg\" = the camels; \"tirsa\" = gave.\n\nExample 9: \n\"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n\"ay\" = I; \"hanuːg\" = will strike; \"bijomri\" = the donkey.\n\nExample 10: \n\"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n\"sarkaːyi\" = cowards; \"aygi\" = are giving; \"beyyeːcciːg\" = the necklaces; \"adeːnda\" = to me.\n\nKey pattern:\n- The verb has a prefix indicating person or number, e.g., \"ay\" (I), \"man\" (he), \"wal\" (dog).\n- Objects are marked with a possessor or direct object marker.\n- The \"for\" or recipient construction appears as a postpositional element: \"for the X\" = \"Xsu\" or \"Xg\" depending on object.\n- Verb aspect and mood: \"will\" = \"waliːg\", \"are\" = \"aygi\", \"am\" = \"beyyeːcciːg\" (in example 5), \"is\" = not directly seen.\n\nNow examine how \"for\" is expressed:\n- In (1): \"jaːnticcirsu\" = for the neighbours → \"kamiːg jaːnticcirsu\"\n- In (4): \"maːgtirsu\" = for the young man → \"kadeːcciːg maːgtirsu\"\n- In (6): \"eldeːnsu\" = for me → \"baːbiːg eldeːnsu\"\n- In (10): \"adeːnda\" = to me → \"beyyeːcciːg adeːnda\"\n\nThus, \"for\" is expressed with a postposition: [object] + [recipient] → Object + [postposition for recipient].\n\nPattern for \"X is giving Y to Z\" = [subject] + [verb] + [object] + [postpositional phrase for recipient]\n\nPattern for \"buying\" = [I] + [beyyeːcciːg] + [object]\n\nPattern for \"steal\" = [he] + [jahalgi] + [object] + [for recipient]\n\nPattern for \"strike\" = [I] + [hanuːg] + [object]\n\nPattern for \"found\" = [subject] + [aygi] + [object] + [for recipient]\n\nSo general structure:\n- Subject + verb + object + for recipient (if any)\n\nNow translate (b):\n\n16. The neighbours are giving the necklace to the owner.\n\nSubject: \"the neighbours\" → \"jaːnticcirsu\" (from example 1) → \"jaːnticcirsu\" or \"jaːnticciri\" → from example, \"kamiːg jaːnticcirsu\", so noun \"kamiːg\" = the camels, \"jaːnticcirsu\" = neighbours.\n\nSo \"the neighbours\" = \"jaːnticcirsu\"\n\n\"are giving\" → similar to (10): \"sarkaːyi aygi beyyeːcciːg\" → cowards are giving → \"aygi\" = are giving.\n\n\"the necklace\" → \"beyyeːcciːg\" from example 5 → \"beyyeːcciːg\" = the necklaces.\n\n\"to the owner\" → \"tirt\" = owner → \"tirsa\" from example 8 → \"tirt\" is owner, \"magaski\" = to the thief → so \"to the owner\" = \"magaski tirt\" (possibly \"magaski tirtsu\", with a su suffix)\n\nIn (8): \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"magaski kamiːg tirsa\" → \"magaski\" = to the thief.\n\nSo \"to the owner\" = \"magaski tirt\"\n\nThus:\n\nThe neighbours are giving the necklace to the owner \n→ \"jaːnticcirsu aygi beyyeːcciːg magaski tirt\"\n\nCheck: subject (neighbours) + (are giving) + object (necklace) + to (owner)\n\nYes.\n\n17. The young man bought the dog for us.\n\nSubject: \"the young man\" → \"jahali\" (example 3)\n\nVerb: \"bought\" → in example 1: \"ar kanarriːcciːg\" → bought → \"kanarriːcciːg\"\n\nObject: \"the dog\" → in (2): \"kadeːg\" = repaired the dress → \"kadeːg\" = dress; probably \"waliːg\" = dog? Example 3: \"darbadki biticcirra\" → \"biticcirra\" = chicken; so likely \"tirsa\" = dog?\n\nIn (7): \"magas ikki waliːg ticcirsu\" → \"gave you the dogs\" → \"waliːg\" = the dogs → so \"waliːg\" = the dog (plural or singular?)\n\nHypothesize: \"waliːg\" = dog\n\nSo object: \"waliːg\"\n\n\"for us\" → \"us\" = plural of \"me\" → in (6): \"eldeːnsu\" = for me → \"adeːnda\" = for me → \"adeːnda\" for me → \"adisa\" or \"adiːg\"?\n\nIn (10): \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"for us\" → perhaps \"adeːnda\" (to me), but \"us\" is plural → in (3): \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → \"to the dogs\" → not explicitly marked.\n\nBut (6): \"found the doors for me\" → \"eldeːnsu\" → for me.\n\nSo \"for us\" — likely \"adisa\" or \"adisug\"? No such form. \"Us\" = plural pronoun.\n\nPossibility: \"adeːnda\" might be used with plural — or \"akadeːnda\"?\n\nNo indication. But in (8): \"gave to the thief\" → \"magaski\" + noun → \"magaski tirt\"\n\nSo recipient = [postposition] + [noun]\n\n\"for us\" = \"for the people\" → but not spelled out.\n\nTry plural: in (10), \"sarkaːyi (the cowards) are giving me\" → \"adeːnda\" = to me\n\nIn (6), \"found the doors for me\" → \"eldeːnsu\"\n\nIn (7), \"gave you (pl.) the dogs\" → \"waliːg\" already includes plural.\n\nSo object = \"dog\" → \"waliːg\"\n\n\"for us\" → is \"ulisi\" or \"adisug\"? Not in examples.\n\nBut in (4): \"stole the dresses for the young man\" → \"maːgtirsu\"\n\n\"for the young man\" → \"maːgtirsu\"\n\nSimilarly, \"for us\" → \"us\" = plural → \"waliːg\" (plural), so \"for us\" → \"waliːg\" + ? → not likely.\n\nAlternative: in (6): \"found the doors for me\" → \"eldeːnsu\" → so \"eldeːnsu\" = for me\n\nIn (10): \"giving me the necklaces\" → \"adeːnda\"\n\nSo \"for us\" = \"adisa\"? No such word.\n\nPerhaps \"adeːnda\" is used for \"to us\" — plural.\n\nExample (10): \"the cowards are giving me\" → \"adeːnda\" = to me\n\nBut if \"us\", it might be \"adeːnda\" with plural, or a different form.\n\nNo clear plural form.\n\nBut check (3): \"will give the chicken to the dogs\" → \"arr\" or not?\n\nNo direct example.\n\nAssume that \"for us\" is expressed as \"adeːnda\" → but that’s for me.\n\nWait: \"us\" = plural, so perhaps \"adeːnda\" is used for \"to us\" — possibly.\n\nBut in (10), it's \"giving me\" → \"adeːnda\"\n\nIn (6), \"for me\" → \"eldeːnsu\"\n\nSo \"for us\" → not seen.\n\nWait: in (9): \"I will strike the donkey\" → no recipient.\n\nBut in (4): \"stole the dresses for the young man\" → \"maːgtirsu\"\n\nSo for a person → \"maːgtirsu\" → \"for X\"\n\nSo for a group? No.\n\nBut \"us\" → likely the same as \"me\" in a general sense.\n\nPerhaps \"adeːnda\" is used for \"to us\", treating \"us\" as plural.\n\nPossible.\n\nSo \"for us\" = \"adeːnda\"\n\nSo: \"jahali kanarriːcciːg waliːg adeːnda\"\n\n\"the young man bought the dog for us\"\n\nYes.\n\n18. We will steal him.\n\n\"We\" → \"ar\" (example 1)\n\n\"will\" → \"waliːg\" (example 3)\n\n\"steal\" → in (4): \"man jahalgi kadeːcciːg\" → \"he stole\"\n\n\"jahalgi\" = steal\n\n\"him\" → \"him\" = \"maːgtirsu\"? \"for the young man\" → \"maːgtirsu\"\n\nSo \"him\" → likely \"maːgtirsu\"\n\nSo: \"ar waliːg jahalgi maːgtirsu\"\n\n19. The owners struck the thieves.\n\nSubject: \"the owners\" → \"tirt\" = owner → plural? \"tirt\" is singular → owners: plural → in (2): \"the owner\" → tirt → so \"tirtsu\" or \"tirsa\"?\n\nIn (8): \"the men gave to the thief\" → \"iːdi\" = men → plural\n\nIn (2): \"the owner\" → \"tirt\"\n\nSo \"owners\" → plural → \"tirtsu\" or \"tirtsu\"?\n\nNot marked.\n\nIn (8): \"iːdi\" = men → plural → so noun particles?\n\n\"owners\" = \"tirt\" with plural marker?\n\nPossibly \"tirtsu\" → like \"tirt\" → \"tirtsu\"?\n\nAlternatively, \"tirt\" is used for owners.\n\nBut no plural form.\n\nAssume \"tirt\" = owner → \"owners\" = \"tirtsu\"?\n\nLook at (6): \"the dog found the doors for me\" → \"wal\" = dog → singular.\n\nNo plural.\n\nBut in (10): \"the cowards\" → \"sarkaːyi\" → plural noun.\n\nSo noun \"owners\" → possible \"tirtsu\"\n\nBut not supported.\n\nAlternatively, \"owners\" = \"tirt\" → kept as such.\n\nBut in (8): \"the men\" = \"iːdi\"\n\nIn (2): \"the owner\" = \"tirt\"\n\nSo \"the owners\" = \"tirtsu\"?\n\nPossibility: suffix \"s\" or \"su\" → \"tirtsu\"\n\nSo \"tirtsu\"\n\n\"struck\" → in (9): \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\n\"hanuːg\" = strike\n\nSo \"the owners struck\" → \"tirtsu hanuːg ticcirsu\"\n\n\"the thieves\" → \"thieves\" → \"magas\" = thief → plural → \"magas\" plural?\n\nIn (7): \"the thief gave you the dogs\" → \"magas\"\n\nSo plural \"thieves\" = \"magas\" → possibly singular only.\n\nNo plural.\n\n\"the thieves\" → in absence of plural marking → \"magas\" → singular?\n\nBut \"the thieves\" is plural.\n\nPossibly \"magas\" is used for plural too.\n\nOr marked with suffix.\n\nIn (7): \"magas\" = thief → singular.\n\nIn (8): \"iːdi\" = men → plural.\n\nSo no consistent.\n\nBut \"thieves\" = plural → must be \"magas\" with plural form?\n\nPossibly \"magas\" is used for plural.\n\nIn example 7: \"the thief\" → \"magas\"\n\nBut not plural.\n\n\"the owners\" → \"tirtsu\"\n\n\"thieves\" → \"magas\" (same)\n\nSo \"tirtsu hanuːg magas\"\n\n\"struck the thieves\" → \"tirtsu hanuːg magas\"\n\nYes.\n\n20. The dogs found the chickens for the coward.\n\nSubject: \"the dogs\" → in (3): \"the young men\" = \"jahali\"; dogs? Not seen.\n\nIn (7): \"the thief gave you the dogs\" → \"waliːg\" = the dogs → \"waliːg\"\n\nSo \"the dogs\" = \"waliːg\"\n\n\"found\" → \"aygi\" (example 6)\n\nObject: \"the chickens\" → (3): \"give the chicken\" → \"biticcirra\" = chicken → so \"biticcirra\"\n\n\"for the coward\" → \"the coward\" → in (10): \"the cowards\" → \"sarkaːyi\"\n\nSo \"the coward\" = \"sarkaːyi\"\n\n\"for the coward\" → \"magaski sarkaːyi\"\n\nSo: \"waliːg aygi biticcirra magaski sarkaːyi\"\n\nNow compile:\n\n16. The neighbours are giving the necklace to the owner \n→ \"jaːnticcirsu aygi beyyeːcciːg magaski tirt\"\n\n17. The young man bought the dog for us \n→ \"jahali kanarriːcciːg waliːg adeːnda\"\n\n18. We will steal him \n→ \"ar waliːg jahalgi maːgtirsu\"\n\n19. The owners struck the thieves \n→ \"tirtsu hanuːg magas\"\n\n20. The dogs found the chickens for the coward \n→ \"waliːg aygi biticcirra magaski sarkaːyi\"\n\nNow verify against patterns:\n\n- (16): subject + \"aygi\" (are giving) + object (necklace) + \"magaski\" + recipient → yes \n- (17): subject (young man) + verb (bought) + object (dog) + \"adeːnda\" (for us) → supported by me-in-examples \n- (18): \"we\" + \"waliːg\" (will) + \"jahalgi\" (steal) + \"maːgtirsu\" (for him) → fine \n- (19): \"tirtsu\" (owners) + \"hanuːg\" (struck) + \"magas\" (thieves) → \"magas\" used as plural → plausible \n- (20): \"waliːg\" (dogs) + \"aygi\" (found) + \"biticcirra\" (chickens) + \"magaski sarkaːyi\" (to coward) → yes\n\nAll verbs and object markers consistent with provided examples.\n\nFinal answers:\n\nb.1 / 16: jaːnticcirsu aygi beyyeːcciːg magaski tirt \nb.2 / 17: jahali kanarriːcciːg waliːg adeːnda \nb.3 / 18: ar waliːg jahalgi maːgtirsu \nb.4 / 19: tirtsu hanuːg magas \nb.5 / 20: waliːg aygi biticcirra magaski sarkaːyi\n\n\\boxed{b.1: jaːnticcirsu aygi be", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10998.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "iid", + "sample_index": 0, + "output": "We are given English-Kilivila sentence pairs, and we are to translate 14–18 into English, noting that one of them has two possible translations.\n\nStep 1: Identify patterns from the given examples.\n\nLook at the structure of key phrases.\n\nIn sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ “One man” = “Bibani navasi” → “navasi” = man, “bibani” = one \n“will catch” = “tetala tau” → “tau” = will, “tetala” = catch \n“four fish” = “yena minasina” → “yena” = four, “minasina” = fish\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n\"Lekota\" = this, \"dimdim\" = white, \"mtona\" = arrived\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n\"Bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n\"Legisi\" = this, \"waga\" = old, \"makesiwena\" = saw, \"namwaya\" = those, \"minana\" = canoes\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"Amtona\" = which, \"tau\" = man, \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n\"Leyamatasi\" = old women, \"teyu\" = looked after, \"tauwau\" = two, \"nunumwaya\" = men\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman, \"minawena\" = will see, \"nakabitam\" = something\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n\"Navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = which, \"waga\" = canoe, \"legisesi\" = the chiefs, \"gweguyau\" = saw\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"Legisi\" = that, \"dakuna\" = beautiful, \"makwena\" = child, \"gwadi\" = child (repetition?), wait — \"gwadi\" = child, \"magudiwena\" = will arrive? But here: \"saw this stone\" — \"gudimanabweta\" = stone.\n\n\"Legisi\" is that, \"dakuna\" = beautiful, \"makwena\" = child? But also \"gwadi\" = child — perhaps \"gwadi\" and \"makwena\" are both used for children.\n\nBut sentence 10: \"saw this stone\" → \"gudimanabweta\" = stone.\n\nSo \"saw\" = \"makesiwena\" in sentence 4 → \"gweguyau\" in sentence 9 → likely \"gweguyau\" = saw.\n\nIn sentence 10: \"makesiwena\" is not used — instead, \"gweguyau\" is used? Wait no: sentence 9 uses \"gweguyau\" = saw, sentence 4 uses \"makesiwena\" = saw — so perhaps \"makesiwena\" and \"gweguyau\" both mean \"saw\", but different contexts.\n\nWait: sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"this old woman saw those canoes\" \nSentence 9: \"Amakena waga legisesi gweguyau?\" → \"Which canoe did the chiefs see?\" → \"gweguyau\" = saw\n\nSo \"gweguyau\" = saw.\n\nSimilarly, sentence 5: \"lekalimati\" = killed\n\nSentence 6: \"teyu\" = looked after\n\nSentence 7: \"minawena\" = will see, \"nakabitam\" = something\n\nSentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"How many things did those white men eat?\" \n\"kwevila\" = how many, \"lekamkwamsi\" = things, \"dimdim\" = white, \"mtosiwena\" = ate\n\nSo \"mtosiwena\" = ate\n\nSentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"naturala\"? \"natala\" = one? \"bunukwa\" = wild pig, \"gagasi\" → \"guyau\" = wild pig? \"guyau\" = wild pig, \"tokabitam\" = killed? But \"lekalimati\" = killed.\n\nIn all, we see fixed word sets:\n\n- \"navasi\" = one (man)\n- \"yena\" = four\n- \"minasina\" = fish\n- \"lekota\" = this\n- \"dimdim\" = white\n- \"mtona\" = arrived\n- \"bikota\" = that\n- \"gwadi\" = child\n- \"magudiwena\" = will arrive\n- \"makesiwena\" = saw\n- \"gweguyau\" = saw\n- \"teyu\" = looked after\n- \"tauwau\" = two\n- \"nunumwaya\" = men\n- \"vivila\" = woman\n- \"kwetala\" = clever\n- \"minawena\" = will see\n- \"nakabitam\" = something\n- \"navila\" = how many\n- \"ka’ukwa\" = dogs\n- \"lekotasi\" = arrived\n- \"amtona\" = which\n- \"lekalimati\" = killed\n- \"nayu\" = two (but earlier \"yena\" = four? Inconsistency?)\n\nWait: in sentence 1: \"yena minasina tetala tau\" → \"four fish\" → \"yena\" = four \nSentence 5: \"nayu bunukwa\" → \"two pigs\" → \"nayu\" = two\n\nSo \"yena\" = four, \"nayu\" = two\n\nSimilarly, \"tauwau\" = two men (sentence 6)\n\nSo numbers: \n- yena = four \n- nayu = two \n- tauwau = two \n- \"tau\" = will \n- \"mtona\" = arrived\n\nNow go to the target sentences:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"Navila\" = how many \n\"vivila\" = woman \n\"biyamata\" = ? \n\"tomwaya\" = ? \n\"mtona\" = arrived\n\n\"vivila\" is woman → so \"a woman\" → \"vivila\" \n\"biyamata\" = ? \nCompare to sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" \n\"vivila\" = woman\n\nIs \"biyamata\" = \"will look after\"? But no.\n\nLook at sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" → \"the old women looked after two men\"\n\n\"teyu\" = looked after\n\nSo \"teyu\" = looked after\n\nBut here: \"biyamata\" — \"bi\" is prefix? \"biyamata\" — perhaps \"bi\" = to, or \"bi\" = of?\n\nAlternatively, \"bi\" = will? In sentence 1: \"tetala tau\" → \"will catch\"\n\nNo \"bi\" in that.\n\nBut sentence 13: \"Navila vivila biyamatasi tau mtona?\" → \"How many women will look after this man?\"\n\nYes! Sentence 13: \n\"The clever chief killed one wild pig.\" → sentence 12 \nBut sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nSo sentence 13: \"Navila vivila biyamatasi tau mtona?\" = \"How many women will look after this man?\"\n\nSo \"biyamatasi\" = will look after, \"tau\" = will, \"mtona\" = this man.\n\nSo \"biyamatasi\" = look after (with \"tau\" being \"will\")\n\nBut in sentence 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n\"biyamata\" — likely a variant of \"biyamatasi\", with \"sasi\" → \"asi\"? Or missing a key?\n\n\"biyamata\" vs \"biyamatasi\" — \"sasi\" → perhaps \"sasi\" is of, \"asi\" is verb?\n\nIn sentence 13: \"biyamatasi\" → \"will look after\" \nIn 14: \"biyamata\" — perhaps missing \"si\"?\n\nBut in sentence 14: \"biyamata\" and \"tomwaya\"\n\n\"tomwaya\" — what is that?\n\nCompare to sentence 4: \"legisi waga makesiwena namwaya minana\" → \"this old woman saw those canoes\" \n\"namwaya\" = those canoes\n\nSo \"namwaya\" = those canoes\n\nSo \"tomwaya\" = that? Or this?\n\n\"tom\" might be related to \"to\", like \"this\"?\n\nSentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\"\n\n\"Legisi\" = that, \"gudimanabweta\" = stone\n\nSo \"tomwaya\" — perhaps \"tom\" = this, \"waya\" = canoes?\n\nIn 4: \"namwaya\" = those canoes → so \"nam\" = those, \"waya\" = canoes\n\nThus, \"tomwaya\" = this canoes? Or \"this\" + \"canoe\"?\n\n\"tom\" could be \"this\", like \"tom\" in \"tomwaya\" → \"this canoe\"?\n\nBut is \"canoe\" used in any place?\n\nYes: \"namwaya\" = canoes → \"waya\" = canoes\n\nSo \"tomwaya\" = this canoe?\n\nBut in sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\"\n\nHere, \"waga\" = canoe\n\nSo \"waya\" → canoe\n\nThus: \"tomwaya\" = this canoe\n\nSo 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n\"Navila\" = how many \n\"vivila\" = women \n\"biyamata\" → likely \"will look after\" (same as \"biyamatasi\", without \"si\")? Or a different verb?\n\nIn sentence 13: \"biyamatasi\" = will look after \nIn 14: \"biyamata\" — missing \"si\"? Or is it a different verb?\n\nBut \"tau\" is also present — \"mtona\" = this man, \"tau\" = will\n\nWait — in sentence 14: \"biyamata tomwaya mtona\" — no \"tau\" here?\n\n\"tau\" is present in the end: \"mtona\" — but not as \"tau\" — mtona is arrived, not will.\n\n\"tau\" = will — in sentence 1: \"tetala tau\" → will catch\n\nIn sentence 7: \"vivila minawena\" → will see\n\nIn sentence 13: \"biyamatasi tau mtona\" → will look after this man\n\nSo \"tau\" = will → present as suffix?\n\nSo in sentence 14: \"biyamata tomwaya mtona\" — no \"tau\"? Then it's not \"will\"?\n\nBut \"mtona\" = arrived — so \"arrived\"?\n\nSo \"how many women arrived at this canoe\"?\n\nBut \"biyamata\" = arrived? Or look after?\n\nBut \"biyamatasi\" = look after → so \"biyamata\" might be a form of arrived?\n\nBut there is no \"arrived\" verb used directly.\n\nLook at sentence 8: \"navila ka’ukwa lekotasi?\" → how many dogs arrived? \n\"lekotasi\" = arrived\n\nSo \"lekotasi\" = arrived\n\nSo \"mtona\" = arrived\n\nTherefore, in 14: \"mtona\" = arrived \nBut \"biyamata\" — possibly \"arrived\" or \"look after\"?\n\nNo direct verb for \"arrived\" used in \"biyamata\" — unless \"biyamata\" is a form of \"arrive\".\n\nBut \"mtona\" is the verb \"arrive\"\n\nSo it is likely that \"biyamata\" is not a verb — perhaps a noun?\n\nBut no.\n\nAlternative: \"biyamata\" = \"these women\" or something?\n\nBut the structure:\n\n\"Navila vivila biyamata tomwaya mtona?\"\n\nCompare to sentence 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\nSo in 13: \"biyamatasi\" + \"tau\" = will look after \nIn 14: \"biyamata\" + \"tomwaya\" + \"mtona\"\n\n\"mtona\" = arrived\n\nSo if \"biyamata\" were \"will arrive\", then it would be \"how many women will arrive at this canoe?\"\n\nBut no \"will\" in the verb — so perhaps \"biyamata\" = arrive\n\nBut in sentence 8: \"lekotasi\" = arrived\n\nSo \"arrived\" is \"lekotasi\"\n\n\"biyamata\" is not a known verb.\n\nBut look at sentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" → \"killed one wild pig\"\n\n\"nagasisi guyau\" — \"guyau\" = wild pig, \"tokabitam\" = killed?\n\n\"lekalimati\" = killed.\n\nSo \"tokabitam\" = killed?\n\nBut in sentence 7: \"nakabitam\" = something\n\nSo different forms.\n\nSo \"biyamata\" — is it a verb?\n\nNow, look at sentence 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n\"bikamkwamsi\" — \"bika\" = that? Like \"bikota\"? \"bikota\" = that\n\n\"bikamkwamsi\" → \"that things\" or \"that things\"?\n\n\"minasina\" = fish\n\nSo \"Bikamkwamsi kweyu vivila minasina\" → \"that things which will catch fish\" or \"that things which will look after fish\"?\n\n\"kweyu\" = will?\n\n\"vivila\" = woman\n\n\"minasina\" = fish\n\n\"bikamkwamsi\" = that things?\n\nBut sentence 15: \"Bikamkwamsi kweyu vivila minasina\" → likely \"That [something] will catch fish\" → but \"vivila minasina\" = woman fish?\n\nNo.\n\nCompare with sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\"\n\nSo \"vivila minawena\" = woman will see\n\nSo \"vivila minasina\" = woman fish? Not possible.\n\nBut \"kweyu\" = will\n\nSo \"Bikamkwamsi kweyu vivila minasina\" → \"those things will catch fish\" → but \"minasina\" = fish — so \"catch fish\"\n\nSo \"kweyu\" = will\n\nSo \"what things will fish catch\" — reversed?\n\nNo — \"Bikamkwamsi kweyu vivila minasina\" → \"those things will catch fish\" → [subject] will catch fish\n\nSo the subject is \"bikamkwamsi\" — \"that things\"\n\nSo \"that things will catch fish\"\n\nBut is \"minasina\" = fish → yes\n\nSo \"vivila minasina\" ≠ woman fish → likely \"vivila\" is not part of it?\n\nWait — in 15: \"Bikamkwamsi kweyu vivila minasina\"\n\n\"vivila\" = woman → so woman catch fish?\n\nBut sentence 1: \"navasi yena minasina tetala tau\" → one man catches fish\n\nSo \"man\" is \"navasi\", \"woman\" is \"vivila\"\n\nSo could \"vivila minasina\" = woman fish? But it's not a phrase.\n\nMore likely: \"vivila\" is an adjective? \"vivila\" = clever? But sentence 7: \"kwetala vivila\" = clever woman\n\nSo \"vivila\" = clever? Or woman?\n\n\"vivila\" appears with \"minawena\" — \"will see\", so woman will see\n\nSo possibly \"vivila\" = woman\n\nSo \"vivila minasina\" → woman fish — likely a mismatch.\n\nBut in sentence 15: \"kweyu vivila minasina\" → will catch fish (by woman)?\n\nBut no such structure.\n\nAlternative: \"Bikamkwamsi kweyu\" = the things will (do something), \"vivila minasina\" = woman fish — doesn't make sense.\n\nOr perhaps \"minasina\" is not fish — but \"minasina\" appears only in fish.\n\nEarlier: sentence 1: \"minasina\" = fish\n\nSo it must be", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11412.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "iid", + "sample_index": 1, + "output": "Start by analyzing the English–Kilivila examples for recurring patterns in word order, morphology, and syntactic structure.\n\nLook at sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n\"navasi\" = man; \"yena\" = one; \"minasina\" = fish; \"tetala\" = four; \"tau\" = will catch → the verb is at the end.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n\"lekota\" = this; \"dimdim\" = white; \"mtona\" = man; \"arrived\" → so \"lekota\" = demonstrative, \"dimdim\" = adjective, \"mtona\" = noun; verb is at end.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n\"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive → verb at end.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n\"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes → verb at end.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs → verb \"lekalimati\" is in middle.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n\"leyamatasi\" = the; \"teyu\" = old; \"tauwau\" = women; \"nunumwaya\" = two men → verb is not at end; \"looked after\" is a verb + object; \"nunumwaya\" = two men.\n\nBut sentence 6: \"looked after\" is not directly visible. \"nunumwaya\" = men, and \"tauwau\" = women → seems like a possession or care structure.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something → verb \"minawena\" is at the end.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n\"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived → so \"how many\" + noun + verb.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"amakena\" = which; \"waga\" = canoe; \"legisesi\" = the; \"gweguyau\" = saw → verb at end.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = this; \"magudiwena\" = saw; \"gudimanabweta\" = stone → verb \"magudiwena\" at end.\n\nSentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n\"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate → verb \"mtosiwena\" at end.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"gagasisi\" = chief; \"tokabitam\" = clever? Seems off.\n\nWait: \"nagasisi guyau\" — likely \"guyau\" = pig; \"takabitam\" = clever → so \"guyau\" = pig, \"tokabitam\" = clever — so \"the clever chief\" = \"gagasisi guyau tokabitam\" — but that's strangely worded.\n\nBetter: look at sentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man → verb \"biyamatasi\" = will look after.\n\nNow, pattern: \n- Verbs often come at the end (e.g., \"will arrive\", \"saw\", \"ate\", \"will look after\"). \n- Nouns and adjectives precede verbs. \n- Demonstratives (this, that, which, how many) often begin sentences or precede nouns. \n- Clauses like \"which X did Y\" or \"how many X did Y\" follow a structure: [quantifier] [noun] [verb].\n\nNow examine each sentence in (a):\n\n14. Navila vivila biyamata tomwaya mtona? \n\"navila\" = how many; \"vivila\" = women; \"biyamata\" = look after; \"tomwaya\" = this; \"mtona\" = man → structure like 13: How many women will look after this man? \n\"biyamata\" = look after; matches \"biyamatasi\" in 13 → \"biyamatasi\" is \"will look after\", so \"biyamata\" = likely \"look after\" (present or future). \n\"tomwaya\" = this; \"mtona\" = man → \"this man\". \n→ So: How many women will look after this man?\n\n15. Bikamkwamsi kweyu vivila minasina. \n\"bikamkwamsi\" = that; \"kweyu\" = two? \"kweyu\" appears in 7 as \"gweyu\" (in \"gweyu minasiwena\") → need to check. \nIn 14: \"vivila\" = woman; \"tomwaya\" = this. \nIn 3: \"bikota\" = that; \"gwadi\" = child \nIn 10: \"legisi\" = that; \"dakuna\" = beautiful \nIn 2: \"lekota\" = this; \"dimdim\" = white man \nSo \"bikamkwamsi\" = that? Maybe same as \"bikota\". \n\"kweyu\" = two? In 12: \"nayu\" = two pigs → \"nayu\" = two \n\"kweyu\" = possibly same as \"kweyu\" — likely \"two\" \n\"vivila\" = woman; \"minasina\" = fish? In sentence 1: \"minasina\" = fish \nBut \"vivila minasina\" = woman fish? No. \nPossibly: \"kweyu vivila minasina\" → two women caught some fish? \nBut \"minasina\" is a noun, so \"vivila minasina\" = women catch fish? \nBut verb should be at end. \nBut here, no verb at end. \nContradiction. \nUnless \"minasina\" is the verb. \nBut \"minasina\" appears in sentence 1: \"minasina tetala tau\" → \"fish will be caught\" → so \"minasina\" = fish? \nBut in 2: \"mtona\" = man; \"dimdim\" = white → no verb. \nIn 1: \"tetala tau\" → \"four will catch\" \nIn 5: \"lekalimati nayu bunukwa\" → \"killed two pigs\" \nIn 11: \"mtosiwena\" = ate \nSo verbs are: \"tau\" (catch), \"mtona\" (arrived), \"magudiwena\" (saw), \"lekalimati\" (killed), \"mtosiwena\" (ate), \"biyamatasi\" (will look after), \"gweguyau\" (saw)\n\nSo in 15: \"bikamkwamsi kweyu vivila minasina\" → no verb at end → must be missing. \nUnless one of the words is verb. \nBut no verb in end. \nSo maybe this is not a full sentence — or \"minasina\" is verb.\n\nBut in sentence 1: \"minasina tetala tau\" → \"fish will be caught\" → so \"minasina\" is not verb.\n\nPossibly a typo or misreading. \nBut look at 16: \"Amagudina gwadi lekota?\" → \"Amagudina\" = which? \"gwadi\" = child; \"lekota\" = this. \n\"amagudina\" → which? \"am\" = which? In 5: \"amtona\" = which (man); in 9: \"amakena\" = which (canoe) \nSo \"amagudina\" = which? \n\"gwadi\" = child; \"lekota\" = this → so \"which child this?\" → \"which child is this?\" \nBut meaning: \"Which child is this?\" → \"Amagudina gwadi lekota?\" \nYes. \nSo 16: Which child is this?\n\n17. Tevila tauwau bigisesi gugwadi gudigasisi? \n\"tevila\" = how many? (from 8: \"navila\" = how many → so \"tevila\" = how many) \n\"tauwau\" = women? (from 6: \"teyu tauwau\" = old women) \n\"bigisesi\" = that? (from 7: \"bigisi\" = that; \"bigisesi\" = that?) \n\"gugwadi\" = what? \"gugwadi\" → similar to \"gwadi\" (child) — so \"gugwadi\" = child? \n\"gudigasisi\" = woman or chief? \"gudigasisi\" → compare to \"gagasisi\" in 12? — seems like \"gagasisi\" = chief → so \"gudigasisi\" = chief? \n\"bigisesi\" = that → \"that woman\"? \nSo: \"how many women will that chief see?\" → \"tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tauwau\" = women? \n\"bigisesi\" = that → \"that\" \n\"gugwadi\" = child? — conflict. \n\"bigisesi gugwadi gudigasisi\" = \"that child chief\"? No. \n\"bigisesi\" = that; \"gugwadi\" = child; \"gudigasisi\" = chief — so \"that child chief\"? No. \nUnlikely. \nAlternatively, is \"gugwadi\" = chief? \nNo, \"gwadi\" = child → \"gugwadi\" = child → consistent. \n\"bigisesi\" = that → \"that\" \nthen \"gugwadi\" = child → so \"that child\" \n\"gudigasisi\" = woman? Chief? \nIn 12: \"gagasisi guyau\" → \"clever chief\" → \"gagasisi\" = chief → so likely \"gudigasisi\" = chief \nSo \"bigisesi gugwadi gudigasisi\" = \"that child chief\"? → grammatically odd. \nPossibility: \"bigisesi\" = that; \"tauwau\" = women; \"gugwadi\" = chief? — no. \nAnother possibility: \"gugwadi\" is a noun, like \"bunukwa\" → pig, \"gagasisi\" = chief. \nBut \"gugwadi\" = child. \nSo perhaps the phrase is: how many women did that chief see? → but \"bigisesi\" = that, \"gugwadi\" = child, \"gudigasisi\" = chief — no. \n\"bigisesi\" likely means \"that\" — \"that woman\"? \n\"bigisesi\" vs \"bigisi\" → \"bigisi\" = that → \"bigisesi\" = that (plural? or same) \n\"tauwau\" = women \n\"gugwadi\" = child → not needed. \n\"Bigisesi gugwadi\" → that child → but \"gudigasisi\" → chief → not clear. \nPossibly: \"how many women will that chief see?\" — but where is the verb? \nThe verb should be at end. \nBut here: \"tevila tauwau bigisesi gugwadi gudigasisi?\" → no verb at end. \nSo verb missing. \nContradiction again.\n\nWait — in sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \nBut in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → verb \"magudiwena\" at end. \nSo any sentence with verb at end must have it. \nSo this sentence has no verb at end → not possible. \nUnless one of the words is verb.\n\nCheck for words that can be verbs: \n- \"bigisesi\" → in 7: \"bigisi\" = that → so not verb \n- \"gugwadi\" → \"gwadi\" = child → not verb \n- \"gudigasisi\" → likely \"chief\" \n- \"tauwau\" → women \n\nNone seem to be verbs.\n\nBut sentence 13: \"Navila vivila biyamatasi tau mtona\" → verb \"biyamatasi\" = will look after → at end \nSentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" → verb \"lekalimati\" = killed → at beginning? \n\"lekalimati\" = killed → at beginning → so not always at end. \nBut in most, the verb is at end.\n\nIn 5: \"amtona tau lekalimati nayu bunukwa?\" → \"lekalimati\" (killed) at middle → not end. \nIn 11: \"kwevila lekamkwamsi dimdim mtosiwena?\" → verb \"mtosiwena\" at end. \nIn 9: \"amakena waga legisesi gweguyau?\" → verb \"gweguyau\" at end. \nIn 10: verb at end. \nIn 8: \"navila ka’ukwa lekotasi?\" → verb at end.\n\nSo in most cases, verbs are at end.\n\nIn 17, no verb at end → likely error or different structure. \nSimilarly, in 15: \"bikamkwamsi kweyu vivila minasina\" — no verb at end → issue.\n\nBut sentence 13: \"Navila vivila biyamatasi tau mtona?\" → verb \"biyamatasi\" at end → works. \nSentence 14: Navila vivila biyamata tomwaya mtona? → verb \"biyamata\" at end → so \"will look after\".\n\n\"biyamata\" vs \"biyamatasi\" — \"biyamatasi\" = look after; \"biyamata\" = perhaps \"look after\" as base form, or for plural? But \"vivila\" = women → plural → so likely same verb.\n\nSo 14: How many women will look after this man?\n\n15: \"Bikamkwamsi kweyu vivila minasina\" → no verb — only if \"minasina\" is verb.\n\nBut in sentence 1: \"minasina tetala tau\" → \"fishing\" or \"fish\" → not verb. \nIn 7: \"vivila minawena nakabitam\" → \"will see\" → verb \"minawena\"\n\nSo only if \"vivila minasina\" = \"women fish\" — that is, \"women will fish\"? \nBut no verb. \nUnless \"kweyu\" is verb.\n\n\"Kweyu\" — in what else? Sentence 5: \"nayu\" = two; sentence 9: \"gweguyau\" → \"saw\" — not \"kweyu\".\n\nNo match.\n\nPossibility: this sentence is misparsed.\n\nAnother idea: word order in Kilivila is subject-verb-object or root-verb in some cases.\n\nIn 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" — \"killed one wild pig\" → verb at beginning → so not consistent.\n\nBut many have verb at end.\n\nTry to map likely translations.\n\nSentence 15: Bikamkwamsi kweyu vivila minasina \n\"bikamkwamsi\" = that \n\"kweyu\" = two \n\"vivila\" = woman \n\"minasina\" = fish\n\n→ \"That two women fish?\" → ungrammatical. \n→ \"Which two women fish?\" → but \"am\" not there. \n\"am\" in 5: \"amtona\" → which \n\"amagudina\" in 16 → which\n\nSo \"bikamkwamsi\" = that → \"that two women fish?\" → not making sense.\n\nPossibility: \"how many fish did that woman catch?\" — but no verb.\n\nWait — in sentence 1: \"minasina tetala tau\" = \"fish will be caught\" → here, \"minasina\" = fish, \"tetala\" = four, \"tau\" = catch\n\nSo \"minasina\" is noun.\n\nSo in 15: \"kweyu vivila", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11181.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Analyze the structure of given English-Kilivila pairs to detect patterns in word order, syntax, and the mapping of semantic roles (subject, object, event, etc.).\n\nObservation 1: In most Kilivila sentences, the word order follows a specific pattern involving:\n- Determiner (which may express “that”, “this”, “which”)\n- Noun phrase (subject or object)\n- Verbal root or verb phrase\n- Adverbial or quantifier elements\n\nNote the use of:\n- \"Navila\" = \"How many\", \"What number?\"\n- \"Bikota\" = \"That\"\n- \"Lekota\" = \"This\"\n- \"Bikamkwamsi\" = \"Which\" (used similarly to \"which\" in English)\n- \"Bigisi\" = \"That\", \"The\"\n- \"Tevila\" = \"How many\"\n- \"Mtona\" = \"man\"\n- \"Minasina\" = \"fish\"\n- \"Dimdim\" = \"white\"\n- \"Gwadi\" = \"child\"\n- \"Magesi\" = \"woman\"\n- \"Waga\" = \"saw\", \"looked at\"\n- \"Tetala\" = \"catch\"\n- \"Minana\" = \"canoes\"\n- \"Tewila\" = \"will arrive\"\n- \"Nunumwaya\" = \"two men\"\n- \"Makwena\" = \"stone\"\n\nClue: Quantifiers like “how many” and “which” are often marked by \"Navila\" or \"Tevila\".\n\nStep 2: Map each sentence in the list to identify patterns.\n\nLook at sentence 8: \n\"8. How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived → verb for arrival\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"Navila\" = how many, \"vivila\" = women, \"biyamatasi\" = will look after, \"tau\" = this, \"mtona\" = man\n\n→ So: Navila = How many? \nvivila = women \nbiyamatasi = will look after \ntau = this \nmtona = man → “This man”\n\nThus, “Navila vivila biyamatasi tau mtona?” = How many women will look after this man?\n\nSentence 14: \n\"Navila vivila biyamata tomwaya mtona?\" \n→ Navila → how many \nvivila → women \nbiyamata → ? \ntomwaya → ? \nmtona → man\n\nFrom earlier: \n\"biyamatasi\" = will look after \n\"biyamata\" → similar form, maybe \"will go\", \"will be\" or \"will see\"?\n\nCheck sentence 15: \n\"Bikamkwamsi kweyu vivila minasina\" \n→ \"Bikamkwamsi\" = which \n\"kweyu\" = will? (matches \"kweyu\" in \"kweyu vivila minasina\") \n\"vivila\" = women \n\"minasina\" = fish\n\n→ So \"Which women will catch fish?\"\n\n\"vivila minasina\" = women catch fish → likely means \"will catch\"\n\nThus, \"kweyu\" is a future auxiliary → will\n\nSo in 15: \"Bikamkwamsi kweyu vivila minasina\" → which women will catch fish?\n\nNow sentence 14: \"Navila vivila biyamata tomwaya mtona?\" \n→ Navila = how many \nvivila = women \nbiyamata = ? \ntomwaya = ? \nmtona = man\n\nCompare \"biyamata\" → likely a variant of \"biyamatasi\" → would mean \"will look after\" \nBut \"biyamata\" is missing the “si” ending → might be a non-future verb? \nPossible: \"biyamata\" = \"will go\", \"will see\", \"will take care of\"?\n\n\"tomwaya\" → what is it? \nCheck sentence 10: \n\"That beautiful child saw this stone.\" \n→ \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n\"makwena\" = stone → \"gwadi magudiwena\" = this child? \n\"makwena\" = stone, \"gudimanabweta\" = beautiful → so vowel patterns suggest \"makwena\" = stone \n\"gwadi\" = child → so “this beautiful child” → \"gwadi magudiwena\"\n\nBack to \"tomwaya\": \nPossible meaning: “man” or “person”? \n\"mtona\" = man → “tomwaya” may be a different form → might be “people”?\n\nBut “mtona” is man → “tomwaya” → similar to “mtona” → could be “man”?\n\nBut it's distinct.\n\nAlternatively: in sentence 14 → \"vivila biyamata tomwaya mtona\"\n\nCould \"biyamata\" = will see, \"tomwaya\" = these, \"mtona\" = man?\n\nBut “tomwaya” = “these”?\n\nCheck: sentence 4: \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana\" \n\"namwaya\" = those canoes → \"namwaya\" = those\n\nSo \"namwaya\" = “those” → dative or plural possessive?\n\nSimilarly, “tomwaya” may mean “those”?\n\nThus: “Navila vivila biyamata tomwaya mtona” → how many women will (do) those (men) to this man? \nThat doesn’t make sense.\n\nWait — perhaps the word order is flexible and the structure is:\n\n[Quantifier] [subject] [verb] [object] or [descriptor]\n\nIn sentence 4: Legisi waga makesiwena namwaya minana → woman saw those canoes\n\nSo \"waga\" = saw, \"makesiwena\" = old woman → possibly \"magesi\" = woman, \"makesi\" = old → so \"makesiwena\" = old woman\n\n→ \"waga makesiwena\" = saw the old woman → confusing.\n\nWait — \"Legisi waga makesiwena namwaya minana\" \n→ \"Legisi\" = that \n\"waga\" = saw \n\"makesiwena\" = old woman? \n\"namwaya\" = those \n\"minana\" = canoes\n\nSo “that old woman saw those canoes”\n\nSo \"makesiwena\" = old woman → “makesi” = old, “wena” = woman?\n\nSo “makesi” = old, “wena” = woman → “makesiwena” = old woman\n\nSo the Noun phrase: [adjective] + [noun] = compound\n\nThus:\n- \"dimdim\" = white → \"dimdim mtona\" = this white man\n- \"gwadi\" = child → \"gwadi magudiwena\" = that child\n- \"bigisi\" = that → \"bigisi gwadi\" = that child\n- \"legisi\" = that → \"legisi\" = that\n- \"lekota\" = this\n\nThus, adjectives modify nouns.\n\nNow verb:\n- \"waga\" = saw\n- \"tetala\" = catch\n- \"mtona\" = man\n- \"nakabitam\" = will see\n\n\"nakabitam\" = will see? In sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\" → \"kwetala\" = clever → so \"kwetala\" = clever, \"vivila\" = woman, \"minawena\" = something, \"nakabitam\" = will see\n\nSo \"nakabitam\" = will see\n\n\"makena\" = see? In sentence 9: \"which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" → \"amakena\" = see, \"waga\" = did, \"legisesi\" = that, \"gweguyau\" = canoe\n\nSo \"waga\" = saw, \"amakena\" = see (past tense)\n\nThus verb forms:\n- \"waga\" = saw\n- \"tetala\" = catch\n- \"nakabitam\" = will see\n- \"kweyu\" = will (in sentence 15)\n\nSo future tense = kweyu, nakabitam\n\nNow analyze sentence 14: \n\"Navila vivila biyamata tomwaya mtona?\"\n\n\"Navila\" = how many \n\"vivila\" = women \n\"biyamata\" = ? \n\"tomwaya\" = ? \n\"mtona\" = man\n\n\"biyamata\" — plausible derivative from \"biyamatasi\" which means \"will look after\" \n\"biyamatasi\" → future, \"will look after\"\n\nSo \"biyamata\" → possibly future with shorter form? Or might mean \"will see\"?\n\nBut \"biyamata\" → no clear association with \"look after\"\n\nAlternatively, look at sentence 13: \n\"Navila vivila biyamatasi tau mtona?\" → How many women will look after this man?\n\nSo \"biyamatasi\" = will look after\n\nSentence 14: \"Navila vivila biyamata tomwaya mtona\" → how many women will (do) tomwaya to this man?\n\n\"tomwaya\" — compare to \"namwaya\" = those → “tomwaya” may mean “those”?\n\nIn sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" \n→ \"leyamatasi\" = old women looked after \n\"teyu\" = two \n\"tauwau\" = men \n\"nunumwaya\" = two men\n\n\"tauwau\" = men → so \"tau\" is man, \"wau\" = plural?\n\n\"nunumwaya\" = two men\n\nSo numerals: \"teyu\" = two, \"nunumwaya\" = two men\n\nSo \"tomwaya\" → possibly not \"those\", but another noun?\n\nPossibility: \"tomwaya\" = \"this\" or \"that\"?\n\nBut \"mtona\" is “this man” → already present\n\nCould \"tomwaya\" be a typo or variant of \"mtona\"?\n\nLikely not.\n\nAlternative proposal: Word order ambiguity\n\nLook at sentence 17: \n\"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n\"Tevila\" = how many \n\"tauwau\" = men \n\"bigisesi\" = that chief \n\"gugwadi\" = that child \n\"gudigasisi\" = ? — likely “saw” or “looked at”\n\n\"bigisesi\" = that chief → similar to \"bigisi\" → that\n\n\"gugwadi\" = that child → “gugwadi” = that child?\n\n\"gudigasisi\" → may mean \"saw\" — similar to \"gudimanabweta\" → stone\n\nIn sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → saw this stone\n\n\"gwadi\" = child, \"magudiwena\" = beautiful → \"gudimanabweta\" = stone? → perhaps \"gudima\" = stone\n\nSo \"gudigasisi\" → possible = saw?\n\nThus: \"gugwadi gudigasisi\" = that child saw\n\nBut “gugwadi” = that child → “gugwadi” = child → “gudigasisi” = saw\n\nSo \"bigisesi gugwadi gudigasisi\" = that chief saw that child?\n\nBut then: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" → How many men did that chief see that child?\n\nThat doesn’t make sense — men see child? Could fit.\n\nBut the grammar is: [how many] [X] [did Y] [see] [Z]\n\nSo: How many men did that chief see that child?\n\nGrammatically acceptable.\n\nSentence 18: \"Legisesi ketala waga vivila minasiwena\"\n\n\"Legisesi\" = that \n\"ketala\" = ? \n\"waga\" = saw \n\"vivila\" = women \n\"minasiwena\" = ? — pattern: \"minasina\" = fish, \"minawena\" = something\n\n\"minasiwena\" → likely \"something\" → \"minasina\" = fish, so “minasina” = fish → so “minasiwena” = something\n\n\"ketala\" — check sentence 2: \"This white man arrived\" → \"lekota dimdim mtona\" → \"lekota\" = this\n\n\"ketala\" — could be verb?\n\n\"tetala\" = catch \n\"ketala\" → possibly “will catch”?\n\nSentence 7: “will see” → “nakabitam”\n\nSo “ketala” → perhaps “will catch”?\n\nThen: \"Legisesi ketala waga vivila minasiwena\" → that [will catch] saw women something?\n\nNo — doesn’t make sense.\n\nCould be: \"that woman will catch these women\"?\n\nNo.\n\nAlternative: \"ketala\" = \"will arrive\"? \"lekotasi\" in sentence 8 = arrived\n\n\"ketala\" = not matching.\n\nPossibility: word order reversal — object before subject?\n\nLook at sentence 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = see, \"waga\" = did, \"legisesi\" = that, \"gweguyau\" = canoe\n\nSo: \"did the chiefs see that canoe?\" → “did” + subject + verb + object\n\nBut in Kilivila, it's \"Amakena waga legisesi gweguyau?\" → \"see did that canoe?\" → not matching.\n\nWait — \"Amakena waga\" → \"see did\" → verb before subject?\n\nSo: “see did” → same as “did see” — possibly a back-verb structure.\n\nSo verb at start.\n\nLikely pattern: verb is placed at beginning — \"waga\", \"amakena\", \"tetala\" — all verbs, often at start.\n\nSo sentence 14: \"Navila vivila biyamata tomwaya mtona?\" \n→ \"Navila\" = how many \n\"vivila\" = women \n\"biyamata\" = ? \n\"tomwaya\" = ? \n\"mtona\" = man\n\nCompare to sentence 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\nSo \"biyamatasi\" = will look after\n\n\"biyamata\" → missing final -si → possible inflection for non-future?\n\nBut “kweyu” is future → so \"biyamata\" might be non-future?\n\nBut “navila” = how many → quantifier → so must have future or present?\n\nCrucial: in sentence 15: \"Bikamkwamsi kweyu vivila minasina\" → which women will catch fish?\n\nSo \"kweyu\" = will\n\nSentence 14: no \"kweyu\", so possibly not future.\n\n\"biyamata\" → could be \"will go\", \"will take care of\", \"will visit\"?\n\nBut \"tomwaya\" — parallels “namwaya” = those\n\nSo “tomwaya” = those?\n\n“mtona” = man → “those men”?\n\nSo “how many women will those men have with this man?” — not sensible.\n\nAlternative: \"tomwaya\" = “this”?\n\n→ “how many women will this man have?” → makes sense.\n\n“biyamata” = “have”?\n\n“biyamatasi” = look after → “have care for”\n\n“biyamata” = less complete → maybe “previously” or “possess”?\n\nCould “biyamata” mean “have”?\n\nIn sentence 13: “will look after” → biyamatasi\n\nBut \"biyamata\" → is a variant with different verb?\n\nPossibility: missing \"-si\" → indicative or non-future?\n\nBut still, in context of question, this may be ambiguous.\n\nSentence 16: \"Amagudina gwadi lekota?\"\n\n\"Amagudina\" = which (from \"bikamkwamsi\"? → \"bikamkwamsi\" = which)\n\n\"Amagudina\" = which? — present form?\n\n\"gwadi\" = child \n\"lekota\" = this\n\nSo \"which child this?\" → which child is this?\n\nOr \"which child?\" → ambiguous.\n\nCould be \"which child is this?\" or \"which child this?\"\n\nBut \"which child this\" → awkward.\n\nMore likely: \"which child is this?\" — the referent is clear.\n\nNow, back to sentence 14: \n\"Navila vivila biyamata tomwaya mtona?\"\n\nIn previous sentence 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\n\"biyamatasi\" = will look after \n\"biyamata\" = missing -si → perhaps future with reduced form?\n\nOr perhaps it's a different verb meaning “will see”?\n\nBut “tomwaya” is problematic.\n\nAnother possibility: among these, one sentence has two possible translations due to ambiguity in word order or reference.\n\nLook at sentence 18: \"Legisesi ketala waga vivila minasiwena\"\n\n\"legisesi\" = that \n\"ketala\" = ? \n\"waga\" = saw \n\"vivila\" = women \n\"minasiwena\" = something\n\n\"ketala\" — compare to \"tetala\" = catch \n\"nakabitam\" = will see\n\n\"ketala\" → could be “catch”?\n\nSo \"that [will catch] saw women something\"?\n\nNo.\n\nCould be: \"that saw women something\" → what?\n\nPerhaps: \"that woman saw these women\"?\n\nBut “vivila” = women → object\n\n\"minasi", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11957.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Analyze the given English-Kilivila pairs to detect patterns in word order, case markers, and semantic role.\n\nLook at (1): \nOne man will catch these four fish. \nBibani navasi yena minasina tetala tau. \n→ \"navasi\" = man; \"yena\" = these; \"minasina\" = four; \"tetala tau\" = fish. \nSo: \"navasi\" (man) + \"yena\" (determiner for 'these') + \"minasina\" (number) + \"tetala tau\" (fish).\n\n(2): This white man arrived. \nLekota dimdim mtona. \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\n(3): That child will arrive. \nBikota gwadi magudiwena. \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = arrive.\n\n(4): This old woman saw those canoes. \nLegisi waga makesiwena namwaya minana. \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = woman; \"namwaya\" = those; \"minana\" = canoes.\n\n(5): Which man killed two pigs? \nAmtona tau lekalimati nayu bunukwa? \n→ \"amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\n(6): The old women looked after two men. \nLeyamatasi teyu tauwau nunumwaya. \n→ \"leyamatasi\" = the; \"teyu\" = old; \"tauwau\" = women; \"nunumwaya\" = two; \"men\".\n\n(7): That clever woman will see something. \nBigisi kwetala vivila minawena nakabitam. \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = something; \"nakabitam\" = will see.\n\n(8): How many dogs arrived? \nNavila ka’ukwa lekotasi? \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\n(9): Which canoe did the chiefs see? \nAmakena waga legisesi gweguyau? \n→ \"amakena\" = which; \"waga\" = canoe; \"legisesi\" = the; \"gweguyau\" = chiefs; \"see\".\n\n(10): That beautiful child saw this stone. \nLegisi dakuna makwena gwadi magudiwena gudimanabweta. \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = this; \"magudiwena\" = saw; \"gudimanabweta\" = stone.\n\n(11): How many things did those white men eat? \nKwevila lekamkwamsi dimdim mtosiwena? \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = men; \"ate\".\n\n(12): The clever chief killed one wild pig. \nLekalimati natala bunukwa nagasisi guyau tokabitam. \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever; \"tokabitam\" = killed.\n\n(13): How many women will look after this man? \nNavila vivila biyamatasi tau mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nNow look for structural patterns:\n\n- Determiners: \"le\" (that), \"bi\" (this), \"navi\" (how many), \"am\" (which), \"lekota\" (this), \"legisi\" (that), \"bikota\" (that), \"navila\" (how many).\n- Possessive/possessive-like markers: \"waga\", \"gwadi\", \"gwen\", \"gudim\".\n- Quantifiers: \"yena\" (these), \"minasina\" (four), \"nayu\" (two), \"nunumwaya\" (two), \"natala\" (one).\n- Verbs: \"minasina\" = catch? \"tetala\" = fish → possibly \"tetala\" = fish, \"mtona\" = arrive, \"makesiwena\" = saw, \"magudiwena\" = arrived, \"waga\" = old, \"gweguyau\" = see.\n- Noun phrases: often structured as [determiner] [adjective] [noun] or [determiner] [noun] [verb].\n\nNow look at the questions:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = look after? (cf. biyamatasi in 13); \"tomwaya\" = this; \"mtona\" = man. \n\"bityamata\" → likely \"look after\" (plural morpheme). \nSo: \"How many women will look after this man?\"\n\n→ This matches (13) exactly, but with \"biyamata\" vs \"biyamatasi\". \"biyamatasi\" = will look after (in 13), so \"biyamata\" might be \"look after\" (infinitive form). Could this be passive?\n\nBut in (13), the sentence is “How many women will look after this man?” — so this is parallel. \nBut the question says one sentence has two possible translations.\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? or \"that things\"? \"kweyu\" = will? or possessive? \"vivila\" = woman? \"minasina\" = four. \nWait: in (1), \"minasina\" = four fish. \nIn (13), \"tau\" = man; \"mtona\" = man. \n\"vivila\" → woman. \n\"minasina\" → four. \nSo “Bikamkwamsi” likely = that women? or “that” + “women”? \nBut \"bikamkwamsi\" → \"bikota\" is \"that\", \"makwamsi\" → possibly \"thing\" or \"woman\"? \nCompare with (7): \"vivila\" = woman, \"minawena\" = something. \nSo \"minasina\" = four (number). \n\"bikamkwamsi\" → could be \"that thing (woman)\" or \"that woman (something)\"? \nBut \"kweyu\" = will? or \"will\" in future? \n\nWait: \"kweyu\" appears in (11): \"kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n\"kwevila\" = how many; \"lekamkwamsi\" = things. \nSo \"lekamkwamsi\" = things. \nNow in (15): \"bikamkwamsi kweyu vivila minasina\" → “that women will catch four?” \nBecause “kweyu” = will, “vivila” = woman, “minasina” = four. \nSo “that woman will catch four”. \nCould be: “Which woman will catch four fish?” — but “kweyu” is not “which”.\n\n“Am” = which, “bi” = that. \nIn (5): “amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \nSo \"amtona\" = which.\n\nIn (15), \"bikamkwamsi\" — \"bikota\" = that → \"bikamkwamsi\" = that thing (woman)? \nBut “minasina” = four. \nSo \"that woman will catch four\"? — but what? Fish? \nOriginal (1): “one man will catch these four fish” — “tetala tau” = fish. \nSo likely: “That woman will catch four fish.” \nBut “vivila” = woman, not “tetala”.\n\nSo possibly: “That woman will catch four fish.” — but “minasina” is not “fish”.\n\nWait: is “minasina” used only for numbers? \nYes: (1) “minasina” with fish; (4) “namwaya minana” → canoes; (6) “nunumwaya” → two men; (5) “nayu” → two pigs; (12) “natala” → one pig.\n\nSo “minasina” = \"four\" — number. \nThen “tetala” = fish. \nIn (15), “minasina” = four, but not with fish. \nSo the noun must be missing.\n\nBut the structure: “bikamkwamsi” = that woman? \n“kweyu” = will catch? or will? \nWait: in (1), “navasi yena minasina tetala tau” → “man these four fish” → so “minasina” modifies “tetala tau”. \nSo “minasina” = number, precedes noun.\n\nIn (15): “bikamkwamsi kweyu vivila minasina” → does “vivila” get modified by “minasina”? \nBut “vivila” is already a noun — woman. \nSo probably not.\n\nAlternatively: “bikamkwamsi” = that woman / that thing; “kweyu” = will; “vivila” = fish? no, “vivila” = woman.\n\nWait — \"vivila\" is only used for woman.\n\nIs there a noun for fish? “tetala tau” = fish.\n\nSo likely: “that woman will catch four fish” — but “vivila” is woman, not fish.\n\nSo unless “vivila” is a misreading.\n\nPossibility: typo? or \"vivila\" = fish? — no, in (7): \"vivila\" = woman.\n\nSo contradiction.\n\nAlternatively: “kweyu” = how many? — but “kwevila” = how many.\n\n\"kweyu\" is not in the how-many set.\n\nSo all signs point to: “that woman will catch four fish” — but \"vivila\" is not fish.\n\nWait — is “vivila” used for fish? No, only in (7) as woman.\n\nWhat is the word for fish? “tetala tau” — “tetala” = fish.\n\nSo possibly “minasina” is the number, and fish is missing — so cannot be.\n\nUnless the sentence is: “That woman will catch (something) with four” — no.\n\nAnother possibility: the noun is implied — but only if “tetala” is missing.\n\nBut no direct reference.\n\nWait — look at (4): “legisi waga makesiwena namwaya minana” — “woman saw canoes”.\n\nIn (10): “legisi dakuna makwena gwadi magudiwena gudimanabweta” — “that beautiful child saw this stone”.\n\nSo prepositions: “makesiwena” = saw, “magudiwena” = saw.\n\nSo verb “saw” = magudiwena.\n\nSo \"kweyu\" = not a verb here.\n\nCould “kweyu” = will look after? → in (13): “biyamatasi” = will look after.\n\nSo “kweyu” = future tense?\n\nYes — in (7): “kwetala vivila minawena nakabitam” — “clever woman will see something”.\n\nSo future marker: “nakabitam” — will see.\n\nSimilarly, (12): “guyau tokabitam” — “clever chief killed” — “tokabitam” = killed (future form? or past).\n\nBut in (7), “nakabitam” = will see.\n\nSo “kweyu” = will.\n\nThen “bikamkwamsi” = that woman? → “bikota” is “that”, so “bikamkwamsi” = that thing? or “that woman”?\n\nBut “makwamsi” = woman? — (11): “lekamkwamsi” = things.\n\nSo \"makwamsi\" = things, plural.\n\nSo \"bikamkwamsi\" = that things? → that things → that thing (in singular)? → ambiguous.\n\nSo sentence: “That things will catch four?” → grammatically odd.\n\nSo better: “That woman will catch four fish” — missing fish.\n\nBut no fish.\n\nAlternatively: the noun is implied to be “fish” — based on previous patterns.\n\nSo likely: “That woman will catch four fish.”\n\nIs this the only interpretation?\n\nAnother: could \"vivila minasina\" = woman with four → still no.\n\nNo match.\n\nBut look at 16: Amagudina gwadi lekota?\n\n\"amagudina\" — “am” = which, “gudina” = stone? “gwadi” = this, “lekota” = this.\n\n\"gudina\" → compare \"gudimanabweta\" in (10): “stone”.\n\n“gudim” → stone → “gudimanabweta” → stone.\n\nSo “gudina” = stone? or “gudina” = saw?\n\nNo — “gudim” is root.\n\nSo “amagudina” → possibly “which stone” or “which thing”?\n\n“gwadi” = this, “lekota” = this → two “this”?\n\n“amagudina gwadi lekota” → “which stone this this” — redundant.\n\nAlternatively: \"amagudina\" = which woman? “gudina” not a woman.\n\nNo.\n\nPossibility: \"amagudina\" = which women? — but “gudina” not woman.\n\nBack to 15: the only plausible translation is “That woman will catch four fish.”\n\nBut is another possible?\n\nPossibility: “That woman (has) four [men]?” — no.\n\nNo.\n\nSo only one.\n\nNow 16: Amagudina gwadi lekota?\n\n→ \"am\" = which; \"gudina\" = stone? or tree? or seen thing?\n\n“gudim” is in “gudimanabweta” = stone.\n\nSo “gudina” = stone (singular).\n\n“gwadi” = this, “lekota” = this → “this this”? redundant.\n\nSo “which stone (is) this (this)”? — odd.\n\nCould it be “which stone did this this see”? → no.\n\nBut (10): \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → “that beautiful child saw this stone”\n\nSo verb \"magudiwena\" = saw.\n\nSo \"amagudina\" = which stone.\n\n“gwadi lekota” = this this → possibly just “this”?\n\nBut both “gwadi” and “lekota” are determiners.\n\nIn (2): \"lekota dimdim mtona\" → “this white man”\n\n(3): \"bikota gwadi magudiwena\" → “that child will arrive”\n\nSo “gwadi” = this, “lekota” = this — both are determiners.\n\nSo “gwadi lekota” → “this this” — redundant — could be “this one”.\n\nSo “which stone this this” → odd.\n\nAlternatively: “which stone did this this see?” → missing verb.\n\nBut sentence has no verb.\n\nSo likely: “Which stone is this?” or “Which stone is this one?”\n\nBut no verb.\n\nMost plausible: “Which stone is this?” — in a question about identity.\n\nBut also possible: “Which stone did this (person) see?” — but no subject.\n\nSo only one translation: “Which stone is this?”\n\nBut is there another?\n\nPerhaps “which stone did this one see?” — but no reference to agent.\n\nNo clear agent.\n\nSo one translation.\n\nNow 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n\"tevila\" = how many; \"tauwau\" = women; \"bigisesi\" = chiefs? \"gugwadi\" = that? \"gudigasisi\" = women?\n\nWait: in (13): \"navila vivila biyamatasi tau mtona\" → “how many women will look after this man?”\n\n“gudigasisi” — in (12): \"guyau tokabitam\" → \"clever chief\" — “guyau” = clever.\n\n“gugwadi” — similar to “gwadi” = this.\n\n“gudigasisi” — “gudigasi” = woman? “sisi” → suffix?\n\nIn (4): \"legisi waga makesiwena namwaya minana\" — “this old woman saw those canoes”\n\n“gudigasisi” — \"gudigasi\" → woman?\n\nCompare: (7): “bigisi kwetala vivila minawena” → “that clever woman”\n\n“bigisi” = that; “kwetala” = clever; “vivila” = woman.\n\nSo “gudigasisi” = woman?\n\n“gugwadi” = that?\n\n“bigisesi” = that chief?\n\nIn (9): “amakena waga legisesi gweguyau?” → “which canoe did the chiefs see?”\n\n“legisesi” = the chiefs.\n\nSo “bigisesi” = chief?\n\nYes — “bigisi” = that, “gisi” = chief.\n\nSo “bigisesi” = that chief.\n\n“gugwadi” = that (adjective) — “gugwadi” = this?\n\nNo — in (10): “legisi dakuna makwena gwadi” → “that beautiful child” → “gwadi” = this.\n\nBut “gugwadi” = “gugwadi” — different.\n\n“", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11585.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "iid", + "sample_index": 0, + "output": "Step 1: Identify common patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"how many [subject] [verb] [object]\" structure is reflected in questions like \"How many canoes did those old women see?\" — likely \"Navila [object] [subject] [verb]?\" or \"Navila [canoes] [old women] [see]?\"\n\nIn sentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" = how many \n\"ka’ukwa\" = dogs \n\"lekotasi\" = arrived \n→ Pattern: \"Navila [NOUN] [VERB]?\" → \"How many [NOUN] [VERB]?\"\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"makesiwena\" = saw \n→ \"waga\" = old woman \n→ \"namwaya minana\" = those canoes \n\nSo: \"subject + saw + object\" → \"legisi + subject + makesiwena + object\"\n\nSentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which \n→ \"tau\" = man \n→ \"lekalimati\" = killed \n→ \"nayu bunukwa\" = two pigs\n\nSo: \"Amtona [noun] [verb] [object]\" → which [subject] [verb] [object]\n\nSentence 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"Amakena\" = which \n→ \"waga\" = chiefs \n→ \"legisesi\" = see \n→ \"gweguyau\" = that canoe \n→ So \"Amakena [subject] [verb] [object]\" = \"Which [subject] [verb] [object]?\"\n\nSentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"Navila\" = how many \n\"vivila\" = women \n\"biyamatasi\" = will look after \n\"tau mtona\" = this man \n→ Pattern: \"Navila [noun] [verb] [object]?\" → \"How many [noun] [verb] [object]?\"\n\nThus, the structure for how many X did Y do? is:\n**Navila [X] [Y] [verb] [object]** \nMore precisely: Navila [count noun] [agent] [verb] [object]\n\nBut in sentence 19: \"How many canoes did those old women see?\" \n→ Object: canoes \n→ Agent: old women \n→ Verb: see\n\nIn sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"legisi\" = see, \"waga\" = old woman → \"legisi waga makesiwena\" = the old woman saw (something)\n\nBut actually \"makesiwena\" = saw, so \"legisi\" is not the verb? Wait: \n\"legisi waga makesiwena\" → \"legisi\" = that, \"waga\" = old woman, \"makesiwena\" = saw — so \"waga makesiwena\" = the old woman saw\n\nSo verb = \"makesiwena\" = saw\n\nSo structure: [subject] + [verb] + [object] \nSo \"Legisi [subject] [verb] [object]\" — but \"legisi\" may be marker or determiner.\n\nBut in sentence 9: \"Amakena waga legisesi gweguyau?\" → which canoe did the chiefs see? \n\"legisesi\" = see → verb\n\nSo in all cases with \"see\", verb is \"makesiwena\" or \"legisesi\"?\n\nSentence 4: \"makesiwena\" \nSentence 9: \"legisesi\" \nSentence 12: \"gweguyau\" = that old man? — no, \"gweguyau\" = that old man? \nSentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"nagasisi guyau\" = killed that old man? → \"guyau\" = old man \nBut \"nagasisi\" = killed?\n\nWait, let’s extract verb patterns:\n\n- \"catch\" in sentence 1 → \"navasi\" → \"catch\"? → \"navasi\" in \"Bibani navasi yena minasina tetala tau\" → \"navasi\" = catch? \n→ \"timasina\" is not present — no. \nWait: \"Bibani navasi yena minasina tetala tau\" \n\"navasi\" = catch? \nYes, likely \"navasi\" = catch.\n\nSentence 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n\"gwadi\" = child? \"magudiwena\" = saw? \nWait: \"magudiwena\" = saw? \nEarlier: \"makesiwena\" = saw. So \"magudiwena\" = saw? Possibly variant?\n\nBut sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"makwena\" = beautiful? \n\"gwadi\" = child \n\"magudiwena\" = saw? \nYes — so \"magudiwena\" = saw.\n\nThus, saw = makesiwena / magudiwena / legisesi?\n\nSentence 4: \"waga makesiwena\" — the old woman saw \nSentence 9: \"legisesi\" = see — probably see = \"legisesi\" or \"makesiwena\"?\n\nActually, \"legisesi\" = \"see\" and \"makesiwena\" = \"saw\"? Possibly different.\n\nBut sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" + \"waga makesiwena\" → \"legisi\" may be \"that\" or \"the\", \"waga makesiwena\" = the old woman saw.\n\nSo the verb \"see\" is encoded as \"makesiwena\" or \"magudiwena\" depending on context.\n\nNow for seeing: \nSentence 2: \"This white man arrived\" → \"lekota dimdim mtona\" → \"lekota\" = this, \"dimdim\" = white, \"mtona\" = arrived\n\nSentence 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\" → \"bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive?\n\n\"magudiwena\" is used in both seeing and arriving — so verb form may be a class.\n\nIn sentence 2: \"mtona\" = arrived \nSentence 3: \"magudiwena\" = will arrive → so \"magudiwena\" = arrive or will arrive?\n\nSentence 4: \"makesiwena\" = saw → past? \nSentence 10: \"magudiwena\" = saw — this indicates \"magudiwena\" is not just arrive.\n\nPossible: \"magudiwena\" = saw \n\"mtona\" = arrived\n\nBack to seeing pattern.\n\nIn sentence 19: \"How many canoes did those old women see?\" \n→ Pattern from example 4: \"Legisi waga makesiwena namwaya minana\" — \"waga\" = old woman, \"makesiwena\" = saw, \"namwaya minana\" = those canoes\n\nSo structure: [det] [subject] [verb] [object]\n\nSo for \"How many canoes did those old women see?\" → likely: \n\"Navila namwaya minana waga makesiwena?\"\n\nBut order? In example 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, which may be presence marker.\n\nIn example 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived\n\nSo \"Navila [NOUN] [VERB]\" — no subject.\n\nBut in sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"Navila\" = how many, \"vivila\" = women, \"biyamatasi\" = will look after, \"tau mtona\" = this man\n\nSo in questions with \"how many\", it is: \nNavila [noun] [verb] [object]? \nBut in arriving, no subject — just Navila [NOUN] [VERB]?\n\nIn sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → no agent — so only \"Navila [NOUN] [VERB]\"?\n\nBut in sentence 19: \"How many canoes did those old women see?\" — agent present — so needs agent.\n\nSo likely: \"Navila [object] [agent] [verb]\"? \nOr \"Navila [object] [agent] [verb]\"?\n\nExample 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo object = \"namwaya minana\" (those canoes) \nAgent = \"waga\" (old woman) \nVerb = \"makesiwena\" (saw)\n\nSo order: [det] [agent] [verb] [object]\n\nBut in sentence 4: \"Legisi waga makesiwena namwaya minana\" — so \"waga makesiwena\" = agent + verb → then object\n\nSo for 19: \"Navila namwaya minana waga makesiwena?\" \nBut \"Navila\" is how many, so likely \"Navila [object] [agent] [verb]\" — that is, how many canoes did those old women see?\n\nBut is \"navila\" parallel to \"navila\" in 8?\n\nIn 8: \"Navila ka’ukwa lekotasi?\" — how many dogs arrived? \n→ No agent — just \"Navila [NOUN] [VERB]\"\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man? \n→ \"vivila\" = women, \"biyamatasi\" = look after, \"tau mtona\" = this man \n→ Agent present → so structure: \"Navila [agent] [verb] [object]?\"\n\nTherefore, general rule: \n- For \"how many [X] did [Y] [verb]?\" → \"Navila [X] [Y] [verb]\" \nBut in 13: it's \"Navila vivila biyamatasi tau mtona\" → agents with verbs \nIn 8: \"Navila ka’ukwa lekotasi\" → no agent → so when agent omitted, just \"Navila [NOUN] [VERB]\"\n\nBut in this case, 19 has agent — so need agent.\n\nSo for 19: \"How many canoes did those old women see?\" \n→ \"Navila namwaya minana waga makesiwena?\"\n\nBut order: in example 4: \"Legisi waga makesiwena namwaya minana\" → agent first, then verb, then object.\n\nSo for question: \"Navila namwaya minana waga makesiwena?\" — object first, then agent, then verb → may be awkward.\n\nBut in 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → child saw stone → \"gwadi magudiwena\" = child saw? Or \"gwadi\" = child, \"magudiwena\" = saw?\n\nActually: \"gwadi magudiwena\" — \"gwadi\" = child (subject), \"magudiwena\" = saw (verb) → then object → \"gudimanabweta\" = this stone\n\nSo structure: [subject] [verb] [object]\n\nBut in sentence 4: \"waga makesiwena namwaya minana\" → \"waga\" = subject, \"makesiwena\" = verb, \"namwaya minana\" = object\n\nSo verb is \"makesiwena\" or \"magudiwena\" → both mean \"saw\"\n\nSo verb = \"makesiwena\" (saw)\n\nSo in 19: \"How many canoes did those old women see?\" → \"Navila namwaya minana waga makesiwena?\"\n\nYes — \"Navila\" = how many, \"namwaya minana\" = canoes, \"waga\" = old women, \"makesiwena\" = saw\n\nBut is \"namwaya minana\" the object? Yes.\n\nBut in sentence 4: the object is \"namwaya minana\", so it's fine.\n\nSo 19: \"Navila namwaya minana waga makesiwena?\"\n\nEnsure tone: all questions start with \"Navila\" for how many.\n\nNow 20: \"These four white men will look after this clever child.\"\n\n→ \"these four\" → in sentence 2: \"This white man arrived\" → \"lekota dimdim mtona\" \n\"lekota\" = this \n\"dimdim\" = white \n\"mtona\" = arrived\n\n\"these four\" → similar to \"this\" or \"that\" — \"these\" = \"yena\"? Or \"weni\"?\n\nSentence 1: \"one man\" → \"bibani\" — \"one\" \nBut \"four\" — not in examples.\n\nBut in sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"nayu\" = two\n\nSo numbers: \"one\", \"two\", \"four\" → possibly \"tetala\" in sentence 1: \"tetala\" → four\n\nSentence 1: \"one man will catch these four fish\" → \"Bibani navasi yena minasina tetala tau.\" \n\"tetala\" = four\n\nSo \"tetala\" = four\n\n\"white\" → \"dimdim\"\n\n\"man\" → \"tau\"\n\n\"will look after\" → in sentence 13: \"will look after\" = \"biyamatasi\"\n\nSentence 13: \"The clever chief killed one wild pig\" → \"lekalimati natala bunukwa nagasisi guyau tokabitam\" → \"nagasisi\" = killed, \"guyau\" = old man\n\nSentence 13: \"Navila vivila biyamatasi tau mtona?\" → \"will look after\"\n\nSo \"biyamatasi\" = will look after\n\n\"this clever child\" → \"gwadi\" = child, \"kwetala\" = clever? Sentence 7: \"That clever woman\" → \"Bigisi kwetala vivila minawena nakabitam\" → \"kwetala\" = clever\n\nSo \"kwetala\" = clever\n\n\"this\" → \"tau\" or \"gwadi\"? \"gwadi\" = child, \"tau\" = man\n\nIn sentence 3: \"That child\" → \"Bikota gwadi magudiwena\" → \"bikota\" = that, \"gwadi\" = child\n\nIn sentence 5: \"Which man\" → \"Amtona tau\" → \"tau\" = man\n\nSo \"this\" or \"that\" = \"lekota\", \"bikota\", \"amtona\"\n\nHere: \"these four white men\" → \"yena\"? Or \"lekota\"?\n\n\"these\" → \"yena\" in sentence 1: \"yena minasina tetala tau\" → \"yena\" = these\n\nYes — \"yena\" = these\n\n\"white men\" → \"dimdim tau\"\n\n\"will look after\" → \"biyamatasi\"\n\n\"this clever child\" → \"gwadi kwetala\"\n\nSo structure: [yena] [dimdim tau] [biyamatasi] [gwadi kwetala]\n\nSo 20: \"yena dimdim tau biyamatasi gwadi kwetala\"\n\nBut must be in Kilivila syntax.\n\nIn example 5: \"which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which, \"tau\" = man, \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\nSo \"subject verb object\" with quantifier.\n\nIn 20: \"these four white men will look after this clever child\" \n→ \"yena dimdim tau biyamatasi gwadi kwetala\"\n\nBut is \"gwadi\" = this child? Yes.\n\nSo 20 = \"yena dimdim tau biyamatasi gwadi kwetala\"\n\nNow 21: \"How many children will eat these pigs?\"\n\n→ How many children will eat these pigs?\n\nPattern: like sentence 8 — \"how many [NOUN] [VERB] [object]?\" \nBut with agent (children) and object (pigs)\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim\" = white men \n\"mtosiwena\" = ate \n\nSo structure: \"Kwevila [NOUN] [agent] [verb] [object]?\" \n\"Kwevila\" — is that same as \"Navila\"?\n\nIn sentence 8: \"Navila ka’ukwa lekotasi?\" → \"how many dogs arrived\" \nSentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\"\n\n\"Kwevila\" and \"Navila\" — are they different?\n\n\"Navila\" appears in 8,13,19 \n\"Kwevila\" in 11\n\nBoth mean \"how many\"?\n\nPossibly \"Kwevila\" is the question word for \"how many\" when the verb is \"eat\", etc.\n\nBut in 19: we used \"Navila\"\n\nIn 11: \"Kwevila\"\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11683.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "iid", + "sample_index": 1, + "output": "Step 1: Analyze the English-to-Kilivila translations to identify patterns.\n\nLook at the structure of the given examples. Note that questions starting with \"How many...\" often use the form \"Navila [noun] [something]?\" or \"Kwevila [something]?\" (e.g., 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\").\n\n- In (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n → \"Navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived (a verb in past tense with aspect).\n\nSimilarly, (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"Kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white men; \"mtosiwena\" = ate.\n\nPattern: \"How many X did Y do?\" → \"Kwevila X Y do?\" or \"Navila X Y?\" — with \"kwevila\" or \"navila\" followed by noun and agent.\n\nBut for (19): \"How many canoes did those old women see?\" \n→ \"Navila [canoes] [old women] see?\"\n\nIn example (4): \"That old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n\"Legisi\" = that old woman; \"waga\" = saw; \"makesiwena\" = those canoes.\n\nSimilarly, in (10): \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n\nSo the structure: [Determiner + noun] + [verb] + [object].\n\nFor questions, the pattern for \"how many X did Y see?\" is likely: \n\"Navila [X] [Y] [verb]?\" — where \"navila\" = how many; verb is the past tense verb of seeing.\n\nIn (4): saw → \"makesiwena\" (those canoes) \nIn (10): saw → \"makwena\" (this stone)\n\nSo, \"see\" is expressed by a verb (e.g., \"makesiwena\"/\"makwena\").\n\nThus, in (19): \"How many canoes did those old women see?\" \n→ \"Navila namwaya lekisi waga?\" \nWait — \"lekisi\" = old women?\n\nCheck (3): \"That child will arrive\" → \"Bikota gwadi magudiwena\" \n\"Bikota\" = that; \"gwadi\" = child; \"magudiwena\" = arrive.\n\n(4): \"That old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana\" \n→ \"Legisi\" = that old woman; \"waga\" = saw; \"makesiwena\" = those canoes; \"minana\" = plural marker?\n\n\"minana\" may mark plurality.\n\nSo \"namwaya\" = canoes; \"minana\" = plural.\n\nIn (5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"Amtona\" = which man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\n\"Which man X did?\" = \"Amtona X?\" \n\nSo \"which X did Y\" = \"Amtona X?\"\n\nSimilarly, (9): \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"Amakena\" = which canoe; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = saw?\n\nWait: \"gweguyau\" looks like a verb.\n\n\"Amakena\" likely means \"which canoe\" — similar to \"Amtona\" for \"which man\".\n\nSo in (9), \"which canoe did chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n\"Amakena\" = which canoe; \"waga\" = saw (main verb); \"legisesi\" = chiefs; \"gweguyau\" = saw?\n\nSo \"waga\" is the verb \"saw\", and \"gweguyau\" may be a variant or second form.\n\nWait — in (4): \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nCompare to (10): \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\"\n\n\"makwena\" = saw; \"gwadi\" = child; \"gudimanabweta\" = this stone\n\nSo \"makwena\" = saw; \"makesiwena\" = saw canoes (map to object)\n\nSo when seeing, the verb is \"waga\" or \"makwena\"/\"makesiwena\"\n\nBut in (9): \"Amakena waga legisesi gweguyau\" — \"Amakena\" = which canoe; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = saw?\n\nThis seems redundant — perhaps \"gweguyau\" is a variant of \"waga\" or the verb in transitive form.\n\nPossibly, the structure is:\n\n\"Which [X] did [Y] [verb]?\" → \"Amakena [verb] [Y] [object]?\" — but no object.\n\nLikely, for questions like \"which X did Y see\", the word order is \"Amakena waga [agent] [object]\" or \"Amakena [agent] waga [object]\"?\n\n(9): \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n→ suggests \"Amakena\" = which canoe; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = (proposed) saw?\n\nActually, likely \"gweguyau\" is the verb form, and \"waga\" is a prefix or auxiliary.\n\nBut look at (4): \"Legisi waga makesiwena namwaya minana\" — agent + verb (waga) + object (makesiwena) + plural?\n\n\"makesiwena\" is the object noun.\n\nSo verb is \"waga\", object is \"makesiwena\" (canoes)\n\nThus, \"see\" is expressed with \"waga\", and object is marked in a noun form.\n\nSo for \"which woman caught those beautiful fish?\", — \"caught\" → compare with (1):\n\n(1): \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\"\n\n\"navasi\" = one; \"yena\" = man; \"minasina\" = these; \"tetala\" = four; \"tau\" = fish → \"tetala tau\" = four fish.\n\nSo \"catch\" → \"yena\" man; \"minasina\" = these; \"tetala\" = four; \"tau\" = fish.\n\nIn (12): \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"lekalimati\" = killed; \"natala\" = clever; \"bunukwa\" = wild pig; \"nagasisi\" = one; \"guyau\" = chief? \"guyau\" = man?\n\n\"tokabitam\" = clever?\n\nSo \"lekalimati\" = killed; \"bunukwa\" = wild pig; \"guyau\" = man; \"tokabitam\" = clever.\n\nSo \"killed\" is \"lekalimati\"; \"caught\" is not directly in data — but (1): \"will catch\" → \"navasi yena minasina tetala tau\" — \"yena\" = man; \"minasina\" = these; \"tetala\" = four; \"tau\" = fish.\n\nSo \"will catch\" has no verb with \"yena\" — the verb is implied or in the form of \"minasina tetala tau\".\n\nBut is there a verb like \"catch\"? In (1), \"catch\" is not a separate verb — only \"will\" and object.\n\nBut in (1), \"Bibani navasi yena minasina tetala tau\" — likely \"Bibani\" = one; \"navasi\" = man; \"minasina\" = these; \"tetala\" = four; \"tau\" = fish.\n\nNo verb of catch? But it must be a verb.\n\nWait — maybe \"yena\" is a verb? No — \"yena\" = man.\n\n\"minasina\" = these; \"tetala\" = four; \"tau\" = fish.\n\nMay need to back-translate.\n\nBut perhaps an alternative: action verbs are in certain forms.\n\nGather verb patterns:\n\n- Arrive: \"magudiwena\" (in 3, 4, 10)\n- See: \"waga\", \"makwena\", \"makesiwena\" — \"waga\" + object\n- Kill: \"lekalimati\" — in (5), (12)\n- Look after: \"teyu\" — \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\"\n- Will: \"will\" → appears in (1), (3), (7), (13)\n\n(7): \"That clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"Bigisi\" = that; \"kwetala\" = clever; \"vivila\" = will see; \"minawena\" = something; \"nakabitam\" = will?\n\nNo verb like \"will see\" — \"vivila\" = see; \"minawena\" = something; \"nakabitam\" = will?\n\nSo \"will see\" = \"vivila\" or \"nakabitam\"?\n\n\"nakabitam\" = will? (in example 7)\n\nBut in (13): \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\n\"Navila\" = how many; \"vivila\" = will look after? Or \"vivila\" = will; \"biyamatasi\" = women?\n\n\"biyamatasi\" = women? \"bityamatasi\" → but in (6): \"Leyamatasi teyu tauwau nunumwaya\" → \"The old women looked after two men\" → \"leyamatasi\" = old women; \"teyu\" = look after → verb.\n\nSo \"teyu\" = look after.\n\nSimilarly, \"vivila\" in (7): \"will see\" → likely \"vivila\" = will see.\n\nIn (13): \"Navila vivila biyamatasi tau mtona?\" = \"How many women will look after this man?\"\n\n\"vivila\" = will look after? Or \"vivila\" = will; \"biyamatasi\" = women; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila\" may be the verbal part — possibly \"will look after\" as a verb.\n\nThus, when verb is \"look after\", the verb is \"teyu\" or \"vivila\"?\n\nIn (6): \"Leyamatasi teyu tauwau nunumwaya\" → \"The old women looked after two men\" → \"teyu\" = look after.\n\nIn (13): \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nSo \"vivila\" = will look after?\n\nBut in (7): \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" — \"vivila\" = see? But \"minawena\" = something; \"nakabitam\" = will?\n\nSo \"vivila\" appears across different contexts.\n\nPossibly \"vivila\" means \"will see\" or \"will look after\"? Not consistent.\n\nAlternatively, \"vivila\" is a separate verb for \"able to see\" or \"something\", but not clear.\n\nBut in both (6) and (13), \"vivila\" is used with \"look after\".\n\nIn (13): \"vivila\" = will look after? Possibly.\n\nSo to generalize:\n\n- Future: \"will\" is expressed by \"vivila\" or \"nakabitam\", or implied.\n- \"look after\" = \"teyu\" (in (6)); in (13): \"vivila\" — perhaps a variant?\n\nBut focus on (19): \"How many canoes did those old women see?\"\n\nPattern from (4): \"That old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana\"\n\nStructure: [agent] + [verb waga] + [object makesiwena] + [plurality marker minana]\n\nSo for question: \"How many canoes did those old women see?\"\n\n→ \"Navila namwaya lekisi waga?\"\n\n\"Navila\" = how many; \"namwaya\" = canoes; \"lekisi\" = those old women (from \"legisi\" = that old woman; \"lekisi\" = those old women? — \"legisi\" = that; \"lekisi\" = those?)\n\nIn (4): \"Legisi\" = that old woman; \"lekisi\" = those women? Not directly.\n\nIn (6): \"Leyamatasi\" = old women → so \"leyamatasi\" = old women.\n\nIn (9): \"Amakena waga legisesi gweguyau?\" → \"which canoe did chiefs see?\" → \"legisesi\" = chiefs.\n\nSo \"legisesi\" = chiefs; \"legisi\" = that chief; so \"lekisi\" = those?\n\nLikely, \"lekisi\" = those old women.\n\nThen, \"namwaya\" = canoes.\n\nSo \"Navila namwaya lekisi waga?\"\n\nBut is \"waga\" the verb?\n\nYes — from (4): \"waga\" = saw.\n\nSo \"Navila namwaya lekisi waga?\" → How many canoes did those old women see?\n\nThis matches.\n\nNow (20): \"These four white men will look after this clever child.\"\n\n\"will look after\" = \"vivila\" (as in (13)) or \"teyu\"?\n\nIn (6): \"look after\" = \"teyu\"\n\nIn (13): \"Navila vivila biyamatasi tau mtona\" → \"how many women will look after this man?\"\n\nSo \"vivila\" = will look after.\n\nThus, \"will look after\" is \"vivila\"\n\nSo \"These four white men will look after this clever child.\"\n\n→ Need to express:\n\n\"these four\" → in (1): \"one man\" → \"Bibani navasi yena\" → \"Bibani\" = one; \"navasi\" = man\n\nIn (5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n\"Amtona\" = which man; \"tau\" = man; \"nayu\" = two; \"bunukwa\" = pigs.\n\n\"nayu\" = two — how many?\n\n\"these four\" — in (1): \"these four fish\" → \"tetala tau\" → \"tetala\" = four; \"tau\" = fish.\n\nIn (2): \"This white man arrived\" → \"Lekota dimdim mtona\" → \"lekota\" = this; \"dimdim\" = white; \"mtona\" = man.\n\nSo \"this\" = \"lekota\"; \"these\" → possibly \"lekisi\" or \"navasi\"?\n\n\"navasi\" = one man → not \"these\"\n\nIn (1): \"these four fish\" → \"tetala tau\" — \"tetala\" = four; \"tau\" = fish.\n\nSo likely, \"four\" = \"tetala\"\n\n\"white men\" → \"dimdim\" = white; \"mtona\" = man → so \"dimdim mtona\" = white man\n\n\"these four white men\" → \"tetala dimdim mtona\"?\n\nBut (1): \"Bibani navasi yena minasina tetala tau\" → \"one man these four fish\"\n\nSo \"minasina\" = these.\n\nSo \"these\" = \"minasina\" (these)\n\nSimilarly, in (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"lekamkwamsi\" = things; \"dimdim\" = white men.\n\nSo \"dimdim\" = white men.\n\nSo \"these four white men\" → likely \"minasina tetala dimdim mtona\"\n\n\"minasina\" = these; \"tetala\" = four; \"dimdim\" = white; \"mtona\" = men.\n\nThus, \"minasina tetala dimdim mtona\"\n\nThen \"will look after\" → \"vivila\"\n\n\"this clever child\" → in (3): \"That child will arrive\" → \"Bikota gwadi magudiwena\"\n\n\"bikota\" = that; \"gwadi\" = child\n\nIn (10): \"that beautiful child saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"gwadi\" = child; \"gudimanabweta\" = this stone.\n\nSo \"this\" = \"gudimanabweta\"\n\n\"clever\" → in (7): \"that clever woman\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"kwetala\" = clever\n\nSo \"this clever child\" = \"gwadi kwetala\"?\n\nBut (7): \"vivila minawena\" → \"will see something\" — \"vivila\" = will see; \"minawena\" = something.\n\nIn (10): \"gwadi magudiwena gudimanabweta\" → \"child this stone\"\n\nSo \"this\" = \"gudimanabweta\"\n\nThus, \"this clever child\" = \"gwadi kwetala\" — but \"gwadi\" is child, \"kwetala\" = clever.\n\nBut \"gwadi\" = child; so \"gwadi kwetala\" = clever child.\n\nIn (3): \"that child\" → \"bikota gwadi\"\n\nSo \"this\" → \"gudimanabweta\";", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11612.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "iid", + "sample_index": 2, + "output": "Step 1: Identify key patterns from the given English–Kilivila pairs.\n\nLook at questions involving \"how many\" → always start with *Navila* in Kilivila. \nExample: \n11. How many things did those white men eat? → Kwevila lekamkwamsi dimdim mtosiwena? \n→ \"Kwevila\" = \"how many\", used after a noun phrase.\n\nSimilarly: \n8. How many dogs arrived? → Navila ka’ukwa lekotasi? \n→ \"Navila\" = \"how many\" + noun. \nThus, \"how many X did Y do?\" → *Navila X [verb] [agent]* or *Navila X [agent]* depending.\n\nIn 19: How many canoes did those old women see? \n→ Should follow pattern: *Navila kanu* (canoe) *lekotasi* (those old women) *makwena* (see) \nBut in 4: They saw those canoes → *Legisi waga makesiwena namwaya minana* \n→ \"makesiwena\" = saw, \"namwaya minana\" = those canoes \n→ So \"see\" = *makesiwena* \n\"those old women\" = *legisi waga lekotasi*? Wait — in 3: That child → *Bikota gwadi magudiwena* \n\"that\" → *Bikota*, *gwadi* = that, *magudiwena* = child \nIn 2: This white man → *Lekota dimdim mtona* \nSo: \n- \"this\" = *Lekota* \n- \"that\" = *Bikota* \n- \"those\" = *legisi*? (19: \"those old women\" = \"legisi waga lekotasi\"?) \nIn 4: \"That old woman\" → *Legisi waga* \n→ So \"legisi\" = those, used for plural, \"waga\" = old woman?\n\nIn 4: \"That old woman\" → *Legisi waga makesiwena namwaya minana* \n→ \"legisi\" = that (referring to old woman) \nBut in 6: \"The old women\" → *Leyamatasi teyu tauwau nunumwaya* \n→ \"Leyamatasi\" = the old women? → likely \"leya\" = the, \"matasi\" = old, \"tauwau\" = women? \nWait: \"Leyamatasi\" might be \"the old women\" → so \"leya\" = the, \"matasi\" = old, \"tauwau\" = women? \nBut in 12: \"The clever chief\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" \n→ \"Lekalimati\" = the clever chief → so \"Lekalimati\" = the clever man? \n\nPattern for possession/agent: \n- \"this\" → *Lekota* \n- \"that\" → *Bikota* \n- \"those\" → *Legisi* → in 4: *Legisi waga* → that old woman → but \"legisi\" = that? \nBut in 8: \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?* → \"lekotasi\" = those dogs? → \"lekota\" = this, \"lekotasi\" = those? \nYes, \"lekotasi\" = those, \"lekota\" = this, \"bikota\" = that \n\nSo: \n- \"this\" = *lekota* \n- \"that\" = *bikota* \n- \"those\" = *legisi* \n\nFor possessed noun: \n\"white man\" = *dimdim mtona* → \"dimdim\" = white, \"mtona\" = man \n\"old woman\" = *waga lekotasi* → in 4: \"legisi waga\" → so \"waga\" = old woman → \"waga\" = old woman \n\"child\" = *gwadi magudiwena* → \"gwadi\" = child, \"magudiwena\" = something? \nIn 10: \"that beautiful child saw this stone\" → *Legisi dakuna makwena gwadi magudiwena gudimanabweta* \n→ \"gwadi magudiwena\" = child \n→ So \"gwadi\" = child, \"magudiwena\" = (the) child? \n\nSo: \n- \"man\" → *mtona* \n- \"woman\" → *waga* \n- \"child\" → *gwadi* \n- \"pig\" → *bunukwa* \n- \"dog\" → *ka’ukwa* \n- \"fish\" → *tetala* \n- \"canoe\" → *namwaya* \n\nActions: \n- \"see\" → *makesiwena* \n- \"arrive\" → *lekotasi* (in 2: \"This white man arrived\" → *Lekota dimdim mtona*) → no, in 2: *Lekota dimdim mtona* → only \"arrived\" not in verb \nLook: \n2. This white man arrived → *Lekota dimdim mtona* → \"arrived\" is implicit? No — verb not present \nWait — in 12: \"The clever chief killed one wild pig\" → *Lekalimati natala bunukwa nagasisi guyau tokabitam* \n- \"killed\" = *nagasisi*? \"nagasisi\" → in 12: \"nagasisi guyau\" → \"guyau\" = wild? \nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" \n→ So \"nagasisi\" = killed? \nIn 7: \"That clever woman will see something\" → *Bigisi kwetala vivila minawena nakabitam* → \"kwetala\" = will, \"vivila\" = something? \n→ \"will see\" = *kwetala vivila minawena* — \"minawena\" = something \nIn 13: \"How many women will look after this man?\" → *Navila vivila biyamatasi tau mtona?* \n→ \"look after\" = *biyamatasi*? \nIn 6: \"The old women looked after two men\" → *Leyamatasi teyu tauwau nunumwaya* → \"teyu\" = looked after? \n→ \"teyu\" = looked after? \nIn 13: \"will look after\" → *biyamatasi* — \"biyamatasi\" = look after? \nYes → \"biyamatasi\" = look after \n\"will\" → *kwetala* \n\"see\" → *makesiwena* \n\"arrive\" → not clearly stated, but in 2: \"This white man arrived\" → *Lekota dimdim mtona* — no verb? \nWait — in 2: \"This white man arrived\" → *Lekota dimdim mtona* — only noun phrase? \nIn 1: \"One man will catch these four fish\" → *Bibani navasi yena minasina tetala tau* \n→ \"navasi\" = will? \n\"navasi\" = will? \nIn 1: \"will catch\" → *yena* = catch? \"navasi\" = will? \nIn 7: \"will see\" → *kwetala* \nSo \"will\" = *kwetala* in future or potential \n\"catch\" = *yena*? \nIn 1: \"will catch\" → *navasi yena* → so \"navasi\" = will, \"yena\" = catch \nIn 5: \"Which man killed two pigs?\" → *Amtona tau lekalimati nayu bunukwa?* \n→ \"killed\" = *lekalimati*? → \"lekalimati\" = man? No — \"lekalimati\" appears in 12: \"the clever chief\" → *Lekalimati natala bunukwa* → \"Lekalimati\" = the clever chief \nSo \"Lekalimati\" = the clever man \nIn 5: \"Which man killed two pigs?\" → *Amtona tau lekalimati nayu bunukwa?* \n→ \"Amtona\" = which? (used for \"which\") \n\"tau\" = man \n\"nayu\" = killed? \nIn 12: \"killed one wild pig\" → *nagasisi guyau tokabitam* \n\"nagasisi\" = killed \nSo \"killed\" = *nagasisi* \nThen in 5: \"killed two pigs\" → *nayu bunukwa* → \"nayu\" = killed? \nBut in 12: \"nagasisi guyau tokabitam\" — \"guyau\" = wild, \"tokabitam\" = pig \nSo \"bunukwa\" = pig \nThus, \"killed\" = *nagasisi* \nIn 19: How many canoes did those old women see? \n→ Subject: \"those old women\" → \"legisi waga\" → in 4: *Legisi waga makesiwena namwaya minana* → they saw those canoes \nSo \"see\" = *makesiwena* \n\"how many\" = *navila* \nSo: *Navila namwaya legisi waga makesiwena?* \nBut in 8: \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?* \n→ \"Navila ka’ukwa lekotasi?\" = How many dogs did those (animals) arrive? — wait, \"lekotasi\" = those? \n\"ka'ukwa\" = dogs \n\"lekotasi\" = those \nBut \"arrived\" not expressed — verb missing. \nIn 2: \"This white man arrived\" → *Lekota dimdim mtona* — no verb → must be missing verb? \nWait, perhaps all verbs are implied or part of the structure. \n\nBut in 8: \"how many dogs arrived\" → verb \"arrived\" is missing. \nBut in 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* \n→ \"kwevila\" = how many? \nSo in 11: \"how many things did...\" → *Kwevila* (how many) + noun + \"did\" + agent + verb? \nBut \"did\" is not expressed — it's in question form. \nSimilarly, in 13: \"How many women will look after this man?\" → *Navila vivila biyamatasi tau mtona?* \n→ \"Navila\" = how many \n\"vivila\" = women? \n\"biyamatasi\" = look after \n\"tau mtona\" = this man \nSo verb in form of \"look after\" = *biyamatasi* \n\nThus, general pattern: \n- \"how many X did Y do?\" → *Navila X [agent] verb* \n- If \"do\" is not a verb, or if verb is \"see\", \"look after\", etc., use the corresponding form. \n- \"will\" → *kwetala* \n- \"see\" → *makesiwena* \n- \"look after\" → *biyamatasi* \n- \"killed\" → *nagasisi* \n- \"arrive\" → verb not directly shown, but in analogy: \nIn 2: \"This white man arrived\" → *Lekota dimdim mtona* — no verb → so perhaps \"arrived\" is not expressed as a separate verb, or it's embedded? \nNo — in 4: \"That old woman saw those canoes\" → has *makesiwena* \nSo verbs are: \n- see → makesiwena \n- look after → biyamatasi \n- kill → nagasisi \n- arrive → ? \n\nBut in 8: \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?* → no verb — missing \nBut in 4: \"saw\" has *makesiwena* — not in 8 \nThus, \"arrive\" might be expressed by a separate verb. \n\nLook at 2: This white man arrived → *Lekota dimdim mtona* \nNo verb — so perhaps \"arrive\" is not a separate verb in this form. \nBut in 8: \"how many dogs arrived?\" → *Navila ka’ukwa lekotasi?* \n→ So likely \"arrive\" is implied or embedded in the noun phrase. \nBut perhaps in Kilivila, \"arrive\" is not a verb with its own form; it's part of the noun or phrasing. \n\nBut in 9: \"Which canoe did the chiefs see?\" → *Amakena waga legisesi gweguyau?* \n→ \"gweguyau\" = see? \n\"Amakena\" = which? \n\"legisesi\" = the chiefs? \n\"canoe\" → *namwaya* \nSo \"see\" = *gweguyau*? \nBut in 4: \"saw\" → *makesiwena* \nIn 9: \"see\" → *gweguyau* \nInconsistency? \nIn 4: \"Legisi waga makesiwena namwaya minana\" → saw \nIn 9: *Amakena waga legisesi gweguyau?* → see \nSo \"see\" = both *makesiwena* and *gweguyau* → different forms? \n\nPossibility: \n- \"makesiwena\" = past tense see \n- \"gweguyau\" = present or future see? \nBut in 7: \"will see\" → *kwetala vivila minawena nakabitam* → *kwetala* = will, *vivila minawena* = see something \nNo verb for \"see\" used. \nSo \"see\" = *makesiwena* in past, *gweguyau* in present? \n\nBut in 10: \"that beautiful child saw this stone\" → *Legisi dakuna makwena gwadi magudiwena gudimanabweta* \n→ \"makwena\" = saw? \nYes — \"makwena\" = saw \nSo \"saw\" = *makwena* in 10 \nBut in 4: *makesiwena* → saw \nIn 9: *gweguyau* → see \nSo multiple forms for \"see\"? \n\nPossibility: meaning or context determines verb — or is it a mistake? \n\nWait — in 4: \"That old woman saw those canoes\" → *Legisi waga makesiwena namwaya minana* \n→ \"makesiwena\" = saw \nIn 10: \"that beautiful child saw this stone\" → *Legisi dakuna makwena gwadi magudiwena gudimanabweta* \n→ \"makwena\" = saw \nSo two forms: *makesiwena* and *makwena* — possibly a typo or dialectal variation? \n\nBut in 9: \"Which canoe did the chiefs see?\" → *Amakena waga legisesi gweguyau?* \n→ \"gweguyau\" = see \nSo different forms: \n- *makesiwena* → saw \n- *makwena* → saw \n- *gweguyau* → see? \n\nBut in 7: \"will see something\" → *Bigisi kwetala vivila minawena nakabitam* \n→ \"kwetala\" = will \n\"vivila minawena\" = something \n\"nakabitam\" = see? \nNo — \"nakabitam\" = see? \nIn 7: \"will see something\" → *Bigisi kwetala vivila minawena nakabitam* \nSo \"nakabitam\" = see? \nBut in 4: \"saw\" = *makesiwena* \nNow we have: \n- *makesiwena* = saw \n- *makwena* = saw \n- *gweguyau* = see \n- *nakabitam* = see \n\nThis is too many. \nBut note: in 12: \"killed one wild pig\" → *Lekalimati natala bunukwa nagasisi guyau tokabitam* \n→ \"nagasisi guyau tokabitam\" → \"guyau\" = wild, \"tokabitam\" = pig \nBut \"nagasisi\" = killed? \nIn 5: \"which man killed two pigs?\" → *Amtona tau lekalimati nayu bunukwa?* \n→ \"nayu\" = killed \nSo \"killed\" = *nayu* in 5, *nagasisi* in 12? \nInconsistent. \n\nPossibility: verbs depend on agent or context. \nBut in 5: \"killed\" = *nayu*, in 12: \"killed\" = *nagasisi* — different forms. \n\nAlternatively, maybe the verb is fixed, and the form changes based on mood or direction. \n\nLet’s reinterpret: \nPerhaps the verb for \"see\" is *makesiwena* or *makwena* — likely *makwena* is the base. \nIn 4: \"makesiwena\" used — perhaps it's a form of \"see\" — and in 10: *makwena* \nIn 9: *gweguyau* — might be same as *makwena*? \n\nBut let's take the most consistent ones: \nFor 19: How many canoes did those old women see? \n→ *Navila namwaya legisi waga makesiwena?* \nBut in 4: \"those old women\" → \"legisi waga\" → saw canoes → *makesiwena* \nYes — so *navila namwaya legisi waga makesiwena?* \nBut must be grammatical — likely \"navila namwaya legisi waga makesiwena\" → how many canoes did those old women see? \nYes.\n\n20.", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10941.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "iid", + "sample_index": 3, + "output": "Step 1: Identify the structure of questions and translations in the given examples.\n\nLook at how English questions are transformed in Kilivila:\n\n- Questions starting with \"How many X did Y see?\" → Structure: \"Navila X lekota Y?\" or \"Navila X waga Y?\"\n - Example: (8) \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n → \"Navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived \n → So \"Navila X lekotasi\" = \"how many X arrived?\"\n\n- \"Which X did Y see?\" → \"Amtona X waga Y lekota?\" or \"Amakena X waga Y?\"\n - (9) \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n → \"Amakena\" = which; \"waga\" = canoe; \"legisesi\" = the chiefs; \"gweguyau\" = saw\n\n- \"Will X look after Y?\" → \"X tauwau Y\"\n - (6) \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\"\n → \"Leyamatasi\" = old women; \"teyu\" = two; \"tauwau\" = look after\n\n- \"X will see something\" → \"X vivila minawena\"\n - (7) → \"Bigisi kwetala vivila minawena nakabitam\"\n → \"vivila minawena\" = will see something\n\n- \"X killed Y\" → \"X natala Y\"\n - (12) → \"Lekalimati natala bunukwa nagasisi guyau tokabitam\"\n → \"natala\" = killed; \"bunukwa\" = pig; \"guyau\" = wild; \"tokabitam\" = man → \"killed a wild man\"\n\nStep 2: Identify patterns for each sentence.\n\n19. \"How many canoes did those old women see?\"\n\n- Pattern: \"How many X did Y see?\" → \"Navila X waga Y lekotasi?\"\n- But in (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n- In (4): \"This old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana\"\n → \"waga\" = canoe; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes\n\nSo \"waga\" = canoe; \"makesiwena\" = saw; so \"waga\" is noun; \"makesiwena\" is verb.\n\nThus: \"How many canoes did those old women see?\" → \n→ \"Navila waga lekota leyamatasi?\"\n\nBut in (4), \"legisi\" = old woman; \"waga\" = canoe; \"makesiwena\" = saw → \"legisi waga makesiwena namwaya minana\"\n\nSo \"waga makesiwena\" = saw canoes\n\nSo \"how many canoes did those old women see?\" → \n\"Navila waga lekota leyamatasi?\"\n\nCheck: \"Navila waga\" = how many canoes? \n\"lekota\" = saw? \n\"leyamatasi\" = those old women?\n\nYes — this matches (4) pattern.\n\n→ So 19: **Navila waga lekota leyamatasi**\n\n20. \"These four white men will look after this clever child.\"\n\n- Structure: \"X will look after Y\"\n- From (6): \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n → \"tauwau\" = look after\n\nSo: \"X will look after Y\" → \"X tauwau Y\"\n\nNow: \"These four white men\" → \"These\" = \"yena\"? \n(1) \"One man will catch these four fish\" → \"navasi yena minasina tetala tau\"\n\n\"yena\" = these\n\nSo \"these four\" → \"yena tetala\"?\n\n\"white man\" → \"dimdim mtona\" in (2) → \"dimdim\" = white; \"mtona\" = man\n\nSo \"white men\" → \"dimdim mtona\"\n\n\"clever child\" → \"gwadi\" = child; \"kwetala\" = clever? \n(7) \"That clever woman\" → \"Bigisi kwetala\" → \"kwetala\" = clever\n\nSo \"clever child\" = \"gwadi kwetala\"\n\n\"will look after\" = \"tauwau\"\n\nSo: \"yena tetala dimdim mtona tauwau gwadi kwetala\"\n\nBut \"yena tetala\" = these four? → in (1): \"yena minasina\" → \"these four fish\" → \"minasina\" = four\n\nSo \"tetala\" = four? → likely \"tetala\" = four\n\nSo \"these four white men\" = \"yena tetala dimdim mtona\"\n\n\"this clever child\" = \"gwadi kwetala\"\n\nThus: \"yena tetala dimdim mtona tauwau gwadi kwetala\"\n\nOrder: subject → verb → object\n\nKilivila may not require case, but order is subject-verb-object.\n\nSo 20: **yena tetala dimdim mtona tauwau gwadi kwetala**\n\n21. \"How many children will eat these pigs?\"\n\n- Pattern: \"How many X will eat Y?\"\n\nCompare (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim\" = white \n\"mtosiwena\" = ate\n\nSo \"Kwevila X lekamkwamsi Y?\" = how many X ate Y?\n\n\"how many children will eat these pigs?\" → \"Kwevila gwadi lekamkwamsi tetala bunukwa?\"\n\n\"gwadi\" = child \n\"tetala\" = four? But pigs → in (12) \"bunukwa\" = pig → \"bunukwa\" = pig\n\n\"these pigs\" → \"tetala bunukwa\"? \nIn (1) \"these four fish\" → \"minasina tetala\" → so \"tetala\" = four? \nBut here \"these pigs\" → likely \"tetala bunukwa\" = these pigs?\n\nYes — in (1) \"tetala minasina\" → four fish → \"minasina\" = fish (not four)\n\nWait: (1) \"One man will catch these four fish.\" → \"navasi yena minasina tetala tau\"\n\n\"minasina\" = fish \n\"tetala\" = four?\n\nBut (4): \"those canoes\" → \"namwaya minana\"\n\nSo \"tetala\" = four?\n\nThen \"these pigs\" → \"tetala bunukwa\"?\n\nBut (12): \"killed one wild pig\" → \"bunukwa\" = pig → \"one\" = \"nayu\"?\n\n(5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n\"nayu\" = two → so \"nayu\" = two\n\nSo \"one\" → likely not in word form here\n\nSo \"these pigs\" → likely \"tetala bunukwa\"? But \"tetala\" = four?\n\nBut in (1), \"these four fish\" — \"minasina tetala\" → so \"tetala\" = four → so \"these four fish\" = \"minasina tetala\"\n\nSo \"these pigs\" → should be \"bunukwa tetala\"? But \"tetala\" is the number?\n\nBut in (1), \"minasina tetala\" — fish is before number?\n\nBut in (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nSo \"lekamkwamsi\" = things → \"dimdim\" = white men → \"mtosiwena\" = ate\n\nSo \"how many X ate Y?\" → \"Kwevila X lekamkwamsi Y?\"\n\nSo here: \"how many children will eat these pigs?\" → \"Kwevila gwadi lekamkwamsi tetala bunukwa?\"\n\n\"gwadi\" = child \n\"lekamkwamsi\" = eat \n\"tetala bunukwa\" = these pigs?\n\nYes — \"tetala\" = these/four? But in context, \"these\" is with pigs — so it's \"these pigs\", like in (1)\n\nBut \"tetala\" is the number? Wait — in (1): \"these four fish\" → \"minasina tetala\" → so \"tetala\" = four?\n\nBut in (11): \"those white men\" → \"dimdim\" and \"mtosiwena\" = ate → no number\n\nSo in (21), \"these pigs\" — does \"tetala\" mean \"these\" or \"four\"?\n\nIn (1): \"these four fish\" → \"yena minasina tetala\" → so \"yena\" = these; \"tetala\" = four\n\nIn (4): \"those canoes\" → \"namwaya minana\" → \"namwaya\" = those\n\nSo \"these\" = \"yena\"; \"those\" = \"namwaya\"\n\nIn (21): \"these pigs\" → likely \"yena bunukwa\"?\n\nBut \"bunukwa\" = pig → so \"yena bunukwa\" = these pigs?\n\nBut no number — unless \"tetala\" is still used?\n\nIn (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nNo number → so number is not required in \"how many things\" — only in specific questions.\n\nIn (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → no number\n\nSo in (21): no number → \"how many children will eat these pigs?\" → \n\"Kwevila gwadi lekamkwamsi yena bunukwa?\"\n\nYes — \"yena\" = these; \"bunukwa\" = pigs\n\n\"will eat\" = \"lekamkwamsi\"\n\n\"how many children\" = \"Kwevila gwadi\"\n\nSo: **Kwevila gwadi lekamkwamsi yena bunukwa**\n\n22. \"Which woman caught those beautiful fish?\"\n\n- Pattern: \"Which X did Y catch?\" → \"Amtona X waga Y lekota?\"\n\nFrom (9): \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n\"amakena\" = which; \"waga\" = canoe; \"legisesi\" = chiefs; \"gweguyau\" = saw\n\nSo format: \"Amtona X waga Y lekota?\" → but (9): \"Amakena waga legisesi gweguyau?\"\n\n\"amakena\" = which canoe → so \"amakena\" = which\n\n\"catch\" → in (1): \"One man will catch these four fish\" → \"navasi yena minasina tetala tau\"\n\n\"tau\" = catch?\n\nIn (1): \"catch\" → \"tau\"\n\nSo \"caught\" = \"tau\"\n\nSo \"which woman caught those beautiful fish?\"\n\n\"amtona\" = which (like amakena)\n\n\"woman\" → \"bikota\" = that woman? (3) \"That child will arrive\" → \"Bikota gwadi magudiwena\"\n\n\"bikota\" = that\n\nBut \"woman\" → is there a word?\n\n(4): \"This old woman saw...\" → \"Legisi waga makesiwena\" → \"legisi\" = old woman\n\n\"woman\" → likely \"bikota\" for that woman?\n\n(2): \"This white man arrived\" → \"Lekota dimdim mtona\"\n\nSo \"bikota\" = that; \"tato\" or other for woman?\n\nIn (19): \"those old women\" → \"leyamatasi\"\n\n\"woman\" → \"bikota\" might be used for \"that woman\"\n\nBut here \"which woman\" → \"amtona bikota?\"\n\nIn (9): \"which canoe\" → \"amakena\"\n\n\"amakena\" = which\n\nSo likely \"amtona\" = which\n\nIn (5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n→ \"amtona\" = which\n\nSo \"amtona\" = which\n\nSo \"which woman\" → \"amtona bikota?\"\n\n\"captured\" → \"tau\"\n\n\"those beautiful fish\" → \"namwaya\" = those; \"minasina\" = beautiful? (10) \"that beautiful child\" → \"dakuna\" = beautiful\n\nIn (10): \"that beautiful child\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"legisi\" = that woman? → \"dakuna\" = beautiful\n\nSo \"dakuna\" = beautiful\n\nSo \"beautiful fish\" → \"minasina dakuna\"?\n\n\"minasina\" = fish\n\nSo \"those beautiful fish\" → \"namwaya minasina dakuna\"?\n\n\"namwaya\" = those\n\nSo: \"amtona bikota tau namwaya minasina dakuna?\"\n\nBut in (1): \"one man will catch these four fish\" → \"navasi yena minasina tetala tau\"\n\nSo \"tau\" = catch\n\nSo \"which woman caught those beautiful fish?\" → \"amtona bikota tau namwaya minasina dakuna\"\n\nYes — this matches.\n\n23. \"Two wild dogs saw that old man.\"\n\n- Pattern: \"X saw Y\"\n\nFrom (4): \"This old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana\"\n\n\"makesiwena\" = saw\n\nSo \"saw\" = \"makesiwena\"\n\n\"Two wild dogs\" → \"two\" = \"nayu\"; \"wild\" = \"guyau\"; \"dogs\" = \"ka’ukwa\"?\n\n(8) \"How many dogs arrived?\" → \"ka’ukwa\"\n\nSo dogs = \"ka’ukwa\"\n\n\"wild\" → in (12): \"killed one wild pig\" → \"guyau\" = wild\n\nSo \"wild dogs\" = \"nayu guyau ka’ukwa\"\n\n\"that old man\" → \"that\" = \"bikota\"; \"old man\" → (3) \"that child will arrive\" → \"bikota gwadi magudiwena\" → \"bikota\" = that; \"magudiwena\" = child\n\nOld man → \"legisi\" = old woman → so man?\n\n(12): \"clever chief\" → \"lekalimati\" = chief\n\n\"old man\" → \"legisi\" → woman? \"legisi\" = old woman → so old man not directly\n\nIs there a word?\n\n(3): \"that child\" → \"bikota gwadi\"\n\n(5): \"which man\" → \"amtona tau lekalimati\" → \"lekotati\" or \"lekala\"?\n\nWait (2): \"This white man arrived\" → \"Lekota dimdim mtona\" → \"lekota\" = arrived; \"dimdim mtona\" = white man\n\nSo man → \"mtona\"\n\nSo \"old man\" → \"bikota mtona\"?\n\nBut \"old\" → in (4): \"old woman\" → \"legisi\"\n\nSo \"old man\" = \"legisi mtona\"?\n\nBut in (2): \"white man\" → \"dimdim mtona\"\n\nSo \"mtona\" = man\n\n\"legisi\" = old woman — so does \"legisi\" extend to man?\n\nCompare to (13): \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\n\"biyamatasi\" = women; \"mtona\" = man\n\nSo man = \"mtona\"\n\nWomen = \"biyamatasi\"\n\nSo \"old man\" → not directly; but \"legisi\" = old → used for woman\n\nIs there a word for old man?\n\nIn (13): \"this man\" → \"mtona\"\n\nNo \"old\" modifier.\n\nSo likely \"that old man\" → \"bikota mtona\" → \"that man\", and \"old\" is implied?\n\nBut in (4): \"old woman\" → \"legisi\"\n\nSo \"old\" only with woman?\n\nBut (12): \"clever chief\" → \"lekalimati\" — chief; \"wild pig\"\n\nNo \"old\" for man.\n\nPossibly \"old\" is only marked on woman.\n\nBut in (23): \"that old man\" → must exist.\n\nPossibility: \"legisi\" is used for old man?\n\nIn (4): \"old woman\" → \"legisi\"\n\nIn (3): \"that child\" → \"bikota\"\n\nIn (13): \"this man\" → \"mtona\"\n\nSo man → \"mtona\"\n\nThus, \"old man\" → must be \"legisi mtona\"? But not used.\n\nAlternative: \"old\" is a separate adjective.\n\nBut only \"legisi\" = old\n\nSo likely, \"that old man\" = \"bikota legisi mtona\"?\n\nNo — \"legisi\" = old woman\n\nCould \"legisi\" be used for old man? Or is it just for women?\n\nBut in Kilivila, gender may be marked.\n\n(13): \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona\" \n→ \"biyamatasi\" = women; \"mtona\" = man\n\nSo \"mtona\" is man; no \"old\"\n\nSo \"old man\" → must be constructed.\n\nPossibility: \"old\" only with woman → so perhaps in this case \"that man\" is considered old?\n\nBut that's not clear.\n\nCompare (2): \"This white man arrived\" → \"Lekota dimdim mtona\" — man\n\n(4): \"This old woman saw...\" → \"Legisi waga makesiwena\" — woman\n\nSo \"old\" only with woman.\n\nThus, in (23), \"that old man\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11398.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given a list of Rotuman words and their English translations, and asked to determine the *theoretically possible* translations for two English words: \n- \"word\" \n- \"to exhaust\" \n\nWe cannot translate them with certainty from the given data, so we must infer possible forms based on linguistic patterns, morphology, and known word structures.\n\n---\n\n### Step 1: Identify possible morphological roots\n\nWe look for patterns in the given data.\n\n#### Possible root for \"word\":\n- There is no direct word for \"word\" in the list.\n- But \"pala\" means \"to pierce\", \"pogi\" means \"night\", \"nu‘suar tiro\" = \"window\", \"nu‘sura\" = \"door\".\n- \"Mamasa\" = solid, \"ma.tit mamasa\" = ice, \"huli\" = to turn over, \"huni\" = lower end.\n- \"Is 'ā\" = sharp-pointed, \"is susu\" = nipple.\n- \"Poagpoga = palpala\" = covered with holes — possibly a compound.\n\nNo obvious candidate for \"word\".\n\nBut consider: is there a possible root for “to exhaust”?\n\n\"To exhaust\" = to deplete completely.\n\nLook for verbs that suggest depletion, usage, or lack of resource.\n\n- \"fäeag ‘u‘u\" = to use sign language → \"to use\" \n- \"fau\" = year \n- \"a‘öf fau\" = year’s end → suggests a time reference \n- \"hün kia\" = base of the neck \n- \"huag to‘a\" = courageous \n- \"hül ha.fu\" = to blow (of a hurricane) \n- \"pura.ki\" = to boil, to bubble up → suggests energy, eruption \n- \"pulu\" = glue \n- \"ka.lu\" = to encircle \n- \"piri\" = to curl \n- \"muli\" = not present, but \"mamasa\" = solid → perhaps used in compound? \n- \"ma.titi\" = coldness → not directly helpful \n\nNow observe: \"fau\" = year; \"a‘öf fau\" = year’s end → so \"a‘öf\" may mean \"end of\", \"end of year\".\n\nAlso: \"to use\" = \"fäeag 'u'u\", so \"to use\" is a verb.\n\nCould \"to exhaust\" be related to \"to use up\"?\n\nYes — \"to use up\" implies to consume entirely.\n\nIn many languages, \"exhaust\" = to use up completely.\n\nWe see \"fäeag\" = to use.\n\nSo “to use” is a verb root.\n\nCan we infer that “to exhaust” might be “to use up”?\n\nBut “use up” is not directly present.\n\nCould “use up” be formed from \"fäeag\" + something meaning \"up\"?\n\n\"Up\" is not directly present, but note:\n\n- \"lala\" = deep \n- \"ha.fha.fu\" = rocky \n- \"huli\" = to turn over \n- \"huni\" = lower end \n\n\"Up\" might be implied by opposition to \"lower\" (huni), or opposite of \"deep\" (lala).\n\nBut no clear word.\n\nWhat if “exhaust” = “to use up” and “up” is implied by a suffix like -huni or -pala?\n\nStill not clear.\n\nAlternatively: look for verbs that imply depletion.\n\n\"pura.ki\" = to boil, to bubble → energy build-up and release → not exhaustion directly.\n\n\"pulu\" = glue → sticky, adhesion → not clearly related.\n\n\"ka.lu\" = to encircle → not exhaustion.\n\nNo clear verb suggesting depletion.\n\nCould it be derived from a root meaning \"to use\" + \"up\"?\n\nBut we don’t have a word for \"up\".\n\nCould \"to exhaust\" be a compound of \"to use\" and \"up\"?\n\nBut we lack \"up\".\n\nAlternatively, is there a root that means \"to leave\" or \"to run out\"?\n\nNo such word.\n\nBut consider: \"moafmofa\" = littered with rubbish — implies something is left behind, but not about depletion.\n\n\"nu‘suar tiro\" = window → not useful.\n\nNow, consider that Rotuman may use reduplication or affixes to form new meanings.\n\nFor \"word\", there is no direct appearance.\n\nBut consider: in some languages, “word” is derived from “to speak” or “to utter”.\n\nWe see no verb for \"to speak\".\n\nBut \"pala\" = to pierce — perhaps \"to utter\" is related? Not clearly.\n\n\"pala\" could mean \"to pierce\", but \"to speak\" is not represented.\n\n\"to use sign language\" = \"fäeag 'u'u\" → so \"use\" is present.\n\nIs there a word that could mean \"to say\" or \"to utter\"?\n\nNot directly.\n\nCould “word” be derived from “to say”?\n\nNo evidence.\n\nCould \"word\" be a noun with a root like \"tua\" or \"tu\" (common in Austronesian languages)? Not present.\n\nAlternative: look at compound words.\n\n\"nu‘suar tiro\" = window → subject with \"nu‘\" (door/window) + \"tiro\" (spectacles or glasses)\n\n\"nu‘sura\" = door → plural?\n\n\"maf tiro\" = spectacles → so \"tiro\" = spectacles, which may be a noun.\n\n\"nu‘suar tiro\" = window ➝ so \"windows\"?\n\n\"tiro\" = spectacles → not clearly a root for word.\n\nBut \"tiro\" appears in “spectacles” → which is not a word meaning “word”.\n\nCould “word” be formed from a pattern like “to use” + something?\n\nNot supported.\n\nBut observe: \"ma.tit mamasa\" = ice → “coldness” and “solid” → ice formed from water.\n\nNo link.\n\nNow: is there a possible morpheme for \"to exhaust\"?\n\nPossibility: \"to use up\" → if \"use\" is \"fäeag\", and \"up\" is implied, then \"to exhaust\" may be a derived form.\n\nBut in absence of \"up\", can we suggest a form?\n\nIn Austronesian languages, exhaust is often formed via root + suffix for \"up\" or \"to consume\".\n\nWe don’t have a word for \"up\" directly.\n\nBut note: \"huni\" = lower end → so “upper” might be the opposite.\n\n\"ha.fha.fu\" = rocky → not helpful.\n\n\"lala\" = deep → so upper may oppose that.\n\nBut no direct \"up\".\n\nAnother verb: \"pura.ki\" = to boil → may imply energy, boiling up — suggests a form of reaching fullness and release.\n\nBut not exhaustion.\n\n\"to blow\" (hül ha.fu) — could be energy release.\n\nStill not exhaustion.\n\nHence, **\"to exhaust\"** is likely not directly present, but **could be formed from \"to use\" + \"up\"**, or from a root meaning \"to deplete\".\n\nPossible candidate: **\"fäeag\"** (to use) + affix meaning \"up\" or \"to the end\".\n\nBut no such affix.\n\nAlternatively, is there a word like “empty”?\n\nNo.\n\nThus, **\"to exhaust\"** may theoretically be formed as a compound of \"to use\" and \"end\", as in \"use to the end\".\n\n\"Year’s end\" = \"a‘öf fau\" → so \"end\" is a meaningful morpheme.\n\n\"End\" appears in \"a‘öf fau\", with \"a‘öf\" = end.\n\nCould \"to exhaust\" be derived from \"to use to the end\"?\n\nThat is: to use until nothing remains.\n\nTherefore, a possible form could be **\"fäeag a‘öf\"** (to use to the end).\n\nThis is not in the list, but based on known patterns (use + end), it would be a plausible theoretical translation.\n\nSimilarly, for \"word\" — we have no root.\n\nBut look: \"huli\" = to turn over → could imply turning something around?\n\n\"pala\" = to pierce → not related.\n\n\"mamasa\" = solid — could be “solid thing”?\n\n\"rū huga\" = stomach-ache → body pain.\n\nAll other compound words are combinations of nouns or verbs.\n\nBut note: \"pogi\" = night → so \"to night\"? No.\n\nIs there a root for \"thing\"? \"word\" = a verbal or noun object.\n\nIn some Austronesian languages, nouns for “word” are derived from verbs like “to speak”.\n\nWe have no verb for “to speak”.\n\nBut “to use” (fäeag) could be used in a broad sense.\n\nStill, \"word\" is not obviously derived.\n\nCould \"word\" be formed from a root meaning “to say”?\n\nWe have no such root.\n\nBut is there a possibility of a root like \"tua\" or \"tu\"?\n\nNot present.\n\nAlternatively, is \"word\" a rare or unmarked word in Rotuman?\n\nYes — and we are told we cannot translate it with certainty.\n\nSo we ask: what are the *possible* forms?\n\nCould \"word\" be related to \"to speak\"?\n\nWe don’t have that.\n\nAlternatively, in compound forms: \"nu‘suar tiro\" = window, \"nu‘sura\" = door → roots \"nu‘\" = door/window, \"tiro\" = spectacles.\n\n\"tiro\" appears in multiple compounds.\n\nBut “word” — no.\n\nAnother possibility: \"is susu\" = nipple → body part.\n\nBut not \"word\".\n\nPossibly, there is no known root, so theoretically, any noun can be formed via reduplication or affixation.\n\nIn Austronesian languages, often compounds are formed using a root + suffix.\n\nFor example:\n\n- \"to use\" = \"fäeag\"\n- \"to close\" = \"to ha‘ha\" (not present)\n\nBut nothing for \"word\".\n\nHowever, consider that in many languages, “word” can be formed as a noun from a verb of saying.\n\nWe have no verb of saying.\n\nTherefore, **\"word\"** cannot be confirmed.\n\nBut theoretically — could it be formed from \"to speak\" or from a noun root?\n\nWe lack evidence.\n\nBut observe: \"fau\" = year → abstract noun.\n\n\"pala\" = to pierce → verb.\n\n\"pogi\" = night → noun.\n\nSo \"word\" might be a noun, possibly resembling \"night\" in form.\n\nBut no suffix patterns show that.\n\nThus, the only possible theoretical forms are based on patterns in the data.\n\nSo for “to exhaust”:\n\nWe see “to use” (fäeag) and “end” (a‘öf).\n\nThus, “to use to the end” = to exhaust.\n\nTherefore, theoretical form: **fäeag a‘öf**\n\nSimilarly, for “word” — we have no root.\n\nBut could it be related to “speech”?\n\nNo.\n\nCould it be a derivative of “to say”?\n\nNot present.\n\nBut in some languages, “word” = “tua”, “tu”, or “kapa”.\n\nNot in data.\n\nBut is there a possibility that “to blow” or “to pierce” could relate to word?\n\n\"pala\" = to pierce — a sound could be pierced?\n\n\"puri\" = to curl?\n\nNot directly.\n\nNo plausible root.\n\nTherefore, in absence of direct evidence, what would be theoretically possible?\n\nWe must consider morphological patterns.\n\nNote: “fau” = year, “a‘öf fau” = year’s end → so compound of “end” + “year”\n\nSimilarly, “to use sign language” = “fäeag ‘u‘u” → compound of “use” and sign.\n\nTherefore, in compounds, we see: verb + noun, or noun + noun.\n\nFor “to exhaust”, a plausible compound is **to use to the end** → fäeag a‘öf\n\nFor “word” — is there a possible compound?\n\n\"pala\" = to pierce → could “word” be related to “pierce”?\n\n\"pala\" = to pierce — if something is pierced, it has a \"word\" in it?\n\nUnlikely.\n\nAlternatively, \"word\" might be a noun derived from “to say” — but no such verb.\n\nThus, theoretically, if a root exists, it may be formed as a noun with a stem like \"tua\", \"tui\", or \"tui\", but not in data.\n\nWe see no such word.\n\nBut “pogi” = night — a noun.\n\n“lala” = deep — noun.\n\n“mamasa” = solid — noun.\n\nSo nouns appear with no clear root for “word”.\n\nHence, the only theoretically possible forms, based on patterns in the language and assumed derivational patterns, are:\n\n- For “to exhaust”: a verb compound using “to use” + “to end” → **fäeag a‘öf** \n- For “word”: no clear root, but may be a noun like “tua” or “tui” — but not present.\n\nAlternatively, could “word” be formed with a root meaning “to speak”?\n\nNo such root.\n\nBut in Austronesian languages, many nouns are monosyllabic or two-syllabic.\n\nNo word in the list suggests a word for \"word\".\n\nHence, the only plausible theoretical form, based on available morphology, is that “word” could be formed with a root like \"lala\" (deep) or \"pala\" (to pierce), but no direct support.\n\nSo, in absence of evidence, we consider that the possible form for “word” might be a reduplicated noun or a borrowed word, but no derivation.\n\nHowever, the problem says: “theoretically possible translations”.\n\nSo what are possible forms?\n\nWe have no basis to say “word” is derived from anything.\n\nBut perhaps a compound like “to say word”?\n\nNo.\n\nAnother idea: “pala” = to pierce → could “to pierce” relate to “word” in speech? Possibly.\n\nBut not supported.\n\nTherefore, based on available data and morphological reasoning:\n\n- “to exhaust” = likely derived from “to use” + “end” → **fäeag a‘öf** \n- “word” = not directly derivable, but could be a noun formed from a root not in the data — e.g., *tua* or *tui*, but not present.\n\nHowever, in the compound “nu‘suar tiro” = window, the noun “tiro” appears — which is “spectacles”.\n\nSo “tiro” is a noun.\n\nCould “word” be formed like that? Possibly.\n\nBut no evidence.\n\nCould “word” be a root like “tua”?\n\nNot in data.\n\nThus, since no support, theoretically, it might be formed as a standalone noun with no root — or a compound.\n\nBut the most plausible *theoretically possible* form is one that follows a pattern: verb + noun or noun + noun.\n\nFor example: “to exhaust” → verb + noun (use + end)\n\n“word” → could be a noun like “lala” (deep) or “tiro” (spectacles), but not equivalent.\n\nBut none of these are “word”.\n\nTherefore, we conclude:\n\n- The theoretically possible translation of “to exhaust” is **fäeag a‘öf** (to use to the end) \n- The theoretically possible translation of “word” is unknown, but based on patterns, might be a stem like **tua** or **tui**, but no evidence — however, in absence of any form, the only plausible inference is that it is a noun with stem not in data.\n\nBut the problem asks for *theoretically possible* — not necessarily attested.\n\nSo could “word” be formed as a reduplicated form?\n\nFor example, “lala” = deep — reduplicated? “lalalala”?\n\nNot likely.\n\nIs there a pattern of stems?\n\nWe see:\n\n- \"mö\" → not present \n- \"huag\" → courageous \n- \"huli\" → to turn over\n\nAll verbs or adjectives.\n\nNo noun for “word”.\n\nTherefore, the only viable theoretical possibility is that “word” may be **tua**, a base noun in Austronesian for “thing” or “word”.\n\nIn some sources, “tua” = word in Malagasy or other Austronesian languages.\n\nTherefore, in Rotuman, it might be plausible.\n\nBut we have no evidence.\n\nSimilarly, “tui” = common for word.\n\nSo in the absence of evidence, a theoretically possible form for “word” could be **tua**.\n\nFor “to exhaust” — **fäeag a‘öf**\n\nThese are speculative, but based on available patterns.\n\nFinal decision:\n\n- d.1 / word: tua \n- d.2 / to exhaust: fäeag a‘öf\n\nNote: “tua” is not in the list, but plausible as a word for “word” in Austronesian languages.\n\n“fäeag a‘öf” is based on “to use” + “to end” → which is “to use up” → “to exhaust”.\n\nThis is a reasonable theoretical form.\n\n\\boxed{d.1: tua; d.2: fäeag a‘öf}", + "generated_tokens": 3732, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: tua; d.2: fäeag a‘öf", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 13018.0, + "ioling_final_answer_chars": 25.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are asked to find the *theoretically possible* translations of the English words **‘word’** and **‘to exhaust’** into Rotuman, given only the provided vocabulary.\n\nSince direct translations for these two items are not provided, we must infer patterns from the given words based on morphological structure, semantic relation, and possible roots.\n\n---\n\nStep 1: Look for possible roots related to \"word\"\n\n- The word \"word\" in a language is often connected to communication, speech, or expression.\n- In the list:\n - ‘el‘ele — shallow\n - ‘ele — to be near\n - ‘olo — to cut\n - ‘fau — year\n - ‘a‘öf fau — year’s end\n - fäeag ‘u‘u — to use sign language\n - huag ‘el‘ele — impatient\n - huag to‘a — courageous\n - hül ha.fu — to blow (of a hurricane)\n - hün kia — base of the neck\n - huli — to turn over\n - huni — lower end\n - is ‘ā — sharp-pointed\n - is susu — nipple\n - lala — deep\n - maf tiro — spectacles\n - mamasa — solid\n - ma.titi — coldness\n - ma.tit mamasa — ice\n - moafmofa — littered with rubbish\n - niu — copra\n - nu‘suar tiro — window\n - nu‘sura — door\n - pala — pierce\n - piri — to curl\n - poagpoga = palpala — covered with holes\n - pogi — night\n - puhra.ki — to boil, to bubble up\n - pulu — glue\n - ka.lu — bracelet; to encircle\n - riamrima — shiny\n - rū huga — stomach-ache\n - to‘a — hero\n\nNotice: **fäeag ‘u‘u — to use sign language**\n\n“Sign language” is a system of communication — akin to \"word\" in a non-spoken form.\n\nThus, “fäeag” (to use) + “‘u‘u” (sign language) → to use sign language.\n\nThis suggests that **‘u‘u** may be a term for a form of communication.\n\nWhat if “word” is a general term for a unit of communication or expression?\n\nCould “word” be a cognate or a derived form of a communication-related root?\n\nNote: There is no direct word for “word” in the list.\n\nBut consider the root **‘u‘u** = sign language → implies communication.\n\nThere is no direct word like “speech” or “utterance”, but we might infer a related morpheme.\n\nNow, observe **pala — to pierce**. “Pierce” might imply cutting through — a metaphor for forming or making a word?\n\nNot directly.\n\nBut consider **‘olo — to cut**; this is similar in meaning to “to cut” → might be used in the sense of “to carve, to make a mark”.\n\nIn many languages, a “word” is a discrete unit forged or carved — like a “cut” in speech.\n\n“Cut” is a possible root for “word” in some lexical systems (e.g. “a word is cut”).\n\nSo, could “word” be derived from **‘olo**?\n\nBut ‘olo is “to cut” — not a noun.\n\nIs there a noun form for “cut”?\n\nNot directly.\n\nHowever, “to use sign language” uses the verb **fäeag** (to use) with a noun **‘u‘u**.\n\nCould “word” be represented by a derived noun from a root meaning “to cut” or “to mark”?\n\nAlternatively, perhaps a term like **pala** (to pierce) used in metaphor?\n\nStill not strong.\n\nAnother idea: Compare to “is susu — nipple” — body part, possibly a metaphorical root?\n\nUnlikely.\n\nWhat about **nu‘sura — door**? **nu‘suar tiro — window** — both are openings.\n\nBut that seems unrelated.\n\nAlternatively, consider that **“to exhaust”** means to use up, to deplete.\n\nWe see:\n- **pulav aho?** — Not in list.\n- **puhra.ki — to boil, to bubble up** — could this be related to overflowing?\n\n“Exhaust” involves something being used up or gone — like “a thing is burned out”.\n\nBut no direct verb for “exhaust”.\n\nHowever, we see:\n- **mamasa — solid**\n- **ma.tit mamasa — ice** → cold, solid\n- **ma.titi — coldness**\n- **huli — to turn over**\n- **huni — lower end**\n- **hua — to be near?**\n\nNow, **exhaust** may be related to “to burn out”, “to use up”.\n\nWe see **puhra.ki** — to boil, to bubble up — might relate to overflow, to go beyond.\n\nBut \"to exhaust\" is more about depletion.\n\nIn many languages, \"exhaust\" is built from a root of “to use up”, “to consume”.\n\nIs there a verb that means “to consume”?\n\nNot directly.\n\nHowever, “to use” is present: **fäeag** — to use.\n\n“Fäeag” is used in “fäeag ‘u‘u” — to use sign language.\n\nCould “fäeag” be generalized to “to use”? Then “to exhaust” might be a form of using until nothing remains.\n\nPerhaps “to exhaust” is built from **fäeag** + a suffix meaning “until gone”?\n\nBut no such suffix is given.\n\nAlternatively, could “exhaust” be related to “to bleach” or “to burn”?\n\nWe have **pala — to pierce**, **puli — glue**, **puhra.ki — to boil**, **ka.lu — to encircle**.\n\nNo clear match.\n\nBut let’s consider that the problem says: \"you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty\".\n\nThus, we are to give the *theoretically possible* translations — i.e., what could they be based on morphology, semantics, and derivation from the given words?\n\nSo, for **“word”**:\n\n- It may be derived from a root meaning \"to cut\" or \"to mark\" — because a word is like a cut in speech or thought.\n- In many languages, “word” stems from “cut” (e.g. Latin *verbum* from *vocare*, but phonetically not matching).\n- In Austronesian languages, there is often a root for “mark” or “cut”.\n\nWe have:\n- ‘olo — to cut\n- pala — to pierce\n\nPossibly, a noun form of “cut” or “mark” could be the root.\n\nBut no noun form is used.\n\nHowever, **‘elee** = shallow — not relevant.\n\nBut consider: in some languages, “to make a word” is “to put something in a speech form”.\n\nBut nothing supports that.\n\nWhat about **‘u‘u** — sign language?\n\nSign language is a form of communication — thus a \"word\" might be a \"sign\" or \"sign form\".\n\nCould “word” be *‘u‘u*? But that’s already sign language.\n\nSo that’s too specific.\n\nAlternatively, could “word” be rendered as **‘olo**? But ‘olo is “to cut” — a verb.\n\nNo.\n\nWhat about a noun derived from “to be near” — ‘ele?\n\nUnlikely.\n\nIs there any word that might be associated with communication?\n\nOnly **fäeag ‘u‘u** — \"to use sign language\".\n\nSo “sign” is probably “‘u‘u”.\n\nThus, in a broader sense, a “word” might be a “unit of communication” — possibly derived from a root like “utterance” or “speech”.\n\nBut no such word is given.\n\nAlternatively, in Rotuman, a common way to build nouns is via nominalization.\n\nBut we see no clear patterns.\n\nPerhaps the only possible option is that **word** could be poetically or potentially **‘u‘u** — if “word” is a sign — but that’s not a general term.\n\nAlternatively, perhaps **pala** — to pierce — implies making a mark → like a word written or spoken.\n\nStill, no.\n\nWait — consider the word **‘fau’** — year.\n\n**Fau** is used in compound: **a‘öf fau — year’s end**.\n\nSo “fau” is a base.\n\nBut “year” is a time unit.\n\n“Word” is not a time unit.\n\nNo.\n\nBack to **exhaust**: the meaning is to use up.\n\nWe have **fäeag** — to use.\n\nSo “to use” is a verb.\n\nCould “to exhaust” be a form of “to use” extended?\n\nYes — in grammar, “to exhaust” is to use something until it is gone.\n\nSo perhaps “to exhaust” is a form of **fäeag** with a meaning of \"to use until gone\".\n\nBut no such compound is given.\n\nAlternatively, **puhra.ki** — to boil, to bubble up — could be metaphorically related to overflowing — and “exhaust” might mean to overflow of energy?\n\nBut not strong.\n\nAnother possibility: “to blow” — hül ha.fu — to blow (hurricane).\n\nBlow could be to exhale — like to exhaust energy.\n\nSo perhaps “to exhaust” could be related to “to blow”?\n\nBut “to blow” is a technical sense (hurricane).\n\nAlso, “hül” is “to blow”, “ha.fu” is “rocky”.\n\nNo.\n\nBut consider: **huag to‘a** — courageous — not related.\n\nOnly hint: **to use** is available as **fäeag**.\n\nThus, **to exhaust** might be a derived form of \"to use\" with a temporal or quantified extension.\n\nBut with no direct evidence.\n\nSo, what could be the *theoretically possible* translations?\n\nWe must offer plausible derivations based on the patterns.\n\nFor **‘word’**:\n\n- No direct word.\n- However, “sign language” is present as **‘u‘u** → communication.\n- Could “word” be derived from a root meaning “to mark”?\n- We have “to cut” → **‘olo**\n- Could a noun from “to cut” be formed?\n- Possibly, in Austronesian languages, verbal roots are nominalized by adding elements.\n\nBut no such form is visible.\n\nPossibly, “word” is **‘olo** — meaning “cut”, implying a marked division — like a word is a cut in speech.\n\nBut this is a stretch.\n\nAlternatively, “pala” — to pierce — making a hole — could be the formation of a word.\n\nBut again, weak.\n\nBest available candidate: **‘u‘u** — although it means “sign language”, and “word” is broader — but perhaps in context, it is plausible.\n\nAnother idea: **to use** (fäeag) — could be used as a general verb for “to act”, and “word” might be “something that is used” — so “a thing used”.\n\nBut we have no such noun.\n\nNo clear noun.\n\nFor **to exhaust**:\n\nThe most plausible link is **fäeag** — “to use”.\n\nExhaustion is using up.\n\nSo if we have a verb meaning “to use”, then “to exhaust” might be a specialized form of that.\n\nHence, a plausible form could be **fäeag** + a suffix indicating “until gone” or “to consume completely”.\n\nBut no such suffix.\n\nAlternatively, **puhra.ki** — to boil — to bubble — could be \"to reach maximum\", so overflowing — exhaustion?\n\nPossible metaphor.\n\nBut not clear.\n\nNow, notice: **is ‘ā — sharp-pointed**\n\nIs there a word for \"to go to fullness\" or \"to use up\"?\n\nWe have **huli — to turn over**\n\n**huni — lower end**\n\n**ma.tit mamasa — ice** (cold, unchanging)\n\nNo.\n\nBut **ka.lu — to encircle** — could mean wrapping — like using up a resource around?\n\nNot clear.\n\nGiven the constraints, and the fact that we have:\n\n- A verb “to use” → **fäeag**\n- A root for “to cut” → **‘olo**\n- A root for communication → **‘u‘u**\n\nThen the only possible *theoretically possible* translations (in absence of direct evidence) should be derived from known morphemes and their semantic fields.\n\nSo:\n\n- For “word”: could it be **‘u‘u**? (as a unit of communication) — plausible in a narrow sense.\n But “word” is not specifically “sign” — so it’s weak.\n\nAlternatively, is there a word like “utterance”?\n\nNot in list.\n\nBut the concept of a small unit of communication is only present in “sign language”.\n\nTherefore, the only possible word for “word” in the data is **‘u‘u**, though it’s specific.\n\nAlternatively, the word **‘olo** as a sharp, cut — a word may be cut — like a word is a cut — so “word” = **‘olo**?\n\nBut that’s a stretch.\n\nStill, no better option.\n\nPerhaps a noun like **pala** (to pierce) → could be \"a pierced thing\" — like a word carved?\n\nBut unknown.\n\nGiven that, the only *theoretically possible* translation from the given material is that **‘word’** might be a form derived from a communication or marking root.\n\nSince **‘u‘u** is the only word related to communication and expression, and “word” is a unit of expression, **‘u‘u** may be a candidate.\n\nFor **to exhaust**:\n\nWe have **fäeag** = to use.\n\nExhaustion = to use up.\n\nSo “to exhaust” might be a form of **fäeag** with a negating or full use sense.\n\nIs there a word for “to burn out”?\n\nNo.\n\nBut “to boil” (puhra.ki) — to bubble up — could metaphorically mean to overflow — like energy used up?\n\nPossibly.\n\nBut no clear derivation.\n\nAnother possibility: “to use” → **fäeag** → so “to exhaust” could be **fäeag [until gone]**.\n\nBut no such form.\n\nThe only verb root in the list that could be extended for “exhaust” is **fäeag**.\n\nTherefore, **to exhaust** might be a potential form of **fäeag**.\n\nBut since “to use” is already a verb, and “to exhaust” is a stronger form, it might be derived from it.\n\nTherefore, the theoretically possible word for “to exhaust” is **fäeag**, or a form thereof.\n\nBut is there another?\n\nWe have **to‘a** — hero.\n\nNo.\n\n**huli — to turn over** — could mean to go through, to exhaust?\n\nPossibly.\n\nBut not clearly.\n\nIn summary:\n\n- “word” — must be related to communication or marking → best available is **‘u‘u** (sign language)\n- “to exhaust” — must be related to using up → best available is **fäeag** (to use)\n\nTherefore, despite lack of direct evidence, based on morphological and semantic reasoning:\n\n- The theoretically possible translation of **‘word’** is **‘u‘u**\n- The theoretically possible translation of **‘to exhaust’** is **fäeag**\n\nNote: This does not mean they are translations, but that these are the only plausible forms based on existing roots.\n\nThus:\n\n\\boxed{d.1: u‘u; d.2: fäeag}", + "generated_tokens": 3410, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: u‘u; d.2: fäeag", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 12137.0, + "ioling_final_answer_chars": 20.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are asked to find the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, based only on the given examples. Since these words are not directly present, we must infer plausible forms using linguistic patterns in the given data.\n\nStep 1: Identify reusable components and patterns.\n\nLook for words that might relate to \"word\" or \"to exhaust\" via root or derivation.\n\nNote: \"word\" is a general conceptual item. In many languages, \"word\" may be expressed via verbs like \"to speak\", \"to utter\", or nouns like \"speech\", \"term\", \"name\".\n\nCheck for related concepts:\n\n- \"pala\" = pierce\n- \"huli\" = to turn over\n- \"pogi\" = night\n- \"fau\" = year\n- \"a‘öf fau\" = year’s end\n- \"hün kia\" = base of the neck\n- \"pi-ri\" = to curl\n- \"poagpoga = palpala\" = covered with holes\n- \"nu‘suar tiro\" = window\n- \"nu‘sura\" = door\n- \"ka.lu\" = bracelet; to encircle\n- \"riamrima\" = shiny\n- \"rū huga\" = stomach-ache\n- \"to‘a\" = hero\n\nNo direct word or verb for \"word\" appears.\n\nBut consider: “pala” means \"to pierce\", which might be related to \"to utter\" or \"to speak\" — as piercing could metaphorically suggest \"cutting\" a word. \nAlso, \"olo\" = to cut — could be a candidate for a verb of \"to cut a word\", possibly \"to exhaust\" (as in cutting down).\n\nNow for \"to exhaust\": \nExhaust can mean:\n- to use up\n- to drain\n- to deplete\n- to burn out\n\nVerbs in the data:\n- \"olo\" = to cut\n- \"hül ha.fu\" = to blow (of a hurricane)\n- \"puhra.ki\" = to boil, to bubble up\n- \"pogi\" = night\n- \"ka.lu\" = to encircle\n- \"huli\" = to turn over\n- \"huni\" = lower end\n- \"ma.tit mamasa\" = ice\n\nNot directly matching. But notice:\n\"to use sign language\" is \"fäeag ‘u‘u\" — \"fäeag\" = to use; “‘u‘u” = sign language.\n\n\"to use\" is \"fäeag\".\n\nSo \"to use\" = \"fäeag\"\n\n\"to exhaust\" may involve \"to use up\", i.e., to use completely.\n\nThus, \"to exhaust\" might be a compound: \"fäeag [something]\" meaning to use up.\n\nBut the use of a noun meaning \"something to use up\" is missing.\n\nAlternatively, \"to exhaust\" might be a derived form involving \"cut\", \"cut out\", or \"cut down\".\n\n\"Olo\" = to cut — could be used to mean \"to cut down\", i.e., exhaust.\n\nSimilarly, \"ma.tit mamasa\" = ice — coldness and then ice.\n\nNo direct term.\n\nBut \"to use\" is \"fäeag\", and \"to use up\" is a common meaning of \"exhaust\".\n\nAlso, \"a‘öf fau\" = year’s end — \"a‘öf\" may mean \"end of\", and \"fau\" = year.\n\nSo \"a‘öf\" = end of — could \"a‘öf\" be used to form \"end of something\"?\n\nThen \"a‘öf\" or \"a‘öf x\" could mean \"end of x\".\n\nSo if *exhaust* = \"to use up\", then what if a word like \"a‘öf\" can be used to form \"end of life\", \"end of breath\", etc.?\n\nBut \"to exhaust\" is a verb.\n\nWe need to find which morphemes can form it.\n\nIs there a word meaning \"to use completely\"? Only \"fäeag\" = to use — but not \"to use up\".\n\nBut perhaps \"to exhaust\" is \"to use up\" — and the pattern is that \"to use\" + a noun = \"to use\", and if that noun is \"everything\", \"all\", or something like that, it could become \"to exhaust\".\n\nBut we don’t have \"all\" or \"everything\".\n\nAlternatively, look for embedded verbs.\n\nAnother possibility: \"hün kia\" = base of neck — how does that relate?\n\nNo.\n\nWe have \"huli\" = to turn over — \"huag to‘a\" = courageous — structure: adjective + noun.\n\n\"huag el‘ele\" = impatient — adjective + noun.\n\nSo many adjectives are formed by a word + noun.\n\n\"to exhaust\" could be a verb derived from a root.\n\nCould \"exhaust\" be derived from \"to cut\" (olo) — as in \"to cut off\", \"to deprive\"?\n\nYes — in English, \"to exhaust\" can mean \"to cut off a supply\".\n\nThus, \"to exhaust\" might be derived from \"olo\" (to cut), with \"cut off\" = \"exhaust\".\n\nIn that case, \"to cut\" = \"olo\", so \"to cut off\" might be \"olo ‘of\" or \"olo a‘öf\"?\n\nWe have \"a‘öf fau\" = year’s end — \"a‘öf\" precedes \"fau\".\n\n\"a‘öf\" likely = end of.\n\nSo \"a‘öf\" = end of.\n\nThus, \"olo a‘öf\" = to cut off? Possibly.\n\nCould \"olo a‘öf\" = to cut off — to exhaust?\n\n\"to exhaust\" might therefore be \"olo a‘öf\".\n\nSimilarly, what about \"word\"?\n\n\"word\" — is there any verb or noun for \"to speak\"?\n\nWe have \"pala\" = to pierce — maybe \"to pierce\" could be used for \"to cut speech\" — not clear.\n\nWe have \"pogi\" = night — no.\n\n\"nu‘suar tiro\" = window — \"nu‘su\" = door/window? \"nu‘sura\" = door.\n\n\"nu‘suar\" = window.\n\nCould \"word\" be related to \"to speak\", \"to utter\"?\n\nWe have \"pala\" = pierce — and \"to pierce\" might be used metaphorically for \"to speak\" or \"to utter\".\n\nBut also \"pala\" could be a verb for \"to pierce\" or \"to pass through\", so perhaps \"to speak\" = to pass through the air.\n\nNo clear candidate.\n\nBut note: \"to encircle\" = \"ka.lu\"\n\n\"to blow\" = \"hül ha.fu\"\n\n\"to boil\" = \"puhra.ki\"\n\nNo clear link.\n\nNow, look at compound forms.\n\n\"poagpoga = palpala\" — two forms, possibly equivalent. \"palpala\" = covered with holes?\n\n\"covered with holes\" — could mean \"full of holes\", so \"exhausted\" might be a state — full of holes?\n\nBut no.\n\nAlternatively, \"to exhaust\" = \"to use up\" = \"to use\" + \"up\"?\n\nWe have \"fäeag\" = to use.\n\nCould \"fäeag\" be used with a noun to mean \"to use up\" if the noun is \"everything\"?\n\nWe don’t have \"everything\".\n\nBut the pattern is: verbs like \"to use\" are \"fäeag\".\n\nSo perhaps \"to exhaust\" = \"fäeag [something]\" where something is \"all\", \"the whole\", \"supply\".\n\nBut not directly available.\n\nBack to \"word\".\n\nWhat about \"to speak\" or \"to utter\"?\n\nWe have \"pala\" = pierce — could \"to pierce\" mean \"to utter\" in some metaphorical sense?\n\nNot likely.\n\nWe have \"huli\" = to turn over — could be \"to turn over a page\"? Perhaps a metaphor for \"word\" in text?\n\n\"huni\" = lower end — no.\n\n\"is susu\" = nipple — body part, possibly not related.\n\n\"riamrima\" = shiny — \"to shine\" could be related to \"to speak\" — not really.\n\nAnother possibility: \"word\" may be a noun like \"speech\", and no such word exists — so perhaps there is no direct word.\n\nBut the question asks for *theoretically possible translations* — so based on patterns and morphemes, what could it be?\n\nThus, possible forms:\n\nFor \"word\":\n- Could be formed from a root meaning \"to speak\" or \"to utter\"\n- The only verb related to speech is not directly given\n- But \"pala\" = pierce — could be used metaphorically\n- Or \"to cut\" (olo) — \"to cut words\"?\n- \"huli\" = to turn over — \"to turn over a page\" = may refer to a word in a book?\n\nNot strong.\n\nBut in Austronesian languages, roots for speech often involve \"to speak\" or \"to say\".\n\nBut we lack such a root.\n\nBest guess: \"word\" might be derived from \"to speak\", which may not be in the data — but a plausible root could be \"pala\" (to pierce) or \"fa\" (in \"fau\" = year), not clear.\n\nNo clear candidate.\n\nBut perhaps \"to exhaust\" is \"olo a‘öf\" (to cut off).\n\nBecause:\n- \"a‘öf\" = end of\n- \"olo\" = to cut\n- \"to cut off\" = to exhaust\n\nSimilarly, \"a‘öf fau\" = year’s end — so \"a‘öf\" is a suffix or prefix meaning \"end of\"\n\nThus \"olo a‘öf\" = to cut off = to exhaust\n\nSo \"to exhaust\" → olo a‘öf\n\nFor \"word\"?\n\nWe need a noun meaning \"word\".\n\nNo such word.\n\nBut perhaps inspired by \"pala\" = pierce — and speaking is an act of piercing the air?\n\nOr \"to use sign language\" = \"fäeag ‘u‘u\"\n\n\"‘u‘u\" = sign language — a form of \"word\"?\n\nSo \"word\" might be related to sign language.\n\n\"‘u‘u\" = sign language → could \"word\" be \"‘u‘u\"?\n\nBut \"‘u‘u\" is specifically \"sign language\", not general \"word\".\n\nBut a general word might be expressed as \"sign\" or \"language\".\n\nCould \"to exhaust\" be expressed as \"to use up\", and \"to use\" is \"fäeag\"?\n\nSo \"fäeag\" + something?\n\nBut again, not complete.\n\nAnother idea: \"pogi\" = night → not related.\n\n\"lala\" = deep → could \"deep\" relate to thought, word?\n\nNot clear.\n\nBut in sound-based meanings, \"to speak\" often uses a verb like \"to utter\".\n\nIs there any form used for \"to say\"?\n\nNo.\n\nBut \"to use\" is \"fäeag\"\n\nCould \"word\" be formed as a compound or noun?\n\nPossibility: \"to exhaust\" = olo a‘öf\n\n\"word\" = ? \n\nWe have \"aria\" or \"pala\"? No.\n\nBut in Rotuman, some words may be formed by combining roots.\n\nFor \"word\", one possibility: \"to speak\" → not directly given.\n\nAlternatively, \"word\" could be formed from \"fau\" (year) — words are annual? Unlikely.\n\nWait — the word \"is\" appears: \"is\" = sharp-pointed, \"is susu\" = nipple.\n\n\"sharply pointed\" — is that related to word?\n\nNot directly.\n\nBut \"pala\" = pierce → could \"pala\" be used for \"to speak\"?\n\nIn some languages, \"to pierce\" can mean \"to speak\" — e.g. to pierce the air.\n\nSo possibly, \"pala\" = to utter a word.\n\nThus, \"word\" might be \"pala\" or \"pala\" as a noun?\n\nBut \"pala\" is defined as \"to pierce\" — verb.\n\nBut could it be a noun?\n\nNot stated.\n\nSimilarly, \"huli\" = to turn over — could be a noun?\n\nNot listed.\n\nOnly direct verbs are given.\n\nBut the question asks for *theoretically possible* translations — not certain ones.\n\nSo we must pick plausible forms based on patterns.\n\nSo for \"to exhaust\":\n\n- It can be derived from \"to cut\" + \"end of\" = \"olo a‘öf\"\n\nThus, theoretically possible: olo a‘öf\n\nFor \"word\":\n\nPossible verbs related to speech: none.\n\nBut possible compound: if \"to speak\" is missing, we can’t have a direct word.\n\nBut \"sign language\" = \"‘u‘u\" — so \"word\" in sign form?\n\nSo \"‘u‘u\" could be a candidate.\n\nBut \"‘u‘u\" is a noun — meaning \"sign language\", not a general \"word\".\n\nCould \"word\" be \"pala\"? If \"pala\" is used as a noun meaning \"a word\".\n\nBut \"pala\" is a verb.\n\nStill, in some languages, verbs can be used as nouns.\n\nIs there a pattern?\n\nLook at \"huag to‘a\" = courageous — \"huag\" is adjective, \"to‘a\" is noun.\n\n\"huag el‘ele\" = impatient — \"el‘ele\" = shallow → so \"el‘ele\" is a noun.\n\n\"el‘ele\" = shallow — used as adjective.\n\n\"una\" or \"nu\"sura\" are nouns.\n\n\"nu‘sura\" = door — a noun.\n\n\"pala\" = pierce — verb.\n\nSo nouns: fau, huag, hün, huli, huni, is, lala, maf, mamasa, ma.titi, moafmofa, niu, nu’suar, pala, piri, poagpoga, pogi, pulu, rū, to‘a\n\nVerbs: olo, faeag, hül, hün, huli, pala, piri, pogi, puhra.ki, ka.lu, rū\n\nSo \"pala\" is listed as \"to pierce\" — verb.\n\nBut could be a noun?\n\nNo evidence.\n\n\"word\" might be derived from \"to speak\".\n\nNo verb for \"to speak\".\n\nBut \"pala\" could be metaphorically used for \"to speak\" in some contexts.\n\nSo a possible translation for \"word\" is \"pala\"?\n\nAlternatively, no candidate.\n\nBut is there a word like \"speech\"?\n\nNo.\n\nPossible inference: \"word\" may be related to \"sign language\" = \"‘u‘u\", so \"‘u‘u\" is a possible candidate for word — though it's specific.\n\nBut \"word\" as general term?\n\nAlternatively, in derived form.\n\nBut given that \"to use\" = \"fäeag\", and \"to exhaust\" = \"to use up\", perhaps \"to exhaust\" = \"fäeag\" + \"everything\" — but no such word.\n\nGiven the patterns, \"to exhaust\" is likely to be \"olo a‘öf\" — cut off.\n\nFor \"word\", given that \"‘u‘u\" means \"sign language\", which contains words, then \"word\" might be \"‘u‘u\" as a general term?\n\nBut \"‘u‘u\" is a specific form.\n\nAlternatively, \"pala\" as the act of speaking.\n\nBut no direct support.\n\nBut in the absence of a better candidate, and given that the only \"language\" term is \"‘u‘u\", which contains words, it's possible that \"word\" is \"‘u‘u\".\n\nAnother possibility: \"to exhaust\" could be \"puhra.ki\" — to boil, to bubble up — as if boiling nutrients?\n\nUnlikely.\n\n\"puhra.ki\" = to boil — too specific.\n\n\"ka.lu\" = to encircle — not relevant.\n\nThus, most plausible:\n\n- \"to exhaust\" = olo a‘öf\n- \"word\" = ‘u‘u\n\nBecause “u‘u” is a form of word (sign language), and \"word\" in sign language is literally a word.\n\nSo although not general, it is a theoretically possible translation.\n\nAlternatively, is there any root for \"word\"?\n\nNo.\n\nSo final answers:\n\nd.1 / word: ‘u‘u \nd.2 / to exhaust: olo a‘öf\n\n\\boxed{d.1: ‘u‘u; d.2: olo a‘öf}", + "generated_tokens": 3561, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: ‘u‘u; d.2: olo a‘öf", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 11402.0, + "ioling_final_answer_chars": 24.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "solver_checklist", + "sample_index": 3, + "output": "We are to determine the theoretically possible translations of 'word' and 'to exhaust' into Rotuman, based only on the provided vocabulary.\n\nStep 1: Look for morphemes or roots that might relate to 'word' or 'to exhaust'.\n\nFirst, consider words that may contain a root meaning 'to exhaust' or 'word'. In Rotuman, the verb system is rich in derivational forms, and many verbs are formed by affixation.\n\nLook for verbs that might be related to exhaustion or depletion.\n\nWe see:\n- ‘pura.ki’ → to boil, to bubble up → likely not related to exhaustion\n- ‘hül ha.fu’ → to blow (of a hurricane) → not clearly related\n- ‘huag to‘a’ → courageous → not helpful\n- ‘huli’ → to turn over → possibly a verb with motion\n- ‘huni’ → lower end → spatial\n- ‘pala’ → pierce → possibly related to action\n- ‘ma.tit mamasa’ → ice → coldness + solid\n- ‘moafmofa’ → littered with rubbish → not directly related\n- ‘nu‘suar tiro’ → window → spatial\n- ‘nu‘sura’ → door → spatial\n- ‘pogi’ → night → time\n\nNow consider possible roots for 'word'. In many Austronesian languages, a word-form might derive from a stem meaning 'to speak' or 'to say'. But we have no direct verb for 'to say' or 'to speak'.\n\nWe do have ‘fäeag ‘u‘u’ → to use sign language. 'Fäeag' is likely a verb root, possibly 'to use'. 'U‘u' could be a sign or a type of sign. So 'fäeag' (to use) + 'u‘u' (sign) → to use sign language.\n\nNow, consider if any root might mean 'to exhaust'. We see:\n- 'pul’u’? Not present.\n- 'pura.ki' → to boil — boiling can imply exhaustion? Unlikely.\n- 'puhra.ki' → to boil, to bubble up — suggests violent process, not exhaustion.\n- 'huli' → to turn over → could be used metaphorically, but not clearly.\n\nNo direct verb for 'exhaust' is present. Similarly, no root for 'word' is directly given.\n\nNow, consider morphological patterns.\n\nLook for compounds that might form 'word':\n- ‘nu‘suar tiro’ = window\n- ‘nu‘sura’ = door\n- ‘ma.titi’ = coldness\n- ‘ma.tit mamasa’ = ice\n\nIs there a root that means 'to speak'? Not present.\n\nBut in the vocabulary:\n- ‘to‘a’ = hero → could be derived from a root meaning 'courage'\n- ‘el‘ele’ = shallow\n- ‘ele’ = to be near\n- ‘olo’ = to cut\n- ‘ha.fha.fu’ = rocky\n- ‘hün kia’ = base of neck\n- ‘pala’ = pierce\n- ‘piri’ = to curl\n- ‘poagpoga = palpala’ = covered with holes\n\nNote: 'poagpoga' is a compound → 'poa' + 'g' + 'poga'? Possibly phonologically extended. It is equal to 'palpala' — covered with holes.\n\n'palpala' is a root meaning 'covered with holes'. Could this be related to a word for 'surface with holes', or 'an object with openings'? Possible.\n\nNo clear word for 'word' or 'to exhaust'.\n\nWhat about word formation?\n\nConsider: words like 'to‘a', 'faul', etc. — many are single roots or modified by affixes.\n\nNow, consider the root ‘ka’ in ‘ka.lu’ — ‘to encircle’ — which may be a root.\n\nCould 'ka' be a marker for 'to' or 'to do'? Possibly.\n\n‘ka.lu’ = bracelet; to encircle → ‘ka’ might be a root + ‘lu’ = to encircle.\n\nBut no verb with 'to' meaning is given. However, many verbs in Austronesian languages have a base that can be used with particles.\n\nBut 'to exhaust' — in some languages, this is derived from roots meaning 'to use up', 'to deplete', or 'to lose'.\n\nLooking at possible compounds: 'moafmofa' = littered with rubbish — some degree of filling or covering.\n\n'pulu' = glue — adhesive — binding.\n\nIs there a verb that could mean 'to use up'? Not clearly.\n\nCould 'exhaust' be formed from a compound like 'to cut' or 'to blow'? For example:\n\n- 'olo' = to cut → cutting can deplete → so 'to cut' might mean 'to exhaust' in a metaphorical sense?\n\nBut is that sound?\n\nIn particular, in Rotuman, 'to cut' might be used in a broader sense — e.g., \"to cut down\", \"to cut out\", \"to cut through\".\n\nSimilarly, 'to blow' (hül ha.fu) → could mean 'to blow out', like 'to blow out the lamp' — which can mean 'to exhaust'?\n\n'pura.ki' → to boil — might mean 'to bubble' — not exhaustion.\n\nBut: 'hün kia' = base of neck — a body part.\n\n'is susu' = nipple — so ‘is’ might be a root meaning 'sharp' or 'pointed' — also used in 'is ‘ā' = sharp-pointed'.\n\nSo possibly, 'is' is a root meaning 'point' or 'sharp'.\n\nNow, in no example is there a word that directly means 'word' or 'to exhaust'.\n\nBut we need to infer what the *theoretically possible* translations could be.\n\nIn the absence of direct evidence, we must consider plausible morphological roots and affixes.\n\nWhere can we find possible roots?\n\nIn Austronesian languages, many nouns and verbs are formed from roots with derivational affixes.\n\nFor example:\n- 'element' + 'to' → to be near (ele) — 'ele' = to be near\n- 'ele' may be a common root\n- 'huli' = to turn over\n- 'huni' = lower end → could be derived from 'hun' + 'i'\n\nAlso, note 'pali' — possibly a verb meaning 'to pierce' — or 'pala'\n\nCould 'pala' (pierce) be extended to mean 'to break through'? Possibly.\n\nBut no link to 'exhaust'.\n\nWhat about compounds involving 'u' or 'a'?\n\n'faul' → year → so 'fau' = year\n\n'a' is a vowel.\n\nBut 'to exhaust' — could be formed like 'to use up'?\n\nCould 'fäeag' (to use) + 'a' root?\n\nBut no clear compound.\n\nNow, consider that the problem says we **cannot** translate 'word' and 'to exhaust' with certainty — so we must infer based on plausible patterns.\n\nBut what about word formation?\n\nWe see 'is’ = sharp → could be a root for something like 'sharpness'\n\nWe see ‘hün kia’ = base of neck — 'kia' may be a noun\n\nWe see 'mamasa' = solid → so 'mamasa' may be a root\n\n'ma.titi' = coldness\n\n'ma.tit mamasa' = ice — so 'coldness' + 'solid' → ice\n\nSo compound noun formation is present.\n\nNow for 'word' — is there a cognate root?\n\nIn many Austronesian languages, 'word' comes from a root meaning 'to say' or 'to speak'.\n\nBut no such verb is in the list.\n\nCould 'to say' be formed with a root like 'to tell'?\n\nNot present.\n\nIn Rotuman, we might expect a root like ‘sai’ or ‘tala’ or ‘fai’ — but none given.\n\nCould 'word' be a noun derived from 'to speak'?\n\nSo perhaps there is no direct form, but a theoretically possible form could be a noun formed from a root meaning 'to speak'.\n\nBut we have no evidence.\n\nWhat about 'to exhaust'?\n\nCould it be related to 'to use up'? 'to use' is 'fäeag', as in 'fäeag ‘u‘u’ = to use sign language'.\n\nSo 'to use' — 'fäeag' — is a verb.\n\nCan we form 'to use up'?\n\nThat might be 'fäeag + a suffix meaning 'up' or 'out'? Not present.\n\nCould 'to blow' (hül ha.fu) be 'to exhaust' in a metaphorical sense?\n\n'blow out' → like blowing out a candle → to extinguish → to exhaust?\n\nThat seems plausible.\n\nSo 'hül' → to blow → could be extended to 'to exhaust'?\n\n'ha.fu' = rocky → no.\n\nBut 'hül' is the verb root.\n\nSo 'hül' might mean 'to blow out' → which could be a form of 'to exhaust'.\n\nAlternatively, 'pura.ki' → to boil → boiling can deplete — but not clear.\n\nBut in no example is there a verb clearly meaning 'to exhaust'.\n\nSimilarly, for 'word', we have no verb or noun related to speech.\n\nSo what are the theoretically possible forms?\n\nWe must base them on available structure.\n\nPossible root for 'word'?\n\nIn Austronesian, 'word' often comes from roots like *sapa, *pura, or *tala*. But we have no evidence.\n\nBut we do have a verb 'fäeag' = to use.\n\nCould 'to use' be extended to 'to use in speech'?\n\nBut not available.\n\nCould 'o' be a root? 'olo' = to cut — could 'to cut' mean 'to exhaust'?\n\nIn some languages, cutting can mean 'to remove' — so 'to exhaust' = to cut down?\n\nThat’s possible.\n\nSo 'olo' → to cut → could be used metaphorically for 'to exhaust'.\n\nThus, 'to exhaust' might be derived from 'olo' (to cut) with a meaning extension.\n\nSimilarly, for 'word' — could there be a root?\n\nWe have 'nu‘sura' = door — 'nu' may be a root (like in 'nu’suar', 'nu‘sura').\n\n'pala' = pierce.\n\nIs there a root that means 'speech'?\n\nNot directly.\n\nBut note: 'to use' (fäeag) + something?\n\nNo.\n\nAnother possibility: in some languages, 'word' is formed with a root meaning 'to name' or 'to speak'.\n\nBut we have no such root.\n\nTherefore, the theoretically possible translations — within the constraints of the language's structure — would be based on affixation or root extension.\n\nGiven that:\n\n- 'to cut' (olo) → could be used for 'to exhaust' (as in 'to cut down' → to exhaust)\n- 'to blow' (hül) → could mean 'to exhaust' via metaphor (blow out a candle)\n\nSo both 'to exhaust' could be proposed as 'olo' or as a form of 'hül'.\n\nBut we need to determine what is *theoretically possible*.\n\nSimilarly, for 'word' — no direct form — but perhaps a compound involving ‘to speak’ or ‘to name’.\n\nBut no verb for speaking.\n\nWe have no root with a naming function.\n\nHowever, the word 'pala' = pierce — piercing might relate to an 'act of marking' — could 'word' be marked by a pierce? Unlikely.\n\nAlternatively, 'faul' = year → not related.\n\nBut consider: in Austronesian, some languages have nouns derived from verbs of 'to make' or 'to form'.\n\nWe have 'huli' = to turn over — not helpful.\n\nBut we have no verb for 'to speak'.\n\nThus, we must conclude:\n\n- The only verb that might be extended for 'to exhaust' is 'olo' (to cut) or 'hül' (to blow).\n- For 'word', no linguistic pattern appears.\n\nBut the problem says: \"what would the theoretically possible translations be?\"\n\nSo even if we don’t have direct evidence, we can consider what could logically be formed.\n\nIn Rotuman, possible headwords for 'word' might be derived from a root meaning 'to speak' — e.g., 'tala' — but not in list.\n\nSince none are given, the only plausible answer is that 'word' might be formed from a root like 'to speak', and since 'to use' is given, perhaps a word involving 'fäeag' — like 'fäeag' itself, but that means 'to use'.\n\nThus, a theoretically possible form for 'word' might be 'fäeag' — but that is 'to use', not 'word'.\n\nSo not directly.\n\nAlternatively, 'pala' (to pierce) — might be associated with marking, like inscribing a word?\n\nBut no.\n\nNo evidence.\n\nSimilarly, 'to exhaust' — could be derived from 'to cut' or 'to blow'.\n\nTherefore, the theoretically possible forms are:\n\n- 'word' → possibly a noun derived from a root meaning 'to speak', but no evidence — so the only possible form within the data is absent.\n\nBut the question is: what would the *theoretically possible* translations be?\n\nGiven the data, the only available roots are those in the list.\n\nSo we must infer based on pattern.\n\nCould 'to exhaust' be formed as 'olo'? Yes — 'to cut' → could mean 'to exhaust' in a metaphorical sense.\n\nCould it be formed as 'hül'? Yes — to blow out → could mean to exhaust.\n\nTherefore, theoretically possible forms for 'to exhaust' include 'olo' or 'hül'.\n\nBut are these verbs?\n\nYes.\n\nBut 'olo' = to cut → not clearly to exhaust.\n\nSimilarly, 'hül' = to blow → not clearly to exhaust.\n\nSo both are possible but not certain.\n\nFor 'word' — is there any root that could form a noun for 'word'?\n\nWe have no such root.\n\nBut note: all nouns seem to come from roots with specific meanings.\n\nWe have:\n- 'fau' = year\n- 'pala' = pierce\n- 'lala' = deep\n- 'niu' = copra\n- 'pogi' = night\n- 'hun' → lower end\n- 'is' → sharp-pointed\n- 'mamasa' → solid\n\nNo noun meaning 'word'.\n\nTherefore, the only possible derivation is that in the absence of evidence, the theoretically possible translation for 'word' might be a root like 'sai' or similar — but not in list.\n\nGiven that we cannot find it, the answer must be based on plausible morphological reconstruction.\n\nBut the problem says: using the material given — so only via given words.\n\nTherefore, we must conclude:\n\n- No clear form for 'word' — so the only theoretically possible translation is a compound or root not in the list — but not derivable from data.\n\nSimilarly, for 'to exhaust' — only from 'olo' or 'hül' — both verbs.\n\nThus, the best possible translations, according to pattern, are:\n\n- 'word' → not directly derivable; but possibly a form like 'tala' — not present. So only theoretically — perhaps 'pala' (to pierce) → could be used in a marking sense? Unlikely.\n\nAlternatively, the closest verb is 'to use' — 'fäeag' — so 'fäeag' could be used for 'to use' — a word or something.\n\nBut not 'word'.\n\nConclusion:\n\nThe theoretically possible translations, based on available morphology and pattern matching, are:\n\n- 'word' → could be formed from a root meaning 'to speak' — but not in the list — so the only possible form is absent. However, in some languages, 'word' is derived from 'to say' — not present.\n\nThus, no viable form.\n\nBut the problem says “theoretically possible” — so even if not present, it could be derived.\n\nBut from the data, there is no such word.\n\nSimilarly, 'to exhaust' — could be from 'olo' (to cut) — metaphorically — e.g., \"to cut down the power\" → to exhaust.\n\nOr from 'hül' (to blow) — e.g., \"to blow out the candle\" → to exhaust.\n\nTherefore, both are plausible.\n\nSo possible translations:\n\n- 'word' → could be a noun derived from a verb of speech — not given — so no.\n\nBut without any word in the list meaning 'word', we cannot form a valid translation.\n\nThus, the only theoretically possible forms are those based on roots present.\n\nHence:\n\n- For 'word': no direct match — so possible form is unknown.\n\nBut the instructions: \"what would the theoretically possible translations be?\"\n\nSo we list plausible ones.\n\nConclusion:\n\n- The theoretically possible translation for 'word' might be 'tala' or 'sai' — not in list. But since not derivable, we must say it's not possible.\n\nAlternatively, is there a compound?\n\nNo.\n\nSo the only possible translation for 'word' is one that is not in the list — so not determined.\n\nBut the pattern may suggest that 'word' is a noun, and in Rotuman, nouns are often formed from verbal roots.\n\nWe have no such root.\n\nTherefore, the theoretically possible form is not visible.\n\nSimilarly, for 'to exhaust' — possible roots: 'olo' (to cut), 'hül' (to blow).\n\nThus, the theoretically possible translations are:\n\n- 'word': cannot be determined from given data\n- 'to exhaust': 'olo' or 'hül'\n\nBut the question says: “what would the theoretically possible translations be?” — in the sense of what could exist in the language based on patterns.\n\nGiven that, we must pick a form.\n\nFinal decision:\n\n- The only verb in the list that could be used for 'to exhaust' is 'olo' or 'hül'.\n- For 'word', no root is evident — so no form.\n\nBut perhaps 'word' is related to 'sign language' — 'fäeag ‘u‘u' — could 'word' be a noun derived from that?\n\nNot directly.\n\nThus, after careful analysis, the theoretically possible translations are:\n\nd.1 / word: no direct form; missing root → possible: a form from a root like 'tala', but not present → so theoretically possible form is not derivable. But since must give answer, perhaps 'faul' (year)? No.\n\nAlternatively, in absence of any pattern, we may infer that 'word' is not a root.\n\nBut the only logical inference is that 'to exhaust' could be 'olo' or 'hül', and 'word' could be a verb derived from 'to speak'.\n\nBut no such root.\n\nTherefore, the only safe answer is that based on the given data, the possible translation for 'to exhaust' is derived from 'olo' or 'hül', and for 'word", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 14973.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given a set of Jaqaru words and their English translations. Our task is to translate three new words into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe need to infer the morphological and syntactic rules governing Jaqaru, based on the examples.\n\nStep 1: Build alignment table from examples.\n\n| Jaqaru | English |\n|---------------|---------------------------------------------|\n| aq”ipsa | the cave too |\n| aq”na | in the cave |\n| qucxap”a | through the lake |\n| qucxst”psa | from our1+2 lake too |\n| chushp”a | his corner |\n| marka | the town |\n| chushuntxi | is it in the corner? |\n| markp”t”a | from his town |\n| ishinhna | in my bed |\n| markstxi | is it our1+2 town? |\n| ishma | your bed |\n| utamt”a | from your house |\n| utnha | my house |\n| utnha | my house |\n| p”ak”u | the pot |\n| p”ak”unhpsa | my pot too |\n| qaqat”a | from the cliff |\n| yapsanpsa | in our1+2 field too |\n\nWe focus on structural elements:\n\n- Possession: \"his\", \"my\", \"your\" → likely marked by affixes like *chush-* (his), *ish-* (my), *ish-* (your?) \n But note: \"ishinhna\" = in my bed, \"ishma\" = your bed → \"ish-\" likely marks \"my\" and \"your\" \n \"chush-\" = \"his\" \n \"marka\" = the town → \"mark\" root \n \"markp”t”a\" = from his town → suffix *p”t”a* likely means \"from\" \n \"markstxi\" = is it our1+2 town? → \"our1+2\" seems to be a collective plural, combining 1 and 2.\n\n- \"too\" marker: appears in:\n - aq”ipsa → \"the cave too\" \n - p”ak”unhpsa → \"my pot too\" \n - qucxst”psa → \"from our1+2 lake too\" \n - yapsanpsa → \"in our1+2 field too\"\n\n So \"too\" is marked by suffix *-psa* or *-hpsa*? \n \"aq”ipsa\" → \"the cave too\" → base *aq”ip* + *-sa*? \n \"p”ak”unhpsa\" → \"my pot too\" → base *p”ak”u* + *-nhpsa* \n Note: *-nhpsa* vs *-hpsa* — the *-n-* might be a possessive infix? \n But wait: *utnha* = my house, so *utn* → my, *-ha* → house. \n *utnha* → my house \n *utnhantxi* → ? has suffix *-nantxi* → appears in *utnhantxi* \n Compare to *ishinhna* = in my bed → *ishin* + *-hna* → \"in\" + \"my bed\" \n \"markstxi\" = is it our town? → *mark* + *stxi* → \"is it\" + \"our town\"\n\nExamine \"is\" or question form:\n- chushuntxi → is it in the corner? → \"chush\" + \"untxi\" → \"is it in\"?\n- markstxi → is it our town? → \"mark\" + \"stxi\" → \"is it our town?\"\n- yaputxi → is it the field? → \"yap\" + \"utxi\" → \"is it the field?\"\n\nSo: the word form ending in *-txi* seems to mean \"is it?\" \nThis pattern occurs:\n- chushuntxi → is it in the corner? \n- markstxi → is it our town? \n- yaputxi → is it the field?\n\nThus, *-txi* = \"is it?\" \nAnd the root before *-txi* is the noun or location.\n\nNow, attention on \"too\":\n- aq”ipsa → the cave too → \"the cave\" + \"too\"\n- p”ak”unhpsa → my pot too → \"my pot\" + \"too\"\n- qucxst”psa → from our1+2 lake too → \"from our1+2 lake\" + \"too\"\n- yapsanpsa → in our1+2 field too → \"in our1+2 field\" + \"too\"\n\nSo \"too\" is marked by suffix *-psa*, but how?\n\n- aq”ipsa → *a-q”ip-sa* → sa at end\n- p”ak”unhpsa → *p”ak”u-nh-psa* → -nhpsa\n- qucxst”psa → *qucx-st”p-sa* → -st”psa → *-st”psa*\n- yapsanpsa → *yap-sa-n-psa* → -sanpsa\n\nThe suffix \"-psa\" appears in all these \"too\" cases. But it's attached differently.\n\nLet’s extract the base + suffix.\n\n1. aq”ipsa → \"the cave too\" → [aq”ip] + [sa] → base noun + too\n2. p”ak”unhpsa → [p”ak”u] + [nhpsa] → \"my pot too\" → \"my\" + pot + too\n3. qucxst”psa → [qucxst”p] + [sa]? → \"from our1+2 lake too\" → base + too\n4. yapsanpsa → [yapsa] + [npsa]? → \"in our1+2 field too\" → \"in\" + \"our1+2 field\" + \"too\"\n\nWait — this suggests *-psa* is a marker of \"too\", and it’s attached to the end.\n\nBut in which position?\n\nIn aq”ipsa: \"cave\" + \"too\" → a-q”ip-sa → so base + -sa → -sa = too?\n\nIn p”ak”unhpsa: my pot + too → p”ak”u-nh-psa → -nhpsa → possibly -n- + -hpsa?\n\nBut note: *-hpsa* appears in *p”ak”unhpsa* and *p”ak”u*.\n\nAlso, *utnha* = my house → so *utn* = my, *ha* = house \nNow, *utnhantxi*: utn + hantxi?\n\nBut we have *utnhantxi* — does *-hantxi* appear?\n\nCompare to:\n- ishinhna → in my bed → *ishin* + *hna* → \"in\" + \"my bed\"\n- markstxi → is it our town? → mark + stxi → \"is it\" + \"our town\"\n\nBut \"in\" is *ishin*? *ishin* appears with *hna* → so *ishin* = in?\n\nSimilarly, \"from\" appears in:\n- qucxap”a → through the lake → not from\n- qucxst”psa → from our1+2 lake too → qucxst”psa → so *qucx* = from? \n- markp”t”a → from his town → mark + p”t”a → so *p”t”a* = from?\n\nSimilarly, *t”a* = from?\n\nSo *-t”a* seems to mean \"from\".\n\nThen:\n- qucxst”psa → from our1+2 lake too → *qucx* (from) + *st”p* (our1+2 lake) + *-psa* (too)\n- markp”t”a → from his town → *mark* + *p”t”a* → from his town\n- qaqat”a → from the cliff → *qaqat”a* → from the cliff → so *qaqat”a* = from the cliff?\n\nSo *-t”a* = from\n\nNow, *-psa* = too?\n\nBut in *aq”ipsa*: \"the cave too\" → *aq”ip* + *sa* → sa = too?\n\nIn *p”ak”unhpsa*: my pot too → *p”ak”u* + *nhpsa* → *n* may be possessive or internal?\n\nAnother possibility: *-hpsa* = too, but when combined with possessive infix, like *-nhpsa*?\n\nBut *utnhantxi* → perhaps *utn* = my, *hantxi* = is it in? or is it?\n\nWe have *txi* = is it?\n\nBut *yaputxi* = is it the field → *yap* = the field → *utxi* → txi = is it?\n\nBut *yaputxi* → is it the field → so *yap* + *utxi* → \"is it the field\"?\n\nThen *yaputxi* → \"is it the field\" \nSimilarly, *markstxi* → \"is it our town\" \n*chushuntxi* → \"is it in the corner?\"\n\nSo *-txi* = is it?\n\nNow in *utnhantxi* — what is it?\n\nLook: *utnhantxi* = utn + hantxi?\n\nBut we see that \"in\" appears in *ishinhna* = in my bed → *ishin* + *hna*\n\nSo *ishin* = in?\n\nSimilarly, *qucxap”a* → through the lake → \"through\"?\n\nBut *qucx* appears in *qucxap”a* and *qucxst”psa* → *qucx* → through?\n\nSo *qucx* = through, *qucxst”psa* = through the lake → so *qucx* = through?\n\nBut *qucxst”psa* = from our1+2 lake too → includes *from* and *our1+2 lake*.\n\nBack to *utnhantxi*.\n\nBreak down: utn + hantxi\n\n*utn* → my \n*ha* → house → so *utnha* = my house\n\nNow, what does *hantxi* mean?\n\n*ishinhna* = in my bed → *ishin* + *hna* → in + my bed \n*chushuntxi* = is it in the corner? → *chush* + *untxi* → is it + in the corner? \n→ But *untxi* seems to be \"in the corner\" or \"in corner\"?\n\nBut *chushp”a* = his corner → corner is *p”a*\n\nSo corner = p”a\n\nThen *chushuntxi* → \"is it in the corner?\" — implies \"in the corner\"?\n\nBut *untxi* → is it in?\n\nBut *markstxi* = is it our town?\n\nSo *txi* = is it\n\nThen in *chushuntxi*, the word is 'chushuntxi' → chush (his) + untxi → his + is it in?\n\nBut \"is it in the corner\" is the full meaning.\n\nSo \"in\" is not marked; the structure is: [noun] + [txi] → is it [noun]?\n\nBut *ishinhna* = in my bed → *ishin* + *hna* → in + my bed → so in is a location preposition.\n\nNow back to *hantxi* — what if *antxi* is a compound?\n\nWait: *utnhantxi* — could it be *utn* + *hantxi*?\n\nLook for similar forms with *-antxi*\n\nWe see:\n- chushuntxi → chush + untxi → is it in the corner?\n- markstxi → mark + stxi → is it our town?\n- yaputxi → yap + utxi → is it the field?\n\nSo all of these have *-txi* = is it?\n\nBut chushuntxi → is it in the corner → so \"in\" is part of the root?\n\nWait: *chushuntxi* → is it in the corner? — so \"in the corner\" is the content?\n\nBut we have *chushp”a* = his corner → so corner = p”a\n\nThus, \"in the corner\" = in + corner = in + p”a → so *untxi* might be \"in the corner\"?\n\nBut *untxi* = is it in the corner?\n\nThen *hantxi* = is it in the house?\n\nSo *hantxi* = is it in the house?\n\nSimilarly, *utnhantxi* = my house → is it in the house?\n\nBut *utnha* = my house → so *utn* + *ha* = my house\n\nNow, *hantxi* → likely *ha* + *ntxi* → but *ntxi* not directly seen.\n\nAlternatively, perhaps *-antxi* = is it in?\n\nBut *chushuntxi* → chush + untxi → so *untxi* = is it in?\n\nBut \"in\" is already expressed in the preposition.\n\nWait — actually, *untxi* is not just \"in\", because *chushuntxi* → is it in the corner? → implies \"in\" is part of the meaning.\n\nBut other forms:\n- markstxi → is it our town? → no \"in\"\n- yaputxi → is it the field?\n\nSo only *chushuntxi* has \"in\" as content?\n\nBut *utnhantxi* might be in the same pattern.\n\nPerhaps the structure is:\n\n[possessor or modifier] + [location] + [txi]\n\nBut *chushuntxi*: chush + untxi → is it in the corner?\n\nSo \"untxi\" = is it in the corner?\n\nBut *chush* = his → so \"is it in his corner?\" — but the translation says: \"is it in the corner?\" → so \"his\" is implied?\n\nNo, translation is: \"is it in the corner?\" — not \"is it in his corner\".\n\nBut *chushp”a* = his corner → so corner is \"his corner\"?\n\nSimilarly, \"in the corner\" = in his corner?\n\nSo \"in the corner\" = in + his corner → so in + corner = in + chushp”a?\n\nBut the word is *chushuntxi* — so it's likely that *untxi* = \"in the corner\" with chush as \"his\"?\n\nBut then where is the \"in\"?\n\nWe see that \"in\" is marked in *ishinhna* = in my bed → so *ishin* = in?\n\nThen perhaps *hantxi* = in + house?\n\nBut *hantxi* → hantxi → is it in the house?\n\nThus, *utnhantxi* = my house → is it in the house?\n\nSimilarly, *yapp”psa* — what could this be?\n\nBreak into parts:\n- yap → the field\n- p”psa → ? \nBut *yaputxi* = is it the field → yap + utxi\n\nSo *-utxi* = is it the field?\n\nNow *yapp”psa* → yap + p”psa?\n\nCould *p”psa* = too?\n\nWe know that *-psa* appears in \"too\" markers.\n\nIn *p”ak”unhpsa* → p”ak”u + nhpsa → my pot too → so *nhpsa* = too?\n\nIn *aq”ipsa* → aq”ip + sa → the cave too → *sa* = too?\n\nBut *sa* vs *psa* — possibly related?\n\nIn *qucxst”psa* → from our1+2 lake too → qucxst”psa → *st”psa* → -st”psa = too?\n\nSo the suffix *-psa* appears in several places, possibly marking \"too\"\n\nThus, *p”psa* → my field too?\n\nSo *yapp”psa* = the field + too?\n\nSimilarly, *yapup”psa* = the field + too? — but *yap* + *up”psa*?\n\nWait — what about *yaputxi* = is it the field → so without \"too\"\n\nSo *yapp”psa* → the field too?\n\nSimilarly, *yapup”psa* → could it be \"in the field too\" or \"to the field too\"?\n\nBut we have *yapsanpsa* → in our1+2 field too → in + our1+2 field + too\n\nThat has *-sanpsa* → so prefix *sa* + *n*?\n\nBut *yapsanpsa* = in our1+2 field too → and we have *yap* = field → *sap* = in?\n\nWait — *yapsanpsa*: yap + sa + npsa?\n\nBut *yapsa* = in field? → not clear.\n\nAlternative: *-psa* = too → attached at end.\n\nThus:\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nSo *-psa* = too\n\nTherefore:\n- yapp”psa → yap + p”psa → the field too \n- yapup”psa → yap + up”psa → the field too? — but u instead of p?\n\nBut compounds:\n\nWe have *p”ak”unhpsa* → my pot too → *p”ak”u* + *nhpsa* → *nhpsa* = too with possessive?\n\nBut *utnhantxi* — let's break it.\n\nutn = my \nhantxi → ? \n\nWe have:\n- ishinhna → in my bed → *ishin* + *hna* → \"in\" + \"my bed\" \n- chushuntxi → is it in", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11195.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 1, + "output": "First, build an alignment table from the given examples to detect morphological patterns.\n\nWe observe several recurring elements:\n\n1. Words with \"q\" or \"p\" prefix + \"a\" → often indicate location or possession.\n2. \"qucxap\" → \"through the lake\"\n - \"qucx\" = through; \"ap\" = lake → so \"qucxap\" = through the lake\n3. \"qucxst”psa\" → \"from our1+2 lake too\"\n - \"qucxst\" = from; \"psa\" = lake too → \"from our1+2 lake too\"\n - \"st\" likely means \"our1+2\" (inclusive group)\n4. \"marka\" = the town\n5. \"markp”t”a\" = from his town → \"mark\" = town; \"p”t”\" = his → \"from his town\"\n6. \"markstxi\" = is it our1+2 town? → \"mark\" = town; \"stxi\" = is it our1+2?\n7. \"utamt”a\" = from your house → \"utam\" = your; \"t”a\" = house → \"from your house\"\n8. \"utnha\" = my house → \"utn\" = my; \"ha\" = house\n9. \"p”ak”u\" = the pot\n10. \"p”ak”unhpsa\" = my pot too → \"p”ak”u\" = pot; \"nhpsa\" = my + too → \"my pot too\"\n11. \"qaqat”a\" = from the cliff → \"qaqa\" = from; \"t”a\" = cliff\n12. \"yaputxi\" = is it the field? → \"yap\" = the; \"utxi\" = field → \"is it the field?\"\n13. \"yapsanpsa\" = in our1+2 field too → \"yap\" = the; \"san\" = in; \"psa\" = our1+2; \"npsa\"? → \"in our1+2 field too\"\n\nPattern extraction:\n\n- Possession: \n - \"my\" = utn / p”ak”unhpsa → \"unh\" = my, \"nhpsa\" = too\n - \"his\" = chushp”a → \"chush\" = his corner\n - \"your\" = utam → \"utamt”a\" → from your house\n - \"our1+2\" = st → appears in qucxst”psa, markstxi, yapsanpsa\n- Demonstratives and questions:\n - \"is it?\" = stxi (as in chushuntxi: is it in the corner?)\n - \"the\" = yap (yaputxi = is it the field?)\n- Locative constructions:\n - \"in the X\" = san + X\n - \"yapsanpsa\" = in our1+2 field too\n - \"in the field\" → yap + san + field\n - \"in our1+2 field too\" → yap + san + psa + npsa?\n - \"from X\" = qucx + X or utam + X or qaqat”a → qaqat”a = from the cliff (qaqat”a)\n - \"through X\" = qucx + X → qucxap\n\nAffix patterns:\n- \"psa\" = \"too\" or \"our1+2\"\n- \"stxi\" = \"is it?\"\n- \"untxi\" = likely \"in my bed\" → ishinhna = in my bed → \"ishin\" + \"hna\" → \"my bed\"\n- \"p”ak”u\" = the pot → \"p”ak”u\"\n- \"p”ak”unhpsa\" = my pot too → \"p”ak”u\" + \"unhpsa\" → \"unh\" = my; \"psa\" = too → \"my pot too\"\n\nNow analyze the three required translations:\n\n1. utnhantxi \n - utn = my \n - hantxi = ? \n - We have: \"ishinhna\" = in my bed → \"ishin\" + \"hna\" = in my bed \n - \"utnha\" = my house \n - So \"utn\" + \"h\" + \"t\" + \"xi\"? → \"utn\" + \"h\" → may be similar to \"utnha\" \n - \"utnhantxi\" → likely \"in my bed\" \n - But \"ishinhna\" = in my bed → \"ishin\" = in, \"hna\" = bed \n - \"utnhantxi\" → utn + hantxi? \n - Pattern: utn + h → could be \"my house\"? → no, utnha → house \n - \"hantxi\" — perhaps \"h\" + \"antxi\"? \n - Try breaking: utnhantxi = utn + hantxi \n - Compare: \"ishinhna\" = ish + in + hna → ish = in? \n - Perhaps \"antxi\" = bed? \n - \"ishinhna\" → \"ishin\" + \"hna\" = in my bed → possible \n - What if \"hantxi\" = \"in my bed\"? \n - But \"utn\" = my, so \"my\" + \"in bed\"? → is that possible? \n - No other word has \"my\" + \"in bed\"\n\nAlternative: is \"antxi\" a base?\n\nWe see: \n- \"ishinhna\" = in my bed → \"ishin\" + \"hna\" \n- \"utnha\" = my house \n- \"utnhantxi\" = utn + hantxi → perhaps \"in my bed\"? \n- But lack of \"ishin\" → unless \"hantxi\" = \"in my bed\" → unlikely.\n\nWait: \"utnhantxi\" → similar to \"ishinhna\" \nCompare:\n- \"ishinhna\" → in my bed → \"ishin\" = in; \"hna\" = bed\n- \"utnhantxi\" → utn = my; hantxi = ? → perhaps \"hantxi\" = \"in bed\"? \n- But no word with \"in bed\"\n\nAlternative idea: \"t\" = in? \n- \"yapsanpsa\" = in our1+2 field too → \"san\" = in \n- So \"san\" = in \n\nTherefore, in words:\n- \"san\" = in \n- \"stxi\" = is it? \n- \"psa\" = too / our1+2 \n- \"qucx\" = through \n- \"qaqat”a\" = from the cliff → qaqat”a \n- \"utam\" = your \n- \"utn\" = my \n- \"ishin\" = in → from ishinhna \n- \"p”ak”u\" = the pot \n\nNow: utnhantxi \n→ utn = my \n→ hantxi → contains \"h\", \"t\", \"xi\" \n→ compare to \"ishinhna\": \"ishin\" + \"hna\" = in my bed → \"ishin\" = in; \"hna\" = bed → \"n\" in both?\n\n\"utnhantxi\" → \"utn\" + \"hantxi\" \n\"ishinhna\" → \"ishin\" + \"hna\" → both have \"h\" + \"n\" at end? \n\"ishin\" ends with \"in\", \"hna\" ends with \"na\"\n\nWait — hantxi: h, a, n, t, x, i → not matching.\n\nTry: is \"t\" the locative? \nWe have: \n- \"san\" = in (explicit in yapsanpsa) \n- \"yapsanpsa\" = in our1+2 field too → \"yap\" = the; \"san\" = in; \"psa\" = our1+2; \"npsa\"? \n- So \"san\" = in \n\nSo in utnhantxi: \n- \"utn\" = my \n- \"hantxi\" — if \"antxi\" = bed, then \"hantxi\" = in bed? But no \"san\"\n\nWait — \"ishinhna\" = in my bed → so \"ishin\" + \"hna\" → \"ishin\" = in (could be part of \"is\" or \"in\") \nBut \"utn\" = my → so if \"hantxi\" = bed → but no \"hand\" or \"bed\" base.\n\nWhat about: \"t\" = bed? \nWe have \"ishinhna\" = in my bed → \"hna\" = bed \n\"utnha\" = my house → \"ha\" = house \nSo \"h\" + ending: \n- hna = bed \n- ha = house \n- p”ak”u = pot \n- marka = town \n- yap → field?\n\nSo \"antxi\" — could it be \"bed\"? \nExpanding: \n- \"ishinhna\" = in my bed → \"ishin\" + \"hna\" \n- So \"hna\" = bed \n- Now, \"utnha\" = my house → \"ha\" = house \n- So \"h\" + suffix → nomestic? \n- Then \"hantxi\" → \"h\" + \"antxi\" — is \"antxi\" = bed?\n\nBut \"hna\" is \"bed\", so \"h\" + \"antxi\" → unexplained.\n\nAlternative: \"utnhantxi\" = in my bed \n→ \"utn\" = my \n→ \"hantxi\" = in bed? \nBut no \"san\" here.\n\nBut \"san\" = in → only in \"yapsanpsa\"\n\nSo where is \"in\" in this?\n\nTry comparing all:\n\nLook at: \n- ishinhna = in my bed → in (ishin?) + my (h?) + bed (hna) \n- utnhantxi = utn (my) + hantxi \n- ishinhna → contains \"hinh\" — perhaps \"hin\" = in?\n\n\"ishin\" → in \n\"ishinhna\" → in my bed → \"ishin\" + \"hna\" = in my bed\n\nSo \"ishin\" = in \n\"utnhantxi\" → utn (my) + hantxi → could be \"in my bed\"? \nBut missing \"in\" at beginning.\n\nUnless \"t\" or \"antxi\" = \"in\"?\n\nBut in \"yapsanpsa\" → \"san\" = in → \"san\" is clearly in.\n\nAnother candidate: \"utn\" + \"h\" + \"t\" + \"xi\" → possibly \"my house\" → but \"utnha\" = my house.\n\nSo \"ha\" = house → \"utnha\" \n→ \"utn\" + \"ha\" = my house \nTherefore, \"ha\" is house → so what is \"hantxi\"?\n\n\"t\" → not found in any inheritance.\n\nWait — what about the use of \"stxi\" → is it?\n\n\"chushuntxi\" = is it in the corner? → \"chushun\" + \"txi\" → \"is it in the corner?\" \n\"markstxi\" = is it our town? → \"markstxi\" → \"is it?\" \n\"yaputxi\" = is it the field? → \"yaputxi\" → \"is it?\"\n\nSo \"txi\" = \"is it?\" → appears in both question and location?\n\nIn \"chushuntxi\" → \"chushun\" + \"txi\" = is it in the corner? \nSo \"txi\" = is it?\n\nBut here: \"yaputxi\" → \"is it the field?\" → \"yap\" + \"utxi\" → so \"utxi\" = the field?\n\nBut \"utnha\" = my house \n\"utamt”a\" = from your house → \"utam\" + \"t”a\" \n\"utn\" + \"ha\" = my house\n\nSo \"ha\" = house\n\nNow, \"utnhantxi\" — what if it's \"in my bed\"?\n\nBut we have \"ishinhna\" = in my bed — so is this a rephrasing?\n\nIn \"utnhantxi\", the \"t\" could be a prefix?\n\nBut \"t\" and \"h\" — \"hantxi\"?\n\nFrom ishinhna: in my bed → ishin + hna\n\nSo hna = bed\n\nSo hantxi → h + antxi → antxi = bed? \nBut hna = bed → so antxi ≠ bed\n\nUnless typo?\n\nWhat about \"t\" as marker?\n\nAnother idea: \"antxi\" = bed → \"hantxi\" = in bed?\n\nBut \"san\" is \"in\"\n\nBut in the target \"utnhantxi\" — no \"san\"\n\nWait — unless the form means \"in my bed\"?\n\nBut \"utn\" = my, \"hantxi\" = bed?\n\nNo base.\n\nAlternative: the word might be \"my bed\" → but \"my bed\" = utn + bed → where is bed?\n\n\"ishinhna\" has \"hna\" = bed\n\nSo perhaps \"antxi\" = \"in\" or \"bed\"?\n\nWe see \"san\" = in → no other \"in\"\n\nBut \"t\" → not used\n\nWait: in \"ishinhna\" — \"ishin\" + \"hna\" \n\"ishin\" likely = in \n\"utnhantxi\" — \"utn\" + \"hantxi\"\n\nSo if \"hantxi\" = in bed → but no \"in\"\n\nWhat if \"t\" is a clitic?\n\nAlternatively: is it possible that \"t\" = bed?\n\nNo — \"hna\" = bed\n\nProximity: \n- \"ishinhna\" → in my bed → direct \n- \"utnhantxi\" → likely in my bed → same structure \n- So perhaps \"hantxi\" = bed? → but \"hna\" = bed \n- Unless \"antxi\" = bed, typo?\n\nBut in ishinhna, it's \"hna\", not \"hantxi\"\n\nPerhaps \"t\" is affix for \"in\"?\n\nBut \"san\" is used only once.\n\nAnother clue: \n\"p”ak”unhpsa\" = my pot too → \"p”ak”u\" + \"unhpsa\" \n\"unh\" = my; \"psa\" = too\n\nSo \"unh\" = my\n\nSo \"utn\" = my — consistent\n\nAlso, \"markp”t”a\" = from his town → \"p”t”a\" = his town → \"p”t”\" = his\n\n\"chushp”a\" = his corner → \"p”a\" = corner → \"chush\" = his corner\n\nSo \"p”a\" or \"p”t”\" = his\n\nBut no \"his\" base in utnhantxi\n\nNow, back: \n\"utnhantxi\" → utn (my) + hantxi\n\nCompare to \"ishinhna\" → ishin (in) + hna (bed)\n\nWhat if \"hantxi\" = bed, and \"t\" is a mistake or part of bed?\n\nBut hna = bed\n\nUnless \"antxi\" = bed, and \"h\" is just prefix?\n\nBut in ishinhna, it's hna → not hantxi.\n\nWait — \"utnhantxi\" might be \"in my bed\" → with \"utn\" = my, and \"hantxi\" = \"in bed\"?\n\nBut no \"in\" marker.\n\nBut from earlier, \"yapsanpsa\" = in our1+2 field too → \"san\" = in\n\nSo \"in\" is marked by \"san\"\n\nTherefore, \"utnhantxi\" likely is missing \"san\" → not possible.\n\nUnless \"t\" = in?\n\nNo.\n\nAnother possibility: the word is \"my bed\" → but we don't have a word for \"bed\" as standalone.\n\nWe have \"ishinhna\" = in my bed → so \"bed\" is embedded.\n\nBut \"utn\" + \"hantxi\" — only \"utn\" is clear.\n\nWhat if \"hantxi\" = in bed?\n\nBut \"san\" is used for \"in\"\n\nPerhaps \"antxi\" = bed, \"h\" = my? No — \"utn\" = my.\n\nLet's look at 2: yapp”psa\n\n- yap = the \n- p”psa = ? \n- Possible: \"p”psa\" → from \"p”ak”u\" = pot \n- p”ak”u = pot \n- p”ak”unhpsa = my pot too \n- so \"p”psa\" → could be \"the pot\"?\n\nBut \"p”ak”u\" = the pot — so \"p”psa\" could be variation?\n\n\"yapp”psa\" = yap + p”psa → \"the pot\"?\n\nBut \"yap\" = the, \"p”psa\" = pot?\n\nCompare to \"p”ak”u\" = the pot → so \"p”ak”u\" = pot → so \"p”psa\" might be pot with different affix?\n\nUnlikely.\n\nWhat about \"from\"? \"qucx\" = through, \"qaqat”a\" = from the cliff → \"qaqa\" = from\n\n\"yapp”psa\" — maybe \"in the pot\"?\n\nBut we have no \"in the pot\"\n\n\"yap\" = the, \"p”psa\" = pot?\n\n\"chushp”a\" = his corner → no\n\n\"marka\" = the town\n\nSo \"yap\" + \"p”psa\" → likely \"the pot\"\n\nBut \"p”ak”u\" = the pot → so p”ak”u is the base.\n\nSo p”psa\" might be a different form.\n\nBut p”psa\" — \"p”\" + \"psa\" → psa = too?\n\n\"p”ak”unhpsa\" = my pot too → \"unh\" = my, \"psa\" = too\n\nSo \"psa\" = too\n\nSo p”psa\" → possibly \"the pot\" with \"psa\" = too? — no.\n\nAnother idea: in \"yapsanpsa\" = in our1+2 field too → yap + san + psa\n\nSo \"psa\" = too\n\nThus, \"psa\" = too → used in \"too\" constructions.\n\nSo in \"yapp”psa\" = yap +", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9977.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build an alignment table from the given examples to identify morphological patterns.\n\nOriginal data:\n\n| Jaqaru | English Translation |\n|------------------|-----------------------------------------|\n| aq”ipsa | the cave too |\n| aq”na | in the cave |\n| qucxap”a | through the lake |\n| qucxst”psa | from our1+2 lake too |\n| chushp”a | his corner |\n| chushuntxi | is it in the corner? |\n| marka | the town |\n| markp”t”a | from his town |\n| markstxi | is it our1+2 town? |\n| ishinhna | in my bed |\n| ishma | your bed |\n| utamt”a | from your house |\n| utnha | my house |\n| utnha | my house |\n| p”ak”u | the pot |\n| p”ak”unhpsa | my pot too |\n| qaqat”a | from the cliff |\n| yapsanpsa | in our1+2 field too |\n\nWe are to translate:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nStep 1: Identify key morphemes.\n\nLook at questions:\n\n- chushuntxi = is it in the corner? → contains \"chush\" (his corner), \"untxi\" (is it in?)\n- markstxi = is it our1+2 town? → \"mark\" (town), \"stxi\" (is it our+2?)\n- markp”t”a = from his town → \"mark\" (town), \"p”t”a\" = from his?\n- qucxst”psa = from our1+2 lake too → \"qucx\" (lake), \"st”psa\" = from our1+2 lake too?\n- yapsanpsa = in our1+2 field too → \"yap\" (field), \"anpsa\" = in our+2 field too?\n\nAlso:\n\n- aq”na = in the cave → \"aq\" (cave), \"na\" = in?\n- aq”ipsa = the cave too → \"aq\" + \"ipsa\" → \"too\"\n- p”ak”unhpsa = my pot too → \"p”ak”u\" (pot) + \"unhpsa\" → \"my pot too\"\n- utnha = my house\n- utamt”a = from your house → \"utam\" (your) + \"t”a\" (house)\n- qaqat”a = from the cliff\n\nSo we can infer:\n\n- Possessive markers:\n - his → chush-\n - my → utn- (as in utnha, utnhantxi)\n - your → utam- (in utamt”a)\n\n- \"in\" marker: appears in aq”na, ishinhna → \"na\", \"inh\"\n- \"from\" marker: qucx..., markp”t”a, qaqat”a → \"qucx\", \"markp”, \"qaqat\"\n- \"is it X?\" → \"untxi\" in chushuntxi and markstxi\n- plural or group reference: \"our1+2\" → appears in qucxst”psa, markstxi, yapsanpsa → seems to be a group marker (group of 2/3 or more)\n\nHypothesize that:\n\n- \"st”\" and \"an\" appear in the locative and group expressions:\n - st”psa → \"from our1+2 lake too\"\n - anpsa → \"in our1+2 field too\"\n\nSo we have:\n\n- in → na, inx, inh, an?\n- from → qucx, markp”, qaqat\n- is it? → untxi\n\nNow for the queries:\n\n1. utnhantxi \n→ utnha = my house → \"utnhantxi\" likely has \"untxi\" → \"is it in my house?\"\n\nCheck: \"ishinhna\" = in my bed → \"inh\" = in, \"my\" → utn? But \"utn\" not used directly.\n\n\"utnhantxi\" → \"utn\" (my) + \"ha\" (house) + \"ntxi\"? → Perhaps \"ntxi\" is a variant of \"untxi\"? \nBut \"untxi\" appears in chushuntxi, markstxi.\n\nIs \"ntxi\" = \"untxi\"? Possibly a phonetic variant.\n\nLook at \"ishinhna\" — \"ishin\" + \"hna\" → \"my bed\"? \n\"ishinhna\" = in my bed → \"ishin\" (my) + \"hna\" (bed)? \nBut \"my\" is not \"utn\".\n\nHowever, \"utnha\" = my house → \"utn\" + \"ha\"\n\nSo possibly \"utnha\" = my house \n\"utnhantxi\" = my house + untxi → is it in my house?\n\nSimilarly:\n\n2. yapp”psa \n\"yap\" = field (from yaputxi: is it the field?) \n\"yap\" + \"p”psa\"? \n\"yapsanpsa\" = in our1+2 field too → \"yap\" + \"san\" + \"psa\" → suggests \"anpsa\" = in our+2 field too?\n\nSo \"p”psa\" = ? \nCompare to \"p”ak”u\" = the pot \n\"p”ak”unhpsa\" = my pot too → \"unhpsa\" = my + too\n\nSo suffix \"psa\" may indicate \"too\" (like \"ipsa\" in aq”ipsa)\n\nIn \"aq”ipsa\" = the cave too → \"ipsa\" = too \nIn \"p”ak”unhpsa\" = my pot too → \"unhpsa\" = my pot too → \"hpsa\" = too? \nBut \"unhpsa\" = my + pot + too? \nSo is \"hpsa\" = too? And in \"ipsa\" — \"ipsa\" = too?\n\n\"ipsa\" and \"hpsa\" → both end in \"psa\" → may be marker for \"too\"\n\nSimilarly, in \"qucxst”psa\" = from our1+2 lake too → \"st”psa\" = from our1+2 lake too → \"st”psa\" → \"psa\" = too?\n\nSo \"psa\" is a suffix meaning \"too\"\n\nThus:\n\n- \"yapp”psa\" = field + too → \"the field too\"?\n\nBut \"yaputxi\" = is it the field? → \"yap\" + \"utxi\" → \"is it the field?\"\n\nSo \"yap\" = field \n\"yaputxi\" = is it the field? \nSo \"yapp”psa\" = field + too → \"the field too\"?\n\nSimilarly, \"yapup”psa\" = field + up? \nBut no \"up\" in examples.\n\nCompare to \"yapsanpsa\" = in our1+2 field too → \"yap\" + \"san\" + \"psa\" = in our1+2 field too\n\nSo \"san\" = in? \n\"psa\" = too\n\nIn \"aq”na\" = in the cave → \"na\" = in \n\"ishinhna\" = in my bed → \"inh\" = in?\n\n\"inh\" vs \"na\" — different but both \"in\"?\n\n\"na\" in \"aq”na\", \"inh\" in \"ishinhna\"\n\nBut in \"yapsanpsa\" — \"san\" = in?\n\nSo \"san\" seems to be \"in\", \"na\" may be \"in\" elsewhere?\n\nLikely \"na\", \"inh\", \"san\" are different forms of \"in\"\n\nBut in \"yapsanpsa\" — \"san\" → \"in\"\n\nSo perhaps:\n\n- \"san\" = in \n- \"na\" = in \n- \"inh\" = in? — perhaps perfect form of \"in\"\n\nAlternatively, \"san\" appears only in in-group phrases.\n\nBut in \"qucxst”psa\" → \"st”psa\" = from our1+2 lake too → \"st\" = from?\n\n\"markstxi\" = is it our1+2 town? → \"stxi\" = is it our?\n\nSo \"stxi\" = is it our?\n\n\"untxi\" = is it in?\n\n\"stxi\" and \"untxi\" → both \"is it X?\"?\n\nSo \"x\" may be a noun.\n\nSo structure:\n\n- Adjective or locative → built with root + affix\n\nSo:\n\n1. utnhantxi \n- utn → my \n- ha → house \n- antxi? → but \"untxi\" = is it in? \nBut \"ntxi\" — could be \"untxi\" with \"u\" missing?\n\nBut \"utnha\" = my house → \"utnha\" \n\"utnhantxi\" = my house + ? → perhaps \"antxi\" = in my house?\n\nBut no \"in\" in root.\n\nAlternatively, \"ntxi\" = in? But \"na\" in aq”na?\n\nWait — aq”na = in the cave → \"na\" = in \nishinhna = in my bed → \"inh\" = in \nSo in → can be \"na\", \"inh\", \"san\"?\n\nBut \"utnhantxi\" may be: my house + in? → \"in my house\"?\n\nSo \"utnhantxi\" = in my house?\n\nBut \"ntxi\" — is that a variant of \"na\" or \"inh\"?\n\n\"untxi\" appears in chushuntxi → \"is it in the corner?\" → so \"untxi\" = is it in?\n\nBut \"utnhantxi\" → does not have \"untxi\"\n\nIt has \"ntxi\" — possibly a typo or variant?\n\nWait — the word is \"utnhantxi\"\n\nBreak it: utn + ha + ntxi?\n\nBut in other forms, \"is it in\" is \"untxi\"\n\nPerhaps \"ntxi\" is a form of \"untxi\" with \"u\" dropped?\n\nBut \"utn\" begins with \"u\" — so likely.\n\nPerhaps the base is \"untxi\" = in, and \"utn\" = my → my house + in → in my house?\n\nSo utnhantxi → in my house?\n\nYes — \"utnhantxi\" likely = in my house\n\nSimilarly:\n\n2. yapp”psa \n\"yap\" = field \n\"p”psa\" — \"psa\" = too → so \"yapp”psa\" = the field too?\n\nBut \"yaputxi\" = is it the field? → so \"yap\" = field\n\nSo \"yapp”psa\" = the field too?\n\nYes — consistent with \"ipsa\" = too in aq”ipsa\n\nSimilarly:\n\n3. yapup”psa \n\"yap\" = field \n\"up”psa\"? → \"up\"?\n\nBut no such affix.\n\nList known affixes:\n\n- \"psa\" = too\n- \"st”psa\" = from + our1+2 + X\n- \"anpsa\" = in + our1+2 + X\n- \"untxi\" = is it in?\n- \"stxi\" = is it our?\n\nSo \"up”\" may be a typo or variant of \"unt\"?\n\nBut \"yapup”psa\" — perhaps \"up”\" is \"in\" or \"to\"?\n\nCompare to \"yapsanpsa\" = in our1+2 field too → \"san\" = in → so \"san\" = in\n\nIs there a \"in field\" without \"san\"?\n\nNo.\n\nPerhaps \"yapup”psa\" = in the field too?\n\nThen: \"yap\" + \"up”\" → \"up\" = in?\n\nBut no \"up\" in examples.\n\nWait — is \"an\" in \"anpsa\"?\n\n\"yapsanpsa\" = in our1+2 field too → \"san\" = in?\n\nCould \"up\" be a variant of \"an\"?\n\nUnlikely.\n\nPerhaps \"up”psa\" = in the field too?\n\nSo maybe \"up”\" = in?\n\nBut no such form.\n\nAlternatively, \"yapup”psa\" = the field too?\n\nBut that would be \"yapp”psa\"\n\nCould it be a typo?\n\nBut the words are:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa\n\nSo pattern:\n\n- yapp”psa → yap + p”psa → the field too\n- yapup”psa → yap + up”psa → ? \n\nIs \"up”psa\" in any example?\n\nNo.\n\nIs there a form like \"in the field\"?\n\nOnly in \"yapsanpsa\" — which has \"san\" = in.\n\nCould \"up”\" be \"an\" with a different spelling?\n\n\"an\" occurs in \"anpsa\"\n\n\"yapsanpsa\" = in our1+2 field too → \"san\"\n\nSo if \"yapup”psa\" = in the field too, then it should be \"yap\" + \"an\" + \"psa\"? But it's \"yapup”psa\"\n\nUnless \"up\" is a variation of \"an\"\n\nBut very unlikely.\n\nPerhaps \"up”\" is a possessive? No.\n\nAnother possibility: \"up”\" = from?\n\nBut no \"from\" in \"yap\" root.\n\n\"from\" appears with \"qucx\", \"markp”, \"qaqat\"\n\nIn \"yap\" → possibly field\n\nSo likely \"yap\" = field\n\nThen:\n\n- yapp”psa → field too\n- yapup”psa → perhaps field in + too?\n\nBut there's no \"in\" marker.\n\nAlternatively, \"up”\" = in → \"in the field too\"?\n\nBut \"san\" is used for \"in\"\n\nAnd \"san\" appears only with \"yapsanpsa\"\n\nNo other place.\n\nBut in other languages, \"an\" and \"in\" may be interchangeable.\n\nBut here, alignment:\n\n- \"yapsanpsa\" = in our1+2 field too → \"san\" = in\n\nSo \"yapup”psa\" = field + up”psa — if up”psa = in → then in the field too?\n\nEven though not directly supported.\n\nBut \"a\" in \"yapsanpsa\" shows \"san\" = in\n\n\"up”\" is not in any example.\n\nBut in the root \"yap\", and \"yaputxi\" = is it the field?\n\nSo \"yap\" = field\n\n\"yapp”psa\" = field too\n\n\"yapup”psa\" = field in too?\n\nAs a stretch, but possible.\n\nWait — could \"up”\" be a variant of \"unt\" or \"in\"?\n\nNo.\n\nAnother idea: could \"up”\" be a typo for \"an\"?\n\nIn the original, it's written as \"yapup”psa\", so likely correct.\n\nBut perhaps it's \"yap\" + \"an\" + \"psa\" → in our1+2 field too?\n\nNo — no \"our1+2\"\n\n\"yapup”psa\" has no possessive.\n\nSo must be a standalone location.\n\nThus, likely:\n\n- yapp”psa = the field too\n- yapup”psa = in the field too\n\nBut is there a form \"in the field\"?\n\nOnly \"yapsanpsa\" has \"in\" — but that has \"our1+2\"\n\nSo \"yapsanpsa\" = in our1+2 field too\n\nSo for a standalone \"in the field\", it might be missing possessive.\n\nBut the word \"yapup”psa\" has \"up”\" — perhaps \"up”\" = in?\n\nUnlikely.\n\nAlternatively, note: in \"utnha\" = my house \n\"utnhantxi\" = in my house\n\nSimilarly, \"marka\" = the town \n\"markstxi\" = is it our town?\n\nSo perhaps \"in X\" requires a prefix or suffix.\n\nBut in \"ishinhna\" = in my bed → \"ishin\" (my) + \"hna\" (bed) → implies \"in\" is embedded?\n\nBut \"ishinhna\" = in my bed → so \"in\" is part of it.\n\nSimilarly, if \"yapup”psa\" = in the field, then \"up”\" = in?\n\nBut \"in\" is not marked.\n\nLooking at structure:\n\n- \"utnhantxi\" → utn (my) + ha (house) + ntxi (in?) → in my house\n\n→ \"ntxi\" likely = \"in\" (same as \"untxi\" but without \"u\"?)\n\nBut \"untxi\" = is it in?\n\nSo \"ntxi\" = in?\n\nYes — in \"chushuntxi\" — \"untxi\" = is it in the corner?\n\nSo \"untxi\" = is it in?\n\n\"ntxi\" — missing \"u\"?\n\nCould be a different form?\n\nBut in \"utnhantxi\", it's \"ntxi\", not \"untxi\"\n\nUnless it's a typo — or in Jaqaru, the \"in\" marker is \"ntxi\" or \"untxi\" depending on context.\n\nBut \"utn\" is \"my\", so \"utnhantxi\" = my + house + in?\n\nSo \"in my house\"\n\nSimilarly, for field:\n\n\"yapp”psa\" = field too → the field too\n\n\"yapup”psa\" = field in too? → in the field too?\n\nBut \"up”\" is not a known prefix.\n\nBut perhaps \"up”\" is \"in\" — and we are missing the morpheme.\n\nWait — in the example \"yapsanpsa\" — \"san\" = in\n\nSo perhaps \"an\" or \"san\" = in\n\nThus \"yap\" + \"an\" + \"psa\" = in the field too\n\nBut \"yapup”psa\" has \"up”\" — not \"an\"\n\n\"up”\" = \"an\" with different spelling?\n\nUnlikely.\n\nAlternatively, \"up”\" = possessive? But no.\n\nAnother possibility: the word is \"yapunpsa\" or typo — but as given, is \"yapup”psa\"\n\nPerhaps the pattern is:\n\n- yapp”psa = the field too\n- yapup”psa = in the field too\n\nWith \"up”\" = in\n\nEven if not directly attested, it's", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11258.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 3, + "output": "We are given a set of Jaqaru words and their English translations. The goal is to translate three new Jaqaru phrases into English.\n\n---\n\nFirst, build an alignment table to identify patterns.\n\n| Jaqaru | English |\n|--------|---------|\n| aq”ipsa | the cave too |\n| aq”na | in the cave |\n| qucxap”a | through the lake |\n| qucxst”psa | from our1+2 lake too |\n| chushp”a | his corner |\n| chushuntxi | is it in the corner? |\n| ishinhna | in my bed |\n| marka | the town |\n| markp”t”a | from his town |\n| markstxi | is it our1+2 town? |\n| ishma | your bed |\n| utamt”a | from your house |\n| utnha | my house |\n| utnhap”sa | my house too |\n| yaputxi | is it the field? |\n| yapsanpsa | in our1+2 field too |\n| qaqat”a | from the cliff |\n\n---\n\n### Step 1: Identify morphological patterns\n\nLook for recurring morphemes:\n\n- **\"our1+2\"** appears in:\n - qucxst”psa → from our1+2 lake too\n - markstxi → is it our1+2 town?\n - yapsanpsa → in our1+2 field too\n\nSo \"our1+2\" is a group referring to \"our (first and second person singular/plural)\".\n\nNote: \"1+2\" likely means \"first and second person\" — not just \"we\", but possibly \"you and I\".\n\nThus, \"our1+2\" = \"we two\" or \"you and I\".\n\n---\n\nAffixes:\n\n- Postposition \"too\" appears in:\n - aq”ipsa = the cave too\n - qucxst”psa = from our1+2 lake too\n - yapsanpsa = in our1+2 field too\n\n\"too\" seems to be a suffix or postposition marking \"additional inclusion\", like \"also\".\n\nBut in:\n- aq”ipsa = the cave too → not in the cave, but the cave too?\nBut compare:\n- aq”na = in the cave → \"in\"\n- aq”ipsa = the cave too → presence of \"too\"\n\nNote: \"too\" may be a suffix (like -ta, -sa) attached to noun.\n\nLooking at:\n- aq”ipsa → \"the cave too\"\n- aq”na → \"in the cave\"\n- aq”ipsa has suffix -ipsa, aq”na has -na\n\nSimilarly:\n- utnha = my house\n- utnhap”sa = my house too → has -p”sa\n\nSimilarly:\n- yaputxi = is it the field?\n- yapsanpsa = in our1+2 field too → has -anpsa\n\nSo we see:\n- \"too\" appears as a suffix (likely -psa or -sa) added to the noun.\n- \"in\" appears as a preposition (e.g., aq”na, ishinhna, yapsanpsa)\n\nNow, let’s consider question form:\n- chushuntxi → is it in the corner?\n- ishinhna → in my bed → not a question\n- yaputxi → is it the field?\n\nSo \"is it X?\" → is it X? → intermediate form: \"is it\" + noun?\n\nCompare:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nSo pattern: **is it [X]?**\n\nAnd what is X? It is:\n- in the corner → chushuntxi\n- our1+2 town → markstxi\n- the field → yaputxi\n\nSo the structure is: **is it [place]?**\n\nBut in some cases, it is **in [place]** — like aq”na = in the cave\n\nSo when the word is used as \"in\", it has a prepositional structure.\n\nNow, the key morphemes:\n\n1. **\"in\"** is attached as a prefix or in a structure?\n - aq”na = in the cave → \"in the cave\"\n - ishinhna = in my bed\n - yapsanpsa = in our1+2 field too\n\nSo \"in\" appears with the place, in some cases with \"our1+2\"\n\n2. \"too\" appears as a suffix (in -ipsa, -p”sa, -anpsa)\n\n3. The root place names:\n - cave → aq”\n - corner → chushp”\n - bed → ishi-, ishinhna → ishina? morpheme?\n - town → marka\n - field → yapu?\n\nLooking at:\n- aq”ipsa → the cave too → meaning the cave (also)\n- aq”na → in the cave\n\n→ \"in\" + noun\n\n- chushp”a → his corner\n- chushuntxi → is it in the corner?\n\n→ \"corner\" seems to be the base\n\n- marka → town\n- markp”t”a → from his town → from + his + town\n- markstxi → is it our1+2 town? → is it + our1+2 + town\n\nSo again, \"is it X?\" with X being a place.\n\nNow, look at the compound:\n\n- yaputxi = is it the field?\n- yapsanpsa = in our1+2 field too\n\n→ \"field\" base = yapu?\n\nSo yapu → field\n\nThus: yaputxi = is it the field?\nyapsanpsa = in our1+2 field too\n\nNow, kita analyze the three target forms:\n\n---\n\n**1. utnhantxi**\n\nBreak it down:\n- utnha → my house\n- utnhantxi → likely \"is it in my house?\"\n\nCompare to:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nSo pattern: **is it in [location]?**\n\nHere, the location is \"my house\" = utnha\n\nSo \"is it in my house?\" → utnhantxi\n\n→ The affix \"-txi\" appears in:\n- chushuntxi, markstxi, yaputxi\n\nBut:\n- chushuntxi = is it in the corner?\n- markstxi = is it our1+2 town?\n- yaputxi = is it the field?\n\nSo the \"-txi\" is the question form: **is it in X?**\n\nBut in the base:\n- chushuntxi → target is \"corner\" → base \"chushp”a\"\n- utnhantxi → target is \"house\" → base \"utnha\"\n\nSo the pattern is:\n- **is it in [Noun]?** → Noun + -txi\n\nYes — in all examples:\n- chushuntxi → corner → is it in the corner?\n- markstxi → town → is it our1+2 town?\n- yaputxi → field → is it the field?\n\nSo for utnhantxi → \"is it in my house?\"\n\nYes.\n\n**Answer 1: is it in my house?**\n\n---\n\n**2. yapp”psa**\n\nWe see:\n- yapsanpsa = in our1+2 field too → base \"yapu\" + \"an\" + \"psa\"\n- yaputxi = is it the field?\n\nyapp”psa → what matches?\n\nLook at:\n- aq”na → in the cave\n- aq”ipsa → the cave too\n\nDoes \"p”psa\" appear?\n\nWe have:\n- utnhap”sa = my house too → my house + too\n\nSo \"-p”sa\" appears as a suffix marking \"too\"\n\nSimilarly:\n- aq”ipsa = the cave too → cave + too\n- aq”na = in the cave → cave + in\n\nNow, aq”ipsa → the cave too → the noun + too\n\nSo \"too\" is marked by suffix -psa\n\nThus, yapp”psa → likely the field too?\n\nBut field base is \"yapu\"\n\nSo yapu + psa = yapp”psa → the field too?\n\nIs that consistent?\n\nCheck:\n- aq”ipsa = the cave too → cave + too\n- utnhap”sa = my house too → house + too\n- qucxst”psa = from our1+2 lake too → lake + too\n- yapsanpsa = in our1+2 field too → field + in + our1+2\n\nSo \"too\" = suffix -psa\n\nTherefore, yapp”psa = the field too\n\nBut is \"the field\" the base?\n\nYes — yapu → field\n\nThus, yapu + psa → yapp”psa → the field too\n\nSo translation: the field too\n\n**Answer 2: the field too**\n\n---\n\n**3. yapup”psa**\n\nAgain, base is \"yapu\" → field\n\nWe have:\n- yaputxi = is it the field?\n- yapp”psa = the field too → yapu + psa\n\nWhat about yapup”psa?\n\nIs there a parallel?\n\nWe have:\n- chapu? → not in list\n- chushp”a → his corner → chush + corner\n\nBut yapup”psa → appears to be \"yapu\" + up”psa?\n\nNote: \"p”psa\" is \"too\" suffix, as above\n\nBut yapup”psa — possibly a compound?\n\nCompare to:\n- p”ak”u → the pot\n- p”ak”unhpsa → my pot too → pot + my + too?\n\nSo \"my pot too\" — morphologically: pot + my + too\n\nSimilarly:\n- utnha → my house\n- utnhap”sa → my house too\n\nSo here: yapup”psa — field + my?\n\nNo — \"my\" is not present.\n\nBut is there a base that combines \"my\" + \"field\"?\n\nCompare:\n- ishinhna → in my bed\n- ishma → your bed\n\nNo \"my field\"\n\nBut what about in the list?\n\nIs there a structure like \"in my field\"?\n\nWe have:\n- yapsanpsa → in our1+2 field too\n\nBut no \"my field\"\n\nIs there a form like: \"in my field\" or \"is it in my field\"?\n\nWe must infer.\n\nWait: is there a word like \"yapu\" with \"my\"?\n\nNo such base.\n\nAlternatives:\n\nCould \"yapup”psa\" be a variant of \"the field too\" with a different morpheme?\n\nBut \"yapp”psa\" is already \"the field too\"\n\nWhat about \"yapup”psa\" — the \"p”\" might be a different affix?\n\nCompare with:\n- aq”ipsa → cave too → aq” + ipsa\n- aq”na → in the cave → aq” + na\n\nSo \"na\" = in, \"ipsa\" = too?\n\nNow, \"yapp”psa\" → yapu + p”psa?\n\nBut \"p”psa\" is the \"too\" suffix.\n\nSimilarly, \"yapup”psa\" → yapu + up”psa?\n\nThat seems like a different suffix.\n\nIs there a parallel in \"in the field\"?\n\nWe have: yapsanpsa → in our1+2 field too\n\nCould \"up”\" be a variant of \"in\"?\n\nBut no.\n\nWait: in the list:\n- chushuntxi → is it in the corner?\n\nSo \"in\" is a preposition.\n\nBut all \"in\" forms appear to be with a specific word.\n\nIs there a \"my field\" form?\n\nWe have no such word.\n\nBut perhaps \"yapup”psa\" is \"in my field\"?\n\nBut the base is not \"in\" — \"in\" is a separate affix.\n\nIs there a structure where \"in\" is attached?\n\nExample: yapsanpsa = in our1+2 field → \"in\" + our1+2 + field\n\nSo structure: in [group] [field]\n\nBut no \"in my field\"\n\nAlternatively, could \"yapup”psa\" be \"in the field\"?\n\nBut that would be like \"yaputxi\" → is it the field?\n\nNo.\n\nWait — what about \"in the field\"?\n\nWe don’t have a word for \"in the field\".\n\nWe have:\n- yapsanpsa = in our1+2 field too → in + our1+2 + field\n\nSo the only \"in\" form is with \"our1+2\"\n\nNow, is there a \"my\" form?\n\nWe have:\n- ishinhna = in my bed → in + my + bed\n\nSo pattern: \"in\" + my + noun\n\nSo inferring: \"in my field\" = in + my + field\n\nBut the word \"my\" in Jaqaru?\n\nWe have:\n- utnha = my house\n- ishinhna = in my bed → \"my\" is attached to \"bed\"\n\nBut no standalone \"my\"\n\nIn \"ishinhna\", \"my\" is part of \"bed\"\n\nSimilarly, we see:\n- ishinhna = in my bed → in + my + bed\n\nSo possible: in my field → in + my + field\n\nBut how is \"my\" encoded?\n\nIn \"ishinhna\" → ishinhna → base: ishi (my) + nha (bed)\n\nSimilarly, utnha = my house → utn + ha\n\nSo \"my\" is embedded in the noun.\n\nThus, \"in my field\" = in + field → but no word.\n\nWe have a word where \"in\" appears: yapsanpsa = in our1+2 field → so \"in\" is a prefix.\n\nBut no \"in my field\" form.\n\nBack to yapup”psa.\n\nWe must find a parallel.\n\nWhat is the morphological structure?\n\nCompare with:\n- aq”na → in the cave\n- utnhap”sa → my house too\n\nNow, possible: \"my field\" → has \"my\" and \"field\"\n\nBut is \"my\" in the base?\n\nWe don’t have a word like \"my field\"\n\nBut we have:\n- yapu → field\n- yaputxi → is it the field?\n\nWhat about \"in my field\"? That would be like \"in + my + field\"\n\nBut we don’t have that structure.\n\nWait — note that the prefix \"in\" might be marked in a different way.\n\nBut in all cases with \"in\", it is \"in\" + noun or \"in\" + group + noun.\n\nNow, look at yapup”psa\n\nCould \"up”\" be a suffix?\n\nCompare: in the examples:\n- aq”ipsa → the cave too → aq” + ipsa → base + too\n- aq”na → in the cave → aq” + na → base + in\n- qucxst”psa → from our1+2 lake too → qucx + st”psa → \"from\" + \"our1+2\" + \"lake\" + too\n\nNow, is \"in\" or \"too\" a suffix?\n\n\"na\" → in\n\"ipsa\" → too\n\nSo \"ipsa\" and \"na\" are suffixes meaning \"too\" and \"in\"?\n\nBut \"ipsa\" appears only with \"the cave too\", and it's attached directly.\n\nAnother possibility: \"p”\" is a suffix for \"my\"?\n\nWe have:\n- utnha → my house → utn + ha\n- so \"utn\" = my, \"ha\" = house?\n\nBut in utnhap”sa → my house too → utn + h + p”sa → \"my house too\"\n\nSo \"p”sa\" = too\n\nSimilarly, if we have \"yapu\" + my → \"yapu\" + utn? → not matching.\n\nBut what about \"yapup”psa\"?\n\nPossibility: \"field\" + \"my\" → but no such form.\n\nAlternatively, morphologically: yapu + up”psa\n\nIs \"up”psa\" a known suffix?\n\nWe have:\n- \"ipsa\" → too\n- \"p”sa\" → too (as in utnhap”sa)\n- \"anpsa\" → in + our1+2 + field too\n\n\"anpsa\" → in + our1+2 + field → so \"an\" = in?\n\nYes — yapsanpsa → in + our1+2 + field\n\nSo \"an\" = in (preposition)\n\nSo \"an\" = in\n\nThen, what suffix?\n\nIn the too forms:\n- aq”ipsa → cave + too → \"ipsa\"\n- utnhap”sa → house + too → \"p”sa\"\n- qucxst”psa → lake + too → \"st”psa\"\n\nSo the \"too\" suffix is -psa, and the base is the noun.\n\nTherefore, \"yapup”psa\" → likely field + too → yapu + p”psa\n\nBut that would be \"yapp”psa\"\n\nWe already have yapp”psa as the field too.\n\nSo why two forms?\n\nWait — the word is \"yapup”psa\"\n\nIt has \"up”\" — not \"p”\"\n\nIs it a typo? Or different?\n\nNo — must be exact.\n\nCompare actual words:\n\n- yapp”psa → possible spelling\n- yapup”psa → different\n\nCould \"up”\" be a different morpheme?\n\nIs there a word with \"up\"?\n\nWe have no such word.\n\nBut is there a word like \"in the field\"?\n\nWe have yapsanpsa → in our1+2 field too → so \"in\" is attached.\n\nSo \"in the field\" → would require \"an\" or \"in\"\n\nBut no standalone \"in the field\"\n\nPerhaps \"yapup”psa\" is a marker of \"in my field\"?\n\nBut there's no \"my field\" form.\n\nAlternative: could \"up”\" be for \"my\"?\n\nBut \"my\" is not attached to field.\n\nWait — from the bed example:\n\n- ishinhna → in my bed → \"my\" in \"bed\"\n\nSimilarly, is there a form like \"in my field\"?\n\nWe don’t have that.\n\nBut is there a \"my field\" base?\n\nNo.\n\nHypothesis: The structure is:\n\n- \"in [group] [noun]\" → for group like our1+2\n- \"in + my + noun\" → for personal possession\n\nBut in the", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11714.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given a set of Dyirbal sentences in (a), and we are to translate three new ones in (b) into English. Our task is to infer the linguistic pattern from the examples and apply it to (17), (18), and (19).\n\nStep-by-step pattern analysis:\n\nKey observations from the examples:\n\n1. The basic structure of a sentence is: \n [Subject] [verb] [object] [modifier] \n The verb often modifies or affects the object. \n The structure appears to follow: \n [A] [B] [C] [D] \n where A = subject, B = verb, C = object, D = descriptive or modal adjectives.\n\n2. Morphemes often encode:\n - Subject: balan (strong man), bala (tired), bayi (booze), baNgun (making), etc.\n - Object: yaóaNgu (mother), garandu (smoke), waymin (sugar), etc.\n - Modifications: suffixes or infixes indicate state, action, or relation.\n\n3. Use of affixes:\n - The suffix -NaymuNa, -Nunéañu, -NaymuNagu appears in descriptive phrases (e.g. “that is always being blamed”).\n - These are likely markers of habitual or iterative actions, often with the meaning “that is always doing X”.\n - Example 2: “bimanéalNaymuNa” → “the man that is always blaming”\n - Example 1: “NunéaymuNa” → “that is always being blamed”\n\n4. The verb “baNgul” appears frequently as a transitive verb meaning “to make” or “to cause”.\n - Example 1: “baNgul yaóa” → “is making” \n - Example 3: “baNgul” → “is making the healthy mother-in-law fat” \n → So “baNgul” + noun = “is making [object]”\n\n But in some cases, “baNgul” is not followed by a noun but rather by a descriptive complement (e.g., “is carrying”, “is searching”).\n\n5. Other verbs:\n - “garan” = following\n - “yabu” = blaming\n - “waymin” = sugar\n - “gurugugu” = booze (but also appears in “gurugugu biNgunman” → making tired → used as a noun)\n - “bimabanéal” → strong man\n - “ñalNga” → quiet boy\n - “diban” → fat\n - “bilmbal” → pushing or moving\n\n6. Morphemes denoting state:\n - “biNgunman” → “tired”\n - “éamiman” → “healthy”\n - “guli” → “following”\n - “bimaban” → “strong”\n - “yabu” → “blaming”\n - “diban” → “fat”\n - “bargin” → possibly similar to “bargan” → “looking at”\n - “gubimbulu” → “tired” or “offended”?\n - Example 8: “gurugugu éagunman” → “making the tired doctor” → “éagunman” = tired\n - Example 16: “Numa guli baNgul yaóaNgu banéalmuNagu munduman” → “the man that is always followed is offending the strong father” → “mun-da” appears with “munduman” → “being followed”\n\n7. Adjective phrases: Often post-nominal and appear with -aymuNa, -aymuNagu, etc.\n - Example 2: “bimanéalNaymuNa” → “the man that is always blaming”\n - Example 16: “Numa guli baNgul yaóaNgu banéalmuNagu munduman” → “the man that is always being followed” → “banéalmuNagu munduman” → “being followed”\n\nSo we identify that:\n- The particle -NaymuNa or -NaymuNagu expresses “that is always doing X”\n- The suffix -baNgul means “is causing to become X”\n- The root noun precedes the verb and the descriptor\n\nNow, analyze each requested sentence:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak down:\n- balan → strong man (subject)\n- ñalNga → quiet boy? But “ñalNga” appears in example 15: “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” → “quiet boy is looking at tired lizard”\n → So “ñalNga” likely means “quiet boy” → subject of action?\n- But here: “balan” is subject → strong man\n- baNgul → is making\n- NumaNgu → “the man” (Numa = man)\n- guniymuNagu → “that is always being pursued” or “that is always following”?\n - Example 2: “guli” → following\n - “guli” appears in “guliNgu” → following\n - “guli” + -NaymuNagu → that is always following\n - So “guniymuNagu” → likely a variant form of “guli” → following, with -NaymuNagu → always following\n - Possibly “guni-” = following → “guniymuNagu” = \"that is always being followed\"\n - In example 16: “Numa guli baNgul yaóaNgu banéalmuNagu munduman” → man that is always being followed\n - So “banéalmuNagu” = being followed\n - Similarly, here “guniymuNagu” = being followed (by the strong man?)\n- bambunman → fat\n\nSo: “The strong man is making the man that is always being followed fat.”\n\nBut wait — is it making the man fat? Or the man being followed fat?\n\nThe object is “NumaNgu” + “guniymuNagu” → “the man that is always being followed”\n\nSo: The strong man is making the man that is always being followed fat.\n\n18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n\nBreak down:\n- bala → tired (subject)\n- diban → fat → so “tired fat”?\n- bilmbalmuNa → “that is always pushing”\n - Example 12: “bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban” → “fat doctor is pushing big stone”\n - “bilmban” → pushing\n - So “bilmbalmuNa” → “that is always pushing”\n- baNgun → is making\n- biñéiriñéu → “the lizard”? → from example 9: “bala garan baNgul biñéiriñéu banéan” → lizard is following smoke\n → “biñéiriñéu” = lizard\n- guniñu → “the little feather” → from example 4: “wura” = searching; “guliNgu” = little feather\n\nSo: “The tired fat man (is making) that is always pushing the lizard to look at the little feather”?\n\nBut grammar: likely the structure is: [Subject] is making [object] [modifier]\n\nBut subject = “bala diban” → “tired fat man” — this is a compound subject?\n\nBut “bala diban” → both adjectives of the same subject.\n\nThen “bilmbalmuNa” → “that is always pushing” → object?\n\nThen “baNgun” → “is making”\n\nThen “biñéiriñéu” → “lizard”\n\nThen “guniñu” → “the little feather”\n\nBut it’s: “bala diban bilmbalmuNa baNgun biñéiriñéu guniñu”\n\nStructure: S + A + O + V + O\n\nPossibility: the tired fat man (is making) [that is always pushing] [the lizard] [to look at the little feather]? But “guli” → following, “guni” → little feather\n\nBut “biñéiriñéu” = lizard\n\nSo “making (that is always pushing) the lizard look at the little feather”?\n\nBut that seems odd.\n\nWait — perhaps “bilmbalmuNa” modifies “biñéiriñéu” → “the lizard that is always pushing”?\n\nBut in example 12: “diban éagiñ baNgul gubimbulugu éamiNgu bilmban” → “fat doctor is pushing big stone” → “bilmban” = pushing → direct verb\n\n“bilmba” → to push? So “bilmbalmuNa” → “that is always pushing” → a noun phrase meaning “the one that is always pushing”\n\nSo object of “baNgun” (is making) = “that is always pushing the lizard”?\n\nBut then “biñéiriñéu” and “guniñu” are separate?\n\nAlternatively, perhaps structure is:\n[Subject] is making [object] [do] [X]\n\nBut no such structure.\n\nMore likely: “The tired fat man is making the lizard that is always pushing look at the little feather?”\n\nBut “bilmbalmuNa” describes the lizard → so “the lizard that is always pushing”\n\nThen “biñéiriñéu” = the lizard → so “the lizard that is always pushing”\n\n→ object is “the lizard that is always pushing”\n\nThen “guniñu” = the little feather → what is being looked at?\n\nBut the verb “baNgun” is not followed by a verb — no infinitive.\n\nAnother idea: “baNgun” means “is causing to” or “is making” → makes the object into a state.\n\nBut “biñéiriñéu” = lizard → so perhaps “making the lizard to look at the little feather”? → but no such verb.\n\nIn example 9: “bala garan baNgul biñéiriñéu banéan” → lizard is following smoke → so “garan” = following\n\nSo here, “biñéiriñéu” = lizard → is being followed by?\n\nNo — here we have “bilmbalmuNa baNgun biñéiriñéu” → perhaps “bilmbalmuNa” is a modifier of the lizard → the lizard that is always pushing?\n\nBut “pushing” is an action — not a state.\n\nAlternatively, “bilmbalmuNa” = “the one who is always pushing” → so object is that entity → “making that one (who is always pushing)” → what?\n\nThen “guniñu” → the little feather → perhaps the action is “to look at”?\n\nBut verb not provided.\n\nWait — in example 9: “bala garan baNgul biñéiriñéu banéan” → lizard is following smoke.\n\nSo “garan” = following\n\nIn example 12: “diban éagiñ baNgul gubimbulugu” → “fat doctor is pushing” → so “éagiñ” = pushing\n\nSo “bilmban” = pushing\n\nSo “bilmbalmuNa” = that is always pushing → likely a nominalized form of “pushing”\n\nSo the verb here is “baNgun” — causing.\n\nWhat is causing? The lizard that is always pushing?\n\nThe object of “baNgun” is “the lizard that is always pushing”?\n\nThen “guniñu” is the target of the action?\n\nBut no verb.\n\nAlternative: Perhaps “baNgun” is not making an object, but the verb is implied.\n\nBut in example 4: “bala yila wura baNgul” → “tired wallaby is searching for little feather” — here “wura” = searching for → “baNgul” is followed by object → “searching for” → so “wura baNgul” → searching for the feather.\n\nBut here, no such “searching for”.\n\nAnother possibility: misreading the structure.\n\nSentence: “bala diban bilmbalmuNa baNgun biñéiriñéu guniñu”\n\nStructure:\n- bala diban → subject (tired fat man)\n- bilmbalmuNa → (that is always pushing)\n- baNgun → is making\n- biñéiriñéu → lizard\n- guniñu → little feather\n\nBest fit: “The tired fat man is making the lizard that is always pushing look at the little feather.”\n\nBut “look at” not present.\n\nAlternatively: the man is causing the lizard to push (something)? But what?\n\n“guniñu” is the object → perhaps the lizard is pushing the feather?\n\nBut “bilmbalmuNa” = that is always pushing — so the lizard is pushing the feather?\n\nBut then “baNgun” is not used for pushing — that’s already described.\n\nPerhaps “baNgun” is a attribute — not a verb?\n\nBut it’s attached to “biñéiriñéu” — “making the lizard look at”?\n\nBut no verb of looking.\n\nWait — in example 15: “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” → “quiet boy is looking at the tired lizard”\n\n→ “biñéiriñ” = looking at\n\nSo “biñéiriñ” = looking at\n\nSo in (18): “biñéiriñéu” = lizard → the one being looked at?\n\nIn (15): “biñéiriñ” is verb of looking at\n\nIn (18): “biñéiriñéu” — likely masculine form of “lizard”\n\nSo perhaps “biñéiriñéu” = the lizard → object of a verb meaning “to look at”\n\nBut where is the verb?\n\nPerhaps the structure is: [Subject] [modifier] [verb] [object]\n\nBut here, “baNgun” is between modifier and object.\n\nActually, from pattern, “baNgun” = “is making” → so verb of causation.\n\nThe only plausible meaning is:\n\n“The tired fat man is making the lizard that is always pushing look at the little feather.”\n\nThis is grammatical and matches morphological patterns.\n\nBut is “look at” implied?\n\nIn example 15: “biñéiriñ biNgun baNgul” → “looking at the tired lizard” — verb “biñéiriñ” → looking at\n\nSo perhaps here “biñéiriñ” is missing — no “biñéiriñ”\n\nBut in the sentence: “biñéiriñéu” — so maybe this is a noun form?\n\nBut in example 9: “biñéiriñéu banéan” → lizard is following → so “biñéiriñéu” is the subject — a noun\n\nSo likely here, “biñéiriñéu” is the noun “lizard”, and “bilmbalmuNa” modifies it → “the lizard that is always pushing”\n\nSo object is “the lizard that is always pushing”\n\nVerb: “baNgun” = “is making”\n\nThen “guniñu” = the little feather → what is being made?\n\nBut not clear.\n\nAlternatively, “baNgun” + object = “is causing to become” — thus “making the lizard that is always pushing become [something]” — but what?\n\nNo adjective after.\n\nNo feature like “fat” or “tired” after.\n\nThus, perhaps “guniñu” is the object of a verb, but no verb.\n\nTherefore, more likely: the sentence uses “biñéiriñ” as verb, but it is missing.\n\nWait — the verb “biñéiriñ” appears in example 15 → verb of “looking at”\n\nBut here, “biñéiriñéu” appears as noun.\n\nIn example 9: “garan” = following → so verb\n\n“biñéiriñ” = looking at\n\nSo “biñéiriñéu” is likely a noun form of “lizard”\n\nSo it cannot be the verb.\n\nThus, only plausible translation is:\n\n“The tired fat man is making the lizard that is always pushing look at the little feather.”\n\nBut “look at” is not in the original.\n\nWait — perhaps the verb is “biñéiriñ” minus the “ñ” — but here it’s “biñéiriñéu”\n\nNo.\n\nAlternative: in example 13: “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” → “mother-in-law that is always pushing stones is looking at the smoke”\n\nSo “garan baNgun” → “is looking at” → so “garan” is the verb, “baNgun” is not used directly.\n\nIn that case, “garan” = looking at\n\nIn sentence 18: “biñéiriñéu” = lizard → is this the verb?\n\nNo, because in example 9: “biñéiriñéu” = lizard, not verb.\n\nSo only verb for “look at” is “biñéiriñ”\n\nSo cannot have “look at” here.\n\nPossibility: typo or morphological shift?\n\nAlternatively, “baNgun” may be the verb — meaning “to cause to be” — and “biñéiriñéu” is the object — “making the lizard into something” — but “guniñu” is the object.\n\nBut “guniñu” is the feather — which is not a state.\n\nConclusion: The best grammatical fit is:\n\n“The tired fat man is making the lizard that is always pushing look at the little feather.”\n\nEven if “look at” is not explicitly stated, it is implied by the structure and parallelism.\n\nAlternatively, perhaps it's \"the tired fat man is making the lizard that is always pushing (to look at the feather)\" — but again, no verb.\n\nGiven pattern, likely non-literal.\n\nBut check if “bilmbalmuNa” modifies the lizard → so “the lizard that is always pushing” → and “baNgun” → “is making” → and “biñéiriñéu” → the one being made to look at?\n\nBut no.\n\nAnother idea: perhaps “biñéiriñéu” is the verb form of “look at” — but that is not supported.\n\nIn example 15: “bayi biñ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13066.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "Step-by-step analysis:\n\nFirst, identify recurring structures and morphemes across the examples.\n\nKey morphemes:\n- \"balan\" = strong/active subject (often describes a person or animal)\n- \"bayi\" = substance/entity (like \"booze\", \"smoke\", \"sugar\")\n- \"baNgul\" = makes/afflicts (causative or affecting structure)\n- \"biNgunman\" = tired\n- \"bimabanéalNaymuNa\" = always being blamed\n- \"yabu\" = strong\n- \"guru/gurugugu\" = booze\n- \"éuga\" = sugar\n- \"garan\" = follow\n- \"diban\" = fat\n- \"waymin\" = healthy\n- \"wura\" = search\n- \"guli\" = death adder\n- \"Nunéañu\" = always following\n- \"banéan\" = possum\n- \"yaóaNgu\" = death adder\n- \"dimbañu\" = being ignored\n- \"bimaban\" = always being blamed\n- \"biñéiriñ\" = looking\n- \"ñalNga\" = quiet (from example 15)\n- \"Numa\" = always being followed\n- \"bambunman\" = fat\n- \"gubiN\" = like \"gubimbulu\" — offended\n- \"bargin\" = produce something? Or act of following?\n\nNow inspect the target sentences:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman. \n- \"balan\" = strong subject \n- \"ñalNga\" = quiet \n- \"baNgul\" = makes \n- \"NumaNgu\" = always being followed \n- \"guniymuNagu\" = ?? possibly a form of \"guniñu\" (searching) with suffix? \n- \"bambunman\" = fat \n\nFrom example 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" → dragonfly is searching for stinging tree. \n\"duNan\" = dragonfly, \"yiriñéilagu\" = stinging tree, \"guniñu\" = searching.\n\nSo \"guniymu\" may be a variant or inflection of \"guniñu\" — seeking. \n\"guniymuNagu\" could be a possessive or relational form, likely meaning \"the one that is searching\" or \"the one who searches\".\n\n\"NumaNgu\" = always being followed (from example 16) \n\"bambunman\" = fat \n\nSo: The strong quiet one is making the one that is always being followed (a person) search for the fat thing. \n\nWait — “baNgul” = makes, so “X is making Y do Z”. \n\nSo: The quiet strong one is making the one always being followed search for the fat thing. \n\nBut \"guniymuNagu\" is likely \"searching for\" something. \n\n\"bambunman\" = fat — so what is being searched for? \n\nBut it's \"guniymuNagu bambunman\" — modifying the object? \n\nCould it be: the one that is always being followed is searching for the fat thing? \n\nBut structure: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" → so the subject (balan ñalNga) makes (baNgul) the one always being followed (NumaNgu) do (guniymuNagu) to (bambunman)? \n\nNo — in example 10: \"balan duNan baNgul yiriñéilagu guniñu\" → the dragonfly is searching for the stinging tree. \n\nSo “X is searching for Y” = “X baNgul Y guniñu” — but in that case, the object is \"yiriñéilagu\", and \"guniñu\" is the verb. \n\nBut here: “guniymuNagu” — likely \"gunitu\" → searching for. \n\nPerhaps “guniymuNagu” = “searching for” and the object “bambunman” is the thing being searched for? \n\nSo: The quiet strong one is making the one that is always being followed (searching for) the fat one. \n\nBut “bambunman” is a property — fat. So “the fat one” is the object. \n\nBut who is fat? Or what is fat? \n\nPossibly, “bambunman” is a noun — the fat thing. \n\nBut in example 3: “sugar is making the healthy mother-in-law fat” → \"éugaNgu baNgun waymin baNgu éamiman\" → sugar makes healthy mother-in-law fat. \n\nSo “fat” is a resulting state. \n\nBut in 17, “guniymuNagu bambunman” — if “guniymuNagu” = searching for, then “searching for fat” — what is being searched? \n\nBut “bambunman” is not modified — it may be the object. \n\nBut the structure is: subject → baNgul → object → verb → object? \n\nIn 10: “balan duNan baNgul yiriñéilagu guniñu” → subject is searching for object. But “baNgul” is the causative — not the verb of action. \n\nWait — this may be a misunderstanding.\n\nIn ex. 1: “bayi yaóa ... baNgu gurugugu biNgunman” → booze is making the man tired. \nSo “baNgu” = is making (causative)\n\nLikewise: “balan yabu ... baNgul yaóaNgu” → the strong man is blaming the mother.\n\nSo the causative verb is “baNgul” — the subject is making the object (or causing it to have a property).\n\nIn ex. 4: “bala yila wura baNgul bargandu biNgundu guniñu” \n“bala yila wura” = the tired wallaby \n“baNgul” = is making \n“bargandu” = the little feather \n“biNgundu” = fat? No — “biNgundu” = articulated? Unlikely.\n\nWait — “wura” = searching. In ex.4: “wura” is the verb, not used with “baNgul”.\n\nSo “wura” is the verb — \"is searching\".\n\nBut in ex.5: “balan malayigara baNgu garandu biNgunman” \n\"malayigara\" = smoke \n\"baNgu\" = is making \n\"garandu\" = scorpion \n\"biNgunman\" = tired → smoke is making scorpion tired.\n\nSo pattern: \n[Subject] [causative verb] [object] [resulting state]\n\nIn ex. 1: bayi yaóa → booze is making the man (baNgu) → tired (biNgunman)\n\nSo [X] is making [Y] [to be] [Z]\n\nThus, \"baNgul\" = causative, meaning \"is making\" or \"causes to be\".\n\nSo in sentence 17: \n\"balan ñalNga\" = the quiet strong one \n\"baNgul\" = is making \n\"NumaNgu\" = the one that is always being followed \n\"guniymuNagu\" = ??? — can’t be the resulting state \nBut \"bambunman\" = fat\n\nSo where does \"guniymuNagu\" go?\n\nIn example 10: \"balan duNan baNgul yiriñéilagu guniñu\" \nduNan (dragonfly) is making yiriñéilagu (stinging tree) searching (guniñu) — but that doesn’t make sense.\n\nAlternatively, is “guniymuNagu” a noun? Possibly a different morpheme.\n\nWait — in ex. 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n\"balan baNgay\" = the big grasshopper \n\"waóu\" = is searching \n\"baNgun\" = is making \n\"bundiñéu\" = bent spear \n\"éagiñéu\" = fat? \n\"guniñu\" = stinging tree? — no.\n\nThis is inconsistent.\n\nWait — \"guniñu\" appears multiple times as a verb meaning \"to search\".\n\nSo likely: \"guniymuNagu\" is a variant of \"guniñu\" with different affixes.\n\n\"guniymu\" → \"guniÑu\" → is searching (likely “guniñu”)\n\n“guniymuNagu” → “guniñu” + possessive? Or object?\n\nIn 10: \"yiriñéilagu guniñu\" — stinging tree is being searched → so the object is \"yiriñéilagu\", the verb is \"guniñu\".\n\nBut in that sentence, \"baNgul\" is not present.\n\nIn 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" — the tired wallaby is searching for the little feather. \nHere, \"wura\" is the verb of action — \"is searching\", and \"guniñu\" is the object? — no.\n\n\"biNgundu\" = fat → so \"guniñu\" is not object.\n\nWait — typo? Or in ex.4: “wura” = searching, “guniñu” = little feather? No.\n\nNo — in ex.4: “wura baNgul bargandu biNgundu guniñu” — “wura” is the verb, but it's not with “baNgul”.\n\nActually in ex.4: \"bala yila wura baNgul bargandu biNgundu guniñu\" — likely the structure is: “bala yila” = the tired wallaby, “wura” = is searching, “baNgul” = is making, “bargandu” = little feather, “biNgundu” = fat, “guniñu” = ???\n\nThis seems inconsistent.\n\nWait — actually, in ex.4: “bala yila wura baNgul bargandu biNgundu guniñu” \n→ the tired wallaby is searching for the little feather. \nSo “wura” = is searching \n“baNgul” = is making? — no.\n\nThat can’t be.\n\nSimilarly, ex.10: “balan duNan baNgul yiriñéilagu guniñu” → dragonfly is searching for stinging tree → “guniñu” = searching.\n\nThus, “guniñu” is the verb “to search”.\n\nSo “baNgul” is not used with “guniñu” — it’s a separate causative.\n\nThus, in ex.4: the wallaby is searching for the feather — so “wura” is the verb, and “bargandu” is object.\n\nIn ex.4, “baNgul” is not with “wura” — it’s with “bargandu” → “baNgul bargandu” = is making the feather? But it says \"searching for\".\n\nWait — the sentence says: \"the tired wallaby is searching for the little feather\" — so “wura” is search, “bargandu” is object.\n\nBut “baNgul” appears in between — likely typo or misalignment.\n\nLooking back: \n\"4. bala yila wura baNgul bargandu biNgundu guniñu.\"\n\nIf “wura” is the verb, \"baNgul\" is a separate action.\n\nBut “baNgul” is applied to “bargandu” → makes the feather (fat)? “biNgundu” = fat.\n\nAnd “guniñu” is separate — maybe “guniñu” is for the person?\n\nNo — in the translation: \"the tired wallaby is searching for the little feather\" — so no fatness.\n\nSo possibly, “guniñu” is incorrectly placed — or it's a synonym.\n\nAlternatively, in ex. 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n\"waóu\" = is searching \n\"baNgun\" = is making \n\"bundiñéu\" = bent spear \n\"éagiñéu\" = fat \n\"guniñu\" = stinging tree?\n\nNo — that doesn’t fit.\n\nOnly consistent pattern is: \n- \"baNgul\" = causative: \"is making\" \n- \"guniñu\" = search \n- \"baNgun\" = causative of something else?\n\nNo — in ex. 11: \"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" \n\"éuga\" = sugar \n\"baNgun\" = is making \n\"yabuNgu\" = strong father \n\"NaéilmuNagu\" = being ignored \n\"dimbañu\" = being ignored? Or “dimbañu” = is carrying?\n\nNo — translation: “the mother that is always being ignored is carrying the sugar”.\n\nSo “baNgun” = is making — but in this case, \"is carrying\"?\n\nIn ex. 12: “bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban” \n“diban” = fat \n“éagiñ” = doctor \n“baNgul” = is making \n“gubimbulugu” = offended \n“éamiNgu” = big stone \n“bilmban” = pushing?\n\n“bala diban” = the fat doctor \n“éagiñ” = is pushing? \n\"baNgul\" = is making → makes the doctor push the stone?\n\nBut translation: “the fat doctor is pushing the big stone” — so the verb is \"pushing\", not \"is making\".\n\nThus, “baNgul” is not used as a transitive verb in all cases.\n\nWait — in ex. 1: “bayi yaóa NunéaymuNa baNgu gurugugu biNgunman” \n“baNgu” — not “baNgul” \n“baNgu” = is making? \n“gurugugu” = booze \n“biNgunman” = tired\n\nSo “baNgu” is causative: booze is making the man tired.\n\nSimilarly, in ex. 2: “balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu” \n“balan yabu” = strong man \n“bimabanéalNaymuNa” = always being blamed \n“baNgul” = is making \n“yaóaNgu” = mother \n“guliNgu” = following \n“Nunéañu” = death adders\n\nSo \"the strong man is making the mother follow the death adders\"\n\nAh! So “baNgul” = causative = “is making”.\n\nSo X is making Y do Z.\n\nSo the structure is: \n[Subject] [adjective or modifier] [causative phrase] [object] [verb] [object or state]\n\nIn ex.2: “strong man is making the mother follow the death adders”\n\nSimilarly, in ex.4: “the tired wallaby is searching for the little feather” — no causative.\n\nBut in ex.4: “bala yila wura baNgul bargandu biNgundu guniñu” \n“bala yila” = the tired wallaby \n“wura” = is searching \n“baNgul” = is making \n“bargandu” = little feather \n“biNgundu” = fat \n“guniñu” = ???\n\nBut translation says “searching for the little feather” — so “wura” is the verb.\n\nThe “baNgul” must be misplaced or a variant.\n\nWait — only in 1, 2, 3, 5, 6, 8 have “baNgul” with causative.\n\nIn 3: “sugar is making the healthy mother-in-law fat” → “éugaNgu baNgun waymin baNgu éamiman” \n“baNgun” = is making, not “baNgul”\n\nSo “baNgun” is causative in numerous cases.\n\nIn ex.1: “baNgu” \nex.2: “baNgul” \nex.3: “baNgun” \nex.5: “baNgu” \nex.6: “baNgul” \nex.8: “baNgu” \nex.9: “baNgul” — “bala garan baNgun biñéiriñéu banéan” → lizard is following the smoke → “baNgun” here is not causative.\n\nPattern: \n- “baNgu” and “baNgul” both mean \"is making\" or \"is causing to be\" \n- They are used for causative constructions \n- “guri/gurugugu”, “éuga”, “yabu” etc. are nouns\n\nBack to 17: “balan ñalNga baNgul NumaNgu guniymuNagu bambunman”\n\n- “balan” = strong \n- “ñalNga” = quiet \n- “baNgul” = is making \n- “NumaNgu” = the one that is always being followed \n- “guniymuNagu” = likely “searching for” (guniñu with affix) \n- “bambunman” = fat\n\nSo “the quiet strong one is making the one that is always being followed search for the fat one”\n\nBut “bambunman” is an adjective — fat — so the object is the fat thing.\n\nSo: the quiet strong one is making the one always being followed (search for) the fat thing.\n\nIn example 15: “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” \n“bayi” = the quiet boy \n“biñéiriñ” = is looking \n“biNgun” = is making \n“ñalNgaNgu” = the quiet one \n“mugurugu” = booze \n“buóan” = possum\n\nSo “the quiet boy is making the quiet one drink booze” — no, “m", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11723.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build an alignment table from the examples to identify patterns in structure, affixes, and meaning.\n\nLook for common components:\n\nSubject: \n- \"balan\" = strong man / dragonfly / fat doctor / fat mother-in-law → often describes a subject with a property \n- \"bayi\" = booze / death adder / quiet boy → often a substance or agent \n- \"bala\" = lizard / tired wallaby / mother-in-law → often inanimate or noun subject with state\n\nPredicate: \n- \"baNgul\" = is searching for / is carrying / is making / is following → common verb root or copula \n- \"guli\" / \"yaóa\" / \"yaóaNgu\" → associated with \"following\" or \"blaming\" \n- \"bimabanéalNaymuNa\" = man always following death adders \n- \"biNgunman\" = makes tired → consistent with \"makem\" \n- \"éamiman\" = makes fat \n- \"guri\" / \"gurugugu\" → tied to \"boozing\", appears in 1, 2, 5, 8 → \"boozing\" → \"makes tired\"\n\nKey morphemes:\n\n- \"-NaymuNa\" → often marks a property (e.g., \"always being blamed\") \n- \"-man\" → ends of nouns with states: \"tired\", \"fat\", \"healthy\", \"offended\", \"big\" \n- \"bi-\" → likely marks a verb root (e.g., \"bimabanéalNaymuNa\" → \"the man who is always blaming\") \n- \"baNgul\" → static relational verb: \"is following\", \"is carrying\", \"is making\" \n- \"gurugugu\" → \"boozing\" → \"is making tired\" \n- \"éuga\" → sugar → \"is making fat\" \n- \"diban\" → fat \n- \"waymin\" → searching \n- \"wura\" → searching \n- \"garan\" → following \n- \"malayigara\" → smoke \n- \"bukan\" → not present\n\nNow, segment sentences 17–19 and match to patterns.\n\nSentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\" \n- \"balan\" → strong man \n- \"ñalNga\" → ? (seen in 15: \"biñéiriñ biNgun baNgul ñalNgaNgu\" → \"quiet boy\") → \"quiet\" \n→ so \"ñalNga\" = quiet \n- \"baNgul\" = is following \n- \"NumaNgu\" → \"the man\" (frequent in 16: \"Numa guli baNgul yaóaNgu\" → \"the man that is always followed\") → \"Numa\" marks someone who is always followed \n- \"guniymuNagu\" → likely \"searching for\" (guni is \"searching\", ym = for?) \n→ \"guniymu\" → searching for → \"guniymuNagu\" = searching for the thing \n- \"bambunman\" → makes fat → \"bambun\" = fat; \"man\" → so \"makes fat\" \n\nBut structure: \n\"strong man is following the man that is always being searched for? No\" — wait. \n\"NumaNgu\" = the man \n\"guniymuNagu\" = in search of something? \nWait — perhaps \"guniymuNagu\" = is searching for something → object? \n\nBut earlier in 16: \"Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"the man that is always being followed is offending the strong father\" \n→ \"Numa\" = man always followed \n→ \"guli\" = is being followed \n→ \"baNgul\" = is following \n\nBut in 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n→ \"strong man is following the man that is always being searched for (and makes fat)?\" — makes no sense.\n\nAlternative: \n\"NumaNgu\" → \"the man\" \n\"guniymuNagu\" → \"who is searching for\" → genitive? \nWait — in 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"dragonfly is searching for stinging tree\" \n→ \"baNgul\" = is searching for → \"guli\" = for? Wait: yiriñéilagu = stinging tree → \"baNgul\" + noun → \"is searching for\" \n→ structure: Subject + baNgul + Noun → \"is searching for\"\n\nSo: \"baNgul\" + noun → \"is searching for that noun\"\n\nBut in 17: \"baNgul NumaNgu guniymuNagu bambunman\" \n= \"is following [the man] that is searching for fat man\"? \n\"bambunman\" → \"makes fat\" \nBut \"guniymuNagu\" → likely \"searching for\", and \"bambunman\" is adjective → perhaps \"makes fat man\"?\n\nAlternatively: \nPossibility: \"guniymuNagu\" = is searching for \n→ so: \"strong man is following the man who is searching for the fat man?\"\n\nBut there’s no reference to \"fat man\" — but \"bambunman\" → \"fat man\" → subject of \"makes\"?\n\nBut \"bambunman\" = fat man → noun phrase?\n\nWait: \"bambun\" = fat → \"man\" → \"bambunman\" = fat man\n\nSo \"guniymuNagu bambunman\" → \"searching for the fat man\"\n\nThus: \n\"strong man is following the man who is searching for the fat man\"\n\nIs that possible? Seems odd.\n\nBut check if \"guniymuNagu\" is a noun: in 10, \"guniñu\" = stinging tree, but \"guni\" is root, \"ñu\" = tree? → likely \"guni\" is root for \"searching\", \"guniñu\" = stinging tree, so \"guni\" used as verb or noun?\n\nNo — 10: \"searching for the stinging tree\" — so \"baNgul\" + \"yiriñéilagu\" → \"is searching for stinging tree\"\n\nSo \"baNgul\" is copular verb with object → \"is searching for X\"\n\nSo \"baNgul NumaNgu\" → \"is following the man\" → object = \"NumaNgu\"\n\nThen \"guniymuNagu bambunman\" → \"searching for the fat man\"? But it comes after?\n\nNo — structure is: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n→ Syntax: Subject + adjective + baNgul + object + (searching for) + object?\n\nBut this would be an embedded clause or prepositional?\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"quiet boy is looking at the tired lizard\" \n→ \"biNgun\" = is making tired → \"biNgun baNgul\" = makes tired and is looking at → two verbs?\n\nNo — \"biNgun\" is separate → \"the quiet boy is looking at the tired lizard\" — clean.\n\nBack to 17: likely misread of word order.\n\nMaybe: \"NumaNgu\" is the object of \"baNgul\", and \"guniymuNagu bambunman\" is a modifier: the man who is searching for the fat man?\n\nSo: \"strong man is following the man who is searching for the fat man\"\n\nBut \"guniymuNagu\" → \"searching for\" → must follow the object of \"baNgul\"? Or is \"guniymuNagu\" the object?\n\nBut no — \"guli\" + \"yaóaNgu\" = \"blaming the mother\" → \"guli\" = blaming, \"yaóaNgu\" = mother.\n\nSo likely, \"guni\" is a verb root.\n\nIn 10: \"guniñu\" = stinging tree → so \"guni\" is not used as verb directly.\n\nIn 17, \"guniymuNagu\" → likely \"searching for something\" → so \"guniymuNagu\" = is searching for\n\nBut it comes after the object of \"baNgul\"?\n\nNo — word order: baNgul NumaNgu guniymuNagu bambunman → baNgul + (NP) + (VP)\n\nSo: \"is following [the man] (who is searching for the fat man)\"\n\nYes — that fits pattern.\n\nSo: \"strong man is following the man who is searching for the fat man\"\n\nBut \"bambunman\" = fat man → so \"the fat man\"\n\nThus, 17: \"The strong quiet man is following the man who is searching for the fat man.\"\n\n→ But \"ñalNga\" = quiet → yes from 15: \"biñéiriñ\" = quiet boy → \"ñalNga\" = quiet\n\n\"baNgul\" = is following → yes\n\n\"NumaNgu\" = the man that is always followed → as in 16\n\n\"guniymuNagu\" = searching for → verb form \n\"bambunman\" = fat man\n\nSo 17: The strong quiet man is following the man who is searching for the fat man.\n\nNow sentence 18: \n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\"\n\n- \"bala\" = lizard \n- \"diban\" = fat → adjective \n- \"bilmbalmuNa\" = ? → in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"mother-in-law that is always pushing stones\" → \"dibanbilmbalNaymuNagu\" → \"diban\" + \"bilmbal\" + \"NaymuNa\" → so \"bilmbal\" = pushing? \n\"bilmba\" appears in 12: \"gubimbulugu bilmban\" → \"pushing the big stone\" → \"bilmban\" = big stone → so \"bilmba\" = push? \n→ \"bilmbal\" = pushing? \n→ so \"bilmbalmuNa\" → \"pushing stones\" → so \"diban bilmbalmuNa\" = fat man pushing stones? \nBut subject is \"bala\" (lizard) → \"the fat lizard is pushing stones\"?\n\nWait: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\nStructure: \n\"bala diban\" = fat lizard \n\"bilmbalmuNa\" = is pushing? → \"bilmba\" root → so \"is pushing\" \n\"baNgun\" → is making → \"is making\" \n\"biñéiriñéu\" → \"the quiet one\" → from 15 → \"biñéiriñ\" = quiet → so \"biñéiriñéu\" = quiet one \n\"guniñu\" = little feather → from 4\n\nSo: \"The fat lizard is pushing the quiet one for the little feather?\" → makes no sense.\n\nWait — \"baNgun\" = is making → copula? Or \"is causing\"?\n\nBut in 1, \"bayi yaóa ... baNgu gurugugu biNgunman\" → \"booze is making the man tired\"\n\n\"baNgu\" = making → \"gurugugu\" = booze → \"biNgunman\" = tired\n\nSo \"baNgu\" = is making → applied to something → \"X is making Y\"\n\nSo here: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ \"the fat lizard is pushing the quiet one\" → \"bilmbalmuNa\" = pushing → \"is pushing\"\n\nThen \"baNgun\" = is making → \"is making\" the quiet one fat? → no, object is \"guniñu\" → \"the little feather\"\n\nSo: \"is making the quiet one [something] for the little feather?\"\n\nUnlikely.\n\nAlternative: the word order may be subject + noun + verb + predication.\n\n\"bala diban\" = fat lizard \n\"bilmbalmuNa\" → is pushing → verb? \nBut \"bilmbal\" is verb → \"bilmba\" = push → so \"bilmbalmuNa\" = pushing (with object?) → \"is pushing something\"\n\nBut object? \"baNgun\" → is making → object? → \"biñéiriñéu\" = quiet one → so \"is making the quiet one\" → then \"guniñu\" = for?\n\nPossibility: \"baNgun\" = is making → \"is making [the quiet one]\" → \"guniñu\" = for the little feather\n\nBut then \"bilmbalmuNa\" = is pushing → \"is pushing\" what?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"the fat doctor is pushing the big stone\" \n→ \"bala diban\" + \"éagiñ\" + \"baNgul\" + \"gubimbulugu\" + \"éamiNgu\" + \"bilmban\"\n\nSo \"is pushing\" + \"big stone\"\n\nHere: \"bilmbalmuNa\" → similar to \"bilmban\" → \"bilmba\" root → \"pushing\" → object implied?\n\nBut here, after \"bilmbalmuNa\", we have \"baNgun\" → which is \"making\"\n\nSo perhaps: \"the fat lizard is pushing [something], and is making the quiet one for the little feather\"? → no.\n\nAlternatively, affix: \"baNgun\" = is making → and the object is \"biñéiriñéu\" → so \"is making the quiet one\" → \"guniñu\" = for the little feather?\n\nBut no sign of \"for\".\n\nIn 5: \"balan malayigara baNgu garandu biNgunman\" → \"smoke is making the scorpion tired\"\n\nSo \"X is making Y tired\"\n\nSo here, \"X is making [object] fat\" — \"is making the quiet one fat\"?\n\nThen \"guniñu\" = for the little feather?\n\nBut \"for\" not triggered.\n\nPossibility: misreading the word \"bilmbalmuNa\"\n\nIn 13: \"dibanbilmbalNaymuNagu\" → \"always pushing stones\" → so \"diban\" + \"bilmba\" + \"NaymuNa\" → \"pushing stones\" → verb form\n\nSo \"bilmbalmuNa\" = pushing stones\n\nSo: \"the fat lizard is pushing stones, and is making the quiet one for the little feather\"? — still odd.\n\nWait — could \"baNgun\" be part of the verb?\n\nBut \"baNgun\" is only used in \"making\" constructions.\n\nIn 3: \"bambun baNgu éugaNgu éamiman\" → sugar is making the healthy mother-in-law fat → \"baNgu\" = making → \"éamiman\" = fat\n\nSo \"baNgun\" = \"making\"\n\nSo \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\" \n→ The fat lizard is pushing stones and is making the quiet one fat? → but \"guniñu\" is last.\n\nBut \"guniñu\" is not an adjective → it's a noun → \"little feather\"\n\nSo likely: \"is making the quiet one [something with little feather]\"\n\nBut no such construction.\n\nAnother idea: the verb is \"is causing to do\", and \"biñéiriñéu\" is the one being affected.\n\nBut \"guniñu\" might be the object of \"making\".\n\nBut no direct evidence.\n\nHold.\n\nNow 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\"\n\n\"bayi\" = booze \n\"bargan\" = ? → not in list \n\"baNgul\" = is following \n\"yaóaNgu\" = mother (in 2) \n\"gubimbuluNunéanaymuNagu\" → \"the man that is always being blamed\"? \nIn 2: \"baban yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" → \"blaming mother that is always following death adders\" \n\"guliNgu\" = following death adders\n\nSo \"gubimbulu\" = in 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" → \"offended father is carrying booze\" \n\"gurugu\" = offended — \"gubimbulu\" not seen.\n\nIn 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" → \"booze is making the tired doctor fall asleep\" → \"gubimbulu\" = tired?\n\nWait: \"biNgun\" = is making tired → so \"gubimbulu\" = tired?\n\nYes — in 8: \"gubimbulu\" = tired → so \"is making the tired doctor fall asleep\"\n\nSo \"gubimbulu\" = tired\n\nThus \"gubimbuluNunéanaymuNagu\" = the man that is always being blamed → from \"NunéanaymuNagu\" = always being blamed\n\nSo → \"the man that is always being blamed\" — so the object of \"yaóaNgu\" — \"is following the mother that is always being blamed\"?\n\n\"baNgul\" = is following → so \"booze is following the mother that is always being blamed\"\n\nAnd \"banéan\" = possum → from 7: \"the death adder that is always searching for scorpions is following the possum\" → \"banéan\" = possum\n\nSo: \"booze is following the mother that is always being blamed\" — that makes sense.\n\nBack to 18: \n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\nKnown: \n- \"diban\" = fat \n- \"bilmbalmuNa\" = is pushing stones? \n- \"baNgun\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11998.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "Start by building a morphological and syntactic alignment from the given examples to determine how the Dyirbal sentences structure their semantic content.\n\nKey observations:\n\n- Subject-initial structure: Most sentences start with a subject (e.g., \"bayi\", \"balan\", \"bala\").\n- The following element often indicates a core action or state:\n - \"baNgul\" commonly follows a subject and introduces an object or state: \"X is [doing something] to Y\".\n - \"baNgu\" typically introduces a state or condition: \"is making [something] [X]\".\n- The item being modified (e.g., tired, fat, healthy) is often marked by a suffix or internal morpheme.\n- The word \"gurugugu\" appears in multiple sentences (e.g., 1, 8) and is consistently translated as \"tired\", thus likely encodes the state \"tired\".\n- \"yabu\" appears in 2 and 11: \"strong man\", \"being ignored\" — likely signals an attribute of the subject.\n- \"yabu\" + \"bimabanéalNaymuNa\" = \"the strong man\", suggesting \"yabu\" = strong; in 11, \"NaéilmuNagu\" = \"always being ignored\".\n- \"bambun\" appears in 3 as \"sugar\", and in 17 as \"bambunman\" → likely means \"fat\".\n- \"biNgunman\" = \"is making tired\" → \"biNgun\" base + \"man\" → \"making tired\" → state is being affected.\n- Affixes show a pattern: \n - Attribute + linker / stated condition + verb + object → standard pattern.\n - Postpositional elements like \"guliNgu\", \"guniñu\", \"bunéan\" act as object or location.\n\nNow analyze each sentence:\n\nSentence 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired\" \n→ \"bayi\" = booze, \"yaóa\" = man, \"NunéaymuNa\" = always being blamed, \"baNgu\" = is making, \"gurugugu\" = tired, \"biNgunman\" = (it) is making him tired. \nThus: \n- \"baNgu\" = \"is making\", followed by state of object \n- \"gurugugu\" = tired → consistently used for tiredness \n- \"bambun\" = fat → appears in 3 and 17 → likely \"fat\" \n- \"bilmban\" appears in 12: \"pushing the big stone\" → \"pushing\" \n- \"biñéiriñéu\" appears in 9 and 18: \"following\" → consistent \n- \"biñéiriñ\" = \"looking at\" → in 15 and 18\n\nNow analyze the target sentences:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n- \"balan\" = subject → likely \"the strong\" or \"the one who is strong\" \n- \"ñalNga\" = ? → appears only here; in 15: \"biñéiriñ\" (quiet boy), so \"ñalNga\" may be \"quiet\" \n- \"baNgul\" = verb → meaning \"is searching for\" \n- \"NumaNgu\" = \"always being followed\" → from 16: \"the man that is always being followed\" \n- \"guniymuNagu\" = ? → in 14: \"guniñu\" = little feather, \"guni\" = little; \"guniymu\" → \"little\" + \"arm\"? → likely \"little [something]\" \n- \"bambunman\" = fat → so \"is making [someone] fat\"\n\nBut grammatically: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"the [quiet] man is searching for the one who is always being followed, [who is] little, making fat\" \nNot logical.\n\nAlternative: maybe attributes are attached to the object.\n\nTry breaking down: \n\"balan\" = subject \n\"ñalNga\" = attribute: \"quiet\" (from 15: \"the quiet boy\") \n\"baNgul\" = verb: \"is searching for\" \n\"NumaNgu\" = object: \"the one who is always being followed\" \n\"guniymuNagu\" = adjective: \"little\" \n\"bambunman\" = state: \"fat\"\n\nBut \"making fat\" only applies to the object?\n\nBut the object is \"NumaNgu\" → \"the one who is always being followed\" \nSo: \"the quiet man is searching for the one who is always being followed, who is little, making him fat\" → illogical.\n\nWait — perhaps \"bambunman\" is not \"making fat\" but part of the subject.\n\nAnother option: \"bambunman\" = \"the fat man\" \nThen: \"the quiet man is searching for the one who is always being followed, who is little, the fat man\"? No.\n\nAlternative: \"guniymuNagu\" = \"little [thing]\" → like \"little spear\" → in 14: \"guniñu\" = little feather → \"guni\" = little \nSo \"guniymuNagu\" = \"little thing\" → likely a noun phrase.\n\nSo structure: \nSubject: balan (strong man?) \nAttribute: ñalNga (quiet) \nVerb: baNgul = is searching for \nObject: NumaNgu (always being followed) → \"the one who is always being followed\" \nModifier: guniymuNagu = little \nState: bambunman = fat\n\nBut fat not being assigned.\n\nWait — is \"bambunman\" the state of the object? → \"searching for the little one who is fat\"?\n\nYes — plausible. \nSo: \"the quiet man is searching for the one who is always being followed, who is little, and is fat\".\n\nBut \"bambunman\" is a suffix? No — \"bambun\" is a noun in 3.\n\nIn sentence 3: \"sugar is making the healthy mother-in-law fat\" → \"sugar\" + \"baNgu\" + \"mother-in-law\" + \"éugaNgu\" (healthy?) + \"éamiman\" (fat) → so \"fat\" is a state.\n\nSo \"bambunman\" → \"fat man\"?\n\n\"bambun\" = fat → so \"bambunman\" = \"the fat man\"\n\nBut in 17, is it \"making fat\"? No.\n\nThe verb is \"baNgul\" → \"searching for\", not \"making\".\n\nSo the object is \"the one who is always being followed\" (NumaNgu), and part of it has attributes: little (guniymuNagu) and fat (bambunman).\n\nSo: \"The quiet man is searching for the one who is always being followed, who is little and fat.\"\n\nBut is \"guniymuNagu\" modifying the one who is always being followed?\n\nYes — likely.\n\nThus: \n17. The quiet man is searching for the one who is always being followed, who is little and fat.\n\nNow 18: bala diban bilmbalmuNa baNgun biñéiriñéu guniñu \n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ? → in 12: \"bila mbal\" → \"big stone\", so \"bilmban\" = big, \"bimbaltu\" → big? \n\"diban\" = fat \n\"bilmbalmuNa\" → \"the big stone\" → likely \"the big stone\" \n\"baNgun\" = is making \n\"biñéiriñéu\" = following → from 9 and 18 \n\"guniñu\" = small feather → in 4: \"little feather\" → so \"guniñu\" = little feather\n\nSo: \"the fat man is making the big stone follow the little feather\"\n\nBut in 9: \"the lizard is following the smoke\" → \"is following\"\n\nSo: \"is making\" → \"causing to follow\"\n\nSo: \"the fat man is making the big stone follow the little feather\"\n\nBut is \"bilmbalmuNa\" = \"the big stone\"? Yes.\n\n\"baNgun\" → causes → \"is making\"\n\nSo: \"The fat man is making the big stone follow the little feather.\"\n\nNow 19: bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan \n\"bayi\" = subject → booze \n\"bargan\" = ? → in 16: \"Numa\" = always being followed → \"gubimbulu\" = tired \n\"baNgul\" = is searching for \n\"yaóaNgu\" = man (from 1) \n\"gubimbuluNunéanaymuNagu\" → related to \"gubimbulu\" → \"tired\", \"NunéanaymuNagu\" → \"always being blamed\"? \nLooking at 8: \"booze is making the tired doctor fall asleep\" → \"gurugugu\" = tired, \"gubimbulu\" = tired → likely the same \n\"bargan\" → could be \"trying to\" or \"searching\"? Related to \"bargan\"? \nIn 15: \"biñéiriñ\" = looking at → not matching.\n\nBut \"bargan\" → never appears in the examples.\n\nWait — 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\" \nSubject: booze \n\"bargan\" → new root? \n\"baNgul\" → is searching for \n\"yaóaNgu\" → man \n\"gubimbuluNunéanaymuNagu\" → \"the tired man who is always being blamed\"? \n\"banéan\" = the smoke → in 9: \"the lizard is following the smoke\"\n\nSo: \"booze is searching for the man who is tired and always being blamed, following the smoke\"?\n\nBut \"bargan\" → not in examples. Could be a verb.\n\nIn 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" → \"the offended father is carrying the booze\" → \"baNgul\" = carrying?\n\nIn 1: \"baNgu\" = making, \"baNgul\" = ? → many verbs.\n\n\"baNgul\" appears in 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 — appears with different verbs.\n\nIn 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"tired wallaby is searching for the little feather\" → \"wura\" = searching → so \"baNgul\" = searching for.\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following the smoke\" → so \"baNgul\" = following.\n\nSo \"baNgul\" is a verb that takes a direct object and means \"is [searching for / following / looking at]\"\n\nIn 19: \"baNgul\" → is searching for → so \"booze is searching for the man who is tired and always being blamed, who is following the smoke\"?\n\nBut \"gubimbuluNunéanaymuNagu\" → likely \"the man who is tired and always being blamed\", from 1 and 8.\n\n\"banéan\" = the smoke\n\nSo: \"Booze is searching for the man who is tired and always being blamed, who is following the smoke.\"\n\nBut it's missing the object of search — is the man the object?\n\nYes — \"booze is searching for the man...\"\n\nAnd the man is doing something: \"who is following the smoke\"\n\nSo: \"Booze is searching for the man who is tired and always being blamed, who is following the smoke.\"\n\nAlternatively, if \"gubimbuluNunéanaymuNagu\" = \"the tired man who is always being blamed\", then yes.\n\nSo final translations:\n\n17. The quiet man is searching for the one who is always being followed, who is little and fat. \n18. The fat man is making the big stone follow the little feather. \n19. Booze is searching for the man who is tired and always being blamed, who is following the smoke.\n\nBut check for consistency.\n\nIn 15: \"the quiet boy is looking at the tired lizard\" → \"biñéiriñ\" = looking at → and \"biñéiriñéu\" = following? In 9: \"following\", so possibly a synonym.\n\n\"biñéiriñ\" = looking at → could be used differently.\n\nIn 19: the action is \"searching for\" → from 4,14 → so \"baNgul\" = searching for.\n\nYes — confirmed.\n\nThus:\n\nb.1 / 17.: The quiet man is searching for the one who is always being followed, who is little and fat. \nb.2 / 18.: The fat man is making the big stone follow the little feather. \nb.3 / 19.: Booze is searching for the man who is tired and always being blamed, who is following the smoke.\n\n\\boxed{b.1: The quiet man is searching for the one who is always being followed, who is little and fat.; b.2: The fat man is making the big stone follow the little feather.; b.3: Booze is searching for the man who is tired and always being blamed, who is following the smoke.}", + "generated_tokens": 3059, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: The quiet man is searching for the one who is always being followed, who is little and fat.; b.2: The fat man is making the big stone follow the little feather.; b.3: Booze is searching for the man who is tired and always being blamed, who is following the smoke.", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9569.0, + "ioling_final_answer_chars": 268.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "Align the given verb forms with their English translations to identify patterns in subject, aspect, manner, and object.\n\nTarget translations:\n\n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out \n\nStep 1: Identify \"begin\" verbs \n- \"kewǣpeqtaq\" = we1+2 begin \n- \"kewǣpānæhkæq\" = we1+2 begin to dig \n→ \"kewǣp\" + \"eqtaq\" = begin; \"kewǣpān\" + \"æhkæq\" = begin to dig \n→ \"begin\" is kewǣp- (we1+2) or likely kewǣp- for \"I begin\" (using same root)\n\nSo \"I begin to eat it\" → likely derive from \"kewǣp\" root, with \"eat\" as object. \nLook for \"eat\" or \"bite\" verbs.\n\nFind verbs involving \"eat\", \"bite\", or \"gnaw\":\n\n- \"kekēskahtæq\" = we1+2 bite it through \n- \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it \n→ \"k-ēskaht\" or \"kēskaht\" = bite, gnaw\n\n\"ketāwahtæq\" = we1+2 bite, gnaw \n→ \"ketā\" or \"ket\" + \"waht\" = gnaw \n\nBut \"I begin to eat it\" → need \"begin\" + \"eat\" \n\"begin\" → root: kewǣp- \n\"eat\" → likely from \"kēskaht\" or \"ketāwaht\" \n\nBut no \"begin to eat\" directly.\n\nInstead, \"begin to eat\" could be a compound of \"begin\" and \"eat\" via an aspectual or transitive form.\n\nLooking at \"kekēskahtæq\" = we1+2 bite through → \"bite\" with \"through\"\n\nBut \"eat\" is not directly present.\n\n\"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths → “come eating” → eating is implied.\n\nBut “I begin to eat” is not directly in the list.\n\nIs there a verb for \"begin\" + \"eat\"?\n\nPossible derivation: use \"kewǣp\" for \"begin\", and attach \"eat\" verb.\n\nBut in Menominee, verbs often have aspect and manner.\n\n\"begin\" appears in: \n- kewǣpeqtaq → we1+2 begin \n- kewǣpānæhkæq → we1+2 begin to dig \n\nSo base form: \"kewǣp\" (begin)\n\n\"eat\" or \"gnaw\" → in \"ketāwahtæq\" = bite/gnaw a hole in it → a type of eating?\n\nBut “begin to eat” may be formed with \"begin\" + \"bite/gnaw\" → possibly \"kewǣp\" + \"kēskaht\" (bite)\n\nNo exact verb, but no other choice.\n\nSo likely: I begin to eat it → kewǣp + kēskaht / kēskahtæq? \nBut \"kēskahtæq\" is \"we1+2 bite through\"\n\n\"begin\" subject is \"I\", not \"we1+2\"\n\nSo must use a subject-specific root.\n\n\"we1+2 begin\" = kewǣpeqtaq → kewǣp + eqtaq\n\n\"we1+2 begin to dig\" = kewǣpānæhkæq → kewǣp + ān + æhkæq\n\nSo \"begin\" base is kewǣp\n\nBut \"I\" → need first person singular?\n\nNo direct \"I begin\" verb.\n\nOnly \"we1+2\" and \"he\", \"I\" verbs exist.\n\nI verbs:\n- nepītohnæm = I walk here \n- nekǣtahan = I pry it out by tool \n- nekāweqtam = I lie down \n- newāckesan = I cut around it \n- nekāwāhpem = I fall over laughing \n\nSo \"I\" verbs have a \"ne\" root.\n\n\"begin\" for \"I\"?\n\nNo \"I begin\" in examples.\n\nBut \"begin\" in \"we1+2\" is kewǣp.\n\nNo \"I begin\" verb.\n\nSo possibly, \"begin\" is used with an object verb.\n\nBut in \"kepītahtæq\", we1+2 come eating → eating is central.\n\nPerhaps \"I begin to eat it\" = \"I begin\" + \"to eat\"\n\nBut no \"I begin\" form.\n\nIs there a verb for \"begin\" with \"I\"?\n\nPossibility: use \"kewǣp\" with \"I\" subject?\n\nBut \"kewǣpeqtaq\" is for \"we1+2\"\n\nNo individual \"I begin\"\n\nBut perhaps \"kewǣp\" is used with first person in some alignment?\n\nNo evidence.\n\nAlternative: use \"begin\" + \"bite\" or \"gnaw\" as \"eating\"\n\n\"ketāwahtæq\" = we1+2 bite/gnaw a hole in it\n\n→ \"bite/gnaw\" is the action of eating.\n\nSo \"I begin to eat it\" → likely \"I begin to gnaw it\" or \"I begin to bite it\"\n\nSo form: \"kewǣp\" + \"ketāwaht\"?\n\nBut subject is \"I\"\n\nNo \"I begin\" form.\n\nSearch for verbs that match \"I lay it flat\"\n\n\"we1+2 lay it flat by hand\" → who does \"lay it flat\"?\n\n\"lay\" → no direct verb.\n\nBut \"walk\" is: \n- nepītohnæm = I walk here \n- kekǣtohnæq = we1+2 walk out \n- wǣpohnæw = he begins walking \n- pāhkeqtaw = he opens up \n- pītenam = he passes it here \n\n\"lay flat\" → \"place flat\" — no verb.\n\n\"walk\" — \"walk\" is common.\n\n\"lay it flat\" → possibly \"place\" or \"set\"?\n\n\"pāhkeqtaw\" = he opens up → not lay \n\n\"nekāweqtam\" = I lie down — not lay\n\n\"we1+2 lay it flat by hand\" → likely from a verb meaning \"place\" or \"set down\"\n\nNo direct verb.\n\nBut \"walk\" has \"we1+2 walk out\" = kekǣtohnæq\n\nSo \"he walks out\" = kekǣtohnæq\n\n\"we1+2 lay it flat by hand\" → must be a verb for place or position.\n\nLook for verbs with “lay”, “place”, “set”\n\nNone given.\n\n\"pāhkaham\" = he opens it by tool → opening\n\n\"nektāwāh\" or \"nekāwāhpem\" → no.\n\n\"cut\" verbs: \n- pahkǣsam = he cuts it off \n- tawǣsam = he cuts a hole in it \n- newāckesan = I cut around it \n- nekǣtahan = I pry it out by tool \n\n\"dig a hole\" → \"dig\" not directly listed.\n\n\"he digs a hole\" → no direct \"dig\" verb.\n\nBut \"he cuts a hole in it\" = tawǣsam\n\n\"dig\" and \"cut\" may be related?\n\nIn context, \"dig a hole\" → likely 'dig' → a hole\n\n\"tawǣsam\" = cuts a hole → so cuts a hole\n\n\"dig\" may be synonymous with \"cut\" in this context?\n\nBut \"dig\" is usually for soil, not cut in wood.\n\nIn Menominee, \"tawǣsam\" = he cuts a hole in it → action of cutting a hole\n\nSo \"he digs a hole\" → may be tawǣsam?\n\nBut \"dig\" has no direct form.\n\n\"dig\" may be inferred from context.\n\nSimilarly, \"he walks out\" = kekǣtohnæq (we1+2 walk out)\n\n\"we1+2\" = we and you\n\n\"he walks out\" = only \"he\"\n\nSo \"kekǣtohnæq\" = we1+2 walk out\n\n\"he walks out\" → must be a different form.\n\nIs there a verb meaning \"he walks out\"?\n\nOnly \"kekǣtohnæq\" for \"we1+2 walk out\"\n\nSo subject must be changed.\n\nPossibly, the verb \"walk\" is in a base form with subject marking.\n\n\"nepītohnæm\" = I walk here (to this place) → \"I walk here\"\n\n\"kekǣtohnæq\" = we1+2 walk out → \"we1+2 walk out\"\n\nSo \"walk\" root is \"kētohn\" or \"kētoh\" \n\n\"kekǣtohnæq\" = we1+2 walk out → kekǣtohnæq\n\nSo \"he walks out\" → would be \"kētohnæq\" with \"he\"?\n\nBut no such form.\n\n\"ke\" = he?\n\n\"nepītohnæm\" = I walk → ne + pītohnæm\n\n\"kekǣtohnæq\" = we1+2 walk → ke + kǣtohnæq\n\nSo \"ke\" = we1+2\n\n\"ne\" = I\n\n\"He\" → not labeled.\n\n\"he\" verbs:\n\n- kawāham = he fells it by tool \n- kēskenam = he breaks it through by hand \n- pahkǣsam = he cuts it off \n- pītenam = he passes it here \n- wackōhnæw = he walks roundabout, by a detour \n- pāhkaham = he opens it by tool \n- ketǣnam = he takes it out by hand \n- ketāwahtæq = we1+2 bite, gnaw a hole in it \n- wǣpohnæw = he begins walking \n\nSo \"he walks out\" — not directly stated.\n\nBut \"wackōhnæw\" = he walks roundabout → not \"out\"\n\n\"pītenam\" = he passes it here → passes\n\n\"kektāwahtæq\" = we1+2 bite\n\nOnly \"wǣpohnæw\" = he begins walking\n\nNo \"he walks out\"\n\nBut \"kekǣtohnæq\" = we1+2 walk out\n\nSo \"he walks out\" → perhaps form from stem, with \"he\" prefix?\n\nLet’s assume that all verb stems are transferable with subject prefixes.\n\nSubjects:\n\n- \"we1+2\" → ke in some verbs: kekǣtohnæq \n- \"I\" → ne: nepītohnæm \n- \"he\" → ? → no prefix in examples\n\nIn \"kawāham\" = he fells it by tool → no marked prefix\n\n\"kēskenam\" = he breaks it through by hand → no prefix\n\nSo \"he\" verbs start with k, or no prefix?\n\n\"pahkǣsam\" = he cuts it off → starts with p\n\n\"pītenam\" = he passes it here → starts with p\n\nSo he verbs are not prefixed with a marker — so perhaps the entire verb is a base with no subject marker?\n\nBut that would suggest that the subject is implied or from context.\n\nFor example, \"he walks out\" → likely \"kekǣtohnæq\" with \"he\" as subject? But \"kek\" means \"we1+2\"\n\nSo no \"he walk\" form.\n\nBut in the list, no \"he walk\" exists.\n\nMost verbs have subject prefixes:\n\n- kewǣpeqtaq → we1+2 begin \n- kawāham → he fells it \n- nepītohnæm → I walk here \n- kēskenam → he breaks \n- pahkǣsam → he cuts \n- kekǣtohnæq → we1+2 walk out \n- kewǣpānæhkæq → we1+2 begin to dig \n- tawǣsam → he cuts a hole \n- nekǣtahan → I pry \n- pāhkaham → he opens \n- kekēskahtæq → we1+2 bite \n- wackōhnæw → he walks roundabout \n- newāckesan → I cut around \n- ketǣnam → he takes \n- ketāwahtæq → we1+2 bite \n- wǣpohnæw → he begins walking \n- nekāweqtam → I lie down \n- pāhkeqtaw → he opens up \n- kepītahtæq → we1+2 come eating \n- nekāwāhpem → I fall over laughing\n\nSo \"he walks out\" → only in \"kekǣtohnæq\" for \"we1+2\"\n\nBut \"wackōhnæw\" = he walks roundabout\n\n\"he begins walking\" = wǣpohnæw\n\n\"walk\" appears as a root.\n\n\"walk out\" → related to \"walk out\"\n\nSo \"he walks out\" → no verb listed, but likely a variant of \"walk\".\n\nBut no \"he walks out\".\n\nPerhaps \"kektāwaht\" or something else.\n\nNo.\n\nAnother possibility: \"lay it flat by hand\" → \"place it flat\"\n\n\"place\" not in list.\n\nBut \"walk\" verbs are only with \"we1+2\", \"I\", and \"he\" with different walks.\n\n\"lay\" is not present.\n\nBut \"cut\" appears for \"dig a hole\"?\n\n\"he digs a hole\" → is that \"tawǣsam\"?\n\n\"tawǣsam\" = he cuts a hole in it → matches \"digs a hole\" in meaning?\n\n\"cut a hole\" = \"dig a hole\" in a non-literal way.\n\nIn context, \"dig a hole\" may be translated as \"tawǣsam\"\n\nSimilarly, \"I begin to eat it\" → since \"bite\" is used for \"eat\", and \"begin\" is in \"kewǣp\", but \"I\" not in \"kewǣp\"\n\n\"we1+2 begin to eat\" = kekēskahtæq? But it's \"we1+2 bite it through\"\n\n\"biting\" = eating\n\nSo \"I begin to eat it\" → \"I begin to bite it\"\n\nSo use \"kewǣp\" with \"I\" subject?\n\nBut no \"I begin\"\n\nOnly \"I walk\" exists.\n\nSo likely, \"begin to eat\" is formed from \"kewǣp\" + \"bite\" verb, with subject \"I\"\n\nBut no such verb.\n\nAlternatively, \"eat\" may be expressed via \"eat in mouth\"\n\n\"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\nSo \"eating\" is in \"kepītahtæq\"\n\n\"come eating\" = eating with the body\n\nBut not \"begin to eat\"\n\n\"begin to eat\" → may be \"I begin to eat\" = \"I begin\" + \"eat\"\n\nWith no \"I begin\" form, but with \"I walk\", \"I cut\", etc.\n\nPerhaps \"begin\" is used with a root that means \"eat\"\n\nBut no.\n\nAnother idea: in \"kewǣpeqtaq\" = we1+2 begin → so \"kewǣp\" is the root\n\n\"begin\" = kewǣp\n\n\"eat\" = in \"ketāwaht\" or \"kēskaht\"\n\nSo \"begin to eat\" = kewǣp + ketāwaht → but subject?\n\nSo the verb form must have subject prefix.\n\n\"we1+2\" uses \"ke\" → ke + wǣp → kewǣp\n\n\"I\" uses \"ne\" → ne + pītohn → nepītohn\n\nSo \"I begin\" → ne + wǣp → \"newǣp\"?\n\nBut not in list.\n\nLikely not.\n\nPerhaps \"I begin to eat it\" is not possible with given forms.\n\nBut must solve.\n\nAll verbs have:\n\n- Subject marker (we1+2, I, he)\n- Verb root\n- Object (if any)\n\nFor:\n\n1. I begin to eat it → likely uses \"eat\" root. \"eat\" is in \"bite/gnaw\" verbs.\n\n\"ketāwahtæq\" = we1+2 bite/gnaw a hole in it\n\nSo \"bite/gnaw\" = eat\n\nSo \"begin to bite\" → begin + bite/gnaw\n\nSubject \"I\" → ne\n\nSo \"ne\" + \"wǣp\" + \"kēskaht\" → but \"wǣp\" is \"begin\"\n\n\"begin\" root: kewǣp\n\nSo for \"I begin\", the form is ne + wǣp\n\nThen \"to bite\" = kēskaht\n\nBut \"bite\" is in \"kēskaht\"\n\nSo \"ne wǣp kēskaht\"?\n\nBut not in list.\n\n\"ketāwahtæq\" = we1+2 bite/gnaw → ke + tāwaht\n\n\"tāwaht\" = bite/gnaw\n\nSo root: tāwaht\n\n\"begin\" root: wǣp\n\nSo \"I begin to eat it\" = ne + wǣp + tāwaht?\n\nBut no such form.\n\nPerhaps the verb is derived from \"kewǣp\" with \"tāwaht\" and subject.\n\nBut what is the structure?\n\n\"we1+2 begin to eat\" = kewǣp + tāwaht? Not in list.\n\nOnly \"kekēskahtæq\" = we1+2 bite through\n\n\"ke\" + \"kēskaht\" → kēskaht\n\nSo format is: subject marker + root\n\nFor \"I begin to eat it\", assume it is \"ne wǣp tāwaht\" or \"ne wǣp kēskaht\"\n\nBut \"wǣp\" for \"begin\" is used in \"wǣpohnæw\" = he begins walking\n\nSo \"wǣp\" is a root for \"begin\"\n\nSo \"I begin to eat it\" = ne + wǣp + tāwaht?\n\nBut is there a verb with that?\n\nNo.\n\nBut in the list, \"newāckesan\" = I cut around it → \"new\" + \"āckesan\"\n\n\"ne\" + \"w\" in \"newāckesan\"\n\nSo \"ne\" + \"w\" → \"new\"\n\n\"w\" = \"cut\"\n\nSo subject + root.\n\nLikely, \"I begin\" = \"ne wǣp\"\n\n\"begin to eat\" = \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11061.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given verb forms in Menominee and asked to translate four English phrases into Menominee.\n\nStep-by-step alignment based on the given verb forms:\n\n1. \"I begin to eat it\" \nLook for verbs meaning \"begin\" or \"start\" and involving \"eating\". \nWe have: \n- *kewǣpeqtaq* = \"we1+2 begin\" \n- *kewǣpānæhkæq* = \"we1+2 begin to dig\" \n- *wǣpohnæw* = \"he begins walking\" \n- *kekēskahtæq* = \"we1+2 bite it through\" \n- *ketāwahtæq* = \"we1+2 bite, gnaw a hole in it\" \n\n\"Begin to eat\" is not directly listed, but \"bite\" and \"gnaw\" are similar to eating, and \"begin\" is a semantic root. \n\"Begin\" is reflected in *kewǣ* + suffix for aspect/subject. \nFor \"I\", we need first-person singular. \nThe verb *kewǣ* is used in first-person forms with modifiers. \n\nWe need a verb that combines \"begin\" and \"eat\". \n\"Ketāwahtæq\" has \"we1+2 bite, gnaw a hole in it\" — \"bite\" is related to eating. \nBut \"begin\" is separate. \n\nLook for a form of \"begin\" for first person. \nOnly *kewǣpeqtaq* has \"begin\", and it is second-person plural (we1+2). \nDo we have a first-person singular \"begin\"? \n\nWe see *nekāweqtam* = \"I lie down\" → different root. \nNo direct form for \"I begin\". \n\nBut “begin to eat” may be formed from \"begin\" + \"eat\". \n\"Ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" is a verb involving eating. \n\"Begin\" is a separate root. \n\nIs \"eat\" expressed as \"bite\"? Possibly. So \"I begin to eat\" → \"I begin to bite\"? \n\nBut \"begin\" is only in forms with \"we1+2\". \nWe do not have a first-person form of \"begin\", only in \"we1+2\". \n\nWait: is there a first-person \"begin\" with \"bite\"? \n\nNo direct match. \n\nBut look at: \n*kekēskahtæq* = \"we1+2 bite it through\" → \"bite through\" → more like eat through. \n\nStill, no \"begin\" + \"eat\" in first person. \n\nAlternative: perhaps “begin to eat” is expressed as \"begin to bite\" → use root *kewǣ* (begin) with object \"it\", and subject \"I\". \n\nIs there a form with \"I begin\"? \n\nWe are missing that. \n\nHowever, in the list, we see *kewǣpānæhkæq* = \"we1+2 begin to dig\" → so \"begin\" is marked with *kewǣ*. \n\nWe may assume that \"begin\" is formed with *kewǣ*, and \"to eat\" is a root verb like *ketāwahtæq*. \n\nBut *ketāwahtæq* is already \"we1+2 bite, gnaw\" — not the same. \n\nBut perhaps *ke* prefix for \"eat\"? No. \n\nWait — \"bite\" is a verb for eating. So \"I begin to eat\" might be formed as *kewǣ* + *kē* (stem) for biting. \n\nWe don’t have a first-person \"begin\" form. \n\nPerhaps the verb stem for \"begin\" is *kewǣ* and it is used with a different object. \n\nBut we are missing a first-person \"begin to eat\". \n\nAlternative hypothesis: the verb \"begin\" is the same as \"start\", and for \"I\", we use a different subject marking. \n\nBut none of the examples show first-person \"begin\" with an act of eating. \n\nWait: is there a verb meaning \"eat\" or \"consume\"? \n\nWe have: \n*ketāwahtæq* = we1+2 bite, gnaw a hole in it → likely consumes something \n*kekēskahtæq* = we1+2 bite it through → eats through \n\nBut no verb for \"begin to eat\" with first person. \n\nCould \"I begin to eat it\" be formed from *kewǣ* (begin) + a stem for eating? \n\nWe note that *kewǣ* is used in: \n- *kewǣpeqtaq* — begin (we1+2) \n- *kewǣpānæhkæq* — begin to dig (we1+2) \nSo the root *kewǣ* is shared. \n\nSo likely, \"begin\" is *kewǣ*. \n\nWe need to attach the verb for \"eat\" — which is likely *ketāwaht* or *rekēskaht*. \n\nBut \"I\" is first person, so we need a first-person singular suffix. \n\nNo clear form. \n\nBut what about *ketāwahtæq* = we1+2 bite, gnaw a hole in it — so \"bite\" or \"gnaw\" is a verb for eating. \n\nSo perhaps \"begin to eat\" = \"begin to bite\" → use *kewǣ* + *tāwāh* (bite) + 'it'. \n\nBut without a first-person version of \"begin\", we must look for a pattern. \n\nObservation: the verb *nekāwāhpem* = \"I fall over laughing\" — first person, separate verb. \n\nSimilarly, *nekāweqtam* = \"I lie down\" — first person. \n\nSo verbs do have first-person forms. \n\n\"Begin\" appears only in \"we1+2\" so far. \n\nIs there a first-person realis form of \"begin\"? \n\nNo. \n\nBut perhaps \"begin to bite\" is formed using *kewǣ* as root, and with object, and first person marker. \n\nWe have *kekēskahtæq* = we1+2 bite it through. \n\nBut \"begin to bite\" = begin + bite. \n\nLikely: *kewǣ* + *tāwāh* + object? \n\nBut no such form. \n\nWait — is there a form for \"I begin to cut\"? *kewǣpānæhkæq* = we1+2 begin to dig — digging. \n\nBut no \"begin to eat\". \n\nAlternative: maybe \"begin to eat\" is not a single verb but constructed. \n\nBut we have no form. \n\nPerhaps the verb *ke* is used for \"eat\" or \"consume\". \n\nLook at *kekēskahtæq* = we1+2 bite it through — \"bite\" is common. \n\nBut \"begin\" is *kewǣ*. \n\nSo perhaps: *kewǣ* + *kēskaht* → but that doesn’t match. \n\nWait: *kewǣpānæhkæq* = we1+2 begin to dig — dig is a different verb. \n\nNo verb combining \"begin\" and \"eat\". \n\nBut maybe \"begin to eat\" is just \"begin\" with object, and \"eat\" is implied. \n\nBut the task is to translate. \n\nPerhaps the verb for \"begin\" is used with a stem meaning \"eat\". \n\nBut no such stem. \n\nWait — *ketāwahtæq* = we1+2 bite, gnaw a hole in it → so \"bite\" and \"gnaw\" are used for eating. \n\n\"Begin to eat\" → might be *kewǣ* + *tāwāh* (bite) + object. \n\nBut we need first person. \n\nIs there a form for \"I begin to bite\"? \n\nWe have *ne* for first person: *nekāweqtam* = I lie down, *nekǣtahan* = I pry it out by tool. \n\nSo *ne* is first person. \n\nSo perhaps \"I begin to eat\" = *ne* + *kewǣ* + *tāwāh* + object. \n\nBut is there a form like that? \n\nWe don’t have such a form. \n\nBut perhaps the pattern is: the root *kewǣ* means \"begin\", and when combined with a verb root, it forms \"begin to V\". \n\nSo for \"eat\" → \"bite\" (as in *ketāwahtæq*), so \"I begin to bite it\" → *ne* + *kewǣ* + *tāwāh* + *it*. \n\nBut what is the verb for \"bite\"? In *ketāwahtæq*, it's \"bite, gnaw a hole in it\" — likely the stem is *tāwāh*. \n\nSo verb \"bite\" is *tāwāh*? \n\nBut \"bite\" is in *ketāwahtæq* — present. \n\nSo for \"I begin to bite\", we attach *kewǣ* to *tāwāh*. \n\nSo structure: *ne* + *kewǣ* + *tāwāh* + object. \n\nBut in the data, *kewǣpeqtaq* is \"we1+2 begin\" — no verb. \n\nSo perhaps the root *kewǣ* is used only with an action verb. \n\nIn *kewǣpānæhkæq*, it is \"we1+2 begin to dig\" — dig is the verb. \n\nSo \"begin to dig\" = *kewǣ* + *pānæhk* (dig). \n\nSo \"begin to eat\" → need a verb stem for \"eat\". \n\nIn *ketāwahtæq*, \"we1+2 bite, gnaw a hole in it\" → stem might be *tāwāh*. \n\nSo \"I begin to eat\" → *ne* + *kewǣ* + *tāwāh* + object. \n\nBut no object marker shown. \n\nIn *kewǣpeqtaq*, no object — \"we begin\" — so object \"it\" is implied. \n\nIn *kewǣpānæhkæq*, \"begin to dig\" — object \"it\" implied. \n\nSo \"begin to bite\" likely has object \"it\". \n\nThus, first translation: *ne kewǣ tāwāh it*? But real structure may be in one word. \n\nBut no such word given. \n\nAlternative: perhaps \"begin to eat\" is *kekēskahtæq* with \"begin\"? No. \n\nWait — perhaps the verb \"eat\" is *ke* + stem — but no. \n\nAnother possibility: *ketāwahtæq* = we1+2 bite, gnaw — so \"eat\" is embedded. \n\nBut we need \"begin to eat\". \n\nWe don’t have a first-person \"begin to eat\", so must construct based on pattern. \n\nGiven: \n- \"I lie down\" → *nekāweqtam* \n- \"I pry it out\" → *nekǣtahan* \n- \"I fall over laughing\" → *nekāwāhpem* \n\nSo first-person has *ne* prefix. \n\n\"Begin\" has *kewǣ* in we1+2 forms. \n\nSo likely, \"I begin\" would be *nekewǣ*? \n\nBut not given. \n\nIs there a form like *ne kewǣ*? \n\nWe don’t have it. \n\nBut *kewǣ* is used as root. \n\nSo perhaps \"I begin\" is *ne kewǣ*, and \"to eat\" is the verb. \n\nBut no verb for \"eat\". \n\nLooking at *ke* verbs: \n- *kekǣtohnæq* = we1+2 walk out \n- *ke* in *ketāwahtæq* — \"bite, gnaw\" \n- *ke* in *kekēskahtæq* — \"bite through\" \n\nSo \"ke\" may be root for \"bite\" or \"eat\". \n\nThus, \"eat\" = *ketāwaht* or similar. \n\nSo \"I begin to eat\" = *ne kewǣ ketāwaht*. \n\nBut will this be accepted? \n\nWait — *kewǣ* + *ketāwaht* would be \"begin to bite\" — plausible. \n\nAnd \"I\" is first person. \n\nSo likely: **ne kewǣ ketāwaht** \n\nBut object \"it\" is missing. \n\nIn *kewǣpeqtaq*, \"we begin\" — no object. \n\nIn *kewǣpānæhkæq*, \"we begin to dig\" — \"dig\" is verb. \n\nSo if \"eat\" is the verb, object \"it\" may be implied. \n\nBut the object is not in the translation. \n\nThe phrase is \"I begin to eat it\" — object \"it\" is present. \n\nSo must include. \n\nBut we don't have a marker for \"it\". \n\nIn *kekēskahtæq*, \"we1+2 bite it through\" — object \"it\" is marked. \n\nSimilarly, *pahkǣsam* = \"he cuts it off\" — object \"it\". \n\nSo object is marked. \n\nTherefore, \"I begin to eat it\" → *ne kewǣ ketāwaht it*? \n\nBut is it one word? \n\nLikely word form: from *kewǣ* + *ketāwaht* with object. \n\nBut no such word. \n\nPerhaps the verb \"bite\" is *tāwāh*, and the root is *kewǣ*. \n\nStill, first person *ne* needed. \n\nWe accept that the verb \"begin\" is *kewǣ* with first person *ne*, and \"eat\" is *tāwāh*. \n\nSo → **ne kewǣ tāwāh it** \n\nBut in *ketāwahtæq*, it's \"bite, gnaw\" — so \"tāwāh\" may be root. \n\nThus — b.1: ne kewǣ tāwāh it \n\nBut check with the pattern in the data: \n- *kewǣpeqtaq* = we1+2 begin → no object \n- *kewǣpānæhkæq* = we1+2 begin to dig → \"dig\" verb \n\nSo \"begin to eat\" with first person → likely *ne kewǣ* + verb for eat \n\nVerb for eat = *tāwāh* (from *ketāwahtæq*) \n\nSo b.1: ne kewǣ tāwāh it \n\nNow, second: \"we1+2 lay it flat by hand\" \n\nWe have: \n- *pītenam* = he passes it here → \"pass\" \n- *nekāweqtam* = I lie down \n- *pāhkeqtaw* = he opens up \n- *pahkǣsam* = he cuts it off \n- *pekāwāhpem* = I fall over laughing \n\nIs there a verb for \"lay flat\"? \n\n\"Flat\" and \"by hand\"? \n\nLook at: \n*nepītohnæm* = I walk here (to this place) — walk \n*kekǣtohnæq* = we1+2 walk out \n\nNo \"lay\" or \"place\". \n\nBut \"lay it flat\" → place it down. \n\nWe have *pāhkeqtaw* = he opens up → \"open\" \n\n*kepītahtæq* = we1+2 come eating it; bring in mouths → bring \n\n\"Bring in\" → \"bring\" — perhaps similar to \"lay\"? \n\nBut \"lay\" is set down. \n\nIs there a verb for \"place\" or \"put down\"? \n\nNo direct verb. \n\nBut \"by hand\" suggests \"with hands\". \n\nWe have: *nekǣtahan* = I pry it out by tool → with tool. \n\n*kepītahtæq* = bring it in mouths → with mouth \n\nBut no verb with \"hand\" or \"place\". \n\nWait — *pāhkaham* = he opens it by tool → with tool. \n\nNo verb for \"lay flat by hand\". \n\nPossibility: \"lay flat\" might be formed from a verb for \"place\" or \"set down\". \n\nWe don’t have such a form. \n\nAlternative: could \"lay\" be \"put\" or \"place\", and in Menominee, the root might be from *kewā* or *pī*? \n\nWe have *pītenam* = he passes it here — pass. \n\nNo match. \n\nWait — *nepītohnæm* = I walk here — walk to place. \n\nNo. \n\nBut is there a stem for \"place\"? \n\nNot present. \n\nCould \"lay it flat\" be expressed as \"we1+2 set it down\"? \n\nWe don’t have that. \n\nBut look at *kekēskahtæq* = we1+2 bite it through — not relevant. \n\nAnother idea: \"lay flat\" might be similar to \"pass\" or \"bring\", but not. \n\nBut in the data, we have forms with \"by hand\". \n\nFor example: \n- *ne* + *kāwāh* = I fall over laughing → laughing \n- *ne* + *kǣtah* = I pry it out by tool → by tool \n\n\"By hand\" is not spelled in any form. \n\n\"By hand\" may be marked by absence of tool. \n\nWe have *pahkǣsam* = he cuts it off — by hand? (not specified) \n\n*kepītahtæq* = we1+2 come eating it → bring in mouth \n\nNo. \n\nWait — *pāhkeqtaw* = he opens up — open \n\nNo. \n\nNo verb matches. \n\nBut perhaps \"lay it flat\" is not in the data, so we must infer from patterns. \n\nIs there a verb with \"set down\"? \n\nNo. \n\nAlternative: \"lay flat\" could be a physical action, and in Menominee, such verbs may be missing. \n\nBut we must translate. \n\nPerhaps \"lay it flat\" is formed with verb like *pī* or *ke* with \"flat\". \n\nNo. \n\nWait — *nepītohnæm* = I walk here — walk to place. \n\nCould \"lay\" be a form of \"put\"? \n\nNo. \n\nPerhaps the verb is *kewā* or something. \n\nAnother idea: \"we1+2 lay it flat by hand\" — \"by hand\" may be implied", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11811.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build alignment table from given examples:\n\n| English | Menominee | Notes |\n|--------|-----------|-------|\n| we1+2 begin | kewǣpeqtaq | plural subject, begin (action) |\n| he fells it by tool | kawāham | tool used: \"by tool\" |\n| I walk here (to this place) | nepītohnæm | \"I\", place: \"here\" |\n| he breaks it through by hand | kēskenam | hand used: \"by hand\" |\n| he cuts it off | pahkǣsam | cutting, separation |\n| we1+2 walk out | kekǣtohnæq | we1+2, \"walk out\" |\n| he passes it here | pītenam | \"passes it here\" |\n| we1+2 begin to dig | kewǣpānæhkæq | begin + dig |\n| he cuts a hole in it | tawǣsam | cuts a hole |\n| I pry it out by tool | nekǣtahan | \"I\", tool used |\n| he opens it by tool | pāhkaham | tool used |\n| we1+2 bite it through | kekēskahtæq | plural, bite through |\n| he walks roundabout, by detour | wackōhnæw | detour walking |\n| I cut around it | newāckesan | \"I\", cut around |\n| he takes it out by hand | ketǣnam | hand used |\n| we1+2 bite, gnaw a hole in it | ketāwahtæq | plural, bite/gnaw hole |\n| he begins walking | wǣpohnæw | begins walking |\n| I lie down | nekāweqtam | \"I\", lie down |\n| he opens up | pāhkeqtaw | \"he\", opens up |\n| we1+2 come eating it; we1+2 bring it in our mouths | kepītahtæq | plural, eating, bringing in mouth |\n| I fall over laughing | nekāwāhpem | \"I\", laughter |\n\nNow, analyze each target translation:\n\n1. \"I begin to eat it\" \n - \"begin\" appears in: kewǣpeqtaq (we1+2), kewǣpānæhkæq (we1+2 begin to dig) \n - \"eat\" is not directly listed, but \"bite\" appears: \"we1+2 bite it through\" = kekēskahtæq, \"bite, gnaw a hole\" = ketāwahtæq \n - \"come eating\" = kepītahtæq → \"we1+2 come eating it\" \n - \"I\" is \"ne-\" prefix (e.g. nekāweqtam: I lie down, nekǣtahan: I pry it out) \n - \"begin to eat\" → need a verb with \"begin\" + \"bite/eat\" \n - kewǣpānæhkæq = begin + dig; suggest pattern: \"begin\" + verb \n - Look for \"begin\" + \"bite/eat\" → no direct match \n - But \"come eating\" implies eating actively \n - \"kepītahtæq\" = we1+2 come eating → implies \"come to eat\" \n - \"I begin to eat\" → base structure: \"begin\" + \"eat\" \n - \"eat\" is similar to \"bite\" or \"gnaw\" → use \"bite\" as primary verb \n - \"I begin to bite it\" → could be derived from \"begin\" + \"bite\" \n - \"begin\" = kewǣpā- (in kewǣpānæhkæq) \n - \"bite\" = kēska- or keta- \n - \"we1+2 bite it through\" = kekēskahtæq → \"we\" + \"bite through\" \n - \"I bite\" (root) → \"nekēskaht\" (replace we with ne?) \n - In \"nekāweqtam\" → \"I lie down\", \"nekāwāhpem\" → \"I fall laughing\" \n - Subject marker: \"ne-\" for \"I\" \n - So \"I begin to bite\" = ne + begin + bite → ne + kewǣpā + kēska? \n - kewǣpānæhkæq = we1+2 + begin + dig → \"begin\" affix: kewǣpā- \n - \"bite\" → kekēskahtæq = we1+2 + bite + through \n - \"begin\" + \"bite\" → need a form like \"kewǣpā + kēska\" \n - But the verb \"bite\" does not appear separately \n - Instead, \"kepītahtæq\" = \"we1+2 come eating\" → eating is present \n - \"I begin to eat it\" → likely \"I begin to bite it\" → use \"bite\" as proxy \n - Best fit: \"ne + kewǣpā + kēskaht\" → but not known \n - Look at \"kepītahtæq\": \"we1+2 come eating\" → combines \"eating\" into a verb \n - But \"begin to eat\" = likely \"begin\" + \"eat\" → if \"eat\" = \"bite\", then use bite \n - Most plausible: \"ne\" + \"kewǣpā\" + \"kēskaht\" → \"I begin to bite it\" \n - But \"kēskaht\" is in kekēskahtæq (we1+2 bite through) \n - Drop \"through\" → \"kēskaht\" = bite \n - \"I begin to bite\" → ne + kewǣpā + kēskaht → nekewǣpkēskaht? \n - But no such form in examples \n - Alternative: perhaps \"begin to eat\" = \"begin to take\" \n - \"he takes it out by hand\" = ketǣnam → \"take out by hand\" \n - \"begin to take\" → no form \n - Reexamine: \"we1+2 come eating it\" = kepītahtæq → \"come eating\" \n - \"begin\" may not have a direct form \n - But \"kewǣpeqtaq\" = \"we begin\" \n - \"begin to eat\" → could be a derivation of \"begin\" + eating \n - Eating = \"come eating\" → so \"I begin to come eating\"? Unnatural \n - Best pragmatic choice: use the verb \"bite\" as representative of eating \n - So: I begin to bite it → ne + kewǣpā + kēskaht → nekewǣpkēskaht \n\nBut check: is there a simpler pattern?\n\n\"we1+2 begin to dig\" = kewǣpānæhkæq → kewǣpā- + -næhkæq \n\"he walks out\" = kekǣtohnæq → we1+2 walks out \n\"he begins walking\" = wǣpohnæw → \"he begins walking\" → singular, not plural \nSo \"begin\" exists as root: wǣpohnæw = he begins walking\n\nThus: \"he begins walking\" = wǣpohnæw → so \"begin\" root is wǣp-? wǣpohnæw → wǣpo + -hnæw\n\nBut kewǣpeqtaq = we1+2 begin → kewǣp- + eqtaq \nSo \"begin\" stem is kewǣp- (we1+2), wǣpo- (he)\n\nSo \"I begin\" → ne + wǣpo + ? \n\"he begins walking\" = wǣpohnæw → wǣpo + hnæw → \"begins walking\" \n→ so \"begin\" stem: wǣpo- for \"he\" \nFor \"I\" → ne + wǣpo + ? → ne + wǣpo + hnæw = \"I begin walking\"? But we need \"begin to eat\"\n\nBut no verb for \"eat\" directly\n\nHave \"come eating\" = kepītahtæq → involves \"eating\" \n\nPerhaps \"begin to eat\" = \"begin to come eating\" → ne + wǣpo + kepītaht? → newǣpōkepītaht?\n\nBut not supported\n\nAlternative: eat = \"bite\" → so \"I begin to bite it\" → ne + wǣpo + kēskaht? \n\nBut kēskaht is in kekēskahtæq → we1+2 bite through \n\n\"bite\" = kēska- \n\nSo \"I begin to bite\" = ne + wǣpo + kēskaht → newǣpōkēskaht \n\nBut not in examples – is it plausible?\n\nYes, given the pattern of \"begin\" affix and \"bite\" root.\n\nSo → nekewǣpkēskaht? But that uses \"kewǣp\" which is for \"we\" \n\nOnly \"we\" and \"he\" are given \n\n\"we1+2 begin\" = kewǣpeqtaq → kewǣp- is only for we \n\n\"he begins\" = wǣpohnæw → wǣpo- \n\nSo for \"I\" → must use different prefix? \n\nThe prefixes: \n- ne- = I \n- kew- = we1+2 \n- k- = he? → kawāham = he fells it \nYes: kawāham → \"k\" = he \nSo he = k- \nI = ne- \n\nThus: \n- \"he begins\" = wǣpohnæw = wǣpo + hnæw \n- \"begin\" stem = wǣpo- \n- \"bite\" = kēskaht (in kekēskahtæq) \n- So \"I begin to bite\" = ne + wǣpo + kēskaht → newǣpōkēskaht \n\nBut is there a verb for \"eat\" as \"bite\"? In context, yes – biting/eating is implied \n\nSo accept: **newǣpōkēskaht**\n\n2. \"we1+2 lay it flat by hand\" \n- \"lay flat\" → not in list \n- \"walk here\" = nepītohnæm → \"I walk here\" \n- \"cut through by hand\" = kēskenam → \"he breaks through by hand\" \n- \"take it out by hand\" = ketǣnam → \"by hand\" \n- \"lay flat by hand\" → may be equivalent to \"place flat by hand\" \n- \"flat\" not available \n- \"lay\" → not directly \n- But \"place\" → similar to \"set down\" \n- \"we1+2\" = kew- \n- \"by hand\" = kēskenam → \"break through by hand\" → hand used \n- So \"by hand\" = kēsken- or kēska-? \n- kēskenam = he breaks through by hand \n- \"break\" may be used for \"lay\"? Unlikely \n- Alternative: \"pītenam\" = he passes it here → \"passes\" \n- \"pāhkeqtaw\" = he opens up \n- Perhaps \"lay flat\" = \"place down\" \n- No such verb \n- But look at \"we1+2 walk out\" = kekǣtohnæq → \"walk out\" \n- \"we1+2 walk here\" → not given \n- Only \"walk here\" is with \"I\" \n- \"we1+2 walk out\" = kekǣtohnæq \n- So no \"lay\" \n- Is \"lay flat\" ≈ \"set down\"? \n- Equivalents: \"take it out\", \"cut it off\" \n- Perhaps \"lay flat\" = \"cut it down\", \"flatten\"? \n- \"cut a hole\" = tawǣsam → cuts a hole \n- \"cut around\" = newāckesan → cut around \n- \"cut it off\" = pahkǣsam → cut off \n- \"lay flat\" → not directly \n- Is there a verb like \"place\" or \"put\"? \n- \"pass it here\" = pītenam \n- \"open it\" = pāhkaham or pāhkeqtaw \n- No \"lay\" \n- But consider \"begin to dig\" = kewǣpānæhkæq \n- \"dig a hole\" = next item \n- Perhaps \"lay flat\" is approximated by \"break it through\" or \"cut\"? \n- No \n- Alternative: in some contexts, \"lay\" = \"set\" → perhaps from \"pass\" or \"bring\" \n- We have \"we1+2 come eating it\" = kepītahtæq → bring in mouth \n- But not laying \n- After analysis: no exact match \n- But \"lay it flat by hand\" → possibly \"he breaks it down\" or \"opens it\" \n- \"he opens it by tool\" = pāhkaham → by tool \n- \"by hand\" → kēskenam (by hand) \n- But \"lay flat\" → unfamiliar \n- Is there a verb for \"to place flat\"? \n- Look at \"we1+2 walk out\" = kekǣtohnæq → walk out \n- \"walk here\" = nepītohnæm → I walk here \n- Perhaps \"lay\" ≈ \"set\" = absent \n- But perhaps a morpheme can be derived: \"we1+2\" + \"place\" + \"by hand\" \n- No such form \n- Final idea: perhaps \"lay\" is a synonym for \"put\", and \"flat\" is \"down\" \n- \"we1+2 put it down by hand\" → could be derived from \"take it out\" or \"pass it\" \n- \"pass it here\" = pītenam → “passes it here” → \"here\" is location \n- \"put it down\" → could be a verb not listed \n- Given no example, perhaps it is kēskenam with different object – but location not matched \n- Wait: \"cut a hole in it\" = tawǣsam → cuts hole \n- \"cut it off\" = pahkǣsam \n- \"cut around\" = newāckesan \n- \"lay flat\" → not directly possible \n- But think: in farm/settlement contexts, \"lay\" might be like \"set flat\" \n- Could it be equivalent to \"break it through\"? Not really \n- Perhaps \"lay flat\" = \"open it\" → but \"open\" ≠ \"lay flat\" \n- Is \"pāhkeqtaw\" = \"he opens up\" → opening \n- \"lay flat by hand\" → may be morphed as \"we lay it flat by hand\" → kew- + lay + by hand \n- But no such verb \n- After review: no verb for \"lay\" \n- However, perhaps \"lay\" is missing and must be inferred from onset \n- But no example has \"lay\" \n- Alternative: \"we1+2 place it flat\" → by hand → use verb from \"break\" or \"cut\"? \n- Final decision: look for a match to \"by hand\" and \"place\" \n- \"by hand\" = kēskenam → kēsken- \n- \"we1+2\" = kew- \n- But \"kewēskenam\"? Is that a form? \n- kēskenam = he breaks through by hand → k + e + s + k + en + am \n- kewēskenam → we1+2 break through by hand? \n- Not in list \n- But \"break through\" = kēskenam \n- \"lay flat\" is not \"break through\" \n- After careful thought: no example matches \n- Perhaps \"lay flat\" is equivalent to \"set down\" → and \"set down\" may be absent \n- But \"we1+2 come eating\" → involves bringing in mouth \n- Perhaps \"lay\" is not needed, but the task is to translate \n- Must find a form \n- Given no direct, perhaps it's \"we1+2 lay it flat by hand\" = kewēskenam? \n- But \"break\" not \"lay\" \n- Or: \"we1+2 open it flat\" → not supported \n- Conclusion: no match → but must infer \n- Perhaps \"lay flat\" = \"begin to place\" → no \n- Abandon: likely a misreading \n- Wait: \"we1+2 walk out\" = kekǣtohnæq \n- \"he walks roundabout\" = wackōhnæw → detour \n- No \n- Final: no direct verb → revert to \"by hand\" affix and subject \n- Best available: perhaps \"kewēskenam\" but it means \"break through\" \n- Not valid \n- Alternative idea: \"lay\" might be derived as \"set\", like \"place\" \n- But no \n- Perhaps \"dig a hole\" is related — for hole, not flat \n- After full analysis: no candidate \n- But compare to \"we1+2 come eating it\" = kepītahtæq \n- \"kepītahtæq\" = we1+2 come eating → eating is central \n- Perhaps \"lay it flat\" is not expressible \n- But must provide answer \n- Given that no such form exists, and \"by hand\" appears in kēskenam, and \"we1+2\" in kew- \n- Perhaps: kewēskenam → we1+2 break through by hand → not \"lay flat\" \n- Final decision: likely a different verb; no evidence \n- Perhaps \"lay flat\" = \"set down\" → use \"put\" → absent \n- After rechecking: no example \n- Wait — \"we1+2 walk here\" = nepītohnæm → \"walk here\" \n- \"here\" = to this place \n- \"lay flat\" = to this place? \n- Only matching: no \n- Final: assume \"lay flat by hand\" = kewēskenam is not correct \n- Maybe \"pāhkeqtaw\" = open up → not relevant \n- After deep analysis: skip and come back \n- Actually, \"lay it flat\" may be equivalent to \"place it down\" \n- No such", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11318.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "Step 1: Analyze the given verb forms and their translations to extract core morphological patterns.\n\nWe are to translate: \n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out\n\nWe look for relevant verb forms in the data:\n\n- “kewǣpeqtaq” = we1+2 begin → base: *kewǣp* (begin) + *eqtaq* (we1+2) \n- “kewǣpānæhkæq” = we1+2 begin to dig → so *kewǣpān* (begin to dig), derived from *kewǣp* + *ān* (dig) \n- “kekǣtohnæq” = we1+2 walk out → *kekǣ* (walk) + *tohnæq* (out) \n- “pahkǣsam” = he cuts it off → cutting action \n- “tawǣsam” = he cuts a hole in it → cuts a hole \n- “nekāweqtam” = I lie down → lying down, not relevant \n- “wǣpohnæw” = he begins walking → begin walking \n- “kepītahtæq” = we1+2 come eating it; we1+2 bring it in our mouths → eating action \n- “kēskenam” = he breaks it through by hand → breaks by hand \n- “pītenam” = he passes it here → motion \n- “nektāwahtæq” = we1+2 bite, gnaw a hole in it → gnawing \n- “nekǣtahan” = I pry it out by tool → using tool \n- “pāhkaham” = he opens it by tool \n\nNote: There is no direct “eat” or “lay flat by hand” verb in the given list. But “kekāwāhpem” = I fall over laughing — not relevant. “kepītahtæq” = we1+2 come eating it — implies eating. So eating is expressed via “come eating it” (i.e., bring in mouth). “begin to eat” → likely related to “begin to do something” with action being \"eat\".\n\nLooking for a root meaning “begin” and “eat” or “consume”.\n\nFrom “kepītahtæq” = we1+2 come eating it; bring it in mouth → suggests “consume” via mouth.\n\nAlso, for “begin to do” — we find:\n- “kewǣpeqtaq” = we1+2 begin\n- “wǣpohnæw” = he begins walking\n→ “begin” appears with *kewǣp* (or *wǣp*)?\n\nBut “begin to dig” → “kewǣpānæhkæq” = we1+2 begin to dig\n\nSo “begin to” = *kewǣp* + root verb?\n\nBut for “begin to eat” — if “eating” is “come eating it”, then \"come\" might be related to \"bring or eat\" — but not \"begin to eat\".\n\nWe need a verb for “begin to eat”.\n\nBut no direct match. However, “kepītahtæq” contains \"eating\", so the verb for eating must be built with *tahtæq* — possibly of root *taht* or *hāt*, as in “come eating it”.\n\nIs there a root for “eat”?\n\nWe can build from: “kepītahtæq” = we1+2 come eating it → implies eating is part of the verb.\n\nIf \"begin to eat\" = “begin” + “eat”, and “begin” is \"kewǣp\", and eating is \"taht\", then \"kewǣp\" + \"taht\"?\n\nBut there’s no direct form.\n\nAnother idea: “begin” verbs in Menominee often use *kewǣp* or *wǣp* → “wǣpohnæw” = he begins walking → suggests *wǣp* + *ohnæw* = begins walking.\n\nSimilarly, “kewǣpeqtaq” = we1+2 begin → *kewǣp* + *eqtaq* → so the root “begin” is *kewǣp*.\n\nSo \"begin to eat\" → possibly *kewǣp* + *tahtæq* (eating), if \"tahtæq\" is \"eat\" or \"come eating\".\n\nBut we have “kepītahtæq” = we1+2 eat (come eating) → so the verb is “tahtæq” or “pihtæq”?\n\nRoots: “pi” might be for “pass”, “ta” might be for “eat”.\n\nBut “nektāwahtæq” = we1+2 bite/gnaw a hole → “waht” might be “bite”.\n\nSo “taht” → possible for “eat” or “bite”.\n\nThis is not clear.\n\nAlternative: Perhaps “begin to eat” is not directly available — but maybe “we1+2 come eating it” is the closest. But we need “I begin to eat it”.\n\nCould “I begin to eat” be built from “begin” + “eat”, and “eat” is a root?\n\nWe see “nekāweqtam” = I lie down — not relevant.\n\nWe see “pītenam” = he passes it here — motion.\n\nWe have “kēskenam” = he breaks it through by hand → breaks by hand.\n\nWe have “pītenam” = he passes it here → movement.\n\nFor “lay it flat by hand” — “flat” and “by hand”.\n\nWe have “kēskenam” = breaks through by hand → “by hand” marked with “by hand”.\n\nAlso, “nekāweqtam” = I lie down — lying, not laying flat.\n\n“pāhkeqtaw” = he opens up → opening.\n\n“pāhkaham” = he opens it by tool.\n\n“kewǣpānæhkæq” = we1+2 begin to dig → “dig” root is *ān*.\n\nSo “dig” = *ān* (as in *pahkǣsam* = cuts off; *tawǣsam* = cuts a hole).\n\nWe have no verb for “dig a hole” — but “tawǣsam” = cuts a hole → that is “cut a hole in it”. Could “dig a hole” be synonymous with “cut a hole” in this context?\n\nPossibly, in some usage, “dig a hole” = “cut a hole in the ground”.\n\nBut “tawǣsam” = he cuts a hole in it → “in it” — the object is not specified. So “he cuts a hole in it” is given.\n\nBut “he digs a hole” → if “dig” is “cut a hole”, then likely *tawǣsam* (he cuts a hole in it) → can be used.\n\nBut we need to specify the object? The translation is “he digs a hole” — no object mentioned — so general.\n\nSo: “he digs a hole” → possibly *tawǣsam*, if “a hole” is implied.\n\nBut is there a better match?\n\nWe have “kewǣpānæhkæq” = we1+2 begin to dig → begins digging.\n\nSo “dig” = *ān*, in form *pahkǣsam*? No — *pahkǣsam* = cuts off.\n\nWait — *pāhkaham* = he opens it by tool.\n\nPerhaps *ān* is from *kewǣpān* (begin to dig), so root *ān*.\n\nIs “dig” directly from *ān*?\n\nWe have no standalone “dig”.\n\nBut “tawǣsam” = cuts a hole — likely same as digging a hole.\n\nSo likely, “he digs a hole” → *tawǣsam*.\n\nBut object is missing — we assume “in it” is implied.\n\nSo conclusion: (3) he digs a hole → *tawǣsam*\n\n(4) he walks out → we have “kekǣtohnæq” = we1+2 walk out → so “he walks out” → *kekǣtohnæq* → subject is “he” → possible with *kekǣ* for “walk” + *tohnæq* for “out”.\n\nSo “he walks out” → *kekǣtohnæq*\n\nNow (2) we1+2 lay it flat by hand.\n\n“lay flat” → flat → no direct verb.\n\nBut “by hand” — we have “breaks through by hand” = *kēskenam*\n\n“break” → *kēs* or *kēske*?\n\n“kēskenam” = he breaks it through by hand → so “by hand” is marked in the verb.\n\nSimilarly, “pāhkeqtaw” = he opens up — “opens up” → not by hand.\n\n“nektāwahtæq” = we1+2 bite, gnaw a hole — not flat.\n\nBut “lay flat” → perhaps related to “break” or “pass”?\n\nWe have “pītenam” = he passes it here → “passes here”.\n\nNo “flat” or “lay”.\n\nBut perhaps “way to lay flat” is equivalent to “place on a plane”.\n\nIs there a verb with “by hand”?\n\nWe have “kēskenam” → breaks by hand → so “by hand” appears with “kēs” (break) root.\n\nBut could “lay flat” be built from “place” or “set down”?\n\nNo direct verb.\n\nBut perhaps “lay” is similar to “break” in the use of “by hand”.\n\nNote: “lay it flat” → likely a physical movement.\n\nAlso, “come eating it” is given — so eating is done with mouth.\n\nBut “begin to eat” → we need a verb combining “begin” and “eat”.\n\nThe only verb with “eat” is “kepītahtæq” → we1+2 come eating it.\n\nSo “come eating” implies eating.\n\nBut “begin to eat” — “begin” is encoded in *kewǣp*.\n\nIs there a form like *kewǣp + taht*?\n\nNo such form directly.\n\nBut “wǣpohnæw” = he begins walking → so “begin” = *wǣp*.\n\n“kewǣpeqtaq” = we1+2 begin → *kewǣp*.\n\nSo “begin” is expressed through *kewǣp*.\n\nNow for eating — if “come eating” is the expression, maybe “begin to eat” is *kewǣp* + *taht*?\n\nBut no such form exists.\n\nPerhaps “begin to eat” is “we1+2 begin to eat” — meaning “we and you begin to eat it” — but subject is “I”.\n\nSo “I begin to eat it” → must be first person singular.\n\nWe don’t have a form for “I” + “begin” + “eat”.\n\nBut focus on available morphemes.\n\nWe have: \n- “begin” = kewǣp (we1+2) or wǣp \n- “eat” → from “kepītahtæq” — the root is likely *taht* \n- “by hand” = in “kēskenam” — “break by hand” → so “by hand” is a suffix or prefix?\n\nLooking at “kēskenam” — *kēs* (break) + *ken*? *kēske*? *kēskenam* — likely *kēs* + *kenam* → \"break through by hand\"\n\nSimilarly, “kawāham” = he fells it by tool → “by tool”\n\n“nekāweqtam” = I lie down → no tool or hand.\n\nSo “by hand” is a mode marker.\n\nNow, we need “lay it flat by hand” → action \"lay flat\", at a certain location.\n\nIs there a verb meaning “place”?\n\nNot directly.\n\nBut “lay flat” might be like “pass” or “set down”.\n\nWe have “pītenam” = he passes it here → “passes here” — movement.\n\nNo “lay flat”.\n\nBut “flat” is not directly expressed.\n\nAlternative: maybe “lay flat” is equivalent to “place it down” or “set on plane”.\n\nBut no verb.\n\nWe may need to infer that “by hand” is present, so use a verb with “by hand” affix.\n\nWe have no verb meaning “lay flat”.\n\nBut perhaps “break” is used for “lay flat” incorrectly?\n\nUnlikely.\n\nWait — “kewǣpānæhkæq” = we1+2 begin to dig → *kewǣp* + *ān* + *æhkæq*\n\n“dug” is not there.\n\nBut perhaps “dig a hole” = “cut a hole” = tawǣsam\n\nSo (3) he digs a hole → tawǣsam\n\n(4) he walks out → kekǣtohnæq\n\n(1) I begin to eat it → from “kepītahtæq” = we1+2 come eating it → so “come eating” = eating action.\n\n“begin to eat” → perhaps not directly, but use *kewǣp* + *taht*?\n\nWe have no verb with “kewǣp” + “taht”.\n\nWe have *kewǣp* + *eqtaq* = begin\n\n*kewǣp* + *ānæhkæq* = begin to dig\n\nSo “begin to eat” → possibly *kewǣp* + *tahtæq*\n\nBut “tahtæq” appears in “kepītahtæq” = we1+2 come eating it\n\nSo *tahtæq* = come eating → so eating with *taht*.\n\nThus, “I begin to eat” → first person? \"I\" — so object is “it”\n\nWe know no first person form for “begin” or “eat”.\n\nBut perhaps “begin” is *wǣp* (he begins walking)\n\nWe have “wǣpohnæw” = he begins walking → *wǣp* + *ohnæw*\n\nSo “begin” = *wǣp* or *kewǣp*\n\nFor first person, no form.\n\nBut “I” is “ne” in subject? “nekāweqtam” = I lie down — so “ne” is first person.\n\nSo perhaps first person “begin” is *ne* + *wǣp*?\n\nBut not given.\n\nPerhaps “begin to eat” is not directly available — but the only eating verb is *taht* — so use “begin” with that.\n\nWe have no data for \"I begin to eat\".\n\nAlternative: perhaps in Menominee, “begin to eat” is expressed as “come eating” when done in a group — but “I” makes it different.\n\nBut in absence, perhaps the closest is to form from known roots.\n\nNote: “kepītahtæq” = we1+2 come eating it → so the verb “come eating” exists.\n\n“come eating” = “begin to eat” in some contexts?\n\nPossibly.\n\nBut “I” not present.\n\nAnother idea: perhaps “begin to eat” is “I start eating it” — and “start” = “begin”, so *ne* + *wǣp* + *taht*?\n\nNo such form.\n\nBut there is no direct verb.\n\nPerhaps in this language, “begin to eat” is not marked with “begin” but by being initiated — so use “come eating” as a default.\n\nBut topic is translation.\n\nWe must find the most plausible form.\n\nLet’s try to form each:\n\n(1) I begin to eat it \n→ likely *ne* + *wǣp* + *taht* → but no such form \n→ is there a verb like “ne” + “kewǣp”?\n\nWe have “nekāweqtam” = I lie down → “ne” + “kāw”?\n\nNo “kewǣp”\n\nWe have “ne” in “nekāweqtam” and “nekāweqtam” — so “ne” is first person.\n\nBut “ne” + “wǣp” = I begin?\n\nWe have “wǣpohnæw” = he begins walking → not “I”\n\nNo first person for “begin”.\n\nThus, perhaps “begin” is expressed differently.\n\nBut “kewǣpeqtaq” = we1+2 begin → so “we1+2” = plural inclusive.\n\nSo for “I”, no “begin” form in data.\n\nThis suggests that “begin to eat” may not be directly formable — but perhaps the verb “come eating” is used with “begin” meaning.\n\nAlternatively, perhaps “eat” is not the verb — “bite” is there — “nektāwahtæq” = bite, gnaw.\n\nBut “eat” is likely “taht”.\n\nGiven the lack of a form, perhaps it is inferred that “begin to eat” uses the structure of “we1+2 begin” with the eating root.\n\nBut for first person, we are forced to assume that the morpheme for “begin” is shared.\n\nPerhaps in Menominee, “begin” is used with the action verb.\n\nAnother possibility: “I begin to eat it” = “I start eating it” → and “start” is equivalent to “begin”.\n\nBut without a first person “begin”, the only way is to use a verb like “ne” + “wǣp” + “taht”.\n\nSince no such form is given, but the pattern of root combinations shows that “begin” is attached to the action via root.\n\nWe can proceed cautiously:\n\n(1) I begin to eat it → ne + wǣp + taht → but we have no “ne” + “wǣp” form.\n\nHowever, “wǣpohnæw” = he begins walking → so “wǣp” + “ohnæw” = begins walking → so “begin” = *wǣp*\n\nSo “I begin” = *ne* + *wǣp*\n\nThen “to eat” = “taht” → so *ne wǣp taht*?\n\nBut no such form.\n\nBut “kepītahtæq” = we1+2 come eating it → suggests *taht* is the root.\n\nSo likely \"begin to eat\" = “begin” + “taht”\n\nWe have only “we1+2” for “begin”.\n\nBut “I” is “ne”.\n\nNo data.\n\nPerhaps “I begin to eat” is built as “ne” + “kewǣp”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11835.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 0, + "output": "First, build an alignment table from the given examples to extract patterns in time expressions and verb constructions in Nooni.\n\nKey days used:\n- Bvutfu: Day 1 (used in 1, 2, 5, 13)\n- Bvusɔw: Day 2 (used in 2, 4, 5, 6, 7)\n- Bvuzhi: Day 3 (used in 3)\n- Bvuŋka: Day 4 (used in 4, 5, 12, 13, 14, 15)\n- Bvuŋkaden: Day 5 (used in 8, 9, 10, 11)\n\nFrom the examples:\n- The day names are followed by “nú” or “nú” + a suffix indicating reference time.\n- Time references use prefixes: “ntfǔː” = tomorrow; “cɛ́” = today; “wɔ̀” = yesterday; “fɔ̀ shě” = day after tomorrow; “kefwé” = day before yesterday.\n\nBreak down time markers:\n- \"ntfǔː nú X\" → Tomorrow is X\n- \"fɔ̀ shě ntfǔː nú X\" → The day after tomorrow is X\n- \"kefwé cí nú X\" → The day before yesterday was X\n- \"me nú mbóy ncáw mutù X\" → On X, I will choose the car\n- \"wvù tɔ̀ nɔ̂ː ...\" → He found the book on X\n- \"kwɔ᷆ːn nǔ bóy fí me X\" → On X, the woman will help me\n- \"bèsèn\" = today? Used in \"bèsèn nǔ géː\" → today we will steal\n\nNote: \"bèsèn\" = today; \"me nú\" = I will; \"kwɔ᷆ːn nǔ\" = the woman; \"fí me\" = will help me\n\nNow observe the time expressions in relation to days.\n\nExample 8: \"ntfǔː nú bvûŋka᷆ːde᷆n\" → Tomorrow is Bvuŋkaden → Bvuŋkaden = tomorrow of Bvuŋka\nSo:\n- Bvuŋka → Day 4\n- Bvuŋkaden → Day 5\n\nExample 11: \"kefwé cí nú bvûŋka\" → The day before yesterday was Bvuŋka → Bvuŋka was two days before the current day → So current day is Bvuŋkaden → consistent\n\nThus, days are ordered:\n- Bvutfu → Day 1\n- Bvusɔw → Day 2\n- Bvuzhi → Day 3\n- Bvuŋka → Day 4\n- Bvuŋkaden → Day 5\n\nNow analyze the sentences spoken on Bvuŋkaden (Day 5).\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ \"On Bvusɔw, the day after tomorrow is [something]\" \nWait: \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow is [X]\" \nBut this seems to be a noun clause. \nCompare to 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → The day after tomorrow is Bvutfu \nSo, “fɔ̀ shě ntfǔː” = day after tomorrow → “fɔ̀ shě ntfǔː nú X” = day after tomorrow is X \n\nBut here: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → On Bvusɔw, the day after tomorrow is [something]? \nNo, structure is “BVUSOW NỮ FŌ ŠĒ NTFU” \nMore likely: “On Bvusɔw, the day after tomorrow is [something]” → but what?\n\nWait: In example 5, we have “fɔ̀ shě ntfǔː nú bvútfu᷅” → the day after tomorrow is Bvutfu \nBut here: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — perhaps the day after tomorrow is Bvusɔw? \nNo, that would be ungrammatical.\n\nAlternative: \"nǔ\" = subject? \"bvúsɔ̀w\" = subject, \"nǔ\" = \"you\"? But \"nǔ\" is used with \"you(sg)\" in example 2.\n\nWait: Example 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → On Bvusɔw, you will steal the yam. \nSo \"nǔ\" = you (sg) \n\"nǔ\" may be a subject marker.\n\nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → On Bvusɔw, you (sg) will [do] the day after tomorrow?\n\nDoesn't parse.\n\nWait — perhaps it's \"On Bvusɔw, the day after tomorrow is [X]\" — but X is missing.\n\nBut no noun after. So maybe it's a broken translation?\n\nWait — other example: 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → On Bvutfu, the woman saw the market.\n\nPattern: [noun] cǐ nɔ̂ː [object] wáy [place] → On X, the woman saw the place.\n\n\"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → On Bvutfu, the woman saw the market\n\nSo: [subject] cǐ nɔ̂ː [object] wáy [place] → On X, subject saw object at place\n\nBut here: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → On Bvusɔw, you (sg) will [day after tomorrow]? \n\nWait — perhaps “fɔ̀ shě ntfǔː” is a time expression, and the whole is saying \"On Bvusɔw, the day after tomorrow is [something]\" — but no [something].\n\nPerhaps it’s missing a day name.\n\nBut look at example 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → day after tomorrow is Bvutfu\n\nSo “fɔ̀ shě ntfǔː nú X” = the day after tomorrow is X\n\nHere, it’s “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — possibly “on Bvusɔw, you will be on the day after tomorrow”?\n\nNot clear.\n\nAnother possibility: the structure \"X nǔ Y\" where X is a day and nǔ is a verb?\n\nIn example 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → On Bvuzhi, the woman will help me.\n\nSo \"X nǔ Y\" = On X, Y will do something.\n\nBut \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — On Bvusɔw, you will [be] the day after tomorrow?\n\nNo.\n\nWait — “fɔ̀ shě ntfǔː” is “the day after tomorrow” → this is a time noun.\n\nSo “bvúsɔ̀w” is the day. “nǔ” is the verb? Then what is the verb?\n\nCompare: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → On Bvusɔw, you will steal the yam.\n\nSo \"on X, you (nǔ) will steal Y\"\n\nThus, \"nǔ\" is a subject marker (you), not a verb.\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → On Bvusɔw, you (sg) will be [the day after tomorrow]? Unlikely.\n\nPerhaps it's a typo or misorder.\n\nWait — another possibility: “fɔ̀ shě ntfǔː” is the day after tomorrow → so on Bvusɔw, the day after tomorrow is [something]?\n\nBut no object.\n\nCheck if \"ntfǔː\" can be used as a place.\n\nIn 13: “yɛ᷅n wáy é bvútfu᷅” → saw the market at Bvutfu\n\nSo indicating location at a day.\n\nBut here, only time.\n\nBut in 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” — woman saw market at Bvutfu\n\nSo time expressed as \"on Bvutfu\"\n\nSimilarly, in 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → perhaps it's \"On Bvusɔw, the day after tomorrow is [something]\" — but what?\n\nUnless the “fɔ̀ shě ntfǔː” is a noun phrase meaning \"a day\" and is being associated.\n\nBut missing object.\n\nWait — in example 13, \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" — the woman saw the market at Bvutfu\n\nSo structure: [subject] cǐ nɔ̂ː [object] wáy [place] → saw object at place\n\nBut in 16: no object.\n\nAnother idea: the pattern might be \"X nǔ Y\" where Y is a verb form.\n\nBut “fɔ̀ shě ntfǔː” is a time expression.\n\nPerhaps it’s a copy error.\n\nLook at 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = I will \n“ŋgéː” = steal (from \"cɔ́ŋ\" in example 2) \n“nyɛ́n” = the (demonstrative?) \n“kèŋkfǔ” = yam \n“lé” = the (something) \n“ɛ̀bɛ̀n” = woman\n\nSo: “I will steal the yam from the woman” — makes sense.\n\nOriginal: 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → you will steal the yam on Bvusɔw\n\nSo “cɔ́ŋ” = steal, “kèŋkfǔ” = yam\n\nSo “ŋgéː” = steal? Possibly variant.\n\n“nyɛ́n” = “the” (demonstrative) — likely \"the\" before \"kèŋkfǔ\"\n\nSo: “I will steal the yam from the woman”\n\nBut \"from\" is \"lé\"? In example 17, “lé ɛ̀bɛ̀n” — \"from the woman\"\n\nYes — analogous to “in example 2”, “cɔ́ŋ kèŋkfǔ” → steal the yam\n\nSo 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → On Bvuŋkaden, I will steal the yam from the woman.\n\nNow 18: “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn”\n\n“wvù” = he \n“tɔ̀” = found \n“nɔ̂ː” = the \n“yɛ᷅n” = the (demonstrative) \n“bèsèn” = today \n“ě” = at \n“bvúmbòn” = Bvumbon\n\nSo: “He found the market today at Bvumbon”\n\nBut “bèsèn ě” = today at → “bèsèn” = today, “ě” = at\n\nSo “he found the market at Bvumbon today” → possibly “at Bvumbon today”\n\nBut in example 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → on Bvuŋka, he found the book\n\nSo pattern: “wvù tɔ̀ nɔ̂ː [object] [place]” → he found the object at the place\n\nSo here: “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn” → he found the market at Bvumbon today\n\nSo “bèsèn ě” = at today → can be parsed as “at today” or “today at”\n\nSo: “He found the market today at Bvumbon” — but Bvumbon is a day, so it’s “at Bvumbon” on “today”\n\nBut in example 1: “fɔgò cǐ nú bvúmbòn” → Yesterday was Bvumbon\n\nSo Bvumbon is a day.\n\nThus, “he found the market at Bvumbon today” → no, “today” is not a day.\n\nBut Bvumbon is a day, and now we are on Bvuŋkaden.\n\nSo this is saying he found the market at Bvumbon **today** — i.e., on the day of Bvumbon, which is Day 1.\n\nBut Bvumbon is Day 1.\n\nSo in this day (Day 5), on Bvuŋkaden, he found the market at Bvumbon yesterday (Bvumbon was day 1, day 4 before).\n\nBut “bèsèn” = today, so it must be today.\n\nBut Bvumbon is a day name.\n\nSo the sentence is: he found the market at Bvumbon today — meaning on today (Bvuŋkaden), at Bvumbon? But Bvumbon is a day.\n\nConfusing.\n\nAlternative: “bèsèn ě bvúmbòn” = “today at Bvumbon” → “at Bvumbon today”\n\nBut Bvumbon is a day, so it's a place?\n\nIn example 4: “bɔ᷅ŋ ŋwà” = book → so place is book → but here “yɛ᷅n” = market.\n\nSo “he found the market at Bvumbon today” — the market is at Bvumbon?\n\nBut in example 1: “Yesterday was Bvumbon” → so Bvumbon is a day, not a place.\n\nConflict.\n\nUnless Bvumbon is both a day and a place.\n\nBut in example 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → on Bvuŋka, he found the book — so place is “bvûŋka” = Bvuŋka, which is a day — so days can act as places?\n\nYes, possibly.\n\nSo in 18: “he found the market at Bvumbon today” → on Bvuŋkaden, he found the market at Bvumbon (as a location)\n\nBut in example 1: “Yesterday was Bvumbon” — Bvumbon is a day\n\nSo “places” are days.\n\nSo “at Bvumbon” means “at the location named Bvumbon”\n\nSo sentence 18: He found the market at Bvumbon today.\n\nBut “today” and “at Bvumbon” — at Bvumbon on today?\n\nYes — so it's fine.\n\nNow 19: “bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n”\n\n“bèsèn” = today \n“nǔ” = you (sg) \n“bóy” = woman \n“tɔ́” = will help \n“fɔ̀wǎy” = market \n“bvúzhı᷇ːde᷆n” = Bvuzhi? → but earlier Bvuzhi was Day 3\n\nWait, “bvúzhı᷇ːde᷆n” — similar to “bvûŋka᷆ːde᷆n” in 8: “bvûŋka᷆ːde᷆n” = tomorrow of Bvuŋka\n\nSo likely suffix “-de” means “tomorrow” or “next”, like “-de” = next day\n\nIn 8: “bvûŋka᷆ːde᷆n” = tomorrow\n\nSo “bvúzhı᷇ːde᷆n” = tomorrow of Bvuzhi\n\nBvuzhi = Day 3 → tomorrow = Day 4 → Bvuŋka\n\nYes → so “bvúzhı᷇ːde᷆n” = Bvuŋka\n\nSo: “you will help me at the market tomorrow of Bvuzhi” → tomorrow of Bvuzhi is Bvuŋka\n\nSo “you will help me at the market on Bvuŋka”\n\nThus, 19: “Today, you will help me at the market on Bvuŋka”\n\nNow back to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have:\n- “bvúsɔ̀w” = day name (Bvusɔw, Day 2)\n- “nǔ” = you (sg)\n- “fɔ̀ shě ntfǔː” = the day after tomorrow is X? Or a verb?\n\nBut no object.\n\nIn example 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” = the day after tomorrow is Bvutfu\n\nSo “fɔ̀ shě ntfǔː nú X” = day after tomorrow is X\n\nSo “fɔ̀ shě ntfǔː” is the noun phrase meaning “the day after tomorrow” and needs a day.\n\nBut here no day.\n\nPossibly typo — perhaps it's “On Bvusɔw, the day after tomorrow is Bvutfu”?\n\nBut Bvutfu is Day 1, Bvusɔw is Day 2 → day after tomorrow of Day 2 is Day 4 → Bvuŋka, not Bvutfu.\n\nSo no.\n\nDay", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9872.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, a day in the Nooni week.\n\nWe must analyze the linguistic patterns from the given examples to determine how references to time (e.g., \"today\", \"yesterday\", \"tomorrow\", \"day after tomorrow\") are formed, and how verbs are structured with subjects, objects, and time references.\n\n---\n\n**Step 1: Identify the days and their temporal relationships**\n\nFrom the examples:\n\n- \"Yesterday was Bvumbon\" → (1)\n- \"On Bvusɔw, you will steal the yam\" → (2)\n- \"On Bvuzhi, the woman will help me\" → (3)\n- \"On Bvuŋka, he found the book\" → (4)\n- \"The day after tomorrow is Bvutfu\" → (5)\n- \"On Bvutfu, I will choose the car\" → (5)\n- \"Today, he killed the woman\" → (6)\n- \"You heard the thief a long time ago\" → (7)\n- \"Tomorrow is Bvuŋkaden\" → (8)\n- \"On Bvuŋkaden, the thief will find us\" → (8)\n- \"Today, I chose the book\" → (9)\n- \"The man is about to see him\" → (10)\n- \"The day before yesterday was Bvuŋka\" → (11)\n- \"I am about to help the man\" → (12)\n- \"On Bvutfu, the woman saw the market\" → (13)\n- \"Today, we will steal the car\" → (14)\n- \"They saw me at the market just now\" → (15)\n\nFrom (8): \"Tomorrow is Bvuŋkaden\" — So Bvuŋkaden is the day after the current day.\n\nSo, order of days:\n\nLet’s assign sequence based on temporal anchors.\n\n- Bvutfu is mentioned in several places: yesterday (1), day after tomorrow (5), and in future (13).\n- (5) says: \"The day after tomorrow is Bvutfu\" → So Bvutfu = day after tomorrow.\n- (8) says: \"Tomorrow is Bvuŋkaden\" → Bvuŋkaden = tomorrow.\n- (11): \"The day before yesterday was Bvuŋka\" → Bvuŋka = day before yesterday.\n- (4): \"On Bvuŋka, he found the book\" → already in the past.\n\nSo we can build the timeline:\n\nAssume current day is **Bvuŋka** (from (11): day before yesterday was Bvuŋka).\n\nThen:\n- Day before yesterday = Bvuŋka → (11)\n- Yesterday = Bvumbon → (1)\n- Today = Bvusɔw → (2,6,7)\n- Tomorrow = Bvuŋkaden → (8)\n- Day after tomorrow = Bvutfu → (5)\n\nWait — (5) says \"The day after tomorrow is Bvutfu\" → so Bvutfu = day after tomorrow.\n\nNow (8): \"Tomorrow is Bvuŋkaden\" → so Bvuŋkaden = tomorrow.\n\nThus, timeline:\n\n| Day (Nooni) | Temporal Position |\n|----------------|-------------------------------|\n| Bvumbon | Yesterday |\n| Bvusɔw | Today |\n| Bvuŋka | Day before yesterday |\n| Bvuŋkaden | Tomorrow |\n| Bvutfu | Day after tomorrow |\n\nWait: (11): \"The day before yesterday was Bvuŋka\" → so if today is Bvusɔw, then:\n- Day before yesterday = Bvuŋka\n- Yesterday = Bvumbon\n- Today = Bvusɔw\n- Tomorrow = Bvuŋkaden\n- Day after tomorrow = Bvutfu\n\nYes — this fits with (1), (2), (4), (5), (8), (11).\n\nSo the days are ordered as:\n- Bvuŋka (day before yesterday)\n- Bvumbon (yesterday)\n- Bvusɔw (today)\n- Bvuŋkaden (tomorrow)\n- Bvutfu (day after tomorrow)\n\n---\n\n**Step 2: Identify temporal markers in the language**\n\nWe examine how time is expressed in the language using the known sentences.\n\nLook at sentence 8:\n- \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → “Tomorrow is Bvuŋkaden”\n\nSentence 5: \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSentence 11: \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka᷆ː\" → \"The day before yesterday was Bvuŋka\"\n\nSo time expressions:\n- \"Tomorrow\" → \"ntfǔː nú ...\"\n- \"The day after tomorrow\" → \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow\"\n- \"The day before yesterday\" → \"kefwé cí nú ...\"\n\n\"kefwé\" = day before yesterday?\n\"fɔ̀ shě\" = day after tomorrow?\n\nYes.\n\nSo:\n- \"ntfǔː\" = tomorrow\n- \"fɔ̀ shě\" = day after tomorrow\n- \"kefwé cí\" = day before yesterday\n\nSo the structure is:\n- [day marker] + [day name] or [day name] is [time marker]\n\nSentence 3: \"On Bvuzhi, the woman will help me\" → verb of future\n\nSentence 14: \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\nSentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n\nSo \"Today\" = \"wɔ̀ tɔ̀ nɔ̂ː\" — in sentence 6: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"You(sg) heard the thief a long time ago\"\n\nWait — that's not today.\n\nIn (6): \"Today, he killed the woman\" → must be \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — this is likely \"Today, he killed the woman\"\n\nSo \"Today\" = \"wvù bɛ̂ː\" or \"wɔ̀ tɔ̀ nɔ̂ː\" is not stated.\n\nWait — sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → matches \"Today, he killed the woman\"\n\nBut there is no explicit \"today\" in the sentence — it's implied.\n\nSimilarly, sentence 9: \"Today, I chose the book\" → \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\"\n\nSo “me mbɛ̂ː” = “I chose”\n\nThus, “Today” is expressed via the verb form or via context.\n\nBut for future or past time, we see:\n\n- \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → shows \"On [day], [I will] do X\"\n\n- \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\nSo \"On [day], [subject] will [verb] [object]\" is a pattern.\n\nSimilarly, \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\nSo \"On [day], [subject] [verb] [object]\"\n\nAlso, \"just now\" appears in (15): \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nSo present perfect / immediately past.\n\nIn (10): \"The man is about to see him\" → \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" → \"is about to\"\n\nIn (12): \"I am about to help the man\" → \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo “is about to” = “nú” or “nú” as affix\n\n“nú” = about to?\n\nUsed in:\n- (12): \"me nú nfí dìɛ̀msɛ̌n\" → I am about to help\n- (10): \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" → the man is about to see\n\nSo “nú” indicates future immediate (in progress)\n\n---\n\n**Step 3: Analyze the requested sentences (16–19), all spoken on Bvuŋkaden**\n\nBvuŋkaden = tomorrow → so all these are about tomorrow.\n\nWe now translate each one.\n\n---\n\n**16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː**\n\nBreak down:\n- \"bvúsɔ̀w\" = Bvusɔw (day)\n- \"nǔ\" = you (sg)\n- \"fɔ̀ shě ntfǔː\" = the day after tomorrow\n\nSo: \"On Bvusɔw, the day after tomorrow\"\n\nBut that’s not a grammatical sentence.\n\nWait — is it a noun phrase?\n\n\"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → likely a statement like \"On Bvusɔw, the day after tomorrow\"\n\nBut \"on Bvusɔw\" is a day, and \"the day after tomorrow\" is another.\n\nBut \"on Bvusɔw\" is today, and \"the day after tomorrow\" is future.\n\nSo what could this mean?\n\nWait — perhaps it is a time expression meaning \"The day after tomorrow is Bvusɔw\"\n\nBut \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → might be: \"The day after tomorrow is Bvusɔw\"\n\nYes — because in sentence (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo pattern: \"fɔ̀ shě ntfǔː nú [day]\" = \"The day after tomorrow is [day]\"\n\nSo here: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → likely meaning: \"The day after tomorrow is Bvusɔw\"\n\nBut Bvusɔw is today — so this would mean \"The day after tomorrow is today\" — logically inconsistent.\n\nBut is it a translation error?\n\nWait — could it be a mistake in word order?\n\nLook at (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo word order: [day marker] + [day name]\n\nSimilarly, (8): \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"Tomorrow is Bvuŋkaden\"\n\nSo pattern: [time] + nú + [day name]\n\nBut in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"day + you + day after tomorrow\"\n\nDoesn't match.\n\nAlternative: could \"bvúsɔ̀w\" be a verb?\n\nNo — \"bvúsɔ̀w\" is also a day name (in (2): \"On Bvusɔw, you will steal the yam\")\n\nSo it's a day.\n\n\"nǔ\" = you (sg)\n\n\"fɔ̀ shě ntfǔː\" = the day after tomorrow\n\nSo: \"You, on the day after tomorrow\"\n\nBut that’s not grammatical.\n\nAlternatively, is there a verb?\n\nNo.\n\nWait — in (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo structure: [subject] + [verb] + [object] + [on day]\n\nAlternately, for time references, a common pattern is:\n\n- [day name] + [time marker] → e.g., \"on Bvusɔw\" = \"on today\"\n\nSo perhaps the sentence is \"On the day after tomorrow, [X]\"\n\nBut what is X?\n\nOnly \"nǔ\" → \"you\"\n\nSo: \"On the day after tomorrow, you [something]\"\n\nBut verb missing.\n\nWait — another idea: maybe \"bvúsɔ̀w\" is a verb?\n\nBvúsɔ̀w = \"on Bvusɔw\" — no, it's a day.\n\nBut in (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo \"on Bvusɔw\" is a locative time marker.\n\nSo \"bvúsɔ̀w\" in (16) is likely part of \"on Bvusɔw\", but here it's not with \"nú\"\n\nAlternative: perhaps it's a verb meaning \"to steal\" or something?\n\nNo, \"wɔ̀ nǔ yúː cɔ́ŋ\" = \"you will steal\"\n\n\"bvúsɔ̀w\" = Bvusɔw (day)\n\nSo in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → may be missing verb.\n\nBut no verb given.\n\nWait — is it a typo? Or misalignment?\n\nCompare with known patterns.\n\nLook at sentence (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo time phrase is: [on day]\n\nSimilarly, (4): \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka\" → \"On Bvuŋka, he found the book\"\n\nSo the pattern is: [subject] or [verb] begins with time reference\n\nBut in (16), no subject or verb present.\n\nUnless \"nǔ\" is the subject.\n\nSo perhaps: \"On Bvusɔw, you will steal the day after tomorrow\"?\n\nNo — \"fɔ̀ shě ntfǔː\" is a time expression, not an object.\n\nAnother idea: perhaps “fɔ̀ shě ntfǔː” is the day name?\n\nNo — “ntfǔː” is tomorrow.\n\n“fɔ̀ shě” is day after tomorrow.\n\nSo it's a time marker.\n\nOnly possibility: could this be a statement like “The day after tomorrow is Bvusɔw”?\n\nIf so, mirror of sentence (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nSo if the sentence is “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — then is it “bvúsɔ̀w” + “nǔ” + “fɔ̀ shě ntfǔː”?\n\nBut no structure.\n\nWait — in sentence (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is [day]\"\n\nSo when the time marker is first, it's \"the day after tomorrow is X\"\n\nSo in (16), \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — if we rephrase: \"On Bvusɔw, the day after tomorrow\"?\n\nBut that doesn’t make sense.\n\nCould it be a misordering? Maybe it should be \"fɔ̀ shě ntfǔː nú bvúsɔ̀w\"?\n\nThat would make sense — \"The day after tomorrow is Bvusɔw\"\n\nBut the sentence is written as \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" is \"you\" — why?\n\nUnless \"nǔ\" is a verb?\n\nBut in other sentences, \"nǔ\" is a pronoun.\n\nAnother possibility: in (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo the structure is [time] + [subject] + [verb] + [object]\n\nBut here, there is no verb.\n\nSo perhaps this is not a full sentence.\n\nWait — perhaps \"bvúsɔ̀w\" is not a day, but a verb?\n\n\"bvúsɔ̀w\" is used as a day name in other contexts.\n\nUnless it's a verb like \"to occur\" or something.\n\nBut no evidence.\n\nAnother idea: perhaps the sentence is \"You are stealing (or on) the day after tomorrow\" — but no.\n\nWait — is \"fɔ̀ shě ntfǔː\" a day name?\n\nIn (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly time expression.\n\nSo only possibility: this is a time-of-day statement.\n\nIn English, \"The day after tomorrow is Bvusɔw\" — which is logically impossible (today is Bvusɔw).\n\nBut based on pattern: sentence (5): \"The day after tomorrow is Bvutfu\"\n\nSo likely (16) is: \"The day after tomorrow is Bvusɔw\"\n\nThus, despite the word order, the intended meaning is: \"The day after tomorrow is Bvusɔ̀w\"\n\nThus, translation: \"The day after tomorrow is Bvusɔw\"\n\nBut Bvusɔw is today — so this would be false.\n\nBut in the context of language pattern, we follow form.\n\nSo we accept: \"The day after tomorrow is Bvusɔw\"\n\n---\n\n**17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n**\n\nBreak down:\n- \"me\" = I\n- \"n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11240.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, using linguistic patterns derived from the provided examples.\n\nWe begin by building a pattern-based alignment from the given examples.\n\n---\n\n### Step 1: Identify days and their relational terms\n\nWe see the following days:\n\n- Bvutfu: \"Yesterday\" (1), \"The day after tomorrow\" (5), \"Tomorrow\" (not directly), \"The day before yesterday\" (11), \"Today\" (not directly), \"Today\" (9)\n- Bvusɔw: (2), (4), (6), (7)\n- Bvuzhi: (3)\n- Bvuŋka: (4), (5), (6), (7), (12), (13), (14), (15)\n- Bvuŋkaden: (8), (9), (10), (11)\n\nWe observe that:\n\n- \"Tomorrow\" = \"Bvuŋkaden\" (8: \"Tomorrow is Bvuŋkaden\")\n- \"The day after tomorrow\" = \"Bvutfu\" (5: \"The day after tomorrow is Bvutfu\")\n- \"The day before yesterday\" = \"Bvuŋka\" (11: \"The day before yesterday was Bvuŋka\")\n- \"Yesterday\" = \"Bvumbon\" (1: \"Yesterday was Bvumbon\")\n- \"Today\" = the day of utterance\n\nSo the days are cyclical. The day-to-day relationships are:\n\n- Yesterday → Bvumbon\n- Today → ?\n- Tomorrow → Bvuŋkaden\n- Day after tomorrow → Bvutfu\n- Day before yesterday → Bvuŋka\n\nFrom this, we can deduce the calendar order:\n\nLet’s assign a place in the week:\n\nAssume the utterance occurs on Bvuŋkaden → today.\n\nThen:\n\n- Yesterday = Bvumbon → (1)\n- Today = Bvuŋkaden → (8)\n- Tomorrow = Bvuŋkaden → next day → Bvuŋkaden\n- Day after tomorrow → Bvutfu (5 says: \"The day after tomorrow is Bvutfu\")\n- Day before yesterday → Bvuŋka (11 says: \"The day before yesterday was Bvuŋka\")\n\nThus, day order:\n\n1. Bvumbon → yesterday \n2. Bvuŋka → day before yesterday \n3. Bvuŋkaden → today \n4. Bvutfu → day after tomorrow \n5. Bvusɔw → ??? \nBut we see: On Bvusɔw → day (2,4,6,7)\n\nWait: sentence (2): \"On Bvusɔw, you(sg) will steal the yam\" → spoken on Bvusɔw\n\n(4): \"On Bvuŋka, he found the book\" → spoken on Bvuŋka\n\nSo days are: Bvumbon, Bvusɔw, Bvuzhi, Bvuŋka, Bvutfu, Bvuŋkaden?\n\nBut the week is only 7 days. Let's assign a sequence.\n\nFrom:\n\n- Bvumbon = yesterday (1)\n- Bvuŋka = day before yesterday (11)\n- Bvutfu = day after tomorrow (5)\n- Bvuŋkaden = today (8)\n\nSo:\n\n- Day before yesterday → Bvuŋka \n- Yesterday → Bvumbon \n- Today → Bvuŋkaden \n- Day after tomorrow → Bvutfu \n\nSo the order is:\n\n1. Bvuŋka (day before yesterday) \n2. Bvumbon (yesterday) \n3. Bvuŋkaden (today) \n4. Bvutfu (day after tomorrow)\n\nBut there's no Bvusɔw or Bvuzhi assigned to a fixed position.\n\n(3): \"On Bvuzhi, the woman will help me\" → spoken on Bvuzhi (day)\n\n(2): \"On Bvusɔw, you will steal the yam\" → spoken on Bvusɔw\n\n(4): \"On Bvuŋka, he found the book\" → spoken on Bvuŋka\n\n(5): \"The day after tomorrow is Bvutfu\" → spoken on Bvusɔw (sentence 4: on Bvuŋka, sentence 5: on Bvusɔw)\n\nWait: sentence 5 is said on Bvusɔw.\n\nConclusion: sentences 4,5,6,7 are spoken on Bvusɔw.\n\nSo:\n\n- Day: Bvusɔw → (2),(4),(5),(6),(7)\n\nThen, when spoken on Bvusɔw:\n\n- \"The day after tomorrow is Bvutfu\" → so today (Bvusɔw) → day after tomorrow = Bvutfu\n\nSo:\n\n- Bvusɔw → today \n- Bvutfu → day after tomorrow \n- Bvuzhi → ? \n- Bvuŋka → ? \n- Bvumbon → ? \n\nBut on Bvusɔw: \"On Bvuzhi, the woman will help me\" → (3) → this is spoken on Bvusɔw, so Bvuzhi is some past day.\n\nSimilarly, (4): \"On Bvuŋka, he found the book\" → spoken on Bvusɔw → so Bvuŋka is a day in the past\n\nSo again, days are not fixed in sequence. But we need to determine the relative timing from the expressions.\n\nWe now focus on how relative days are expressed.\n\n---\n\n### Step 2: Look at time expressions used in the examples\n\nWe extract patterns for time expressions:\n\nCommon time expressions:\n\n- \"Tomorrow\" = Bvuŋkaden → (8: \"Tomorrow is Bvuŋkaden\")\n- \"The day after tomorrow\" = Bvutfu → (5: \"The day after tomorrow is Bvutfu\")\n- \"The day before yesterday\" = Bvuŋka → (11: \"The day before yesterday was Bvuŋka\")\n- \"Yesterday\" = Bvumbon → (1: \"Yesterday was Bvumbon\")\n\nSo:\n\n- Tomorrow → Bvuŋkaden \n- Day after tomorrow → Bvutfu \n- Day before yesterday → Bvuŋka \n- Yesterday → Bvumbon \n\nSo we have a mapping:\n\n| Time reference | Day |\n|---------------|-----|\n| Yesterday | Bvumbon |\n| Day before yesterday | Bvuŋka |\n| Today | ? (day of utterance) |\n| Tomorrow | Bvuŋkaden |\n| Day after tomorrow | Bvutfu |\n\nThis suggests a consistent cycle.\n\nWhen speaking on a day, we can refer to other days with fixed relative terms.\n\nThus, we can derive the time expressions in the target sentences.\n\nNow we analyze each target sentence, spoken on Bvuŋkaden (today):\n\n---\n\n### Sentence 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\nBreakdown:\n\n- bvúsɔ̀w → day (previously used in 2: \"On Bvusɔw, you will steal the yam\")\n- nǔ → subject (you sg)\n- fɔ̀ shě ntfǔː → \"the day after tomorrow\" (from 5: \"The day after tomorrow is Bvutfu\")\n\nSo \"On Bvusɔw, the day after tomorrow is Bvutfu\"? But that doesn’t parse.\n\nWait: \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nBut \"fɔ̀ shě\" appears in 5: \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" = Bvutfu\n\nBut the structure is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nLikely: \"On Bvusɔw, [the day after tomorrow] is [something]\"\n\nBut no object or predicate.\n\nWait — in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, the day after tomorrow?\"\n\nNo — \"nǔ\" is subject. So it must be \"On Bvusɔw, you (sg) will have the day after tomorrow?\" — illogical.\n\nAlternative: misreading of structure.\n\nPerhaps it's: \"On Bvusɔw, the day after tomorrow is [a day]\" — missing object?\n\nBut no object.\n\nWait: sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me.\"\n\nSo structure: \"On [day], [subject] will [verb] [object]\"\n\nIn this case: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nPossibly: \"On Bvusɔw, you (sg) will [have] the day after tomorrow\"?\n\nBut \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\", which is a day.\n\nSo the sentence may be: \"On Bvusɔw, you (sg) will have the day after tomorrow\"\n\nBut that doesn't make sense.\n\nAlternatively, maybe \"fɔ̀ shě ntfǔː\" is a fixed phrase meaning \"the day after tomorrow is ___\", so the sentence is asserting that.\n\nBut no complement.\n\nWait — sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" is a noun phrase meaning \"the day after tomorrow\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) have the day after tomorrow\" — awkward.\n\nAlternatively, could \"nǔ\" be part of a verb?\n\nPerhaps the full structure is: \"On Bvusɔw, you will have the day after tomorrow\" — but what does \"have\" mean?\n\nNo such use found.\n\nPerhaps a typo? Or misread.\n\nWait — \"fɔ̀ shě\" may mean \"the day after tomorrow\" as a temporal reference, and \"ntfǔː\" is the day name.\n\nBut \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" could be: \"On Bvusɔw, the day after tomorrow is Bvutfu\"\n\nBut it’s missing \"nú\" (is)\n\nIn (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo likely, in (16), the structure is missing \"nú\" — but it's not written.\n\nThus, we assume: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, [the day after tomorrow is Bvutfu]\"\n\nBut why \"nǔ\"?\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you(sg) will steal the yam\"\n\nSo \"nǔ\" = you(sg)\n\nSo in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) have the day after tomorrow?\"\n\nNo.\n\nPerhaps it's a misplacement.\n\nAlternatively, maybe \"fɔ̀ shě ntfǔː\" is not \"the day after tomorrow\", but something else.\n\nAnother possibility: \"fɔ̀ shě\" = \"the day after\", and \"ntfǔː\" = a name — but no.\n\nFrom sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nThus \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo it's a noun phrase.\n\nIn sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo format: [preposition] [day], [subject] [verb] [object]\n\nSo in (16), \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — subject missing.\n\nPossibly typo. But likely, the intended meaning is that \"the day after tomorrow is Bvutfu\", and it's being said on Bvusɔw (a day in the past or future relative to Bvuŋkaden).\n\nBut the sentence is being spoken on Bvuŋkaden.\n\nSo from the perspective of Bvuŋkaden:\n\n- Bvusɔw is in the past or future?\n\nWe have:\n\n- Bvuŋkaden = today\n- Bvusɔw = ? \nFrom earlier: on Bvusɔw, they said \"The day after tomorrow is Bvutfu\" \nSo when speaking on Bvusɔw, \"day after tomorrow\" is Bvutfu → so Bvutfu is after Bvusɔw\n\nSo Bvusɔw < Bvutfu\n\nAlso, Bvutfu is after Bvusɔw.\n\nThen, from sentence 11: \"the day before yesterday was Bvuŋka\" → so Bvuŋka < Bvutfu\n\nWe have:\n\n- Bvuŋka → day before yesterday (relative to when spoken)\n- Bvumbon → yesterday\n- Bvuŋkaden → today\n- Bvutfu → day after tomorrow (from Bvusɔw)\n\nSo we can chain:\n\nOn Bvusɔw (day): \n- Day after tomorrow → Bvutfu \n→ so Bvusɔw → is two days before Bvutfu\n\nSo Bvutfu = Bvusɔw + 2\n\nAlso, on Bvuŋkaden (today), we want to know what day Bvusɔw is.\n\nWe don’t have a fixed order, but we can derive relative timing from known facts.\n\nFrom (11): \"The day before yesterday was Bvuŋka\" → so Bvuŋka = two days before today \n→ today is Bvuŋkaden → so Bvuŋka = Bvuŋkaden - 2\n\nFrom (1): \"Yesterday was Bvumbon\" → Bvumbon = Bvuŋkaden - 1\n\nFrom (5): \"The day after tomorrow is Bvutfu\" → Bvutfu = Bvuŋkaden + 2\n\nFrom (8): \"Tomorrow is Bvuŋkaden\" → Bvuŋkaden = today\n\nThus, all days are assigned:\n\n- Bvumbon = Bvuŋkaden - 1 \n- Bvuŋka = Bvuŋkaden - 2 \n- Bvutfu = Bvuŋkaden + 2 \n- Bvusɔw = ? → unknown from this\n\nBut from (2): on Bvusɔw, \"you will steal the yam\" → so Bvusɔw is a day when the speaker said that\n\nWe need to find where Bvusɔw is in the sequence.\n\nWe have:\n\n- Bvumbon = -1 \n- Bvuŋka = -2 \n- Today = 0 \n- Bvutfu = +2\n\nThe days must be ordered in a week.\n\nWe also have (3): \"On Bvuzhi, the woman will help me\" → spoken on Bvuzhi (some day)\n\nFrom sentence 3: \"On Bvuzhi, the woman will help me\" — on Bvuzhi\n\nOn Bvuzhi, a future or past event?\n\nWe don't have full information.\n\nBut structure of time expressions suggests a fixed set:\n\nThe days are:\n\n- Bvumbon \n- Bvuzhi \n- Bvusɔw \n- Bvuŋka \n- Bvutfu \n- Bvuŋkaden\n\nFrom timing:\n\n- Bvuŋka = -2 \n- Bvumbon = -1 \n- Bvuŋkaden = 0 \n- Bvutfu = +2\n\nSo the remaining day, Bvusɔw, must be either -3, +1, or +3.\n\nBut the week is 7 days — likely all are present.\n\nLet’s assume a linear order:\n\nLet’s assign:\n\nPosition from today:\n\n| Day | Offset |\n|------------|--------|\n| Bvuŋka | -2 |\n| Bvumbon | -1 |\n| Bvuŋkaden | 0 |\n| Bvutfu | +2 |\n| Bvusɔw | ? |\n| Bvuzhi | ? |\n\nIs there a day with offset +1?\n\nWe see no sentence with \"today +1\" or \"today -3\"\n\nBut sentence 13: \"On Bvutfu, the woman saw the market\" → spoken on Bvuŋka\n\nSo when speaking on Bvuŋka, they report something about Bvutfu.\n\nIn that case, Bvutfu is in the future from Bvuŋka (since they say \"on Bvutfu\", future).\n\nSimilarly, on Bvusɔw, they say \"on Bvusɔw\" — so it's a day referenced.\n\nBut to find Bvusɔw relative to Bvuŋkaden:\n\nOnly known: on Bvusɔw, \"the day after tomorrow is Bvutfu\"\n\nSo when on Bvusɔw, Bvutfu is day after tomorrow.\n\nSo Bvutfu = Bvusɔw + 2\n\nWe have Bvutfu = Bvuŋkaden + 2\n\nSo:\n\nBvusɔw + 2 = Bvuŋkaden + 2 → Bvusɔw = Bvuŋkaden\n\nBut that means Bvusɔw = today → but we are speaking on Bvuŋkaden today, and the sentence is about Bvusɔw.\n\nContradiction?\n\nWait — no: the sentence 16 is being spoken on Bvuŋkaden.\n\nIt says: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nIf \"fɔ̀ shě ntfǔː\" = \"the day", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11349.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 3, + "output": "First, identify the key linguistic pattern in the Nooni sentences. The sentences refer to days of the week and use a consistent structure involving time references and verbs.\n\nObserve the time markers:\n\n- \"Yesterday\" → \"fɔgò cǐ nú bvúmbòn\" → on Bvumbon\n- \"On Bvusɔw, you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → so \"fɔ̀ shě\" = \"the day after tomorrow\"\n- \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"ntfǔː\" = tomorrow\n- \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\" → \"kefwé cí\" = day before yesterday\n- \"Today\" → \"wvù tɔ̀ nɔ̂ː\" → \"today\"\n\nNow, time expressions and related structure:\n\n- \"fɔ̀ shě\" = the day after tomorrow\n- \"ntfǔː\" = tomorrow\n- \"fɔgò cǐ\" = yesterday\n- \"kefwé cí\" = day before yesterday\n- \"wvù tɔ̀ nɔ̂ː\" = today\n\nAll time expressions are topic-marked with \"nú\" + day name (i.e., \"on [day]\") or compound time phrases.\n\nNow, look at the verbs and their use:\n\n- \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → \"On Bvumbon, I came to the market\"\n- \"wvù tɔ̀ nɔ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed the woman\"\n- \"me nú mbóy ncáw mutù bvútfu᷅\" → \"On Bvutfu, I will choose the car\"\n- \"cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n\" → \"On Bvuŋkaden, the thief will find us\"\n- \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → \"Today, I chose the book\"\n\nPattern: all days are marked with \"nú\" or prefixed with time expressions.\n\nNow, the day names:\n\n- Bvumbon → yesterday\n- Bvusɔw → current day (from sentence 2)\n- Bvutfu → day after tomorrow (sentence 5)\n- Bvuŋka → current day (sentence 4)\n- Bvuŋkaden → tomorrow (sentence 8)\n\nSo: \n- Bvumbon = yesterday \n- Bvusɔw = day of sentence 2 → not today \n- Bvutfu = day after tomorrow \n- Bvuŋka = day of sentence 4 → today \n- Bvuŋkaden = tomorrow\n\nNow, we are to translate sentences spoken on **Bvuŋkaden** (tomorrow). So all the translations must be interpreted from the point of view of \"tomorrow\".\n\nNow, evaluate each sentence:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n\"bvúsɔ̀w\" = Bvusɔw (a day) \n\"nǔ\" = you (sg) \n\"fɔ̀ shě\" = the day after tomorrow \n\"ntfǔː\" = tomorrow \n\nBut \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow is tomorrow\"? That can't be. \nBut \"fɔ̀ shě\" means \"the day after tomorrow\" → so \"the day after tomorrow is tomorrow\" is a contradiction.\n\nWait — perhaps the structure is: \"On [day], [subject] will do [action]\"?\n\nBut the sentence is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nNo \"nú\" or \"on\" — but look at structure.\n\nCompare with: \nSentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" is a time-expression used to refer to \"the day after tomorrow\"\n\nThus, the sentence: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → likely means \"On Bvusɔw, you will [do something] with the day after tomorrow?\"\n\nBut what verb?\n\nWait — perhaps typo in understanding. There is no verb. This seems incomplete.\n\nNow check sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" = the day after tomorrow \n\"ntfǔː\" = tomorrow \n\"nú\" = on\n\nBut the structure of 16 is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — missing a verb?\n\nWait — perhaps the pattern is missing. Try other sentences.\n\nLook at sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nStructure: [time] [subject] [verb] [object]\n\nSentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo: Subject (bɔ́) + verb (nɔ̂ː) + object (yɛ᷅n me) + place (lé fɔ̀wǎy)\n\nBack to 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — no verb.\n\nWait — perhaps it's a typo or misreading. Look at original:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\nCompare sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo “fɔ̀ shě ntfǔː” = time phrase meaning “the day after tomorrow” — or perhaps “the day after tomorrow is [day]”\n\nBut in sentence 16, it's \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — if there is no verb, it's incomplete.\n\nWait — look at sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me nú\" → I on \n\"ŋgéː\" → verb: to see or to look at \n\"nyɛ́n\" → the thief \n\"kèŋkfǔ\" → the yam \n\"lé\" → at \n\"ɛ̀bɛ̀n\" → the woman\n\n\"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"On Bvutfu, I saw the thief at the yam (place?)\"\n\nBut \"kèŋkfǔ\" might be \"the yam\", \"lé\" = \"at\", \"ɛ̀bɛ̀n\" = woman?\n\nWait — sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\n\"yúː cɔ́ŋ\" = steal \n\"kèŋkfǔ\" = yam\n\nSo in 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → similar structure: I saw the thief at the yam of the woman?\n\nPerhaps “kèŋkfǔ” is a place, like “the yam market” or “the yam place”.\n\nSimilarly, sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\"\n\n\"wvù tɔ̀ nɔ̂ː\" = today \n\"yɛ᷅n\" = he \n\"bèsèn\" = will \n\"ě\" = at \n\"bvúmbòn\" = yesterday\n\n\"Today, he will see at yesterday\" — doesn’t make sense.\n\n\"bèsèn ě\" = will go to or will be at?\n\n\"bèsèn\" = will \n\"ě\" = at \n\"bvúmbòn\" = yesterday\n\nSo \"today, he will be at yesterday\" — still doesn’t make sense.\n\nBut consider: “bèsèn” + preposition?\n\nCompare sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSo \"bèsèn\" = will (future)\n\n\"bèsèn nǔ\" = we will\n\nLikely \"bèsèn\" = \"will\", \"nǔ\" = \"we\"\n\nSo in 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" → \"Today, he will be at yesterday\"\n\nBut “be at yesterday” is odd.\n\nUnless \"bvúmbòn\" is not \"yesterday\" but a day name.\n\nBut in context, it's spoken on Bvuŋkaden, so \"bvúmbòn\" refers to a day — yesterday from today?\n\nYesterday from Bvuŋkaden is Bvuzhi?\n\nWait — from sentence 3: \"On Bvuzhi, the woman will help me\" — so Bvuzhi is a day.\n\nBut no direct link.\n\nTime mapping across days:\n\nFrom the text:\n\n- On Bvumbon → yesterday\n- On Bvutfu → day after tomorrow\n- On Bvusɔw → current day (sentence 2)\n- On Bvuŋka → today (sentence 4)\n- On Bvuŋkaden → tomorrow (sentence 8)\n\nSo when speaking on Bvuŋkaden (tomorrow), the time expressions are shifted:\n\n- \"yesterday\" = Bvumbon\n- \"today\" = Bvuŋka (was today, now is tomorrow)\n- \"day before yesterday\" = Bvuŋka → no\n- Sentence 11: \"kefwé cí nú bvûŋka\" → day before yesterday was Bvuŋka\n\nSo Bvuŋka = day before yesterday\n\nBut Bvuŋka was, in sentence 4, the day of \"on Bvuŋka\", which was today.\n\nNow we are speaking on Bvuŋkaden.\n\nThus, time reference:\n\n- Today: Bvuŋkaden \n- Yesterday: Bvuŋka \n- Day before yesterday: Bvumbon \n- Tomorrow: Bvutfu \n- Day after tomorrow: Bvutfu\n\nYes — from sentence 5: \"The day after tomorrow is Bvutfu\"\n\nSo mapping:\n\n| Date |\tTime |\n|---------------|------|\n| Bvumbon | yesterday |\n| Bvusɔw | (unknown) |\n| Bvutfu | day after tomorrow |\n| Bvuŋka | day before yesterday |\n| Bvuŋkaden | today |\n\nIn sentence 4: on Bvuŋka, he found the book → so Bvuŋka = day before yesterday \nSentence 5: day after tomorrow is Bvutfu → so Bvutfu = day after tomorrow \nSentence 11: day before yesterday was Bvuŋka → confirms \nSo Bvumbon = yesterday (Bvuŋkaden's yesterday) \nBvusɔw = ? \nSentence 2: on Bvusɔw, you will steal the yam — no day reference, so it's a separate date.\n\nBut for translation, we only care about the time relations.\n\nNow, for each sentence, reconstruct meaning.\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \nWait — \"fɔ̀ shě ntfǔː\" — from sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" as a phrase = \"the day after tomorrow\"\n\nBut what about \"bvúsɔ̀w nǔ\" — \"on Bvusɔw, you\"?\n\nBut nothing follows. So likely, it's missing a verb.\n\nBut look at the parallel in sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nStructure: [day] [subject] [verb] [object] [place]\n\nSo sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — likely missing verb.\n\nBut each sentence has a verb. So perhaps \"fɔ̀ shě ntfǔː\" is not a time phrase, but the verb?\n\nBut in sentence 5, \"fɔ̀ shě\" is a time, \"ntfǔː\" is a time.\n\nBut no verb.\n\nWait — perhaps the structure is: \"On [day], [subject] will [do] [time phrase]\" — not possible.\n\nBetter to assume the pattern is coordination between time and action.\n\nLook at sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → On Bvusɔw, you will steal the yam\n\nSo \"wɔ̀ nǔ\" = you (sg) \n\"yúː cɔ́ŋ\" = steal \n\"kèŋkfǔ\" = the yam \n\"bvúsɔ̀w\" = on Bvusɔw\n\nSimilarly, sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nSo verb is in middle.\n\nIn sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — \"bvúsɔ̀w\" = day \n\"nǔ\" = you \n\"fɔ̀ shě ntfǔː\" = ??? — possibly \"the day after tomorrow\" is the object?\n\nBut what verb?\n\nCompare with sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nStructure: day + subject + verb + object + location?\n\n\"kwɔ᷆ːn cǐ\" = the woman \n\"cǐ\" = saw \n\"nɔ̂ː\" = the market \n\"wáy é\" = at the place?\n\n\"yɛ᷅n\" = the man?\n\n\"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the man at the market\"\n\nSo \"cǐ\" = saw\n\nLikely verbs: \n- \"cɔ́ŋ\" = steal \n- \"bóy fí\" = help \n- \"ŋgéː\" = see \n- \"wvù\" = found \n- \"bɛ̂ː\" = killed \n- \"tɔ̀\" = heard \n\nSo verbs are in the middle.\n\nNow sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — missing verb.\n\nBut look at 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"On Bvutfu, I saw the thief at the yam of the woman?\"\n\n\"kèŋkfǔ\" = yam — can it be a place?\n\n\"lé\" = at \n\"ɛ̀bɛ̀n\" = woman\n\nSo likely: at the yam of the woman? Or at the woman’s yam?\n\nBut in English, \"the yam market\" or \"the yam place\".\n\n\"nyɛ́n\" = the thief \n\"kèŋkfǔ\" = the yam \n\"lé\" = at \n\"ɛ̀bɛ̀n\" = woman\n\nSo likely: \"I saw the thief at the woman's yam\"\n\nBut yam is not a place.\n\nMore likely: \"I saw the thief at the yam market\" — “kèŋkfǔ” as a place name.\n\nIn sentence 2: \"you will steal the yam\" → “kèŋkfǔ” is object — the yam.\n\nSo in 17, \"kèŋkfǔ\" is likely object of \"saw\" — \"the yam\"\n\n\"lé ɛ̀bɛ̀n\" — at the woman → so \"at the yam of the woman\"?\n\nProbable: “I saw the thief at the woman's yam”\n\nBut that doesn't make sense.\n\nAlternative: “I saw the thief at the market” where “kèŋkfǔ” is “market”?\n\nNo.\n\nAnother possibility: typo or misreading.\n\n“kèŋkfǔ” appears in both sentence 2 and 17 — likely “the yam”\n\nBut in 17, “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” — I saw the thief at the yam at the woman?\n\nUnlikely.\n\nPerhaps \"kèŋkfǔ\" is a place — \"yam market\"\n\nSo \"at the yam market\" (lé kèŋkfǔ) — but “lé ɛ̀bɛ̀n”?\n\n“lé” is one word — “at”\n\nSo “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → the thief, the yam, at the woman?\n\nNot clear.\n\nPerhaps “kèŋkfǔ” is modifier.\n\nTry 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\"\n\n\"wvù tɔ̀ nɔ̂ː\" = today \n\"yɛ᷅n\" = he \n\"bèsèn\" = will \n\"ě\" = at \n\"bvúmbòn\" = yesterday\n\nSo: \"Today, he will be", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10389.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "Step-by-step analysis:\n\nWe are given 12 Inuktitut sentences with English translations. We are to translate 5 new sentences into Inuktitut, based on pattern recognition from the examples.\n\nKey step: Build an alignment table from examples to extract morphological and syntactic patterns.\n\nFirst, extract patterns in subject–predicate–object structure and verb forms.\n\nLook at verb morphology:\n\n1. Qingmivit takujaatit → Your dog saw you \n \"Qingmivit\" = saw (past tense, 3rd person, instrument/agent) → verb stem \"qingmi\" with prefix \"q\" for \"dog\", \"-vit\" for past tense \n \"takujaatit\" = saw you (object)\n\n2. Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor \n \"Inuuhuktuup\" = the boy shot → \"inuuhuk\" (boy) + \"tuup\" (past tense) \n \"qukiqtanga\" = the doctor (object)\n\n3. Aanniqtutit → You hurt yourself \n \"Aanniqtutit\" = you hurt yourself → \"aanniqt\" (hurt) + \"utit\" (past tense, reflexive) \n Synonym of \"hurt\" appears in 19: \"The shaman hurt you\" → will use \"aanniqt\"\n\n4. Iluaqhaijiup aarqijaatit → The doctor cured you \n \"aarqijaatit\" = cured → \"aarqij\" (cure) + \"aati\" + \"t\" (past tense, passive or active) \n Reuse \"aarqij\" as cure\n\n5. Qingmiq iputujait → You speared the dog \n \"iputujait\" = speared → \"iputuj\" (to spear) + \"ait\" (past tense)\n\n6. Angatkuq iluaqhaijimik aarqisijuq → The shaman cured a doctor \n \"Angatkuq\" = shaman → subject \n \"aarqisijuq\" = cured → verb \n \"iluaqhaijimik\" = a doctor → \"iluaqhaiji\" (doctor) + \"mik\" (genitive or possessor)\n\n7. Nanuq qaijuq → The polar bear came \n \"qaijuq\" = came → verb stem\n\n8. Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy \n \"iluaqhaijivit\" = your doctor (see genitive \"v\" or \"vi\") \n \"inuuhuktuit\" = your boy \n \"aarqijanga\" = cured\n\n9. Angunahuktiup amaruq iputujanga → The hunter speared the wolf \n \"iputujanga\" = speared \n \"amaruq\" = wolf \n\n10. Qingmiup ilinniaqtitsijiit aanniqtanga → The dog hurt your teacher \n \"aanniqtanga\" = hurt (reflexive? object) → \"aanniqt\" verb \n \"ilinniaqtitsijiit\" = your teacher → \"ilinniaqt\" (teacher) + suffix \"itsijiit\" (dative/genitive) \n So: object marked with possessive/genitive suffix\n\n11. Ukiakhaqtutit → You fell \n \"ukiakhaqtutit\" → \"ukiakhaq\" (to fall) + \"utit\" (past tense)\n\n12. Angunahukti nanurmik qukiqsijuq → The hunter shot a polar bear \n \"qukiqsijuq\" = shot → \"qukiq\" (to shoot) + \"sijuq\" (past tense)\n\nNow, observe verb roots and tense markers:\n\n- Past tense is commonly marked with -it/-t, e.g., -vit, -utit, -tutit, -it, -anga, -sijuq\n\n- Reflexive or intransitive constructions: \"you hurt yourself\" = aanniqtutit → so \"aanniqt\" + \"utit\"\n\n- Object is marked with genitive or dative suffix: \n example: \"iluaqhaijimik\" = a doctor (genitive) → \"iluaqhaiji\" + \"mik\" \n \"iluaqhaijivit\" = your doctor → \"iluaqhaiji\" + \"vit\" (possessive/possessive object)\n\n- Possessive markers: \n \"your\" = \"vi-\", \"your boy\" = \"inuuhuktuit\", \"your wolf\" = ?\n\n- Verbs:\n - \"to hurt\" = aanniqt (root) → used in 19 and 23 \n - \"to cure\" = aarqij → used in 4, 6, 8 \n - \"to see\" = takujaat → in 1: \"takujaatit\" \n - \"to spear\" = iputuj → in 5, 9 \n - \"to shoot\" = qukiq → in 2, 12 \n - \"to fall\" = ukiakhaq → in 11\n\nNow, translations:\n\n19. The shaman hurt you \n → \"Angatkuq\" = shaman (subject) \n → \"aanniqtutit\" = hurt you (past tense, intransitive, object \"you\") \n → pattern: subject + verb (hurt) + object \n → \"Angatkuq aanniqtutit\" \n → But object \"you\" likely marked by \"takuj\" or \"aanti\"? \n Example: \"you hurt yourself\" = aanniqtutit → object is \"yourself\" → \"utit\" is reflexive \n But here, object is \"you\" → direct object → so need object marker? \n In example 1: \"Qingmivit takujaatit\" → dog saw you → \"takujaatit\" = saw you \n So \"takujaat\" may be \"see you\" → similar structure \n\n Therefore, \"aanniqt\" + \"utit\" is for \"you hurt yourself\" \n For \"the shaman hurt you\" → need \"you\" as object → likely \"aanniqt\" + \"takuj\" or \"tutit\"? \n\n Look at: \"aanniqtutit\" = you hurt yourself → so \"utit\" = reflexive \n In 19: \"hurt you\" = not reflexive → so object is direct \n\n In 10: \"The dog hurt your teacher\" → \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n → \"aanniqtanga\" = hurt teacher → \"aanniqt\" + \"anga\" (likely object marker) \n → \"anga\" appears after verb? In 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → cure + you \n → \"aarqijaatit\" = cured you → \"aatit\" after verb \n\n So verb + object → object marked with -t or -a?\n\n In 8: \"your doctor cured your boy\" → \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"aariqijanga\" = cured (possibly past tense) \n Here, \"aariqijanga\" may be the full verb with object suffix \n\n But in 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"aariqisijuq\" = cured a doctor \n → \"aariqisijuq\" = verb + object (a doctor) \n\n So: verb + object with suffix (like -mik, -it) → so \"aanniqtanga\" = hurt teacher \n → Therefore, \"aanniqtanga\" = hurt teacher \n\n So: \"Angatkuq aanniqtanga\" → shaman hurt teacher? \n But English says \"hurt you\" → object is \"you\"\n\n In 1: \"Qingmivit takujaatit\" → dog saw you → \"takujaatit\" = saw you → so actual object is marked with -it \n\n So in 19: \"Angatkuq aanniqtit\" → no, \"aanniqtutit\" is reflexive \n So need object marker for \"you\" → likely -t or -it \n\n What is the form for \"you\" as object?\n\n In 1: \"takujaatit\" → saw you → \"takuj\" + \"aati\" → \"aati\" is object marker? \n In 10: \"aanniqtanga\" → hurt teacher → \"anga\" seems like object marker \n\n So pattern: verb + object marker → e.g., \"aanniqtanga\" = hurt teacher \n\n \"You\" as object → \"takuj\" or \"takujit\"? \n\n In 3: \"Aanniqtutit\" = you hurt yourself → no object → reflexive \n\n In other examples, direct object: \n - 1: saw you → \"takujaatit\" \n - 4: cured you → \"aarqijaatit\" \n - 6: cured a doctor → \"aarqisijuq\" → object = doctor (a + noun) \n - 8: cured your boy → \"aarqijanga\" = cured → object is \"your boy\" with suffix \n\n So \"takuj\" might be the base form for \"you\"\n\n Example: \"takujatit\" — \"you saw\" — not present.\n\n But in 1: \"takujaatit\" = saw you → object = you → so \"aati\" appears → maybe object suffix \n\n In \"aarqijaatit\" = cured you → object suffix \"aati\"? No, \"aati\" is not in 4 → \"aarqijaatit\" \n\n In 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → \"aarqijaatit\" \n → \"aarqijaat\" + \"it\"? \n\n Omit: in 10: \"ilinniaqtitsijiit aanniqtanga\" → \"aanniqtanga\" = hurt teacher → so object suffix = \"anga\" \n In 1: \"takujaatit\" → object = \"you\" → suffix = \"aati\"? → \"aati\" \n So: verb root + object suffix (like -aati) or -anga?\n\n But in 1: verb = \"takuj\", object = \"you\" → \"takujaatit\" → so \"aati\" → likely object marker \n\n So for \"hurt you\" → verb \"aanniqt\" + \"aati\" → \"aanniqt aati\"? But not found.\n\n In 3: \"aanniqtutit\" = you hurt yourself → self → \"utit\"\n\n In 10: \"aanniqtanga\" = hurt teacher → object \"teacher\" → suffix = \"anga\" → so object suffix varies based on noun?\n\n Actually, look: \n - In 4: \"aarqijaatit\" = cured you → \"aatit\"? \n - In 10: \"aanniqtanga\" = hurt teacher → \"anga\" \n - In 1: \"takujaatit\" = saw you → \"aati\" \n\n So suffix may be based on noun? Or is \"aati\" the suffix for \"you\"?\n\n In 1: \"takujaatit\" → \"aati\" → \"you\" \n In 4: \"aarqijaatit\" → \"aati\"? → probably \"aati\" \n But written as \"aarqijaatit\" → if it's \"aarqijaat\" + \"it\", then \"it\" = tense \n\n So possibly only the verb tense marker is -it, and the object is marked by noun alone.\n\n But in 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"aarqijanga\" = cured → \"anga\" with the verb → object is \"your boy\"\n\n So in all examples, after verb, object is expressed with possessive or direct noun.\n\n Therefore, \"you\" = \"takuj\" as object? But not directly.\n\n In example 1: \"Qingmivit takujaatit\" → \"takujaatit\" = saw you → yes, object is \"you\" → suffix = \"aati\"? or \"takuj\" + \"aati\" → the suffix is attached to the verb?\n\n Try: \"aanniqt + aati\" = hurt you → likely, since \"aanniqtutit\" is reflexive.\n\n In 1: \"takuj\" + \"aati\" = saw you \n In 10: \"aanniqt\" + \"anga\" = hurt teacher \n So object suffix does not depend on the subject.\n\n But no clear pattern for \"you\".\n\n However, in 3: \"Aanniqtutit\" = you hurt yourself → so \"you\" is subject → \"aanniqtutit\" \n In 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"aanniqtanga\" = hurt teacher → object = teacher \n\n So \"you\" as object is likely marked by \"aaniqt\" + \"aati\" — from example 1, similar structure.\n\n So: \n 19. The shaman hurt you → \"Angatkuq aanniqt aati\"? \n But \"aanniqt\" + \"aati\" → hurts you → is \"aati\" a valid object suffix?\n\n In 1: \"takuj aati\" = saw you → exists \n So likely.\n\n But in 1: \"takujaatit\" → it ends in \"it\" — tense \n So perhaps \"aanniqt aati\" is not complete — must include tense.\n\n \"aanniqtutit\" is past tense — has \"-utit\" \n \"takujaatit\" has \"-aati\" → includes tense? \n \"aati\" might be object marker and tense?\n\n In 4: \"aarqijaatit\" → cure you → \"aati\" + \"it\" → so likely \"aati\" = object marker, and \"it\" = past tense\n\n So: verb stem + object suffix + tense marker? Or vice versa.\n\n In \"takujaatit\" → \"takuj\" + \"aati\" + \"it\" → so \"aati\" is object marker, \"it\" = past tense \n In \"aarqijaatit\" → \"aarqija\" + \"aati\" + \"it\" → cured you \n In \"aanniqtanga\" → \"aanniqt\" + \"anga\" + \"a\"? → not marked with \"it\"?\n\n In 10: \"aanniqtanga\" — not ending in \"it\" → but is past tense? \n In 1: ends in \"it\" → tense \n In 4: \"aarqijaatit\" → ends in \"it\" \n In 11: \"ukiakhaqtutit\" → ends in \"utit\" — past tense \n So past tense marker is -it or -utit\n\n So \"aanniqtanga\" → \"anga\" = object marker? \n \"aanniqt\" = hurt → root\n\n So likely: verb root + object marker (e.g., \"aati\" for you, \"anga\" for teacher) \n But in 1: \"takujaatit\" → \"aati\" = object marker → for you \n In 10: \"aanniqtanga\" → \"anga\" = for teacher \n\n So object marker: \n - \"you\" → aati \n - \"a teacher\" → aanga? or \"anga\"? \n - \"a doctor\" → \"mik\" in genitive?\n\n So for \"you\" → \"aati\" is used \n Therefore: \n 19. \"Angatkuq aanniqt aati\" → shaman hurt you \n But \"Angatkuq\" = shaman → subject \n \"aanniqt aati\" = hurt you → but in example 3: \"you hurt yourself\" → \"aanniqtutit\" → reflexive \n\n So \"aanniqt aati\" is not reflexive — it's direct object\n\n Yes — so \"aanniqt aati\" → hurt you\n\n But tense? → \"aanniqt\" + \"aati\" → without past tense? \n In 1: \"takujaatit\" → has \"it\" → tense \n So must add \"it\"\n\n So \"aanniqt aati it\"? → redundant? \n\n In 3: \"aanniqtutit\" → has \"utit\" → past \n In 1: \"takujaatit\" → ends in \"it\"\n\n So likely, tense is marked by \"-it\" at end.\n\n So verb root + object marker + it → e.g., \"aanniqt + aati + it\" → hurt you? \n But \"aanniqt aati it\" = awkward\n\n In 10: \"ilinniaqtitsijiit aanniqtanga\" → \"aanniqtanga\" → no \"it\", but sentence is past?\n\n In 10: \"The dog hurt your teacher\" → past → so \"aanniqtanga\" → likely includes tense?\n\n Perhaps the suffix \"anga\" includes tense.\n\n But in 1: \"takujaatit\" → \"takuj + aati + it\" \n In 4: \"aarqijaatit\" → \"aarqij + aati + it\" \n In 10: \"aanniqtanga\" → \"aanniqt + aanga\" → not ending in \"it\" → perhaps \"anga\" is object marker and tense is separate?\n\n Alternative: in all examples, past tense is marked by \"-it\" at end of verb.\n\n In 1: \"takujaatit\" → \"aati\" + \"it\" \n In 4: \"aarqijaatit\" → \"aati\" + \"it\" \n ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11281.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "Start by building a morphological and syntactic alignment from the provided examples.\n\nObserve the examples:\n\n1. Qingmivit takujaatit. → Your dog saw you. \n → \"Qingmi\" (dog), \"v\" (past), \"takujaatit\" (saw you; \"takuj\" = see, \"-aat\" = 3rd person, \"-it\" = you)\n\n2. Inuuhuktuup iluaqhaiji qukiqtanga. → The boy shot the doctor. \n → \"Inuuhuktui\" (boy), \"qukiqtanga\" = shot doctor → \"qukiqtang\" = shoot, \"-a\" = 3rd person, \"-a\" = object\n\n3. Aanniqtutit. → You hurt yourself. \n → \"Aanniqt\" (hurt), \"ut\" = past, \"it\" = yourself → \"Aanniqtutit\" = you hurt yourself\n\n4. Iluaqhaijiup aarqijaatit. → The doctor cured you. \n → \"Iluaqhaiji\" (doctor), \"aarqijaatit\" = cured you → \"aarqi\" = cure, \"-jaat\" = you, \"-it\" = past\n\n5. Qingmiq iputujait. → You speared the dog. \n → \"iputujait\" = speared dog → \"iputuj\" = spear, \"-a\" = object, \"-it\" = past\n\n6. Angatkuq iluaqhaijimik aarqisijuq. → The shaman cured a doctor. \n → \"Angatkuq\" = shaman, \"iluaqhaijimik\" = a doctor, \"aarqisijuq\" = cured → \"aarqi\" + \"sij\" = past + object, \"uq\" = 3rd person? \n → \"aaruq\" = cure, \"sijuq\" = past? \n\n→ \"aarqi\" appears in both \"cured you\" and \"cured a doctor\"\n\n7. Nanuq qaijuq. → The polar bear came. \n → \"Nanuq\" = bear, \"qaijuq\" = came → \"qaij\" = come, \"uq\" = past\n\n8. Iluaqhaijivit inuuhuktuit aarqijanga. → Your doctor cured your boy. \n → \"iluaqhaijivit\" = your doctor, \"inuuhuktuit\" = your boy, \"aarqijanga\" = cured → \"aarqi\" + \"-janga\" = past, object\n\nCompare translations:\n\nHurt: \nExample 3: Aanniqtutit → \"you hurt yourself\" \nSo \"Aanniqt\" = hurt; \"ut\" = past; \"it\" = yourself (reflexive)\n\nSo for \"the shaman hurt you\" → \nSubject: shaman → from ex. 6: \"Angatkuq\" = shaman \nVerb: hurt → \"aanniqt\" \nPast: \"ut\" \nObject: you → \"it\"\n\n→ \"Angatkuq aanniqtutit\"\n\nBut is \"aanniqtutit\" used only for reflexive? \nIn ex. 3: \"you hurt yourself\" → \"aanniqtutit\" — reflexive \nIn ex. 4: \"doctor cured you\" → \"aarqijaatit\" → object \"you\", not reflexive \nSo \"aanniqtutit\" likely means \"you hurt yourself\", while \"aanniqt\" + object → \"aanniqt\" + object + past?\n\nBut \"aanniqtutit\" has past \"ut\" and \"it\" — \"it\" is reflexive.\n\nSo: hurt someone → use \"aanniqt\" + object + past?\n\nCheck ex. 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n→ \"ilinniaqtitsijiit\" = hurt teacher, → \"ilinniaqtitsijiit\" → aanniqt with object?\n\nWait: \"ilinniaqtitsijiit\" → likely \"ilinniaq\" = hurt, \"tisijiit\" = past?\n\nBut ex. 3 says \"Aanniqtutit\" = you hurt yourself\n\nSo is \"aanniqt\" the base verb?\n\nCheck ex. 8: \"aarqijanga\" = cured → \"aarqi\" base\n\nSo verb base: \n- aanniqt = hurt \n- aarqi = cure \n- iputuj = spear (ex. 5: \"iputujait\" = speared dog)\n\nSo structure: \nSubject + verb root + past + object?\n\nWait: ex. 5: \"Qingmiq iputujait\" → \"you speared the dog\" \n→ \"Qingmiq\" = you (possessive?) → \"Qingmi\" = dog? \nActually: ex. 1: \"Qingmivit takujaatit\" = your dog saw you \n→ \"Qingmivit\" = your dog, \"takuj\" = see, \"aatit\" = you\n\nSo in ex. 5: \"Qingmiq iputujait\" → you speared the dog \n→ \"Qingmiq\" = you (is \"q\" infix?) \nPossibly: \"Qingmi\" (dog) → \"Qingmiq\" = you? \nBut \"Qingmiq\" is not \"you\"\n\nIn ex. 1: \"Qingmivit\" = your dog → uses \"v\" for past? \n\"vit\" = past?\n\nIn ex. 1: Qingmivit → your dog (with past)\n\nEx. 5: Qingmiq iputujait → you speared the dog\n\n\"Qingmiq\" → likely \"you\", \"iputujait\" → \"speared\" (iputuj + past + object)\n\nBut \"Qingmi\" appears as dog.\n\nSo many things have \"Qingmi\" as dog → likely the noun \"dog\" is \"Qingmi\"\n\nLikewise, \"iluaqhaiji\" = doctor\n\nSo nouns:\n- dog: Qingmi\n- doctor: iluaqhaiji\n- boy: inuuhuktu\n- shaman: Angatkuq\n- polar bear: Nanuq\n- wolf: Angunahukti (ex. 9)\n\nNow verbs:\n- see: takuja → takujaatit = saw you\n- shoot: qukiqtanga = shot doctor\n- hurt: aanniqt → aanniqtutit = you hurt yourself\n- cure: aarqi → aarqijaatit = cured you\n\nNow, in ex. 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor \n→ \"Inuuhuktuup\" = boy (with object marker?) → \"up\" = object?\n\n\"iluaqhaiji qukiqtanga\" → doctor shot → \"qukiqtanga\" = shot doctor → verb + object?\n\nWait: \"qukiqtanga\" is the verb phrase — \"qukiqtang\" = shoot, \"a\" = 3rd person, \"a\" = object?\n\nSo verb form: [base] + [past] + [object]?\n\nCheck: ex. 5: \"iputujait\" → \"iputuj\" = spear, \"ait\" = past? → \"ait\" = past, \"it\" = object?\n\n\"iputujait\" = you speared the dog → object is \"the dog\"?\n\nIn ex. 5: \"Qingmiq iputujait\" → you speared the dog → so object is dog? But \"Qingmiq\" may be you.\n\nPossibility: verbs are in a pattern: \n[Subject] + [verb stem] + [past marker?] + [object marker?]\n\nBut in ex. 1: \"Qingmivit takujaatit\" → your dog saw you → subject = Qingmivit, verb = takujaatit → takujaatit = saw you\n\nSo takujaatit = takuja + past + object (you)\n\nSimilarly, ex. 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → aarqijaatit = cured you\n\n→ aarqijaatit = aarqi + ja + atit? \n→ aarqi = cure, \"ja\" = object? \"atit\" = past?\n\nPattern: verb + object + past?\n\nBut \"aanniqtutit\" → hurt yourself → \"aanniqt\" + \"ut\" (past) + \"it\" (yourself)? \nSo reflexive object → \"it\"\n\nSo \"aanniqt\" + object + past?\n\nNow for hurt:\n\n19. The shaman hurt you → \nSubject: shaman → Angatkuq \nVerb: hurt → aanniqt \nObject: you → it \nPast: ut \n\nSo → Angatkuq aanniqtutit\n\nBut in ex. 3: \"Aanniqtutit\" = you hurt yourself → so aanniqtutit = you hurt yourself → this form has \"it\" = reflexive\n\nSo for \"you hurt you\" → aanniqtutit \nFor \"you hurt a person\" → would it be aanniqtit + object?\n\nCheck ex. 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n→ \"Qingmiup\" = the dog? → \"up\" = object marker? \n\"ilinniaqtitsijiit\" = hurt teacher → ilinniaq = hurt, \"tisijiit\" = past?\n\nWait: \"ilinniaqtitsijiit\" → \"ilinniaqt\" = hurt, \"tisijiit\" = past + object → \"siji\" = object?\n\nBut this is a different verb.\n\nSo perhaps two verbs: \n- aanniqt = hurt \n- ilinniaq = hurt?\n\nIn ex. 3: \"Aanniqtutit\" → you hurt yourself \nIn ex. 10: \"the dog hurt your teacher\" → \"Qingmiup ilinniaqtitsijiit aanniqtanga\"? \nNo — the sentence is: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n→ \"ilinniaqtitsijiit\" = hurt your teacher → so \"ilinniaqt\" = hurt, \"tisijiit\" = past + object?\n\nBut \"aanniqtanga\" = hurt? \nWait: \"aanniqtanga\" → is that \"hurt\" + object? → \"aanniqtanga\" = hurt?\n\nBut in ex. 3: \"Aanniqtutit\" = hurt yourself — so \"utit\" = reflexive?\n\nNo — likely \"aanniqt\" is the verb, and the form changes based on object.\n\nIn ex. 3: \"aanniqtutit\" — reflexive \nIn ex. 10: \"ilinniaqtitsijiit\" — object: \"your teacher\" → so \"tisijiit\" = past + object?\n\nBut the structure is \"subject + verb + object\" → and the verb has form depending on object.\n\nBut in ex. 5: \"Qingmiq iputujait\" — you speared the dog → \"iputujait\" → verb with object?\n\n\"Qingmiq\" = you (subject), \"iputujait\" = speared dog → so verb has object?\n\nBut ex. 1: \"Qingmivit takujaatit\" → your dog saw you → verb has object?\n\nSo verb alternates with object markers.\n\nNow, in ex. 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → verb \"aarqijaatit\" = cured you\n\n\"aarqijaatit\" → aarqi (cure) + \"ja\" (object?) + \"atit\" (past)?\n\nIn ex. 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"aaruq\" (cure) → \"aarqisijuq\" → \"sijuq\" = past? \n\"aarqisijuq\" likely = cured (past)\n\nSo in ex. 4: \"aarqijaatit\" = cured you → object = you \nex. 6: \"aarqisijuq\" = cured doctor → object = doctor\n\nSo the verb \"aarqi\" appears with different object markers.\n\nSimilarly, “aanniqt” appears in:\n- ex. 3: aanniqtutit → you hurt yourself \n- ex. 10: ilinniaqtitsijiit → the dog hurt your teacher\n\nBut ilinniaq is different from aanniqt?\n\nWait — perhaps it's a single verb meaning \"hurt\", with two forms:\n\n- aanniqt with suffix: \n - ut + it = you hurt yourself \n - ?? + object = you hurt X\n\nBut ex. 10: \"ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher → but \"ilinniaqtitsijiit\" is the verb phrase?\n\nWait: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n→ This seems to have two verbs?\n\nThat can't be.\n\nPossibly typo or full misreading.\n\nLook again: \n\"10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\"\n\nSo \"ilinniaqtitsijiit\" = the dog hurt your teacher? \nThen why is there \"aanniqtanga\"?\n\nMaybe \"ilinniaqtitsijiit\" = hurt, and \"aanniqtanga\" = hurt again?\n\nNo — likely \"ilinniaqtitsijiit\" is the verb meaning \"hurt\", and \"aanniqtanga\" is a red herring?\n\nNo — the translation is \"The dog hurt your teacher\" — so one verb.\n\nSo likely: \"ilinniaqtitsijiit\" = the dog hurt your teacher\n\nSo verb: ilinniaqt → hurt, with object marker \"tisijiit\" = \"your teacher\"?\n\n\"tisijiit\" = your teacher?\n\n\"tisijiit\" → \"tisiji\" = teacher? \"it\" = your?\n\nIn ex. 1: \"takujaatit\" → saw you → \"atit\" = you \nSo \"atit\" = you, \"it\" = your?\n\nIn ex. 3: \"aanniqtutit\" → you hurt yourself — \"utit\" = reflexive?\n\nSo forms:\n- \"atit\" = you \n- \"it\" = your \n- \"it\" = yourself? \n- \"tisijiit\" = your teacher?\n\nSo object markers: \n- \"it\" = you / yourself \n- \"atit\" = you \n- \"tisijiit\" = your teacher\n\nBut in ex. 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" — the dog hurt your teacher → so one verb: \"ilinniaqtitsijiit\"\n\nSo ilinniaqt + tisijiit → hurt your teacher\n\nSimilarly, in ex. 5: \"Qingmiq iputujait\" → you speared the dog → \"iputujait\" = speared (dog?) → object is dog?\n\nBut no object marker? \"iputujait\" — could be \"iputuj\" + \"ait\" = past + object?\n\n\"ait\" = object?\n\nIn ex. 4: \"aarqijaatit\" = cured you → \"jaat\" = you?\n\nIn ex. 2: \"qukiqtanga\" = shot doctor → \"qukiqtang\" = shot, \"a\" = 3rd person, \"a\" = object?\n\nSo verb has both subject and object graphemes?\n\nPattern: \nFor intransitive verbs (like come): \"Nanuq qaijuq\" → bear came — \"qaijuq\" = came \nFor transitive verbs: verb + object + past?\n\nBut in ex. 1: \"Qingmivit takujaatit\" → your dog saw you → \"takujaatit\" = saw you → so includes object marker\n\nSimilarly, ex. 5: \"iputujait\" = speared (with object?)\n\nSo verb base + past marker + object marker?\n\nVerb stem:\n- takuj → see\n- qukiq → shoot\n- aanniqt → hurt\n- aarqi → cure\n- iputuj → spear\n- ilinniaq → hurt?\n\nBut ex. 10: ilinniaqtitsijiit → \"ilinniaqt\" + \"tisijiit\" → hurt your teacher\n\nSo \"ilinniaqt\" = hurt \n\"tisijiit\" = your teacher\n\nAlso in ex. 1: \"takujaatit\" → \"takuj\" + \"a\" + \"atit\"? → \"a\" = object marker?\n\n\"takuj\" + \"a\" = vu? → no\n\n\"takuj\" + \"a\" + \"atit\" = saw you?\n\nSo object marker may be internal.\n\nFor \"hurt\", we have:\n- ex. 3: aanniqtutit → you hurt yourself \n- ex. 10: ilinniaqtitsijiit → the dog hurt your teacher\n\nSo likely, the root verb is \"aanniqt\" or \"ilinniaq\", but used differently.\n\nBut in ex. 10, \"ilinniaqtitsijiit\" is used — is this from \"aanniqt\" or different?\n\nPerhaps \"ilinniaqt\" is a variant of \"aanniqt\"?\n\nCheck if \"ilinniaqt\" and \"aanniqt\" are the same verb.\n\nIn ex. 3: \"Aanniqtutit\" → you hurt yourself \nIn ex. 10: \"ilinniaqtitsijiit\" → dog hurt your teacher\n\nSo both \"hurt\", but different object forms.\n\nSo verb is \"aanniqt\" with object marking.\n\nIn ex. 3: \"aanniqtutit\" → \"ut\" = past, \"it\" = reflexive object\n\nIn ex. 10: \"ilinniaqtitsijiit\" → \"tisijiit\" = object = your teacher\n\nSo the form is: [verb stem] + [past marker] + [object marker]\n\nFor \"aanniqt\":\n-", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10991.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are translating into Inuktitut, a language with specific morphological patterns based on the given examples.\n\nStep-by-step analysis of the examples:\n\nLook for patterns in verb stems, affixes, cases, and objects.\n\nExample 1: Qingmivit takujaatit → Your dog saw you \n- \"Qingmivit\" = dog + saw (past tense, active) \n- \"takujaatit\" = saw (verb, causative or intransitive, but \"you\" is marked as object via \"takujaatit\"?) \nWait — better: \"takujaatit\" = saw (you) — so the verb has a direct object. \nBut \"Qingmivit\" is subject — \"your dog\" — so \"Qingmivit\" likely is subject marker + dog. \n\"Qingmi\" = dog → \"Qingmivit\" = dog (marked with -vit = past, or additive suffix) \nSimilarly, \"takujaatit\" = saw you → verb form with object \"you\"\n\nExample 2: Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor \n- \"Inuuhuktuup\" = boy (subject) \n- \"iluaqhaiji\" = doctor (object) \n- \"qukiqtanga\" = shot (verb) → -tanga = past tense \n\nExample 3: Aanniqtutit → You hurt yourself \n- \"Aanniqtutit\" = you hurt yourself → self-object → \"aanniqtut\" = hurt + yourself \n- \"aanni\" = you (reflexive) \n- \"qaijuq\" = hurt (verb base)\n\nExample 4: Iluaqhaijiup aarqijaatit → The doctor cured you \n- \"iluaqhaijiup\" = doctor (subject) \n- \"aarqijaatit\" = cured you → verb + object \n- \"aarqi\" = cure, -jaatit = past tense (causative or result)\n\nExample 5: Qingmiq iputujait → You speared the dog \n- \"Qingmiq\" = you (subject) \n- \"iputujait\" = speared (dog?) \n- \"iputuj\" = spear → \"iputujait\" = speared (dog) → object is dog → stem + -ait = past\n\nExample 6: Angatkuq iluaqhaijimik aarqisijuq → The shaman cured a doctor \n- \"Angatkuq\" = shaman (subject) \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured → verb with past tense, causative\n\nExample 7: Nanuq qaijuq → The polar bear came \n- \"Nanuq\" = bear (subject) \n- \"qaijuq\" = came → verb base\n\nExample 8: Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy \n- \"iluaqhaijivit\" = your doctor (subject) \n- \"inuuhuktuit\" = your boy (object) \n- \"aarqijanga\" = cured (past tense, verb)\n\nExample 9: Angunahuktiup amaruq iputujanga → The hunter speared the wolf \n- \"Angunahuktiup\" = hunter (subject) \n- \"amaruq\" = wolf (object) \n- \"iputujanga\" = speared (past tense)\n\nExample 10: Qingmiup ilinniaqtitsijiit aanniqtanga → The dog hurt your teacher \n- \"Qingmiup\" = dog (subject) \n- \"ilinniaqtitsijiit\" = hurt your teacher → verb with object “your teacher” \n- \"aanniqtanga\" = hurt → verb past form\n\nExample 11: Ukiakhaqtutit → You fell \n- \"Ukiakhaqtutit\" = you fell → subject + verb base + past tense suffix\n\nExample 12: Angunahukti nanurmik qukiqsijuq → The hunter shot a polar bear \n- \"Angunahukti\" = hunter \n- \"nanurmik\" = a polar bear \n- \"qukiqsijuq\" = shot (past tense)\n\nVerbs in Inuktitut are marked for person, number, and object. They often take reflexive or possessive prefixes.\n\nPattern for verbs:\n- Root verbs: qaijuq (hurt), iputuj (spear), aarqi (cure), iluaqhaij (doctor), nanuq (bear), etc.\n- Past tense suffix: -tut, -tanga, -tita, -tanga, -tanga, -jiit — seems to vary.\n- But look at:\n - qaijuq → hurt → in Example 3 (\"Aanniqtutit\" = you hurt yourself) → \"aanni\" is you, \"qaijuqtut\" = hurt → so \"-tut\" = past?\n - \"Aanniqtutit\" → \"tutit\" — could be -tut + -it (dual past or intensive)\n - Example 4: \"aarqijaatit\" → \"aarqi\" + \"jaatit\" → past\n - Example 8: \"aarqijanga\" → past tense\n - Example 5: \"iputujait\" → past\n - Example 10: \"ilinniaqtitsijiit\" → hurt → \"ilinniaqtitsijiit\" = past root with object?\n\nLet’s isolate verb forms:\n\n| Base verb | Use | Tense | Object | Example |\n|---------------|-----|-------|--------|---------|\n| qaijuq | hurt | base? | self | 3: aanniqtutit |\n| aarqi | cure | base? | object | 4,6,8 |\n| iputuj | spear | base? | object | 5,9 |\n| iluaqhaij | doctor | noun | — | 2,4,6 |\n| nanuq | bear | noun | — | 7 |\n| ukiakhaq | fall | base? | — | 11 |\n\nNow look at possessive forms:\n- \"Your\" = \"Qingmivit\" (dog) — \"Qingmi\" + \"vit\" → possessive of dog?\n- \"Your boy\" = \"inuuhuktuit\" → \"inuuhukt\" + \"uit\" → possessive marker?\n- \"Your doctor\" = \"iluaqhaijivit\" → \"iluaqhaiji\" + \"vit\"\n- \"Your teacher\" = not present, but \"ilinniaqtutsijiit\" in example 10 — \"ilinniaqt\" = teacher?\n\nIn example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → “The dog hurt your teacher” \n\"ilinniaqt\" = teacher → \"ilinniaqtitsijiit\" = hurt + object = teacher? \n\"ilinniaqtitsijiit\" — likely \"ilinniaqt\" (teacher) + \"tisijiit\" = past tense + object? \nBut \"aanniqtanga\" = hurt → verb form? \nNo — \"ilinniaqtitsijiit\" seems to be the verb form — so \"ilinniaqt\" + \"tisijiit\" → verb \nBut \"aanniqtanga\" is separate → verb \"aanniqtanga\" = hurt → so \"ilinniaqtitsijiit\" = hurt your teacher?\n\nWait — this is inconsistent.\n\nAlternative: verb comes after object? Or object before verb?\n\nCheck:\n- 1: Qingmivit takujaatit → subject (dog) + verb (saw you)\n- 2: Inuuhuktuup iluaqhaiji qukiqtanga → boy (subject) + doctor (object) + shot (verb)\n- 3: Aanniqtutit → you (subject) + hurt yourself (verb)\n- 4: Iluaqhaijiup aarqijaatit → doctor (subject) + cured you (verb)\n- 5: Qingmiq iputujait → you (subject) + speared dog (verb)\n- 6: Angatkuq iluaqhaijimik aarqisijuq → shaman (subject) + doctor (object) + cured (verb)\n\nConclusion: All verbs are on the right, and the verb (with object) appears after the subject, and the object is in the middle or before the verb.\n\nExample 3: Aanniqtutit — reflexive, no object → no noun after verb\n\nExample 4: Iluaqhaijiup aarqijaatit → doctor (subject) + \"aarqijaatit\" = cured you → verb + object at end\n\nIn 10: Qingmiup ilinniaqtitsijiit aanniqtanga → dog (subject) + ilinniaqtitsijiit (hurt your teacher?) → verb? \nBut aanniqtanga is separate → likely verb is “aanniqtanga”, not in ilinniaqtitsijiit.\n\nWait — perhaps the noun-object is immediately before the verb? \nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n→ subject (dog) + object (teacher) + verb? \nBut \"ilinniaqtitsijiit\" is a noun phrase?\n\nBut in example 1: \"Qingmivit takujaatit\" — subject + verb \nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" — subject + object + verb \nIn 4: \"Iluaqhaijiup aarqijaatit\" — subject + object (aarqijaatit?) → no, \"aarqijaatit\" is verb\n\nTherefore, structure is:\n\n[subject] [object] [verb] — when object is present\n\nOr: [subject] [verb] — when no object (reflexive)\n\nBut example 3: “Aanniqtutit” — you hurt yourself → no object → reflexive\n\nExample 11: “Ukiakhaqtutit” → you fell — no object\n\nNow verbs with past tense:\n\n- hurt: qaijuq → qaijuqtutit (with -tutit?) — Example 3: Aanniqtutit → qaijuqtut? But only if “aanni” + “qaijuqtut” \n- → “qaijuq” is root → in past: -tut or -tanga?\n\nExample 3: Aanniqtutit — likely “aanni” (you) + “qaijuqtutit”? \nBut it is one word — so verb = aanniqtutit = you hurt yourself → so verb stem is “qaijuqtutit”\n\nSimilarly, cure: \n- aarqi → aarqijaatit (cured you) — so verb = aarqijaatit \n- aarqisijuq → shaman cured a doctor → verb = aarqisijuq \n- aarqijanga → cured your boy → verb = aarqijanga\n\nSo past tense is marked by suffix: -jaat, -si, -anga, etc.\n\nNote: In 4: aarqijaatit → cured you \nIn 6: aarqisijuq → cured a doctor \nIn 8: aarqijanga → cured your boy \nSo: \n- -jaat → cured (object) \n- -sijuq → cured (object) \n- -janga → cured (object)\n\nBut all are past tense verbs, with object marked.\n\nFor \"spear\":\n- iputujait → speared the dog → in 5 \n- iputujanga → speared the wolf → in 9\n\nSo verb stem: iputuj — past: -ait, -anga\n\nFor \"see\":\n- takujaatit → saw → in 1 \n- takujaat? — no other example\n\nSo verb for “see” is takujaat → past: -jaatit\n\nFor “fall”:\n- ukiakhaqtutit → you fell → verb form\n\nNow for possessive markers:\n- \"your\" = -vit \n- \"your doctor\" = iluaqhaijivit \n- \"your boy\" = inuuhuktuit \n- \"your teacher\" = ilinniaqtitsijiit? — not clear\n\nBut in example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog (subject) + hurt (your teacher)? \n→ probably \"ilinniaqt\" = teacher → \"ilinniaqtitsijiit\" = hurt teacher? \nBut “aanniqtanga” = hurt → so likely the verb is after.\n\nSo verb form is “aanniqtanga” = hurt\n\nThen object is “ilinniaqtitsijiit”? → but that sounds like a full phrase.\n\nWait — in example 10: “Qingmiup ilinniaqtitsijiit aanniqtanga” \n→ The dog hurt your teacher\n\nSo subject → \"Qingmiup\" = you? No — \"Qingmiup\" = dog? \n\"Qingmi\" = dog → so \"Qingmiup\" = dog (subject)\n\nThen \"ilinniaqtitsijiit\" = your teacher? → but \"ilinniaqt\" = teacher → \"tisijiit\" = possessive + past?\n\nBut in example 1: \"Qingmivit\" = your dog \nSo \"vit\" = your → then \"Qingmi\" = dog → so \"Qingmivit\" = your dog\n\nSimilarly:\n- \"inuuhuktuit\" = your boy \n- \"iluaqhaijivit\" = your doctor \nSo object marked with “-vit” for possessive\n\nThen verb comes after, with object or reflexive.\n\nTherefore:\n- For \"The shaman hurt you\" → shaman + hurt + you\n\n\"shaman\" = Angatkuq \n\"you\" = aanni (subject) → but in Example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" — shaman cured a doctor → object = a doctor\n\nSo object = a doctor → iluaqhaijimik → \"iluaqhaiji\" (doctor) + \"mik\" = (a) → possessive marker?\n\nWait — \"iluaqhaijimik\" — “mik” could be article?\n\nIn 4: \"iluaqhaijiup\" = doctor (subject) \nIn 6: \"iluaqhaijimik\" = a doctor (object) → so \"mik\" = article \"a\"\n\nSimilarly, in 12: \"Angunahukti nanurmik qukiqsijuq\" → \"nanurmik\" = a polar bear\n\nSo:\n- \"mik\" = a (singular)\n- \"vit\" = your\n- \"up\" = (in some cases) object marker?\n\n\"up\" as in \"inuuhuktuup\" = boy \n\"up\" → object marker?\n\nIn 2: \"Inuuhuktuup\" = boy (subject), so subject = inuuhuktuup \nIn 4: \"iluaqhaijiup\" = doctor (subject) \nSo \"up\" = subject?\n\nBut in 6: \"iluaqhaijimik\" = a doctor (object) → so object marker is \"mik\" and \"up\" seems to be for subject?\n\nCheck:\n- In 2: Inuuhuktuup (boy) + iluaqhaiji (doctor) + qukiqtanga (shot)\n→ so subject → \"Inuuhuktuup\" — no \"up\"? \"Inuuhuktuup\" ends with \"up\" → likely subject\n\nIn 4: \"iluaqhaijiup\" → doctor (subject) → ending with \"up\"\n\nIn 6: \"iluaqhaijimik\" → object → \"mik\"\n\nSo:\n- Subject: noun + \"up\" (if not already) or just noun?\n- Object: noun + \"mik\" (a) or \"vit\" (your)\n\nSo:\n- \"your doctor\" = iluaqhaijivit \n- \"a doctor\" = iluaqhaijimik \n- \"your boy\" = inuuhuktuit \n- \"your teacher\" = ilinniaqtitsijiit? → but \"ilinniaqt\" is teacher, so with \"tisijiit\"? \n\nWait — in example 10: \"ilinniaqtitsijiit\" → \"ilinniaqt\" + \"tisijiit\" → object?\n\nBut \"aanniqtanga\" = verb — \"aanni\" = you, \"qtaanga\" = hurt\n\nSo structure: [subject] [object] [verb]\n\nWith:\n- subject: noun + (up or not)\n- object: noun + (mik or vit)\n- verb: root + past tense suffix\n\nNow for each translation:\n\n19. The shaman hurt you \n- shaman = Angatkuq \n- hurt = qaijuq → past: qaijuqtutit? \n→ in example 3: \"Aanniqtutit\" = you hurt yourself → “qaijuqtutit” — so “qaijuq” + “tutit”? \nBut in 6: \"aarqisijuq\" → cured → so root + tense suffix\n\nSo \"hurt\" past = qaijuq + taut? \nBut no clear suffix.\n\nLook at past forms:\n- hurt: \n - Example 3: aanniqtutit → \"aanni\" + \"qaijuqtutit\" → → qaijuqtutit \n - No other hurt \n- cure: \n - aarqijaatit → aarqi + jaatit \n - aarqisijuq → aarqi + sijuq \n - aarqijanga → aarqi + janga \n→ So past tense varies per verb\n\nSpear: \n- iputujait → iputuj + ait \n- iputujanga → iputuj +anga\n\nSee: \n- hurt: in 3, aanniqtutit → qaijuqtutit → so qaijuq + tutit?\n\n\"tutit\" = past", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11181.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "We are given examples of Inuktitut sentences with English translations, and we are to translate five new sentences into Inuktitut. The key is to identify the underlying morphological and syntactic patterns.\n\nLet’s build an alignment table using the given sentences.\n\n---\n\n**Step 1: Identify recurring patterns**\n\nLook for noun roles and verbs.\n\nFrom sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you\" \n- \"Qingmivit\" = your dog (possessive + noun, \"qin\" = dog, \"mi\" = possessive, \"vit\" = verb form?) \nWait — actually, \"takujaatit\" = saw (past, active, 3rd person), \"vit\" may be a subject marker? \n\nBut look at the verb forms:\n\n- \"takujaatit\" = saw (past, active, 3rd person) \n- \"aarqijaatit\" = cured (past, active) \n- \"putujait\" = speared (past, active) \n- \"qaijuq\" = came (did come) \n- \"iluaqhaiji\" = doctor \n- \"inuuhuktuup\" = boy → \"inuuhuktuit\" in 8 \n- \"angatkuq\" = shaman \n- \"aanniqtutit\" = hurt yourself (reflexive) \n- \"angunahukti\" = hunter \n- \"qingmi\" = dog \n\nNow, observe verbs:\n\n- hurt → \"aanniqtutit\" (1, 3, 10, 19) \n- saw → \"takujaatit\" (1) \n- cured → \"aarqijaatit\" (4, 6, 8) \n- speared → \"iputujait\" (5, 9, 22) \n- came → \"qaijuq\" (7) \n- fell → \"ukiakhaqtutit\" (11) \n\nSo verbs are transitive, intransitive, or reflexive.\n\nNow, subjects:\n\n| Sentence | Subject | Object | Verb |\n|--------|--------|--------|------|\n| 1 | your dog | you | saw |\n| 2 | the boy | the doctor | shot |\n| 3 | you | yourself | hurt |\n| 4 | the doctor | you | cured |\n| 5 | you | the dog | speared |\n| 6 | the shaman | a doctor | cured |\n| 7 | the polar bear | — | came |\n| 8 | your doctor | your boy | cured |\n| 9 | the hunter | the wolf | speared |\n|10 | the dog | your teacher | hurt |\n|11 | you | — | fell |\n|12 | the hunter | a polar bear | shot |\n\nWe note:\n\n- Possessive markers: \"your\" = \"q\" + possessive prefix (e.g., \"qingmivit\" = \"your dog\")\n- \"Qingmivit\" = your dog → \"qingmi\" + \"vit\" \n- \"Inuuhuktuup\" = the boy — \"inuuhuktuit\" = your boy (possessive)\n- \"Angatkuq\" = the shaman → \"angunahukti\" = the hunter\n- \"Aanniqtutit\" = you hurt yourself → reflexive\n\nPattern: \n- Subject and object are marked with possessive prefixes when referring to \"your\" or \"your\" something.\n- The verb stem changes with transitivity and aspect.\n- \"Hurt\" → \"aanniqtutit\"\n- \"Cured\" → \"aarqijaatit\"\n- \"Saw\" → \"takujaatit\"\n- \"Spear\" → \"iputujait\"\n- \"Fell\" → \"ukiakhaqtutit\"\n- \"Came\" → \"qaijuq\"\n\nAlso, do possessives exist on nouns?\n\nExamples:\n\n- \"Qingmivit\" = your dog → \"qingmi\" (dog) + \"vit\" (possessive suffix?) \nBut “qingmi” in 5 is “qingmiq” in \"qingmiq iputujait\" — you speared the dog.\n\n“qingmiq” = dog? “iputujait” = speared.\n\nSo “qingmiq” is the noun — \"dog\"\n\nIn \"qingmivit\" = your dog → “qingmi” + “vit” → “vit” = possessive suffix?\n\nSimilarly, \"inuuhuktuup\" = the boy → \"inuuhuktuit\" = your boy → \"inuuhuktuit\" = \"inuuhuk\" (boy) + \"tuit\" = possessive?\n\nLikewise:\n\n- \"iluaqhaiji\" = doctor \n- \"iluaqhaijivit\" = your doctor → \"iluaqhaijivit\"\n\nSo pattern:\n\nPossessive suffixes:\n- \"vit\" → \"your\" (used in 1, 8)\n- \"tuit\" → \"your\" (in 8: \"inuuhuktuit\" → your boy)\n- \"ik\" → not clear.\n\nBut look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n→ \"The dog hurt your teacher\" \nSo \"qingmiup\" = \"dog\" + \"up\" → is “up” possessive?\n\n\"Qingmiup\" → \"your dog\" in 1 is \"qingmivit\" → so \"v\" is in \"vit\", not \"up\".\n\nWait: 1 is \"Qingmivit takujaatit\" → your dog saw you \n10 is \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n\nSo in 1: \"qingmivit\" = your dog \nin 10: \"qingmiup\" = dog (without possessive?) — not.\n\nBut \"ilinniaqtitsijiit\" = hurt (verb)? \n\"ilinniaqtitsijiit\" → likely verb form of \"ilinniaq\" = hurt? \n\nYes — in 10: \"ilinniaqtitsijiit\" = hurt (past, transitive)\n\nAnd \"aanniqtanga\" = your teacher → \"aanniqtanga\" → \"aanniqt\" = hurt, \"anga\" = poss.?\n\nIn 3: \"Aanniqtutit\" → you hurt yourself → \"aanniqtutit\" → reflexive form?\n\nIn 10: \"aanniqtanga\" → your teacher → \"aanniqt\" + \"anga\" = poss. suffix?\n\nCompare with 4: \"Iluaqhaijiup aarqijaatit\" → the doctor cured you → \"iluaqhaijiup\" = doctor + \"up\"? \nBut \"iluaqhaiji\" = doctor → \"iluaqhaijiup\" = doctor (with possessive? no)\n\nBut 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"iluaqhaijivit\" = your doctor → \"iluaqhaiji\" + \"vit\"\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → the shaman cured a doctor → \"iluaqhaijimik\" = a doctor? → \"iluaqhaiji\" + \"mik\" → \"mik\" = possessive? No — \"mik\" might be a partitive.\n\nWait — in 6: \"iluaqhaijimik\" → a doctor? \"mik\" = a (partitive) → so \"iluaqhaijimik\" = a doctor\n\nIn 8: \"iluaqhaijivit\" = your doctor → \"iluaqhaiji\" + \"vit\"\n\nSo:\n- \"vit\" = your (possessive)\n- \"mik\" = a (partitive, indefinite)\n- \"up\" = ? — appears in \"qingmiup\"\n\nBut sentence 1: \"Qingmivit\" → your dog \n10: \"Qingmiup\" → dog? Maybe \"up\" is a marker for third-person or subject?\n\nWait — what about the verb?\n\nList verbs:\n\n| Verb | Base form | Examples |\n|------|----------|--------|\n| hurt | aanniqt- | aanniqtutit, aanniqtanga (your teacher) |\n| cured | aarqi- | aarqijaatit, aarqisijuq |\n| saw | takuj- | takujaatit |\n| speared | iputuj- | iputujait, iputujanga |\n| fell | ukiakhaq- | ukiakhaqtutit |\n| came | qaijuq | qaijuq |\n\nNow, notice the verb ending:\n\n- aanniqtutit → “you hurt yourself” → reflexive\n- aanniqtanga → “your teacher” → object\n- aarqijaatit → “the doctor cured you” — object “you”\n- iputujait → “you speared the dog”\n- ukiakhaqtutit → “you fell”\n\nPattern: \nFor verbs with object, we see:\n- \"aanniqtanga\" → object \"your teacher\"\n- \"aarqijaatit\" → object \"you\"\n- \"iputujanga\" → object \"your wolf\"? In 9: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"shot a polar bear\" → \"qukiqsijuq\" = “qukiq” (shot) + “sijuq”?\n\nIn 9: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\"\n\n\"nanurmik\" = a polar bear → \"n\" + \"anurmik\"? \nBut 7: \"Nanuq qaijuq\" → \"the polar bear came\" → \"nanuq\" = polar bear\n\nSo \"nanur\" → polar bear \n\"nanurmik\" → a polar bear (partitive)\n\nSimilarly, 12: \"Angunahukti nanurmik qukiqsijuq\" → the hunter shot a polar bear → \"qukiqsijuq\" = shot? → \"qukiq\" = shoot, \"sijuq\" = object?\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"qukiqtanga\" = the doctor — object marker?\n\nWait — \"qukiqtanga\" → \"qukiq\" + \"tanga\"? \nBut in 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → \"aanniqtanga\" → \"aanniqt\" (hurt) + \"anga\" = your teacher\n\nSo: \n- \"anga\" = your \n- \"tanga\" = your? \nBut in 8: \"inuuhuktuit\" = your boy → \"tuit\" = your \nSo different possessive suffixes?\n\nPossessive suffixes:\n- \"vit\" → your (with noun)\n- \"tuit\" → your (with boy)\n- \"anga\" → your (with teacher)\n\nSo the suffix varies.\n\nBut more importantly: \n- If the subject has possessive, it's marked on the noun: \"iluaqhaijivit\" = your doctor \n- If the object has possessive, it's marked: \"aanniqtanga\" = your teacher\n\nThus, in translation:\n\nFor \"The shaman hurt you\" → \nSubject: the shaman → \"angatkuq\" (from sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor) \nVerb: hurt → \"aanniqt-\" \nObject: you → \"takujait\"? but in 1: \"takujaatit\" = saw you → \"takuj\" + \"aat\" → last form?\n\nIn 3: \"aanniqtutit\" = you hurt yourself → reflexive \nIn 1: \"takujaatit\" = saw you → \"takuj\" + \"aati\"?\n\nPattern: \n- For transitive verbs, verb has object noun with suffix\n- Possessive is on the object or subject\n\nSo build for:\n\n19. The shaman hurt you → \nSubject: \"angatkuq\" (the shaman) \nVerb: \"aanniqt-\" \nObject: \"you\" → \"takujait\"? → no, \"takuj\" is saw → not hurt\n\nWait — hurt is \"aanniqt-\", saw is \"takuj-\"\n\nIn 3: \"Aanniqtutit\" = you hurt yourself → only reflexive \nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher → so \"ilinniaqtitsijiit\" = verb (hurt), \"aanniqtanga\" = object\n\nSo verb is \"aanniqt-\" + suffix?\n\n- in 3: \"aanniqtutit\" → reflexive\n- in 10: \"ilinniaqtitsijiit\" → transitive verb with object → \"ilinniaqtitsijiit\" likely = \"ilinniaq\" (hurt) + \"titsijiit\" → tense?\n\nBut in 1: \"takujait\" = saw → \"takuj\" + \"ait\"\n\nIn 5: \"Qingmiq iputujait\" → you speared the dog → \"iputujait\" = speared\n\nIn 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"aarqisijuq\"\n\nSo verb forms:\n- hurt: aanniqt- → with object → aanniqtanga (for object you), or aanniqtutit (reflexive)\n- cured: aarqi- → aarqijaatit (you), aarqisijuq (a doctor)\n- saw: takuj- → takujaatit (you)\n- speared: iputuj- → iputujait (dog), iputujanga (your wolf?)\n- fell: ukiakhaq- → ukiakhaqtutit (you)\n\nSo active past tense verb endings:\n- -aati / -ait → for transitive verbs\n- -utit → reflexive?\n\nIn 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"aarqijanga\" → verb form (cured) + object?\n\n\"aarqijanga\" → \"aarqi\" + \"janga\"? \n\nCompare with 4: \"Iluaqhaijiup aarqijaatit\" → doctor cured you → \"aarqijaatit\" → \"aarqi\" + \"jaat\"? \n\n\"jaat\" vs \"janga\" — different.\n\nBut in 6: \"angatkuq iluaqhaijimik aarqisijuq\" → \"aarqisijuq\" = cured a doctor\n\nSo \"janga\" → object (your boy) → \"inuuhuktuit\" = your boy → \"janga\" = verb form?\n\nFrom 8: \"aarqijanga\" → cured your boy\n\nIn 10: \"aanniqtanga\" → hurt your teacher → \"anga\"\n\nSo the suffix on the verb may mark the object:\n\n- \"aati\" → \"you\" or \"a person\"\n- \"anga\" → \"your teacher\"\n- \"janga\" → \"your boy\"\n- \"tanga\" → \"your teacher\"?\n\nIn 10: \"aanniqtanga\" → your teacher\n\nIn 8: \"aarqijanga\" → your boy\n\nIn 4: \"aarqijaatit\" → cured you → \"jaatit\"\n\nSo:\n- \"jaatit\" → you\n- \"janga\" → your boy\n- \"anga\" → your teacher\n\nSo object marking is consistent.\n\nThus for \"The shaman hurt you\" → \nSubject: \"angatkuq\" \nVerb: \"aanniqt\" + object suffix for \"you\" → but in 3: \"aanniqtutit\" = you hurt yourself → reflexive\n\nWhat about \"you\" as direct object?\n\nIn 1: \"takujaatit\" = saw you → so \"takuj\" + \"aati\"? → \"aati\" seems to be object marker for \"you\"\n\nBut in 3: \"aanniqtutit\" = you hurt yourself — no separate object → reflexive\n\nIn 10: \"aanniqtanga\" = hurt your teacher → \"anga\"\n\nSo for object \"you\" → what suffix?\n\nIn 1: \"takujaatit\" → saw you → \"aati\"? \nBut 3: \"aanniqtutit\" → you hurt yourself → \"utit\" → reflexive\n\nSo perhaps:\n- \"aati\" → for \"you\" as object\n- \"utit\" → reflexive\n- \"anga\" → your teacher\n- \"janga\" → your boy\n\nBut in 1: \"takujaatit\" — \"aati\" → you \nSo if \"aaniqt\" + \"aati\" = hurt you?\n\nBut no such example.\n\nWe have no direct \"x hurt you\" with \"you\" as object.\n\nBut in 3: \"aanniqtutit\" = you hurt yourself — reflexive\n\nWe need to find a non-reflexive form with \"you\" as object.\n\nWhat about sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → \"doctor\" is object\n\nNo \"you\"\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" — object \"a polar bear\"\n\nSo missing a direct \"x hurt you\"\n\nBut perhaps the form is based on the object's possession.\n\nWait: the verb ending may indicate object type.\n\nBut look at 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher → \"aanniqtanga\"\n\nSo \"aanniqtanga\" = hurt + object \"your teacher\"\n\nSimilarly, 8: \"iluaqhaijivit inuuhuktuit", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10968.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given a set of Nooni sentences across different days of the \"Nooni week\", and we are to translate five sentences into Nooni, spoken on **Bvumbon**.\n\nWe need to derive the linguistic pattern from the examples, particularly regarding:\n\n- Day reference (e.g., \"Yesterday\", \"Tomorrow\", \"Today\", \"The day after tomorrow\")\n- Tense and aspect (e.g., \"will\", \"just now\", \"heard\", \"will kill\", \"saw\")\n- Subject-object relations (e.g., \"I helped the man\", \"the thief stole\", \"the man saw\")\n- Fixed expressions (e.g., \"On Bvusɔw\", \"On Bvuŋkaden\", \"Today\")\n\n---\n\n### Step 1: Identify Day Reference Patterns\n\nFrom the examples:\n\n- \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" \n- \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \n- \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" \n- \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" \n- \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\"\n\nObservation:\n- \"Yesterday\" → fɔgò cǐ \n- \"Tomorrow\" → ntfǔː \n- \"Day after tomorrow\" → fɔ̀ shě \n- \"Day before yesterday\" → kefwé cí \n- \"Today\" → used directly (as in \"Today, I chose the book\") \n- \"On X\" → used as a temporal adverbial (\"On Bvusɔw\", \"On Bvutfu\")\n\nSo temporal expressions:\n- fɔgò cǐ = yesterday \n- ntfǔː = tomorrow \n- fɔ̀ shě = day after tomorrow \n- kefwé cí = day before yesterday \n- Present day = no fixative, just \"Today\"\n\nAlso: \"On X\" → \"nú\" + day-name \n→ e.g., \"On Bvusbɔw, you will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\nNote: \"nú\" = on (temporal adverb)\n\n---\n\n### Step 2: Tense and Aspect\n\nLook at \"just now\", \"will\", \"heard\", \"will kill\", \"saw\"\n\n- \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" \n→ \"heard\" = cɔ̌ŋ (past perfect? long ago) \n- \"The woman saw me at the market just now\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" \n→ \"just now\" = cǐ nɔ̂ː yɛ᷅n me lé → seems to use \"cǐ\" (just) + \"nɔ̂ː\" (now) \n\nWait — \"cǐ\" = just (in some cases) \nBut in “Yesterday was Bvumbon” → \"fɔgò cǐ\" → “fɔgò” = yesterday, \"cǐ\" = adjective or addition? \nNot clear.\n\nAnother clue: \n→ \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" \n→ \"fɔ̀ shě\" = day after tomorrow \n→ \"nú\" = on \n→ So: \"On Bvutfu\" = \"nú bvútfu᷅\"\n\nAlso: \n(8) \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" \n→ \"ntfǔː\" = tomorrow, \"nú\" = on \n\nSo pattern:\n- [Temporal phrase] + nú + day-name\n\nAlso from 21: \"The thief stole the yam just now\" → must contain \"just now\"\n\nIn sentence (7): \"You(sg) heard the thief a long time ago\" → uses \"tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"a long time ago\"\n\nSo:\n- a long time ago → \"tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\"\n- just now → likely \"cǐ nɔ̂ː\" or similar\n\nFrom (15): \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" \n→ \"bɔ́\" = they, \"nɔ̂ː\" = now, \"yɛ᷅n me lé\" = saw me \n→ So \"nɔ̂ː\" is present (now)\n\nThus:\n- \"just now\" = nɔ̂ː (now), possibly with \"cǐ\" for immediacy?\n\nBut (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" \n→ \"kwɔ᷆ːn\" = woman, \"cǐ nɔ̂ː\" = just now, \"yɛ᷅n wáy\" = saw the market\n\nSo \"cǐ nɔ̂ː\" = just now\n\nTherefore:\n- \"just now\" = cǐ nɔ̂ː \n- \"a long time ago\" = tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\nSo for:\n21. \"The thief stole the yam just now\" → \"yo᷅w cɔ̌ŋ kèŋkfǔ yɛ᷅n\" + \"cǐ nɔ̂ː\"\n\nWait — \"thief\" = yo᷅w \n\"stole\" = cɔ̌ŋ \n\"yam\" = kèŋkfǔ \n\"just now\" = cǐ nɔ̂ː\n\nSo: yo᷅w cɔ̌ŋ kèŋkfǔ cǐ nɔ̂ː\n\nThis matches the pattern.\n\n---\n\n### Step 3: Subject-Verb-Object\n\nExamples:\n- \"On Bvusɔw, I came to the market\" → \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" \n→ me = I, ncí = came, nɔ̂ː = to, ntɔ᷅ = market, bvúmbòn = (on) Bvumbon\n\nBut \"on Bvusɔw\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \n→ wɔ̀ = you, yúː = will, cɔ́ŋ = steal, kèŋkfǔ = yam, bvúsɔ̀w = on Bvusɔw\n\nSo verb marked with tense: yúː = will\n\nSimilarly, (3): \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" \n→ kwɔ᷆ːn = woman, nǔ = will, bóy = help, me = I, bvúzhí = on Bvuzhi\n\nSo: [subject] + [tense] + [verb] + [object] + [on X]\n\nBut in \"On Bvusɔw, I helped the man\" (20) → required\n\nWe are to build: \"On Bvusɔw, I helped the man\"\n\nFrom (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" \n→ \"cǐ nɔ̂ː\" = just now, \"yɛ᷅n wáy\" = saw → verb is \"yɛ᷅n\"\n\nAlso in (14): \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" \n→ bèsèn = we, nǔ = will, géː = steal, mutù = car, ɛ̀bɛ̀n = the car\n\nSo: [subject] + [will] + [verb] + [object]\n\nSo \"help\" = bóy (as in \"help me\")\n\n\"helped\" = past tense of \"bóy\" → do we have a past tense?\n\nIn (3): \"the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\" → \"nǔ\" = will\n\nNo past tense marker for \"will help\"\n\nBut (15): \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" \n→ \"yɛ᷅n\" = saw → appears to be a past tense verb\n\nSo \"saw\" = yɛ᷅n\n\n\"helped\" → likely absence of tense? But when a future is needed, \"nǔ\" = will\n\nSo:\n- \"will\" → nǔ \n- \"past\" → no explicit marker; used in present or immediacy\n\nBut (20): \"On Bvusɔw, I helped the man\" → past tense?\n\nCompare to (2): \"On Bvusɔw, you(sg) will steal\" → uses \"nǔ\" for future\n\nSo only future uses \"nǔ\"\n\nSo \"helped\" = present or past? → likely uses the base verb without future marker → base form\n\nBut (14): \"we will steal\" → \"nǔ géː cɔ́ŋ\"\n\nSo present or past use of verb? No vowel change.\n\nPerhaps all verbs are in base form, and tense is marked by auxiliary.\n\nBut future = \"nǔ\"\n\nPresent = implied (without auxiliary)\n\nSo for \"helped\", if past, may be just \"bóy\" + object?\n\nBut (3): \"on Bvuzhi, the woman will help me\" → used \"nǔ\"\n\nSo present tense may not require auxiliary.\n\nSo \"I helped the man\" → me + bóy + man\n\nLikely: me bóy dìɛ̀msɛ̌n\n\n\"man\" = dìɛ̀msɛ̌n\n\nSo (20): \"On Bvusɔw, I helped the man\" → \"me bóy dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nBut is there a marker for past?\n\n(12): \"I am about to help the man\" → \"me nú nfí dìɛ̀msɛ̌n\" \n→ \"nfí\" = about to → near future\n\nSo \"to help\" = nfí, not \"bóy\"\n\nSo \"helped\" is not shown in past — only future via \"nǔ\", present via base\n\nThus, \"helped\" is base verb → \"bóy\" → for past or present\n\nSo (20): me bóy dìɛ̀msɛ̌n nú bvúsɔ̀w\n\n---\n\n### Step 4: 21. \"The thief stole the yam just now\"\n\nFrom (7): \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\"\n\n→ \"yo᷅w\" = thief, \"cɔ̌ŋ\" = heard, \"tɔ̀ nɔ̂ː\" = a long time ago\n\nSo \"heard\" = cɔ̌ŋ\n\n\"stole\" = likely cɔ̌ŋ (same verb?) — check\n\n(2): \"you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\"\n\n\"steal\" = cɔ́ŋ\n\n(7): \"heard\" = cɔ̌ŋ → same verb?\n\nBut different meaning?\n\nLikely same root with different tone or affix?\n\nIn (21): \"thief stole the yam just now\"\n\nSo: yo᷅w cɔ̌ŋ kèŋkfǔ cǐ nɔ̂ː → only if \"cɔ̌ŋ\" = steal\n\nBut (2): \"cɔ́ŋ\" = steal, (7): \"cɔ̌ŋ\" = heard → different tone\n\nSo possibly different verbs or affixes.\n\nBut \"cɔ́ŋ\" vs \"cɔ̌ŋ\" — tone difference\n\nSo \"cɔ́ŋ\" = steal, \"cɔ̌ŋ\" = heard\n\nSo \"the thief stole\" = yo᷅w cɔ́ŋ kèŋkfǔ\n\n\"just now\" = cǐ nɔ̂ː\n\nSo: yo᷅w cɔ́ŋ kèŋkfǔ cǐ nɔ̂ː\n\nNo \"on\" because not tied to a day → just a statement\n\n---\n\n### Step 5: 22. \"On Bvuŋkaden, I will hear the car\"\n\n\"hear\" = cɔ̌ŋ \n\"will\" = nǔ \n\"I\" = me \n\"car\" = mutù or ɛ̀bɛ̀n\n\nFrom (14): \"we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" \n→ mutù and ɛ̀bɛ̀n both mean \"car\"? Possibly equivalent or different\n\n(6): \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" \n→ \"wvù\" = he, \"bɛ̂ː\" = killed, \"yo᷅kwɔ᷆ːn\" = woman, \"ɛ̀bɛ̀n\" = woman? → \"ɛ̀bɛ̀n\" = woman?\n\nBut car is different.\n\nIn (14): \"the car\" = mutù ɛ̀bɛ̀n → both used?\n\n(5): \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\"\n\n→ \"ncáw\" = choose, \"mutù\" = car → so \"mutù\" = car\n\nIn (14): \"steal the car\" → \"mutù ɛ̀bɛ̀n\" → ambiguous\n\nBut in (14): \"we will steal the car\" → \"mutù ɛ̀bɛ̀n\"\n\nSo if \"mutù\" = car, \"ɛ̀bɛ̀n\" = car → may be redundant\n\nAlternatively, \"mutù\" = car, \"ɛ̀bɛ̀n\" = woman\n\nIn (6): \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"ɛ̀bɛ̀n\" = woman\n\nSo \"car\" = mutù only? But \"mutù\" appears with \"car\"\n\nIn (5): \"choose the car\" → ncáw mutù → so \"mutù\" = car\n\nThus, \"hear the car\" → me nǔ cɔ̌ŋ mutù\n\n\"On Bvuŋkaden\" → nú bvûŋka᷆ːde᷆n\n\nSo: me nǔ cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\n\nNote: \"nǔ\" = will\n\n---\n\n### Step 6: 23. \"Today, the woman will kill the man\"\n\n\"Today\" → no marker → \"Today\" = context, not on a day name\n\nIn (9): \"Today, I chose the book\" → \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" \n→ \"mbɛ̂ː\" = chose, \"nca᷅w\" = book, \"ɛ̀bɛ̀n\" = book? redundant\n\nSo \"today\" = context, not explicit in form\n\nSo \"today\" = implied\n\n\"the woman\" = kwɔ᷆ːn \n\"will kill\" = nǔ + bɛ̂ː \n\"the man\" = dìɛ̀msɛ̌n\n\nSo: kwɔ᷆ːn nǔ bɛ̂ː dìɛ̀msɛ̌n\n\nNo \"on X\" — just today\n\nSo: kwɔ᷆ːn nǔ bɛ̂ː dìɛ̀msɛ̌n\n\n---\n\n### Step 7: 24. \"Today, the man saw you(sg)\"\n\n\"the man\" = dìɛ̀msɛ̌n \n\"saw\" = yɛ᷅n \n\"you(sg)\" = wɔ̀\n\nFrom (15): \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n→ \"yɛ᷅n\" = saw\n\nSo: dìɛ̀msɛ̌n yɛ᷅n wɔ̀\n\n\"today\" = implied\n\nSo: dìɛ̀msɛ̌n yɛ᷅n wɔ̀\n\n---\n\n### Final Translations (spoken on Bvumbon)\n\nAll sentences are to be in **Nooni**, spoken on **Bvumbon**, so no day markers for temporal reference unless used.\n\n20. On Bvusɔw, I helped the man → me bóy dìɛ̀msɛ̌n nú bvúsɔ̀w \n21. The thief stole the yam just now → yo᷅w cɔ́ŋ kèŋkfǔ cǐ nɔ̂ː \n22. On Bvuŋkaden, I will hear the car → me nǔ cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n \n23. Today, the woman will kill the man → kwɔ᷆ːn nǔ bɛ̂ː dìɛ̀msɛ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9166.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given a set of Nooni sentences across different days of the week (Bvutfu, Bvusɔw, Bvukema, Bvuzhi, Bvuŋka), and we are to translate five new sentences into Nooni, all **spoken on Bvumbon**.\n\nWe must derive the linguistic patterns step-by-step, focusing on:\n\n- How time references are expressed (yesterday, today, tomorrow, the day after tomorrow, etc.)\n- How tense/aspect is marked (past, present, future)\n- How subject, object, and actions are phrased\n- How verbs are constructed (especially for possession, helping, stealing, hearing, seeing, killing)\n\nWe'll build an alignment table from the given examples and extract patterns.\n\n---\n\n### Step 1: Identify time expressions\n\nFrom the examples:\n\n| Sentence | Day | Time reference |\n|--------|-----|----------------|\n| 1 | Bvutfu | \"Yesterday was Bvumbon\" → \"Yesterday\" = Bvumbon |\n| 2 | Bvusɔw | \"On Bvusɔw, you will steal...\" → \"On X, Y will do Z\" |\n| 3 | Bvusɔw | \"On Bvuzhi, the woman will help me\" → future action on a specific day |\n| 4 | Bvusɔw | \"On Bvuŋka, he found...\" → past on Bvuŋka |\n| 5 | Bvusɔw | \"The day after tomorrow is Bvutfu\" → day after tomorrow = Bvutfu |\n| 8 | Bvukema | \"Tomorrow is Bvuŋkaden\" → tomorrow = Bvuŋkaden |\n| 11 | Bvukema | \"The day before yesterday was Bvuŋka\" → day before yesterday = Bvuŋka |\n| 12 | Bvukema | \"I am about to help the man\" → present continuous (about to) |\n| 13 | Bvukema | \"On Bvutfu, the woman saw the market\" → past on a day |\n| 14 | Bvukema | \"Today, we will steal the car\" → future today |\n\nWe now gather time markers:\n\n- **Yesterday** → Bvumbon (ex. 1)\n- **Today** → \"nú\" or \"wɔ̀\" (examples: 4, 6, 9, 14)\n- **Tomorrow** → Bvuŋkaden (ex. 8)\n- **The day after tomorrow** → Bvutfu (ex. 5)\n- **The day before yesterday** → Bvuŋka (ex. 11)\n\nIn all cases, time markers are expressed with the day name or with a time adverb (like \"tomorrow\", \"today\", \"yesterday\").\n\nTo express time, a structure like **[time adverb] + [day name]** is used.\n\nBut note: \n- In 5: \"The day after tomorrow is Bvutfu\" → \"ntfǔː nú bvútfu᷅\" → “the day after tomorrow” is the time point, “is” = copula.\n- In 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n”\n\nSo pattern: \n**[time] + nú + [day name]**\n\nSo:\n- yesterday → “cǐ nú” ??? Wait.\n\nBut sentence 1: “fɔgò cǐ nú bvúmbòn” → “Yesterday was Bvumbon” \n→ “cǐ nú” = “yesterday” + “was” = past time indicator?\n\nWait, “cǐ” may be “yesterday” (from “fɔgò cǐ nú” = yesterday was).\n\nSimilarly, sentence 11: “kefwé cí nú bvûŋka” → “the day before yesterday was Bvuŋka” → “cí nú” = day before yesterday.\n\nSo:\n\n- “cǐ” = yesterday\n- “cí” = day before yesterday\n- “ntfǔː” = tomorrow\n- “ntfǔː nú” = tomorrow is [day]\n- “ntfǔː nú” + day → tomorrow is X\n- “cǐ nú” → yesterday was X\n- “cí nú” → day before yesterday was X\n\nNow, other time expressions:\n\n- “The day after tomorrow” → translated as: “ntfǔː nú bvútfu᷅” in sentence 5 \n→ so “nú” after “ntfǔː” → “the day after tomorrow is X”\n\nSo “ntfǔː nú” = tomorrow \n“ntfǔː nú” again = tomorrow → but we need “the day after tomorrow”\n\nWait, sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo the structure is: **fɔ̀ shě + ntfǔː + nú + [day]**\n\n→ “fɔ̀ shě” = \"the day after tomorrow\"\n\nSo:\n- \"fɔ̀ shě\" = day after tomorrow (used in 5)\n- \"cǐ\" = yesterday (1)\n- \"cí\" = day before yesterday (11)\n\nSo time markers:\n\n| Time phrase | Morpheme |\n|-----------|---------|\n| yesterday | cǐ |\n| day before yesterday | cí |\n| tomorrow | ntfǔː |\n| the day after tomorrow | fɔ̀ shě |\n\nThus:\n- “The day after tomorrow is X” → “fɔ̀ shě nú X”\n- “Yesterday was X” → “cǐ nú X”\n- “Tomorrow is X” → “ntfǔː nú X”\n- “Today” = without time marker or explicit “wɔ̀” (used in 4,6,9,14)\n\nAnd “on X” is expressed with: **[action] + on + X**, or **on X, [action]**\n\nStructure: “me nú mbóy ncáw mutù bvútfu᷅” → “On Bvutfu, I will choose the car”\n\nSo: [subject] + nú + [verb] + [object] + [on day]\n\nIn 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “On Bvuŋka, he found the book” → pattern: [subject] + [verb] + [object] + [on day]\n\nSo on day = “on X” or “nú X” (sometimes)\n\nNow, what about verb patterns?\n\n---\n\n### Step 2: Verb morphology and aspect\n\nList of verbs:\n\n- **find** → “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà” → “he found the book”\n- **come** → “me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn” → “on Bvumbon, I came to the market”\n- **steal** → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “on Bvusɔw, you will steal the yam”\n- **help** → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “on Bvuzhi, the woman will help me”\n- **hear** → 22: “I will hear the car” → must be “nú” + verb + object\n- **see** → 24: “the man saw you” → “wvù nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “they saw me at the market just now”\n- **kill** → 23: “the woman will kill the man” → “bɛ̀n” = woman?; “bɛ̀n” = woman?; “wɛ̂ː” = kill?\n\nIn sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “Today, he killed the woman” → “bɛ̂ː” = kill \nSo “bɛ̂ː” = kill\n\nLikely:\n- “bɛ̂ː” = kill (with person)\n- “wɔ̀” = “you”\n- “yúː” = steal\n- “cɔ́ŋ” = the yam (possessive?)\n- “kwɔ᷆ːn” = woman\n- “fí” = help\n\nHence, verbs:\n- “cɔ́ŋ” = the yam → noun\n- “wɛ̂ː” = kill\n- “cɔ́ŋ” = steal? in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ” → “you will steal the yam” → “yúː” = steal\n- So: “yúː” = steal\n- “bɛ̂ː” = kill\n- “fí” = help\n- “wvù” = he / find / he saw\n- “ncí” = came\n- “bóy” = woman\n- “bèsèn” = will (future)\n- “me” = I\n- “mbóy” = I chose (in 9)\n- “mbɛ̂ː” = I chose? or “I will choose”\n\nIn 9: “me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n” → \"Today, I chose the book\"\n\nSo:\n- “mbɛ̂ː” = I chose\n- “nca᷅w” = book\n- “ŋwà” = the book\n\nSo verb forms include:\n- Present/future: “nú” + verb → “on X, I will do”\n- Past: “wɔ̀ tɔ̀” = “you heard” (in 7)\n- Present: “wvù” = “he saw”\n- Interrupted past (\"just now\"): “fɔ̀wǎy” → “just now”?\n\nIn 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “They saw me at the market just now”\n\n→ “fɔ̀wǎy” = “just now”\n\nSo “fɔ̀wǎy” = just now → present or immediate past\n\nSimilarly, in 21: “The thief stole the yam just now” → “just now” = fɔ̀wǎy\n\nSo using “fɔ̀wǎy” for “just now”\n\nFor future: “nú” (on a day) → “will”\n\nIn sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “Today, we will steal the car”\n\n→ “bèsèn” = future, “we will steal”\n\nLikely “bèsèn” = future marker? But in 2: “wɔ̀ nǔ yúː cɔ́ŋ” → “you (sg) will steal” → no “bèsèn”\n\nBut 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → future: after “on Bvusɔw”\n\nSo future is marked by context: time reference (like “on Bvusɔw”) → future reference\n\nSome verbs are time-restricted to the day.\n\nBut “on X” = action on that day → future or past?\n\nIn 3: “On Bvuzhi, the woman will help me” → future\n\nIn 4: “On Bvuŋka, he found the book” → past\n\nSo on X can be past or future depending on time.\n\nBut the verb at the end carries aspect.\n\nWe see that:\n- Present (immediate): “fɔ̀wǎy” = just now\n- Future: “nú + day” = on X → will\n- Past: “wvù tɔ̀” = he found\n\nSo:\n\n| Aspect | Marker |\n|-------|--------|\n| past | wvù + verb |\n| present (immediate) | fɔ̀wǎy |\n| future | on X → “nú + day” or “bèsèn” |\n\nBut “bèsèn” appears in 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “we will steal” → so “bèsèn” = future\n\nSo: “bèsèn” = future tense\n\nIn sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ” → no future marker, but time: “on Bvusɔw” → so \"will\" is implied by time.\n\nSo likely:\n- “on X” → future if X is in future (like Bvusɔw), past if X is in past\n\nBut in 13: “On Bvutfu, the woman saw the market” → past → “saw”, not “will see”\n\nSo on X → whether past or future depends on the day\n\nBut for our purpose, we need to translate with appropriate tense.\n\nNow, focus on translations:\n\n---\n\n### (c.1) 20. On Bvusɔw, I helped the man.\n\nWe know:\n- “I helped” → “me” + “fí” (help)\n- “on Bvusɔw” → “nú bvúsɔ̀w”\n\nPattern from 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “on Bvuzhi, the woman will help me”\n\nSo: [subject] + [verb] + [object] + on day\n\nHere: “me fí dìɛ̀msɛ̌n” → “I helped the man”\n\nBut: “fí” = help → verb\n\nBut in 3, “nǔ bóy fí me” → \"the woman will help me\" → so “fí” = help → \"help (someone)\"\n\nSo “me fí dìɛ̀msɛ̌n” = I helped the man\n\nSo full: “me fí dìɛ̀msɛ̌n nú bvúsɔ̀w”\n\nBut does it require “on”?\n\nIn 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “on Bvuzhi, the woman will help me”\n\nSo “on day” = “bvúzhí” after verb\n\nSimilarly, 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “on Bvuŋka, he found the book”\n\nSo verb + object + “on day”\n\nSo for 20: “me fí dìɛ̀msɛ̌n nú bvúsɔ̀w”\n\nWe must include “nú” with day.\n\nSo: **me fí dìɛ̀msɛ̌n nú bvúsɔ̀w**\n\n---\n\n### (c.2) 21. The thief stole the yam just now.\n\n- “the thief” = “yo᷅kwɔ᷆ːn” (from sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “he killed the woman” – “yo᷅kwɔ᷆ːn” = thief)\n- “stole” = “yúː” (from sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ” → “you will steal the yam”)\n- “the yam” = “cɔ́ŋ” (same as in sentence 2)\n- “just now” = “fɔ̀wǎy” (from sentence 15)\n\nSo: “yo᷅kwɔ᷆ːn yúː cɔ́ŋ fɔ̀wǎy”\n\nNo need for “on day” — just now → present, immediate\n\nSo: **yo᷅kwɔ᷆ːn yúː cɔ́ŋ fɔ̀wǎy**\n\n---\n\n### (c.3) 22. On Bvuŋkaden, I will hear the car.\n\n- “on Bvuŋkaden” → “nú bvûŋka᷆ːde᷆n” (from sentence 8: “tomorrow is Bvuŋkaden”)\n- “I will hear” → “me” + “nú” + verb?\n- Verb for “hear”? Not directly given.\n\nWe are missing “hear”. But look at sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → day after tomorrow is Bvutfu\n\nNo “hear” in examples.\n\nBut in sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n” = saw → verb for see\n\nSo “hear” may not be in the list.\n\nWait — in sentence 13: “yɛ᷅n wáy” → “saw the market”\n\nSo “yɛ᷅n” = saw\n\nNo hear.\n\nBut we are to translate “I will hear the car”\n\nIs “hear” a verb? Not present.\n\nBut look: in 9: “me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n” → “I chose the book”\n\nNo “hear”\n\nBut perhaps the verb is “wɛ̂ː” (kill), “yúː” (steal), “fí” (help), “yɛ᷅n” (see)\n\nWe need a verb for “hear”.\n\nWait — “hear” may be “wɛ̂ː” or another form?\n\nNo — “wɛ̂ː” = kill in sentence 6.\n\nPossibly “nɔ̂ː” = heard? In sentence 7: “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “you heard the thief a long time ago”\n\nAh! “nɔ̂ː” = heard → past\n\nSo “nɔ̂ː” = hear (past)\n\nSimilarly, future? Maybe “nú", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9846.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are given a set of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), with English translations. We are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe must deduce the grammatical and morphological patterns from the examples, especially focusing on:\n\n- Time references (yesterday, today, tomorrow, day after tomorrow, etc.)\n- Tense/aspect (past, present, future)\n- Subject–object structure\n- Possession, action, transitivity\n- Marker for \"just now\", \"will\", \"heard\", \"see\", etc.\n\n---\n\n### Step 1: Identify time markers and their forms\n\nFrom the data:\n\n- **Bvutfu**: appears as a day reference\n- **Bvusɔw**, **Bvuzhi**, **Bvuŋka**, **Bvukema** — all appear as days of the week.\n\nLook at **day expressions**:\n\n- (1) \"Yesterday was Bvumbon\" — implies \"Yesterday\" is Bvumbon\n- (5) \"The day after tomorrow is Bvutfu\" → \"ntfǔː nú bvútfu᷅\"\n- (8) \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n- (11) \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\"\n\nWe observe:\n\n- \"Yesterday\" → **kefwé cí**\n- \"The day before yesterday\" → **kefwé cí nú** (same as above)\n- \"Tomorrow\" → **ntfǔː nú**\n- \"The day after tomorrow\" → **fɔ̀ shě ntfǔː nú** (\"The day after tomorrow is Bvutfu\")\n- \"Today\" → used directly: e.g., (6) \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n- \"On X\" → **me nú mbóy** (I will choose the car) → no, \"On X\" often uses **nú** or **cǐ** or **nɔ̂ː**\n\nBut note:\n\n- (1) \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → \"fɔgò cǐ nú\" = yesterday was → **fɔgò cǐ** = yesterday\n- (5) \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"fɔ̀ shě\" = day after tomorrow\n- (8) \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"ntfǔː nú\" = tomorrow\n\nSo:\n\n- **Yesterday** → **fɔgò cǐ**\n- **Tomorrow** → **ntfǔː nú**\n- **The day after tomorrow** → **fɔ̀ shě** (in \"fɔ̀ shě ntfǔː nú\" — \"fɔ̀ shě\" is the time, \"ntfǔː nú\" is the day)\n- **Day before yesterday** → **kefwé cí nú** — (11): \"kefwé cí nú bvûŋka\"\n- **Today** → expressed directly, e.g., \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed the woman\"\n\nAlso, the word **nú** appears with a day: \"nú bvúmbòn\" = \"was Bvumbon\" (in (1))\n\nSo structure of time reference:\n\n- **time marker + nú + day** → e.g., “On X” / “The day X is” (with a verb)\n- For actions, time markers can be used with verbs: e.g., \"On Bvusɔw, you will steal\"\n\nSo time expressions:\n\n| Time | Marker |\n|------|--------|\n| Yesterday | fɔgò cǐ |\n| Today | (implicit or used with \"wvù\", \"me\", \"wɔ̀\", etc.) |\n| Tomorrow | ntfǔː nú |\n| Day after tomorrow | fɔ̀ shě |\n| Day before yesterday | kefwé cí nú |\n\nNote: in (1), \"fɔgò cǐ nú\" = yesterday was → so \"fɔgò cǐ nú\" is the marker.\n\nIn (5): \"fɔ̀ shě ntfǔː nú\" = day after tomorrow is → \"fɔ̀ shě\" + \"ntfǔː nú\"\n\nIn (8): \"ntfǔː nú bvûŋka᷆ːde᷆n\" = tomorrow is → \"ntfǔː nú\" + day\n\nIn (11): \"kefwé cí nú bvûŋka\" = day before yesterday was → \"kefwé cí nú\" + day\n\nSo:\n\n- Time markers: \n - **fɔgò cǐ** = yesterday \n - **fɔ̀ shě** = day after tomorrow \n - **ntfǔː nú** = tomorrow \n - **kefwé cí nú** = day before yesterday \n - **today** = no separate marker; used with verbs or implicitly\n\nTense markers:\n\n- Present: \"I am about to\", \"will\", \"heard\", \"saw\"\n- Past: \"killed\", \"heard a long time ago\"\n- Future: \"will steal\", \"will help\", \"will see\"\n\nTense aspect markers:\n\n- \"will\" → appears with **cɔ́ŋ** in some cases: e.g., (2) \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"just now\" → in (15): \"They saw me at the market just now\" → likely \"fɔ̀wǎy\" or similar\n\nWait: (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\" → \"fɔ̀wǎy\" = just now?\n\nAlso (7): \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"cɔ̌ŋ\" = long time ago?\n\nCould \"cɔ̌ŋ\" mean \"a long time ago\"?\n\nYes: (7) \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" = you heard the thief a long time ago → \"cɔ̌ŋ\" = past, long time ago\n\nBut in (21): \"The thief stole the yam **just now**\"\n\nSo \"just now\" likely = **fɔ̀wǎy** (used in (15))\n\nBack to (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\" → \"cǐ\" = on? → \"cǐ\" is used as \"on\"\n\nAlso (1): \"fɔgò cǐ nú bvúmbòn\" → \"yesterday was\" → again \"cǐ\" = on (or referring to a day)\n\nSo \"on X\" → **cǐ nú** or **cǐ**? \nIn (1): \"fɔgò cǐ nú\" → \"yesterday was\" — here \"cǐ\" is part of the time clause \nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal\" — \"bvúsɔ̀w\" is the day, not preceded by \"cǐ\"\n\nBut (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"on Bvutfu, the woman saw the market\" → \"cǐ\" before day?\n\nSo structure:\n\n- **[subject] [verb] [object] [time marker]** \n or \n- **Time marker + subject + verb + object**\n\nBut \"On X\" seems often structured as **cǐ [day]** for past/future? \n(13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nAlso (4): \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → \"On Bvuŋka, he found the book\" → here, **'nɔ̂ː'** is the verb, not \"cǐ\"\n\nWait — no \"cǐ\" → so is \"cǐ\" only used in some?\n\nActually: (1): \"fɔgò cǐ nú bvúmbòn\" → \"Yesterday was\" — but \"was\" is the verb, \"bvúmbòn\" is the day\n\n(2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal\" → here, **\"cɔ́ŋ\"** = future, **bvúsɔ̀w** = day\n\nSo perhaps **\"cɔ́ŋ\"** is the future marker, used with verb.\n\nSimilarly, (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\" → **\"fí\"** = help → verb, **\"nǔ\"** = woman, \"me\" = me\n\nBut no \"cɔ́ŋ\" here — perhaps \"will\" is implied?\n\nBut (2) has \"cɔ́ŋ\" → future verb marker.\n\n(6): \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed the woman\" → present/past tense? \"bɛ̂ː\" = killed\n\n(7): \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"You heard the thief a long time ago\" → \"cɔ̌ŋ\" = long time ago → past with deferment\n\nSo:\n\n- **cɔ̌ŋ** = long time ago (past, remote)\n- **fɔ̀wǎy** = just now (present, recent)\n- **cɔ́ŋ** = future (will)\n\nNow verb forms:\n\n- Transitive verbs: subject + verb + object → e.g., \"you stole the yam\"\n- Intransitive verbs: e.g., \"saw\", \"helped\"\n\nNote that \"help\" is expressed with \"fí\": (3) \"fí me\" → \"help me\"\n\n\"see\" = \"yɛ᷅n\" → (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\" → \"yɛ᷅n\" = saw\n\n\"kill\" = \"bɛ̂ː\" → (6) \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"he killed the woman\"\n\n\"steal\" = \"cɔ́ŋ kèŋkfǔ\" → (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\nSo:\n\n- \"steal\" = **kèŋkfǔ**\n- \"help\" = **fí**\n- \"see\" = **yɛ᷅n**\n- \"hear\" = **yo᷅w** → (7): \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"heard the thief a long time ago\"\n\nSo now build:\n\n### Subject markers:\n\n- **me** = I\n- **wvù** = he/him\n- **wɔ̀** = you (sg)\n- **nǔ** = woman\n- **dìɛ̀msɛ̌n** = man\n- **kwɔ᷆ːn** = thief\n\n(9): \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → \"Today, I chose the book\" → \"me\" + verb \"mbɛ̂ː\" = chose\n\nSo verb form depends on the action and aspect.\n\nNow, for each translation:\n\n---\n\n### 20. On Bvusɔw, I helped the man.\n\nWe need: **On Bvusɔw, I helped the man**\n\n- Subject: \"I\" → **me**\n- Verb: \"helped\" → past tense — but \"fí\" is base form for help\n- \"helped\" = past of \"fí\"\n- Time: \"On Bvusɔw\" → structure?\n\nFrom (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\" → uses **fí**, no \"cɔ́ŋ\" → so \"will\" only in future?\n\nBut (2): \"will steal\" → \"cɔ́ŋ\"\n\nIn (3): \"the woman will help me\" — does it have \"cɔ́ŋ\"?\n\n(3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" — no \"cɔ́ŋ\" → so might be present or future?\n\nBut \"will\" could be implicit.\n\nAlternatively, in (12): \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\" → \"nfí\" = about to help\n\n\"nfí\" → present continuous/pending\n\n\"help\" = **fí**\n\nIn (12): \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\"\n\nSo \"nfí\" = about to help (present continuous)\n\n\"nú\" = am (present)\n\nSo \"nú\" is used for present continuous?\n\nBut in (9): \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → \"Today, I chose the book\" → present, not with \"nú\"\n\nSo different structures.\n\nBack to (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\" → likely \"bóy\" = will?\n\n\"bóy\" = future?\n\nIn (21): \"The thief stole the yam just now\" → \"just now\" = **fɔ̀wǎy**\n\nIn (15): \"They saw me at the market just now\" → \"fɔ̀wǎy\"\n\nSo \"fɔ̀wǎy\" = just now\n\nNow, \"helped\" → past? How is past expressed?\n\n(13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\" → seen at time with \"yɛ᷅n\"\n\nNo future marker → so perhaps \"will\" is only with \"cɔ́ŋ\"?\n\n(2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → future\n\n(3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"bóy\" = future?\n\n\"bóy\" is used only once.\n\nIn (12): \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help\" → present\n\nSo \"fí\" can be in present, and \"cɔ́ŋ\" or \"bóy\" in future.\n\nBut (3) uses \"bóy\" as future marker?\n\nBut (13) uses no marker: \"cǐ nɔ̂ː yɛ᷅n wáy\" — \"saw\" — present?\n\nSo time is embedded.\n\nFor \"helped\" in past — is there a marker?\n\n(15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"saw me at market just now\" → \"fɔ̀wǎy\" = just now\n\nNo marker for past.\n\nIn (6): \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"today, he killed\" → day-time, not future\n\nSo no clear past marker.\n\nPerhaps all past actions are just simple verb + object.\n\nIn (3): \"On Bvuzhi, the woman will help me\" → uses \"bóy\" — “bóy” is future?\n\nBut not used again.\n\nIs \"bóy\" = will?\n\nBut (3) could be interpreted as present — \"will help\" might be used to mean \"is helping\" or future.\n\nBut \"helped\" is past.\n\nWe see no past tense marker — only aspect markers.\n\nSo perhaps \"helped\" is just \"fí\" without marker — but only in context.\n\nLook at (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\" — no future marker, \"nɔ̂ː\" = saw\n\n\"bóy\" is only in (3)\n\nSo likely, \"fí\" is the base verb, and \"will\" is marked by **cɔ́ŋ** or **bóy**?\n\nBut (3) has \"fí\" with \"bóy\" → \"bóy fí\" → future help?\n\nBut \"bóy\" is not a tense — it may be a locative?\n\nWait — \"bv", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9651.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "solver_checklist", + "sample_index": 3, + "output": "Step 1: Identify the linguistic pattern by analyzing the given examples.\n\nLook for recurring time expressions and actions.\n\nTime markers:\n- \"On Bvumbon\" → appears repeatedly in examples 1, 2, 3.\n- \"On Bvusɔw\", \"On Bvuŋka\", \"On Bvutfu\", \"Tomorrow\", \"The day after tomorrow\", \"The day before yesterday\", \"Today\" — all used in different days.\n- The day markers are embedded in specific structural forms: e.g., \"ntfǔː nú bvútfu᷅\" = \"The day after tomorrow is Bvutfu\" → implies a temporal reference.\n\nTemporal expressions:\n- \"Yesterday\" → \"fɔgò cǐ nú bvúmbòn\"\n- \"Today\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" (he killed the woman today)\n- \"Just now\" → \"bɛ̀n\", \"cɔ̌ŋ\", \"wvù\" in examples 7 and 15\n- \"Tomorrow\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n- \"The day after tomorrow\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n- \"The day before yesterday\" → \"kefwé cí nú bvûŋka\"\n\nCrucially, \"today\" is marked by a clitic or structure, while past or future often involve verbs with tense/aspect markers.\n\nStep 2: Analyze verb forms and aspect markers.\n\nExample 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → On Bvuzhi, the woman will help me → future in passive/active? → \"fí\" likely means \"help\".\n\nExample 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → Today, he killed the woman → past tense, \"bɛ̂ː\" = \"killed\", \"wvù\" = \"he\", \"ɛ̀bɛ̀n\" = \"the woman\"\n\nExample 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → You(sg) heard the thief a long time ago → past, remote → \"cɔ̌ŋ\" = \"heard\", \"yo᷅w\" = \"the thief\"\n\nExample 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → Today, we will steal the car → future → \"bèsèn\" = \"today\", \"géː\" = \"we\", \"cɔ́ŋ\" = \"steal\", \"mutù\" = \"the car\"\n\nExample 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → They saw me at the market just now → present or recent past → \"bɔ́\" = \"they\", \"yɛ᷅n\" = \"saw\", \"me\" = \"me\", \"lé\" = \"at\", \"fɔ̀wǎy\" = \"the market\"\n\nSo \"just now\" appears with:\n- \"yɛ᷅n me\" (saw me)\n- \"wvù\" (he), \"bɛ̂ː\" (killed), \"ɛ̀bɛ̀n\" (woman)\n- \"bɔ́\" (they), \"yɛ᷅n\" (saw)\n\n\"just now\" seems to be marked by the verb yɛ᷅n, with object attached.\n\nBut \"just now\" is also used in 21: \"The thief stole the yam just now\" → likely \"yɛ᷅n\" or similar.\n\nSo from example 15: \"They saw me at the market just now\" → verb \"yɛ᷅n\" with immediate object.\n\nSimilarly, \"he killed the woman a long time ago\" → \"cɔ̌ŋ\" with temporal distance.\n\nBut 21: \"The thief stole the yam just now\" → likely uses \"yɛ᷅n\" or a similar form for \"saw\", but \"stole\"?\n\n\"Stole\" is \"cɔ́ŋ\" — used in example 2: \"you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\nSo \"cɔ́ŋ\" = steal.\n\nSo \"the thief stole the yam just now\" → \"yo᷅w cɔ́ŋ kèŋkfǔ fɔ̀\" → but with \"just now\" marker?\n\nIn example 15 → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"just now\", with event and location.\n\nNo direct \"just now\" + stealing.\n\nBut look at 21: similar to \"they saw me just now\" → so stealing \"just now\" may use \"yɛ᷅n\" or a similar immediate past form.\n\nBut verb for stealing is \"cɔ́ŋ\" — so possibly: \"yo᷅w cɔ́ŋ kèŋkfǔ yɛ᷅n\" → thief stole yam just now?\n\nBut word order?\n\nIn examples, objects follow verbs.\n\nEvidence: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → you will steal the yam (on Bvusɔw)\n\nSo order: subject → verb → object → time?\n\nNo — time is at end: \"on Bvusɔw\"\n\nSo verb-object-time?\n\nIn \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → woman will help me → subject → object → verb → time?\n\nNo: \"kwɔ᷆ːn\" (woman), \"nǔ\" (will), \"bóy\" (the woman?), wait — \"nǔ\" is likely subject? Wait.\n\n\"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nSo: \"kwɔ᷆ːn\" = woman, \"nǔ\" = will, \"bóy\" = the woman? probably \"bóy\" = object? or \"fí\" = help.\n\nPossible structure: [subject] + [auxiliary] + [verb] + [object] → but \"bóy\" is \"the woman\" — could be object?\n\nBut \"kwɔ᷆ːn\" is already subject.\n\n\"bóy\" appears elsewhere as \"the woman\".\n\nLikely: \"kwɔ᷆ːn\" = subject, \"nǔ\" = auxiliary (will), \"bóy\" = \"to help\" — no.\n\nWait — \"fí\" = \"help\", \"me\" = \"me\".\n\nSo: \"the woman will help me\" → subject + (will) + verb + object.\n\nSo: [subject] [aux] [verb] [object]\n\nSimilarly, in ex. 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you will steal the yam\" → you (sg) → will → steal → yam → on Bvusɔw\n\nSo object after verb.\n\nSo word order: subject → auxiliary → verb → object → time\n\nBut time is often attached with \"on X\".\n\nBut some times embedded.\n\nNow for \"just now\" — appears only in 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → they saw me at the market just now → \"yɛ᷅n\" = saw, \"me\" = me, \"lé\" = at, \"fɔ̀wǎy\" = market → so \"just now\" is likely marked by the verb \"yɛ᷅n\" — which is in present, immediate past.\n\nIn 21: \"The thief stole the yam just now\" → similar form: thief + steal + yam + just now?\n\nBut no \"yɛ᷅n\" — unless \"cɔ́ŋ\" is a similar verb.\n\nBut \"cɔ́ŋ\" for \"steal\" — is in remote past in ex. 2: future in ex. 2 — \"you will steal\"\n\nSo future = \"nǔ\" (will), past = without context.\n\nStill, \"just now\" may be marked by a temporal marker.\n\nLook at example 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → you heard the thief a long time ago → past, remote → \"cɔ̌ŋ\" = heard.\n\nSo “a long time ago” = \"nɔ̂ː\" (with tone), possibly \"tɔ̀ nɔ̂ː\" → \"a long time ago\"?\n\n\"nɔ̂ː\" = long?\n\n\"tɔ̀\" = in, before?\n\n\"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → you heard the thief a long time ago → \"tɔ̀ nɔ̂ː\" = a long time ago?\n\nYes — seems \"tɔ̀ nɔ̂ː\" = a long time ago.\n\nThen \"just now\" → opposite → immediate.\n\nIn example 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → they saw me just now → \"yɛ᷅n\" = saw, \"me\" = me → but no explicit \"just now\" in form?\n\n“just now” might be implied in the verb form or after.\n\nBut \"just now\" is not marked with a separate particle — so in the absence of \"tɔ̀ nɔ̂ː\", the immediate past is the default.\n\nSo in 21: \"The thief stole the yam just now\" → likely: yo᷅w cɔ́ŋ kèŋkfǔ yɛ᷅n? or other form.\n\nBut no such structure.\n\nAlternative: “just now” is expressed through verb + object + location or simply through verb choice.\n\nIn ex. 15: “saw me at the market” — the verb is “yɛ᷅n”, which is immediate past.\n\nSimilarly, “stole the yam just now” → use “cɔ́ŋ” with object → but need to mark immediacy?\n\nBut in ex. 2: “you will steal the yam” → future — no immediacy.\n\nWe don’t have a clear “just now” past.\n\nBut in ex. 15: \"they saw me just now\" → verb is \"yɛ᷅n\"\n\nSo perhaps the verb form indicates immediate past.\n\nSo for “just now”, use \"yɛ᷅n\" with object.\n\nThus, for 21: \"The thief stole the yam just now\" → \"yo᷅w cɔ́ŋ kèŋkfǔ yɛ᷅n\"\n\nBut “yɛ᷅n” = saw — not “stole”.\n\n\"stole\" = cɔ́ŋ, so why not use cɔ́ŋ with \"yɛ᷅n\"? That would be redundant.\n\nPossibly, \"yɛ᷅n\" = to see, but \"cɔ́ŋ\" = steal.\n\nDifferent verbs.\n\nSo 21: “stole the yam just now” → does not use “yɛ᷅n” — so perhaps “just now” is not expressed with that verb.\n\nBut in ex. 15: “saw me at the market just now” — uses “yɛ᷅n” and has the structure.\n\nIs there a verb for “stole” that occurs in immediate past?\n\nIn ex. 2: “you will steal the yam” — future.\n\nNo immediate past form.\n\nBut “the thief stole the yam just now” — likely must be expressed with “cɔ́ŋ” and a marking of immediacy.\n\nBut lack of such marking in data.\n\nAlternative: “just now” might be attached via time marker, like “today” or “on X”.\n\nBut in 20, 21, etc., time is different.\n\nAll translations are to be spoken on Bvumbon — so time reference is fixed.\n\nFor 20: “On Bvusɔw, I helped the man.”\n\nWe have data: on Bvusɔw, present or future?\n\nFree: ex. 2: “you will steal the yam on Bvusɔw” — future.\n\nEx. 6: “today, he killed” — past.\n\nSo time is separate from verb tense.\n\nSo for 20: “On Bvusɔw, I helped the man” → likely structurally: [subject] + [aux?] + [verb] + [object] + [on X]\n\nSubject: \"me\" → \"I\"\n\nVerb: “help” → in ex. 3: “bóy fí me” → “help me” → “fí” = help\n\nSo verb is “fí”\n\nObject: “the man” → in ex. 13: “the woman saw the market” → “yɛ᷅n me lé fɔ̀wǎy” → “me” = me, “lé” = at, “fɔ̀wǎy” = market.\n\nSo “the man” → possibly \"dìɛ̀msɛ̌n\" → in ex. 12: “I am about to help the man”\n\nSo “dìɛ̀msɛ̌n” = man\n\nSo \"me fí dìɛ̀msɛ̌n\" = I helped the man\n\nBut in ex. 12: \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\" → \"nfí\" = about to\n\nSo \"fí\" = help\n\nSo for 20: \"On Bvusɔw, I helped the man\" → \"me fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nBut is \"fí\" used with \"nú bvúsɔ̀w\"? Yes — ex. 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\nSo structure: subject + verb + object + on X\n\nBut ex. 2 has \"nǔ\" (will) — auxiliary? Yes.\n\nSo we must include auxiliary for future?\n\nIn ex. 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"the woman will help me on Bvuzhi\"\n\nSo past or future?\n\n\"will\" = nǔ\n\nSo “will” is used for future.\n\nThus for 20: \"On Bvusɔw, I helped the man\" → is it future?\n\nBvusɔw is in the future relative to Bvumbon?\n\nFrom the timeline:\n\n- Bvumbon: day of speaking\n- Bvusɔw: in the past? No — in ex. 1: \"Yesterday was Bvumbon\" — so Bvumbon is yesterday\n\nThen ex. 4: spoken on Bvusɔw → so Bvusɔw is now\n\nEx. 5: \"the day after tomorrow is Bvutfu\" → so Bvutfu is after\n\nEx. 8: \"tomorrow is Bvuŋkaden\" → so Bvuŋkaden = tomorrow\n\nSo days occur in order:\n\n- Bvumbon → yesterday\n- Bvusɔw → today (ex. 4)\n- Bvutfu → day after tomorrow (ex. 5)\n- Bvuŋkaden → tomorrow (ex. 8)\n\nSo Bvusɔw is today.\n\nSo when speaking on Bvumbon, which is yesterday, the statement “On Bvusɔw, I helped the man” → is about today → a future event from Bvumbon's perspective.\n\nSo must use future auxiliary “nǔ”\n\nSo: \"me nǔ fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nYes — like ex. 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you will steal the yam on Bvusɔw\"\n\nSo structure: subject + nǔ (will) + verb + object + on X\n\nThus 20: \"me nǔ fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nNow 21: \"The thief stole the yam just now\"\n\nThe thief = yo᷅w\n\nStole = cɔ́ŋ\n\nYam = kèŋkfǔ\n\n\"just now\" — not marked explicitly.\n\nBut in ex. 15: “they saw me at the market just now” → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n\"nɔ̂ː\" = long time ago? But here used with \"just now\"?\n\n\"nɔ̂ː\" in ex. 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"you heard the thief a long time ago\"\n\nSo \"tɔ̀ nɔ̂ː\" = a long time ago\n\n\"nɔ̂ː\" alone is not “just now”\n\nBut in ex. 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — “just now”?\n\nPossibly, the verb form \"yɛ᷅n\" = saw (immediate past), and \"nɔ̂ː\" may be attached as \"just now\" — but it was used with \"long time ago\" in ex. 7.\n\nBut tone: in ex. 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"nɔ̂ː\" is long, likely with a different tone.\n\nEx. 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"a long time ago\"\n\nBut in 15: the same \"nɔ̂ː\" is used with “just now”?\n\nIn 15: “they saw me just now” — not “a long time ago”\n\nSo perhaps the context makes it distinct — no separate marker for “just now”.\n\nBut is there a different verb form?\n\n“Just now", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10272.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "First, build an alignment table from the examples to identify patterns.\n\n| English | Jaqaru |\n|--------|--------|\n| the cave | aq”ipsa |\n| in the cave | aq”na |\n| through the lake | qucxap”a |\n| from our1+2 lake too | qucxst”psa |\n| his corner | chushp”a |\n| is it in the corner? | chushuntxi |\n| my bed | ishinhna |\n| your bed | ishma |\n| the pot | p”ak”u |\n| my pot too | p”ak”unhpsa |\n| from the cliff | qaqat”a |\n| in our1+2 field too | yapsanpsa |\n| is it the field? | yaputxi |\n| from his town | markp”t”a |\n| is it our1+2 town? | markstxi |\n| from your house | utamt”a |\n| my house | utnha |\n\nNow extract morphological patterns:\n\n1. Possessive markers:\n - \"our1+2\" = \"our1+2\" as a group (mine and yours)\n - Appears in: qucxst”psa (from our1+2 lake too), markstxi (is it our1+2 town?), yapsanpsa (in our1+2 field too)\n\n2. \"too\" suffix appears as:\n - -psa → in \"aqucxst”psa\", \"p”ak”unhpsa\", \"yapsanpsa\"\n - \"too\" seems to be marked by -psa\n\n3. \"in\" = aq”na (in the cave), ishinhna (in my bed), utamt”a is from your house → \"in\" seems to be marked by a prefix or root\n - But \"in the bed\" = ishinhna → so in + bed → ishinhna\n - \"in your corner\" → missing in the examples\n - \"in your corner\" might derive from \"chushp”a\" (his corner), and we need \"your\" and \"in\"\n\n4. \"from\" = qaqat”a (from the cliff), markp”t”a (from his town), utamt”a (from your house)\n - Pattern: from + noun → derived from root with affix\n\n5. \"is it [X]?\" = question form\n - chushuntxi = is it in the corner?\n - yaputxi = is it the field?\n - so \"is it [N]\" = root + untxi\n\n6. Possessive + noun:\n - \"our1+2\" is used as a prefix in:\n - qucxst”psa = from our1+2 lake too\n - markstxi = is it our1+2 town?\n - yapsanpsa = in our1+2 field too\n - all end in -psa → \"too\"\n - \"your\" appears in:\n - ishma = your bed\n - utamt”a = from your house\n - so \"your bed\" = ishma\n - \"your corner\" = ? → noun is chushp”a (his corner)\n\nSo, \"corner\" = chushp”a\n\"your corner\" = ? → likely based on \"chushp”a\" with \"your\" affix\n\nCheck if \"your\" = ish or ishma?\n\n- \"your bed\" = ishma → base is \"isha\"?\n- \"in my bed\" = ishinhna → ish + in + hna\n- \"in your bed\" = not given\n- \"in your corner\" → would be \"in + your corner\"?\n\nPossibility: \"in\" = \"na\" or prefix?\n\n\"aq”na\" = in the cave → \"na\" = in?\n\"ishinhna\" = in my bed → \"inhna\" = my bed?\n\"ishma\" = your bed → \"shma\" = your bed?\n\nSo:\n- \"my\" = inh?\n- \"your\" = shma?\n\nFrom \"ishma\" → your bed → \"isha\" + \"ma\"? But \"ish\" → \"ishma\"\n\nSimilarly, \"chushp”a\" = his corner → \"chush\" + \"p”a\"\n\n\"chushuntxi\" = is it in the corner? → \"chush\" + \"untxi\"\n\n\"markp”t”a\" = from his town → \"mark\" + \"p”t”a\"\n\n\"markstxi\" = is it our1+2 town? → \"mark\" + \"stxi\"\n\nSo:\n- \"his\" → chush, mark\n- \"our1+2\" → mark (in markstxi, markp”t”a)\n- \"your\" → appears in ishma → ish? + ma?\n\nCompare:\n- ishina? → my bed → ishinhna\n- ishma → your bed\n\nPossibly, \"in\" = \"in\" attached to \"bed\" → \"inhna\" → so \"in + hna\"? Then \"your + bed\" = \"ishma\" → so \"ish\" = your?\n\nThen \"in your corner\" = \"na\" + \"ish\" + \"chush\" → \"na\" + \"ish\" + \"chush\"?\n\nBut \"in our1+2 field too\" = yapsanpsa → \"yap\" + \"san\" + \"psa\" → so \"our1+2 field\" → \"san\", then + \"psa\"\n\nSimilarly, \"from our1+2 cliff\" = ?\n\n\"from the cliff\" = qaqat”a → \"qaq\" + \"at”a\"\n\n\"from our1+2 cliff\" → likely \"qaqat”a\" with \"our1+2\" prefix?\n\n\"From our1+2 cliff\" → \"our1+2\" + \"cliff\" → prefix + qaqat”a?\n\nWhere is \"our1+2\" used?\n- qucxst”psa = from our1+2 lake too → so \"from\" + \"our1+2 lake too\"\n- markstxi = is it our1+2 town?\n\nSo \"our1+2\" appears as prefix to \"lake\", \"town\", \"field\"\n\nThus, \"our1+2 cliff\" = qaqat”a with \"our1+2\" prefix → qaqat”a → qaq + a + t”a → so prefix \"our1+2\" → mark?\n\nBut mark appears in \"mark\" + \"p”t”a\" (from his town) → mark is used for \"town\", not \"cliff\"\n\nNo prefix for cliff.\n\nBut \"our1+2\" is used before lake, town, field → all are nouns with possessive attached.\n\nSo pattern: [our1+2] + [noun] → in form Xst”psa for \"from\" and \"in\" with \"too\"\n\nBut 4. \"our1+2 cliff\" = likely \"qaqat”a\" with \"our1+2\" prefix?\n\nBut which affix?\n\nIn \"qucxst”psa\" = from our1+2 lake too → qucx + st”psa → implies \"from\" is qucx, and st”psa = \"our1+2 too\" or with \"too\"?\n\n\"st”psa\" — appears in qucxst”psa, markstxi, yapsanpsa\n\n\"qucxst”psa\" = from our1+2 lake too\n\"markstxi\" = is it our1+2 town?\n\"yapsanpsa\" = in our1+2 field too\n\nSo \"st”psa\" appears when:\n- after \"from\" (qucx) → qucxst”psa = from our1+2 lake too\n- after \"is it\" → markstxi = is it our1+2 town?\n- after \"in\" → yapsanpsa = in our1+2 field too\n\nSo \"st”psa\" = the possessive \"our1+2\" + \"too\"? But markstxi = \"is it our1+2 town\" → not \"too\"\n\nyapsanpsa = \"in our1+2 field too\" → ends in -psa\n\nSo perhaps:\n- -psa = \"too\"\n- -stxi = \"is it\"\n- -na = \"in\"\n- -p”a = \"the\"\n- -t”a = \"from\"\n\nThus:\n- \"from\" = qaqat”a → qaq + at”a\n- \"in\" = aq”na → aq” + na\n- \"is it\" = ? → chushuntxi = chush + untxi\n\nSo:\n4. \"our1+2 cliff\" → from the cliff? or just \"our1+2 cliff\"?\n\nStructure: possessive + noun → our1+2 + cliff → but how written?\n\n\"our1+2 lake\" → in qucxst”psa → qucxst”psa = from our1+2 lake too → so \"from\" + \"our1+2 lake too\"\n\nBut in \"qucxap”a\" = through the lake → no possessive\n\nSo \"the lake\" = qucxap”a\n\nThus, \"cliff\" = qaqat”a\n\nSo \"our1+2 cliff\" = likely qaqat”a with possessive prefix?\n\nIn \"our1+2 field\" = yapsanpsa → yapsanpsa = in our1+2 field too → \"in\" + \"our1+2 field too\"\n\n\"our1+2 field\" = yapsan → yapsan = \"in our1+2 field\" → root \"yap\" + \"san\"\n\nSo \"our1+2\" = part of \"yapsan\"\n\nSimilarly, \"our1+2 lake\" = in qucxst”psa → qucxst”psa = from our1+2 lake too → qucx + st”psa → so qucx is \"from\", st”psa is \"our1+2 too\"?\n\nBut \"markstxi\" = is it our1+2 town → mark + stxi → so \"stxi\" = \"is it\", not \"too\"\n\nSo:\n- -psa = \"too\"\n- -stxi = \"is it\"\n- -na = \"in\"\n\nNow for \"our1+2\" used in:\n- qucxst”psa → from our1+2 lake too → so \"st”psa\"\n- markstxi → is it our1+2 town → \"stxi\"\n- yapsanpsa → in our1+2 field too → \"anpsa\"\n\nSo \"our1+2\" is attached to a root, and the ending indicates the aspect.\n\nSo:\n\"our1+2 + cliff\" = root of \"cliff\" is qaqat”a → qaqat”a = from the cliff\n\nSo \"our1+2 cliff\" = likely qaqat”a with \"our1+2\" prefix?\n\nIn \"our1+2 field\" = yapsanpsa → yapsan = \"in our1+2 field\"\n\nSo root is \"yap\" for \"field\"? \"yaputxi\" = is it the field?\n\n\"yapsanpsa\" = in our1+2 field too → yap + san + psa\n\nSo \"san\" = \"our1+2 field\"?\n\nBut \"field\" = yap → so \"our1+2 field\" = yap + san?\n\nSimilarly, \"our1+2 lake\" → qucx + st”psa → \"st”psa\" = \"our1+2 lake\"?\n\n\"st”psa\" appears in from our1+2 lake too.\n\nSo likely:\n- \"our1+2 + noun\" = root + affix\n- But which affix?\n\nWe have:\n- \"our1+2 lake\" → used with -st”psa → from our1+2 lake too → qucxst”psa\n- \"our1+2 field\" → yapsanpsa → in our1+2 field too → yap + san + psa\n- \"our1+2 town\" → markstxi → is it our1+2 town → mark + stxi\n\nSo the affix differs per word:\n- For \"field\": \"san\" (in our1+2 field)\n- For \"lake\": \"st”psa\" (in from our1+2 lake too)\n- For \"town\": \"stxi\" (is it our1+2 town)\n\nBut pattern:\n- \"lake\" = qucx + st”psa\n- \"town\" = mark + stxi\n- \"field\" = yap + san + psa\n\nSo \"san\" might be \"our1+2\" → then \"field\" = yap-san → our1+2 field\n\nSimilarly, \"cliff\" → qaqat”a = from the cliff → so \"our1+2 cliff\" = qaq + at”a + our1+2?\n\nBut no consistent affix.\n\nAlternative: \"our1+2\" is prefixed to the noun, and the word structure is:\n\n- \"our1+2 + noun\" → root + possessive mark?\n\nBut in qaqat”a, no possessive.\n\nIn the given words, \"our1+2\" appears only in complex constructs with \"in\", \"from\", \"is it\".\n\nTherefore, \"our1+2 cliff\" = likely \"qaqat”a\" with the possessive \"our1+2\" added as a prefix, but which prefix?\n\nIn \"qucxst”psa\", “markstxi”, “yapsanpsa”, the possessive is added to the root with affix.\n\nBut no consistent affix.\n\nWait — \"our1+2\" may be a prefix and attached to the noun.\n\nIn \"yapsanpsa\", it is \"in our1+2 field too\" → the structure is [in] + [our1+2 field] + [too]\n\nSimilarly, \"qucxst”psa\" = [from] + [our1+2 lake] + [too]\n\nSo \"our1+2 field\" = yap + san → so \"san\" = our1+2?\n\nBut \"san\" is not a known root.\n\nIn \"markstxi\" = \"is it our1+2 town\" → mark + stxi → stxi = is it\n\nSo the possessive is not at the end.\n\nThus, the pattern is:\n- For animate or specific nouns, \"our1+2\" is attached via internal affix or prefix?\n\nBut all examples have \"our1+2\" in a specific position.\n\nSo for 4. \"our1+2 cliff\" → from the cliff with possessive?\n\nThe root of \"cliff\" is qaqat”a\n\nIn \"cliff\" only occurs in qaqat”a\n\nSo \"our1+2 cliff\" = qaqat”a with \"our1+2\" → could be qaqat”a with prefix?\n\nBut no example of \"our1+2 cliff\"\n\nNow, try analogical derivation:\n\n- \"our1+2 field\" = yapsanpsa → yap + san + psa → so yap = field, san = our1+2, psa = too\n- \"our1+2 lake\" = qucxst”psa → qucx + st”psa → st”psa = our1+2 lake?\n- \"our1+2 town\" = markstxi → mark + stxi → stxi = our1+2 town?\n\nSo perhaps \"our1+2\" is marked by affix:\n- with -psa → \"too\"\n- with -stxi → \"is it\"\n- with -na → \"in\"\n\nBut not directly.\n\nFor \"our1+2 cliff\", no such example.\n\nBut cliff is a noun like lake and town.\n\nSo likely \"our1+2 cliff\" = qaqat”a with possessive affix → what affix?\n\nIn \"cliff\", the root is qaqat”a (from the cliff)\n\nIn \"field\", yap → \"in our1+2 field\" = yap + san + psa → so san = our1+2?\n\nIn \"lake\", qucx + st”psa → st”psa = our1+2 lake?\n\nIn \"town\", mark + stxi → stxi = our1+2 town?\n\nSo the suffix type depends on context.\n\nBut for \"cliff\", if pattern is similar, \"our1+2 cliff\" = qaq + at”a + st”psa?\n\nBut \"st”psa\" is in \"from our1+2 lake too\"\n\nSo perhaps \"our1+2 cliff\" = qaqat”a + st”psa? But that would be redundant.\n\nAlternatively, \"our1+2\" is used as a prefix, and the word becomes qaqat”a with \"our1+2\" attached → no example.\n\nBest match: structure is that \"in our1+2 field too\" = yap + san + psa → so \"san\" = \"our1+2\"?\n\nBut \"san\" is not used in other cases.\n\n\"chushp”a\" = his corner — so \"corner\" = p”a, chush = his\n\n\"ishma\" = your bed → ish + ma?\n\nSo \"your\" = ish?\n\nThus, \"in your corner\" = in + your + corner = na + ish + chushp”a?\n\nBut in \"ishinhna\" = in my bed = ishinhna → ishi + in + hna?\n\n\"ish\" appears in both.\n\nIn \"ishinhna\" = in my bed — likely \"ish\" = my, \"inhna\" = bed?\n\n\"ishma\" = your bed → \"ish\" + \"ma\" = your bed\n\nSo \"ish\" = shared root for \"my\" and \"your\"?\n\nBut my = ishin? Inh → maybe \"in\" + \"h\" = my?\n\n\"ishinhna\" = in my bed → ish + in + hna\n\n\"ishma\" = your bed → ish + ma\n\nSo \"ish\" is the root for bed — with \"in\" or \"ma\"?\n\n\"my bed\" = ishinhna → so \"in\" + \"my\" + \"bed\"? But \"in\" = already in the word?\n\nPerhaps the structure is:\n- \"in\" = a prefix?\n- \"my bed\" = ishinhna → ish + in + hna\n\n\"your bed\" = ishma → ish + ma\n\nSo \"in\" appears in \"my bed\", not \"your bed\"\n\nThus, for \"in your corner\" → in + your corner", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10510.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "Start by analyzing the given examples to identify consistent morphological patterns in Jaqaru.\n\nFrom the examples:\n\n- \"aq”ipsa\" = the cave too \n- \"aq”na\" = in the cave \n- \"qucxap”a\" = through the lake \n- \"qucxst”psa\" = from our1+2 lake too \n- \"chushp”a\" = his corner \n- \"chushuntxi\" = is it in the corner? \n- \"marka\" = the town \n- \"markp”t”a\" = from his town \n- \"markstxi\" = is it our1+2 town? \n- \"utamt”a\" = from your house \n- \"utnha\" = my house \n- \"p”ak”unhpsa\" = my pot too \n- \"qaqat”a\" = from the cliff \n- \"yapsanpsa\" = in our1+2 field too \n\nStep 1: Identify common morphemes.\n\n- \"our1+2\" = \"mine and yours\" → appears in \"qucxst”psa\", \"markstxi\", \"yapsanpsa\"\n- \"your\" → appears in \"chushp”a\" (his), \"utamt”a\" (your house)\n- \"in\" → \"aq”na\", \"chushuntxi\", \"markstxi\", \"yapsanpsa\"\n- \"from\" → \"qucxst”psa\", \"markp”t”a\", \"utamt”a\", \"qaqat”a\"\n- \"too\" → \"aq”ipsa\", \"p”ak”unhpsa\", \"qucxst”psa\", \"yapsanpsa\"\n- \"is it\" → \"chushuntxi\", \"markstxi\", \"yapsanpsa\"\n- Anaphoric markers: \"our1+2\", \"his\", \"your\", \"my\"\n- The root for \"corner\" is \"chush-\", and for \"lake\" is \"qucx-\", \"cliff\" is \"qaqa-\", \"town\" is \"mark-\", \"house\" is \"utam-\", \"field\" is \"yap-\"\n- \"too\" appears as suffix \"-psa\" in: aq”ipsa, p”ak”unhpsa, qucxst”psa, yapsanpsa\n\nIn \"qucxst”psa\" = from our1+2 lake too → structure: [from] + [our1+2 lake] + [too]\n\nIn \"qucxap”a\" = through the lake → not related to 'from' or 'in'\n\nIn \"markp”t”a\" = from his town → [from] + [his] + [town]\n\nIn \"utamt”a\" = from your house → [from] + [your] + [house]\n\nIn \"qaqat”a\" = from the cliff → [from] + [the cliff]\n\nSo \"from X\" is formed by [from] + [noun]\n\nSimilarly, \"in X\" = \"X\" + \"na\" in examples like \"aq”na\", \"chushuntxi\" (is it in the corner?) — note that \"chushuntxi\" has \"chush\" (corner) + \"untxi\" (is it in?)\n\n\"untxi\" seems to mean \"is it in?\" → use in questions.\n\nAlso: \n\"p”ak”unhpsa\" = my pot too → [my] + [pot] + [too] → my pot + -psa \n\"yapsanpsa\" = in our1+2 field too → [in] + [our1+2] + [field] + [too]\n\nSo for \"too\", suffix \"-psa\" is used after a noun phrase.\n\nPattern for \"too\": suffix \"-psa\"\n\nPattern for \"in X\": X + \"na\"\n\nPattern for \"from X\": \"from\" + X \n\"from\" is not directly given, but in \"utamt”a\" = from your house → \"utam\" = your house → \"utamt”a\" (from your house) → so from + [your house] → derived from \"utamt”a\"\n\nSimilarly, \"qaqat”a\" = from the cliff → \"qaqat”a\" → likely \"qaqa\" (cliff) + \"t”a\" (from)\n\nUse of \"t”a\" for \"from\" in: \n- \"qaqat”a\" = from the cliff \n- \"utamt”a\" = from your house \n- \"markp”t”a\" = from his town \n\nSo suffix \"-t”a\" indicates \"from\"\n\nSimilarly, \"na\" indicates \"in\" (as in \"aq”na\", \"chushuntxi\" → \"chush\" + \"untxi\" → \"is it [in] the corner?\")\n\nThus:\n- \"in\" → used in \"in the cave\" = aq”na \n- \"is it in\" → marker \"untxi\" → appears in: chushuntxi, markstxi, yapsanpsa? yapsanpsa = in our1+2 field too → not a question.\n\nActually: \n\"markstxi\" = is it our1+2 town? → so \"stxi\" = is it? \n\"chushuntxi\" = is it in the corner? → so \"untxi\" = is it in?\n\nWait: \"markstxi\" = is it our1+2 town? → so \"stxi\" = is it?\n\n\"chushuntxi\" = is it in the corner? → \"untxi\" = is it in?\n\nThus, \"stxi\" = is it? \n\"untxi\" = is it in?\n\nSo:\n- \"is it\" = stxi \n- \"is it in\" = untxi\n\nAlso:\n- \"too\" = suffix -psa \n- \"our1+2\" = fixed expression\n\nNow for the questions:\n\n4. our1+2 cliff \n→ from \"qaqat”a\" = from the cliff → so \"cliff\" = qaqa \n→ with \"our1+2\" → as in \"qucxst”psa\" (our1+2 lake too), \"markstxi\" (is it our1+2 town?) \n→ therefore, \"our1+2 cliff\" → qaqa + our1+2 + ? \n\nBut in \"qucxst”psa\" = from our1+2 lake too → no \"from\", just \"our1+2 lake too\"\n\nSo is \"our1+2 cliff\" simply \"qaqat”a\" with our1+2?\n\nBut no structure for \"our1+2 X\" without a modifier.\n\nLook at:\n- \"qucxst”psa\" = from our1+2 lake too → has from, our1+2, lake, too \n- \"markstxi\" = is it our1+2 town? → has \"our1+2\" \n- \"yapsanpsa\" = in our1+2 field too → has \"our1+2\" \n\nSo \"our1+2 X\" can appear independently as a noun phrase.\n\nSo \"our1+2 cliff\" = qaqa + (our1+2) → but is there a word for \"cliff\"?\n\n\"qaqat”a\" = from the cliff → \"qaqa\" = cliff, \"t”a\" = from\n\nSo likely \"qaqa\" = cliff\n\nThen \"our1+2 cliff\" = qaqa + our1+2 → but how?\n\nIn \"qucxst”psa\" = from our1+2 lake → structure is [from] + [our1+2] + [lake]\n\nBut for \"our1+2 cliff\", no prefix, so must be [our1+2] + [cliff]? \n\nBut in \"yapsanpsa\" = in our1+2 field → [in] + [our1+2] + [field]\n\nSo \"our1+2\" appears after modifier or before?\n\nFrom \"markstxi\" = is it our1+2 town? → \"our1+2\" appears before \"town\"\n\nSimilarly, \"yapsanpsa\" = in our1+2 field → \"our1+2\" before \"field\"\n\n\"qucxst”psa\" = from our1+2 lake → \"our1+2\" before \"lake\"\n\nSo \"our1+2\" is a noun quantifier before the noun.\n\nSo \"our1+2 cliff\" = [our1+2] + [cliff] = ? \n\nBut is there a word for cliff? \nFrom \"qaqat”a\" = from the cliff → we know \"qaqa\" = cliff.\n\nSo \"our1+2 cliff\" = our1+2 + qaqa\n\nBut do we need a marker? \nIn other cases, when \"our1+2\" is used with a noun, it’s directly attached.\n\nExample: \"markstxi\" = is it our1+2 town? → our1+2 town — \"our1+2\" + \"town\"\n\nThus, \"our1+2 cliff\" = our1+2 + qaqa\n\nBut is \"qaqa\" a root? Yes.\n\nNow, is there a marking of number or possession? No, \"our1+2\" is a shared possessive.\n\nSo answer for 4: our1+2 + qaqa → \"our1+2 qaqa\"\n\nBut must be written in Jaqaru.\n\nSo: \"our1+2 qaqa\"\n\nBut what about aspiration? In \"qaqat”a\", \"qaqa\" is root, and \"t”a\" is for from. So \"qaqa\" may be unmarked.\n\nSo \"our1+2 qaqa\"\n\nBut in the word \"qucxst”psa\", \"our1+2\" is after \"from\", so \"from our1+2 lake\"\n\nHere \"our1+2 cliff\" is not preceded by \"from\", so just \"our1+2 qaqa\"\n\nThus, b.1: our1+2 qaqa\n\n5. in your corner \n→ \"in\" = infix or suffix? \"aq”na\" = in cave → \"na\" = in? \n\"chushuntxi\" = is it in the corner? → \"untxi\" = is it in?\n\nSo in + X = X + \"na\"? \n\"aq”na\" = in cave → \"aq\" + \"na\"? \n\"chushp”a\" = his corner → no \"na\" \n\"marka\" = the town → no \"na\"\n\nBut \"chushuntxi\" = is it in the corner? → suggests \"untxi\" = is it in?\n\nSo \"in\" may be expressed via \"na\" as a suffix to noun.\n\n\"aq”na\" = in cave → \"aq\" + \"na\"\n\nSo \"in X\" = X + \"na\"\n\nThus, \"in your corner\" = [your corner] + \"na\" \n\"your\" = ? → from \"chushp”a\" = his corner → \"chush\" = corner → so \"chush\" = corner \n\"your\" → from \"utamt”a\" = from your house → \"utam\" = your house → so \"utam\" = your\n\nSo \"your corner\" = \"utam\" + \"chush\" → ? \nBut is there a word for \"your corner\"?\n\nWe don't have it directly, but we have \"his\" = \"chushp”a\" → \"chush\" + p”a → \"p”a\" = his?\n\n\"chushp”a\" = his corner → so \"chush\" + \"p”a\" = his corner\n\nSimilarly, for \"your\" — \"utam\" = your (house)\n\nBut for \"corner\", only \"chush\" appears.\n\nSo \"your corner\" = \"utam\" + \"chushp”a\"? → but that’s redundant.\n\nIs there a third person? \"his\" is \"chushp”a\", so \"your\" might be \"utam chush\"?\n\nBut in \"utamt”a\" = from your house → so \"utam\" = your (house)\n\nSo \"your corner\" = utam + chush → but with affix?\n\n\"chush\" alone = corner? \n\"chushp”a\" = his corner → so corner is \"chush\" with possessive.\n\nSo \"your corner\" = \"utam chush\"?\n\nBut not marked — is \"p”a\" needed?\n\nNo parallel for \"your corner\".\n\nBut in \"chushp”a\" = his corner → so \"chush\" + \"p”a\" = his → \"p”a\" = his possessive\n\nSimilarly, \"your\" in \"utam\" → might have a possessive suffix?\n\nIn \"utamt”a\" = from your house → \"utam\" = your house → \"t”a\" = from\n\nSo \"utam\" = your house\n\nNo possessive suffix on \"your\" — \"your\" is encoded in \"utam\"\n\nSo \"your corner\" = \"utam chush\"? \n\nBut is \"chush\" standalone used?\n\nIn \"marka\" = the town — no possessive\n\nSo likely, \"corner\" = \"chush\" → and possessive adds suffix.\n\nSo \"his\" = chush + p”a \n\"your\" = ? — not directly given.\n\nBut \"utam\" is your house → so perhaps \"utam\" = your (something)\n\nCould \"your corner\" = \"utam chush\"? \n\nBut in \"chushuntxi\" = is it in the corner? → no possessive\n\nIn \"markstxi\" = is it our1+2 town? → possessive for \"us\"\n\nSo for \"your corner\", likely \"utam chush\"\n\nThen in → add \"na\"\n\nSo \"in your corner\" = (utam chush) + na = utam chush na\n\nBut is there any evidence of word order?\n\nIn \"chushp”a\" = his corner → \"chush\" + \"p”a\" → so noun + possessive\n\nSimilarly, \"utam\" = your house → \"utam\" alone\n\nSo for \"your corner\" = \"utam\" + \"chush\"\n\nThen \"in your corner\" = \"utam chush na\"\n\nBut order: is \"utam chush\" acceptable? Or is \"chush\" modified?\n\nNo parallel.\n\nIn \"chushp”a\" = his corner → possessive last.\n\nIn \"markp”t”a\" = from his town → \"chush\" = corner, but \"mark\" = town → so \"markp”t”a\" = from his town → \"mark\" + \"p”a\" → so possessive suffix on noun.\n\nSo when possessive is added, it's added to the noun.\n\nThus, \"your\" is not marked — only when possessive is added.\n\nFor \"your corner\", we use base \"chush\", with \"utam\" as modifier? But no.\n\nAlternative: is there a word like \"your\" affix?\n\nOnly \"p”a\" for \"his\", \"t”a\" for \"from\"\n\nBut no \"your\" affix.\n\nIn \"utamt”a\" = from your house — \"utam\" = your\n\nSo \"utam\" = your (with house)\n\nSo \"your corner\" = utam + chush → unmarked\n\nThen \"in your corner\" = utam chush na\n\nBut \"na\" = in → as in \"aq”na\" = in cave\n\nYes.\n\nThus, b.2: utam chush na\n\n6. in your corner too\n\n\"too\" = suffix \"-psa\"\n\nSo \"in your corner too\" = (in your corner) + too = (utam chush na) + psa = utam chush na psa\n\nSo b.3: utam chush na psa\n\n7. from your corner too\n\n\"from\" = suffix \"-t”a\" \n\"your corner\" = utam chush \n\"too\" = -psa\n\nSo \"from your corner too\" = (your corner) + from + too = utam chush t”a psa\n\nBut is \"from\" attached before or after?\n\nIn \"utamt”a\" = from your house → \"utam\" + \"t”a\" → so \"your house\" + \"t”a\" = from your house\n\nIn \"markp”t”a\" = from his town → \"mark\" + \"p”a\" + \"t”a\"? → no, \"markp”t”a\" — likely \"mark\" + \"p”a\" = his town, then \"t”a\" = from? But \"markp”t”a\" — could be \"mark\" + \"p”t”a\" → but \"p”t”a\" is not seen.\n\nActually, \"markp”t”a\" = from his town → likely \"mark\" + \"p”a\" = his town → and from = \"t”a\" → so \"markp”t”a\" → \"mark\" + \"p”a\" + \"t”a\"? \n\nBut the word is \"markp”t”a\" — so likely \"mark\" + \"p”\" + \"t”a\" → so \"p”a\" may be pronounced as \"p”\" and then \"t”a\"\n\nBut in \"utamt”a\", it's \"utam\" + \"t”a\"\n\nIn \"qaqat”a\" = from the cliff → \"qaqa\" + \"t”a\"\n\nSo \"from X\" = X + t”a\n\nThus, \"from your corner\" = utam chush + t”a\n\nThen \"from your corner too\" = (utam chush t”a) + psa = utam chush t”a psa\n\nSo b.4: utam chush t”a psa\n\n8. is it from the cave?\n\n\"from the cave\" = from + cave → from = t”a, cave = aq”?\n\n\"aq”ipsa\" = the cave too → so \"aq”\" = the cave\n\nThus, \"from the cave\" = aq” + t”a\n\n\"is it\" = stxi (as in \"markstxi\" = is it our1+2 town?)\n\nSo \"is it from the cave?\" = stxi + (from the cave) = stxi + aq” t”a\n\nSo b.5: stxi aq” t”a\n\n9. is it the house?\n\n\"the house\" = utnha → as in \"utnha\" = my house\n\nSo \"is it the house?\" = stxi + utnha\n\nSo b.6: stxi ut", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10485.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build alignment table from given examples:\n\n| English | Jaqaru |\n|--------|--------|\n| the cave | aq”ipsa |\n| in the cave | aq”na |\n| through the lake | qucxap”a |\n| from our1+2 lake too | qucxst”psa |\n| his corner | chushp”a |\n| is it in the corner? | chushuntxi |\n| in my bed | ishinhna |\n| your bed | ishma |\n| the pot | p”ak”u |\n| my pot too | p”ak”unhpsa |\n| from the cliff | qaqat”a |\n| from his town | markp”t”a |\n| is it our1+2 town? | markstxi |\n| from your house | utamt”a |\n| my house | utnha |\n| is it the field? | yaputxi |\n| in our1+2 field too | yapsanpsa |\n\nNow extract patterns:\n\n1. Possession:\n - \"our1+2\" = \"mine and yours\" = used in: qucxst”psa, markstxi, yapsanpsa\n - \"your\" = ishma, utamt”a → \"your house\" = utamt”a, \"your bed\" = ishma\n\n2. Adverbial constructions:\n - \"in\" = aq”na (in the cave), ishinhna (in my bed), markstxi (is it our1+2 town?)\n - \"from\" = qucxst”psa (from our1+2 lake too), markp”t”a (from his town), qaqat”a (from the cliff), utamt”a (from your house)\n\n3. \"too\" = suffix added to base, like:\n - aq”ipsa → aq”ipsa (no \"too\") → aq”ipsa + \"too\" = ? \n - p”ak”u → p”ak”unhpsa → \"my pot too\" → so \"unhpsa\" = \"too\"\n - Also \"yapsanpsa\" = \"in our1+2 field too\" → \"sanpsa\" = \"too\"\n - \"qucxst”psa\" = \"from our1+2 lake too\" → \"st”psa\" = \"too\"\n\nThus, \"too\" = suffix -psa (after vowel or consonant cluster), with aspiration mark if needed.\n\n4. \"is it X?\" → chushuntxi (is it in the corner?) → structure: verb + \"it\" + place? → chushuntxi = \"is it in the corner?\"\n\nBut \"is it X?\" = a question with \"untxi\" = \"is it?\" + noun or locative phrase.\n\nMore clearly:\n- is it in the corner? = chushuntxi → chush- (corner) + untxi\n- is it our1+2 town? = markstxi → mark- (town) + stxi\n\nSo: \"is it X?\" = [noun] + stxi → markstxi, yaputxi (is it the field?), chushuntxi (is it in the corner?)\n\nWait: chushuntxi → chush (corner), untxi → \"is it in\" → so different structure.\n\nBut markstxi → “is it our1+2 town?” → not “in the town”, but “is it our1+2 town?”\n\nSimilarly, yaputxi → “is it the field?”\n\nSo pattern: \"is it X?\" = [X stem] + stxi\n\n- markstxi = “is it our1+2 town?” → mark → town → markstxi\n- yaputxi = “is it the field?” → yapu → field → yaputxi\n- chushuntxi = “is it in the corner?” → chush → corner → chushuntxi → so “untxi” = “is it in”?\n\nContradiction? But chushuntxi → \"is it in the corner?\" → so “in” is part of the word.\n\nBut markstxi → “is it our1+2 town?” → no “in”.\n\nSo two types:\n- “is it in X?” → chushuntxi → uses untxi\n- “is it X?” → markstxi, yaputxi → uses stxi\n\nBut “in the corner” occurs in chushuntxi → so “in” is attached with “untxi”\n\nWhen is “in” used? Only in chushuntxi → “is it in the corner?” → so “in” = untxi?\n\nBut “in our1+2 field too” = yapsanpsa → “in” is there → yapsa = field → “in” + “our1+2” + “field” → so “sanpsa” = “too”\n\nHence: “in” is likely a suffix or prefix.\n\nRecheck:\n\n- in the cave → aq”na\n- in my bed → ishinhna\n- in our1+2 field too → yapsanpsa\n\nSo “in” = morpheme that appears with a noun. In “aq”na → “na” = “in”?\n\n“aq”ipsa = “the cave”, “aq”na = “in the cave” → “na” = “in”?\n\n“ishinhna” = “in my bed” → “inhna” = “my bed”? → inhna?\n\nWait: “ishinhna” → “in + my bed”?\n\nLikely: “in” is expressed via a suffix or bound morpheme.\n\nBut “aq”na = in the cave → “aq” + “na” → “na” = in?\n\nSimilarly, “ishinhna” = “ish” + “inhna” → “ish” = my → “inhna” = bed?\n\nSo “in” may be built into placement.\n\nBut “yapsanpsa” = “in our1+2 field too” → “yap” = field → “sanpsa” = too\n\nSo “in” is not separate — the root contains the “in” when compounded.\n\nBut \"in the cave\" = aq”na → \"in\" is carried in \"na\" → so “na” = “in [the] cave”?\n\nSimilarly, “in my bed” = “ishinhna” → “ish” = my → “inhna” = bed → so “in” not explicitly worded?\n\nBut “in” is not a separate word — it's internalized into noun phrase.\n\nSo probably, the indicator of location (“in” / “from”) is part of the verb or noun stem.\n\nNow for (b):\n\n4. our1+2 cliff → from “from the cliff” = qaqat”a → qaq → cliff → “from”?\n\n“from” = qaqat”a → “qaq” + “at” + “a”?\n\n“qaqat”a = from the cliff → so “qaq” = cliff → with “at” = from? → “at” is a suffix?\n\n“from” = qaqat”a → “at” is a suffix?\n\nCompare:\n- from our1+2 lake too = qucxst”psa → “qucx” + “st” + “psa” → “st” might be “our1+2”, “psa” = too?\n- from the cliff = qaqat”a → “qaq” + “at” + “a” → “at” = from?\n\n“markp”t”a” = from his town → mark → town → “p”t”a” → “p” is possessive?\n\n“markp”t”a” → from his town → so “p” = his? “t”a = town?\n\n“p” in p”ak”u → “p” + “ak”u → pot → “p” is root?\n\nSo: possessive markers:\n- “his” = chushp”a → chush → corner → “p”a → “p”a = his?\n- “his town” = markp”t”a → mark → town → “p”t”a” → “p” → his?\n\nSimilarly, “your” = ishma → “is” + “hma” → “hma” = bed? → “is” = your?\n\n“your house” = utamt”a → “ut” + “am” + “t”a → “am” = your?\n\n“your bed” = ishma → “ish” + “hma” → “ish” = your?\n\nSo: “your” = ish + hma → “h” = your?\n\nBut “our1+2” = not matched directly.\n\nWhere is “our1+2”?\n\n- from our1+2 lake too = qucxst”psa → “qucx” = lake → “st” = our1+2? → “st” = our1+2?\n- is it our1+2 town? = markstxi → “mark” = town → “stxi” → “st” = our1+2?\n\n“qucxst”psa” → “qucx” + “st” + “psa” → “st” = our1+2 → “psa” = too?\n\n“markstxi” → “mark” + “stxi” → “stxi” = our1+2 town?\n\nSo “st” = our1+2?\n\nBut “st” has no aspiration — look at “chushp”a” → chush → his → “p”a → “p” is his?\n\nSo “st” = our1+2?\n\nSo:\n- “our1+2” = “st” → as in qucxst”psa, markstxi\n\nTherefore:\n- 4. our1+2 cliff → take “qaqat”a (from the cliff) → remove “from” → need “our1+2 cliff” → no “from” → so structure?\n\n“from the cliff” = qaqat”a → so base: qaqat”a (from the cliff)\n\nTo get “our1+2 cliff” → without “from” → so “our1+2” + “cliff” → add “our1+2” prefix?\n\nBut “our1+2” is “st” → so “st” + “qaq”?\n\n“st” + “qaq” = stqaq?\n\nDo we have “st” + “qaq”?\n\nLook: “qucxst”psa” → “qucxst”psa” → “qucx” (lake) + “st” (our1+2) + “psa” (too)\n\nSimilarly, “markstxi” → “mark” (town) + “st” (our1+2)\n\nSo “st” is a prefix meaning “our1+2”\n\nSo “our1+2 cliff” = st + qaq → stqaq\n\nBut is “qaq” = cliff? qaqat”a = from the cliff → so “qaq” = cliff?\n\nYes.\n\nSo: stqaq\n\nBut in “qaqat”a” → “at” and “a” → “at” is suffix? → “qaq” = cliff?\n\nIn “qucxst”psa” → “qucx” = lake, “st” = our1+2, “psa” = too → no marking of “in” or “from”\n\nSo “st” is a possessive prefix.\n\nThus, 4. our1+2 cliff → stqaq\n\n→ stqaq\n\nNow 5. in your corner\n\n“in” → appears in “in the cave” = aq”na → “na” = in?\n\n“in my bed” = ishinhna → “inhna” = my bed? → “in” not explicit?\n\nBut “in your corner” → “your corner” = chushp”a → chush = corner → “p”a = his?\n\n“your” = ishma → ish = your?\n\nSo “your corner” = ish + chushp”a? → ishchushp”a?\n\nBut “p”a is in chushp”a → “p”a = his?\n\nSo if “your” is ish → must be ish + chush → ishchush?\n\nThen “in your corner” → needs “in”?\n\n“in the cave” = aq”na → “na” = in?\n\n“in my bed” = ishinhna → “inhna” = in + my bed?\n\nSo pattern: “in + X” = in + noun stem → with specific suffix?\n\n“ishinhna” → ish + in + hna? or ish + in + hna?\n\n“inhna” → likely “in + my bed” → “in” attached?\n\nSo for “in your corner” → we need “in + your corner”\n\nYour corner = ish + chush → but chushp”a → “p”a = his → so does “p”a mean “his” or “corner”?\n\nchushp”a → “chush” = corner, “p”a = his → so “his corner”\n\nSo “your corner” = ? → no word directly.\n\nIs there “your” + “corner”?\n\nNo direct example.\n\nBut “your bed” = ishma → “ish” = your, “ma” = bed?\n\n“your town”? Not given.\n\nBut “in your corner” → likely needs the “in” suffix.\n\nIn aq”na → “na” = “in [the] cave”?\n\nIn ishinhna → “inhna” = “in my bed”?\n\nSo “in” = suffix -hna?\n\nBut “inhna” → in + hna?\n\nBut hna = bed?\n\nSo: in + bed → ishinhna\n\nSimilarly, in + corner → ? → ish + chush + ?\n\nchush has “p”a → his → so if we want “your corner”, we need “your” + “corner”\n\nBut what is the root?\n\nchush → corner — can we make “your” + “corner”?\n\nPossibility: ish + chush → ishchush → then “in” → + in?\n\nBut ishinhna → ish + in + hna?\n\nSo “inhna” = “in + my bed”\n\nSimilarly, “in + your corner” = ish + chush + in?\n\nBut what is the infix?\n\nIn aq”na → “na” = in?\n\nIn ishinhna → “inhna” → in + hna?\n\nSo the “in” is attached to the noun with a suffix?\n\nBut the suffix is different:\n\n- cave → aq”na → aq + na\n- bed → ishinhna → ish + in + hna → “in” is a suffix?\n\nPerhaps all locative expressions have “in” as suffix.\n\nBut in “from” words → “from our1+2 lake too” = qucxst”psa → “qucx” + “st” + “psa” → “st” = our1+2, “psa” = too — no “in” or “from” marked?\n\n“from” is separate.\n\nBut “in” in “in the cave” → “aq”na → “na” = in?\n\nSo likely, “in” is marked in non-“from” forms.\n\nSo for “in your corner”:\n\n- “your corner” = ish + chush? → “ish” = your, “chush” = corner → ishchush?\n\n- then “in” → if “in” is suffix, like “na” or “hna”, → so ishchush + in?\n\nWhat is the suffix?\n\nIn “in the cave” = aq”na → “na”\n\nIn “in my bed” = ishinhna → “inhna” → so “in” + “hna”?\n\nBut “hna” = bed?\n\nSo the noun is the base.\n\nSo “in + my bed” = ish + in + hna\n\n“in + your corner” = ish + in + chushp”a?\n\nBut chushp”a” has “p”a → his → so cannot be used.\n\nNeed “corner” without possessive.\n\nSo is there a base for “corner” alone? chush → corner?\n\nchush → corner — as in chushp”a = his corner → so “chush” = corner?\n\nSo “your corner” = ish + chush → ishchush?\n\nThen “in your corner” = ishchush + in?\n\nBut what suffix? In “in my bed” = ishinhna → so “in” is attached as “in”?\n\nBut “inhna” — where is “in”? It is in the middle?\n\nActually: “ish” + “in” + “hna”?\n\nBut hna not in chush.\n\nIs there a form like “in chush”?\n\nWe don’t have it.\n\nBut “is it in the corner?” = chushuntxi → “chush” + “untxi”\n\nSo “in the corner” = chushuntxi → “untxi” = “in”?\n\nYes.\n\nSo “in” is expressed by “untxi” in questions.\n\nIn statements: “in the cave” = aq”na → “na” = in?\n\n“in my bed” = ishinhna → “inhna” → “in” + “hna”?\n\nSo possible: “in + [noun]” = [possessed noun] + “in” or with a suffix.\n\nBut in “chushuntxi” → “untxi” = “is it in the corner?” → so “untxi” marks “in” for questions.\n\nTherefore, in declarative statements, “in” is marked by a suffix like “na” or “hna”.\n\nBut for “in your corner”, possible form: ishchush + na? → ishchushna?\n\nOr ishchush + in? → no word.\n\n“na” is used for “the cave” → “in the cave” = aq”na\n\n“in my bed” = ishinhna — “hna” = bed\n\nSo no direct “in corner” form?\n\nBut “in your corner” — perhaps ishchushna?\n\nBut “na” is used for “in the cave”, not “in corner”.\n\nHowever, no other form — must be inferred.\n\nLikely, the suffix “na” is used for “in” in general.\n\nBut “in my bed” uses “inhna” → so not “na”.\n\nUnless “in” is not fixed.\n\nAnother idea: “in” is expressed by the suffix of the noun, like “na” for cave, “h", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10495.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "Start by analyzing the given examples to find patterns in word formation, especially regarding possession, location, negation, and questions.\n\nFrom the given:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- chushuntxi = is it in the corner? \n- marka = the town \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishma = your bed \n- utamt”a = from your house \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- qaqat”a = from the cliff \n- yapsanpsa = in our1+2 field too \n\nKey observations:\n\n1. Possession markers:\n - “our1+2” appears in: qucxst”psa (from our1+2 lake too), markstxi (is it our1+2 town?), yapsanpsa (in our1+2 field too)\n - “your” appears in: ishma (your bed), utamt”a (from your house)\n\n2. Location/prepositional markers:\n - “in” is used in: aq”na (in the cave), ishinhna (in my bed), yapsanpsa (in our1+2 field too)\n - “from” is used in: qucxst”psa (from our1+2 lake too), markp”t”a (from his town), utamt”a (from your house), qaqat”a (from the cliff)\n\n3. Demonstratives and adjectives:\n - “too” appears as a suffix: aq”ipsa (the cave too), p”ak”unhpsa (my pot too), qucxst”psa (from our1+2 lake too), yapsanpsa (in our1+2 field too)\n - The suffix “-psa” is used with “too” — appears in aq”ipsa, p”ak”unhpsa, qucxst”psa, yapsanpsa → pattern of -psa = “too”\n\n4. Questions:\n - “is it” is introduced by “untxi” (e.g., chushuntxi = is it in the corner?)\n - So: “is it X?” is formed as “untxi” + locative or possessive phrase\n\n5. Possession:\n - “his” = chushp”a (corner), markp”t”a (from his town)\n - “my” = ishinhna (in my bed), p”ak”unhpsa (my pot too)\n - “your” = ishma (your bed), utamt”a (from your house)\n\n6. Location affix:\n - “in” = introduced by “-na” (e.g., aq”na = in the cave)\n - “from” = introduced by “-p”t”a” or “-t”a” (e.g., markp”t”a = from his town, utamt”a = from your house)\n - “through” = qucxap”a\n\n7. “from” pattern:\n - qaqat”a = from the cliff → base = qaqat”a\n - utamt”a = from your house → base = utam + t”a → tentative: utam = your house, t”a = from?\n - utamt”a = from your house → utam + t”a → “your house” → “t”a” = from?\n\n8. “in” pattern:\n - aq”na = in the cave → aq” + na → “the cave” → “na” = in?\n - ishinhna = in my bed → ishin + hna → “my bed” → “hna” = bed?\n - ishma = your bed → “ishma” → “ish” + “ma” → “your”?\n - So: “bed” = hna or ma?\n\n9. “corner”:\n - chushp”a = his corner → chush + p”a → “corner”\n - so “corner” = p”a\n - chushuntxi = is it in the corner? → chushu (is it) + n + txi → /untxi/ = is it?\n\n10. “field”:\n - yaputxi = is it the field?\n - yapsanpsa = in our1+2 field too → yapsa + n + psa → “in our1+2 field too”\n - So “yapsa” = field?\n\nNow solve each required translation:\n\n4. our1+2 cliff \n→ From qaqat”a = from the cliff \n→ So “our1+2 cliff” → likely qaqat”a with “our1+2” added \n→ In examples: qucxst”psa = from our1+2 lake too → “our1+2” + [place] \n→ So, “our1+2 cliff” = qaqat”a → add “our1+2” prefix? \n→ But qaqat”a = from the cliff → so base = qaqat”a\n\nBut “our1+2” is used in: qucxst”psa, markstxi, yapsanpsa \n→ qucxst”psa = from our1+2 lake too → (qucx + st”psa) → st”psa = from our1+2 lake too → “st”psa” = from our1+2 + lake?\n\nBut “lakes” = qucxap”a (through the lake), qucxst”psa = from our1+2 lake too → so qucx + st”psa\n\nSo the “our1+2” is in the “st” part.\n\nWhat does “st” mean? It’s part of “st”psa — “st” = our1+2?\n\nWait: qucxst”psa = from our1+2 lake too → “st”psa → st = our1+2? \nBut chushp”a = his corner → “p”a = corner\n\nSimilarly, markp”t”a = from his town → “p”t”a” = from his town → p”t”a” = from his town \nSo: \n- qaqat”a = from the cliff → qaqat”a \n- markp”t”a = from his town → mark + p”t”a \n- utamt”a = from your house → utam + t”a \n→ So the “from” phrase is formed as [noun base] + [possession + from marker]\n\nWait — qaqat”a has no possessive — so “the cliff” → “from the cliff”\n\nSo “our1+2 cliff” = just “our1+2” + “cliff”?\n\n→ But no adjective form. \n→ Is there a form for “our1+2 cliff”? \n→ Look: in “qucxst”psa = from our1+2 lake too → “st”psa → we see “st” = our1+2?\n\nBut “st”psa = from our1+2 lake too → so “st” is “our1+2”?\n\nBut “st” appears only in qucxst”psa and possibly others?\n\nWait — what about markstxi = is it our1+2 town? → mark + stxi → stxi = our1+2 town?\n\nBut “our1+2” appears in: \n- qucxst”psa → from our1+2 lake too \n- markstxi → is it our1+2 town? \n- yapsanpsa → in our1+2 field too \n\nSo the pattern is: [noun base] + [our1+2 marker] + [positional suffix]\n\nFor “our1+2 cliff” → we need “cliff” base + “our1+2” → qaqat”a is “from the cliff”, so perhaps the base is “qaqat”?\n\nBut “qaqat”a” — if we remove “a” → qaqat → then add “our1+2” marker?\n\nBut where is “our1+2” marker? In qucxst”psa → “st” — so “st” = our1+2?\n\nIn yapsanpsa → yapsa + n + psa → “in our1+2 field” — so “psa” = too, “n” = in?\n\nWait — yapsanpsa = in our1+2 field too → so “yapsa” = field → “n” = in? → “n” appears to mark “in”?\n\na) in the cave → aq”na → “na” → so “na” = in?\n\nb) in my bed → ishinhna → “hna” → “hna” = in bed?\n\nc) in your corner → we need to find this\n\nSo, for “in your corner” → likely “your” + “corner” + “in”\n\n“corner” = chushp”a → so “p”a = corner\n\n“your” = in ishma = your bed → “isha” or “ish”?\n\nisha = your? → in ishma = your bed → “ish” + “ma” → so “ish” = your?\n\nSimilarly, markp”t”a = from his town → “mark” + “p”t”a” → “p”t”a” = from his?\n\nSo, “in your corner” = in + your + corner\n\n“in” → “na” (from aq”na)\n\n“your” → “ish”?\n\n“corner” → “p”a\n\nSo: ishna + p”a? → ishna = in your?\n\nBut ishinhna = in my bed → ishin + hna → “hin” = my?\n\nSo “my” = ishin? → so “your” = ish?\n\nThen in your corner → ish + na + p”a = ishnap”a\n\nBut ishinhna = in my bed → ishin + hna → so “hna” = bed, “hin” = my\n\nSo “hna” = bed → not in\n\nWait: aq”na = in the cave → “na” = in?\n\nishinhna = in my bed → ishinhna → so “inh” = my bed? “inh” is not separate.\n\nAlternative: “na” = in, “bin” or something?\n\nBack to patterns for “in”:\n\n- aq”na = in the cave → na = in?\n- ishinhna = in my bed → ishinhna → “na” at end → “na” = in?\n\nYes — in both, “na” ends → so “in” = na?\n\nThen:\n- aq”na = the cave in? → but “in the cave”?\n\nActually, all location phrases seem to have a locative marker.\n\nSo:\n- in the cave = aq”na → “na” = in?\n- in my bed = ishinhna → “hna” → “hna” = my bed?\n- in your corner = ? → likely “your” + “corner” → “ish” + “p”a → with “na”?\n\nBut “in” might be part of the base.\n\nLook at qucxap”a = through the lake → not in, but through.\n\nOnly “na” appears in “in”.\n\nIn:\n- aq”na → in the cave\n- ishinhna → in my bed\n- markstxi → is it our1+2 town? → not in\n- markp”t”a → from his town\n\nSo “na” = in?\n\nThus “in your corner” = your corner + in → “ish” + “p”a + “na” → ishnap”a\n\nSimilarly:\n- “in your corner too” = ishnap”a + psa → add “-psa” = too → ishnap”apsa\n\n- “from your corner too” → from + your corner + too → from → “t”a” → from?\n\nFrom:\n- from his town = markp”t”a → mark + p”t”a → p”t”a = from his\n- from your house = utamt”a → utam + t”a → t”a = from your?\n\nSo “t”a = from your?\n\nThen “from your corner” = your corner + from → ishp”a + t”a → ishp”at”a?\n\n“corner” = p”a → so ish + p”a → ishp”a → then from = t”a → ishp”at”a\n\nThen “too” = psa → so from your corner too = ishp”at”a + psa = ishp”at”apsa\n\nBut we have no “your corner” base.\n\nNote: “your” = ish (from ishma = your bed)\n\nSo “your corner” = ish + p”a = ishp”a\n\nThen:\n- from your corner → ishp”at”a\n- from your corner too → ishp”at”apsa\n\n- is it from the cave? → “is it” + from + the cave\n\n“is it” = chushuntxi = is it in the corner? → “untxi” = is it?\n\nSo structure: [untxi] + [from] + [cave]\n\nFrom = t”a? But “from the cave” → where is “the cave”?\n\n“the cave” = aq”ipsa → “ipsa” = cave?\n\naq”ipsa = the cave too → so “ipsa” = cave\n\nTherefore “from the cave” = t”a + ipsa → “t”aipsa\n\nSo “is it from the cave?” = untxi + t”aipsa → untxit”aipsa\n\n- is it the house? = “is it” + “the house”\n\n“the house” = ? → utamt”a = from your house → “utam” = your house\n\nSo “your house” = utam → so “the house” = ? → base?\n\nBut “the” may not be marked; in “from your house”, “utam” = your house\n\nNo “the” elsewhere.\n\nIn “the cave” = aq”ipsa → aq” = the?\n\n“the pot” = p”ak”u → so “p”ak”u” = the pot?\n\nSo “the” is marked by base: aq” = the, p”ak”u = the pot\n\nSo “the house” = likely utam → but “utam” = your house\n\nSo is there a neutral “the”?\n\nOnly when no possession: qaqat”a = from the cliff → so “qaqat”a” → “the cliff”?\n\nYes — so “the” is marked in base word.\n\nThus “the house” = utam → but “utam” = your house → not neutral.\n\nIs there a “the” without possession?\n\nutamt”a = from your house → so “your” is marked.\n\n“the house” is not directly given.\n\nBut: “is it the house?” → likely “untxi” + “the house”\n\n“the house” → what is base?\n\nWe have no standalone “house”\n\nBut: “your house” = utamt”a → base = utam → so “utam” = house?\n\nSo “the house” = utam? → unmarked?\n\nIn qaqat”a = from the cliff → “qaqat”a” → “the cliff” → “qaqat”a” = “the cliff”?\n\nSo “the” is part of base.\n\nSo “the house” = utam → perhaps\n\nBut only “your” is marked.\n\nSo likely, “the house” = utam\n\nThus “is it the house?” = untxi + utam = untxiutam\n\nNow summarize:\n\n4. our1+2 cliff → from examples: qucxst”psa = from our1+2 lake too → “st”psa = from our1+2 lake → so “st” = our1+2?\n\nBut “st” is used in: qucxst”psa, markstxi, yapsanpsa\n\nSo “st” = our1+2?\n\nBut in yapsanpsa = in our1+2 field too → “psa” = too\n\nSo “st” appears as “our1+2” suffix?\n\nSo our1+2 + cliff → qaqat”a with st at beginning?\n\nBut qaqat”a = from the cliff\n\nSo “our1+2 cliff” → likely qaqat”a with “st” prefix? → stqaqat”a?\n\nOr with “st” in location?\n\nBut in qucxst”psa = from our1+2 lake too → “qucxst”psa” → so “st” is attached to “lake”\n\n“lake” = qucxap”a → so “lake” base → qcx?\n\nSo “st” = our1+2 → so “our1+2 lake” = qucxst”psa → so “st” is a possessive suffix?\n\nThus “our1+2 cliff” = qaqat”a with “st” → stqaqat”a?\n\nBut qaqat”a = from the cliff → so does it have a possessive?\n\nNo example shows “our1+2 cliff” directly.\n\nBut we do have “our1+2 field” → yapsanpsa = in our1+2 field too → so “our1+2” marker is in the phrase.\n\nIn yapsanpsa: yapsa (field) + n (in) + psa (too)\n\nNo possessive prefix?\n\nBut we have markstxi = is it our1+2 town? → so “our1+2” appears in the middle?\n\nSo the structure is: [noun] + [possessive marker] → for “our1+2”?\n\nPossessive markers:\n- our1+2 = in “st” in markstxi\n- his = p” in chushp”a\n- your = ish in ishma, utam in utamt”a\n\nSo likely:\n- our1+2 = st\n- his = p\n- your = ish\n\nSo:\n-", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10497.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given a series of Inuktitut sentences with English translations. Our goal is to translate six new sentences (13–18) into English, identifying the underlying grammatical patterns.\n\nStep-by-step pattern analysis:\n\n1. Identify core verbs and their participial or nominal forms:\n - \"takujaatit\" → \"saw\" (1)\n - \"iluaqhaiji\" → \"shot\" (2, 4, 12)\n - \"aanniqtanga\" → \"hurt\" (3, 10)\n - \"aarqijaatit\" → \"cured\" (4, 8)\n - \"iputujait\" → \"speared\" (5, 9, 18)\n - \"qaijuq\" → \"came\" (7)\n\n2. Observe verb roots and affixes:\n - All verbs are derived from root verbs with:\n - -it (past tense or perfective)\n - -up (intransitive or active agent)\n - -mik (possessive or possessive target)\n - -it (in past tense)\n - Common root: \"angunahukti\" → \"hunter\", \"inuuhuktuup\" → \"boy\"\n - \"iluaqhaiji\" → \"shot\" / \"shot the doctor\"\n - \"aarqisijuq\" = \"cured\" (from aarqijaatit)\n - \"iputujanga\" = \"speared\" (from iputujait)\n\n3. Identify subject indicators:\n - \"Qingmivit\" → \"your dog\"\n - \"inuuhuktuup\" → \"the boy\"\n - \"aanniqtutit\" → \"you hurt yourself\" → reflexive\n - \"iluaqhaijiup\" → \"the doctor\"\n\n4. Identify affix patterns:\n - Determiners and possessives:\n - \"your\" = \"Qingmivit\", \"inuuhuktuup\", \"Nanuit\", \"Nanuit\"\n - \"your\" is often prefixed in possessive constructions\n - “your doctor” = iluaqhaijiup aarqijaatit → \"the doctor cured you\" → similar to “your doctor cured you”\n - Plural markers: -sij (e.g., takujanga → saw you)\n - Possessive suffixes: -mik (e.g., inuuhukturmik → your boy)\n - Subject prefixes:\n - \"Amaruup\" = \"the hunter\"\n - \"Nanuit\" = \"the polar bear\"\n - \"Angunahukti\" = \"the hunter\"\n\n5. Apply minimal pairs:\n - (1) Qingmivit takujaatit → your dog saw you\n - (5) Qingmiq iputujait → you speared the dog\n → root \"iputujait\" = \"speared\", subject \"you\"\n → \"Qingmiq\" = \"the dog\"\n\n - (9) Angunahuktiup amaruq iputujanga → the hunter speared the wolf\n - (18) Angunahuktimik aarqisijutit → the hunter cured (someone) → possible reflexive?\n\n - (10) Qingmiup ilinniaqtitsijiit aanniqtanga → the dog hurt your teacher\n → \"ilinniaqtitsijiit\" = hurt (reflexive or transitive?)\n → “ilinniaqtitsiji” → pointer to “hurt”\n\n - (14) Nanuit inuuhukturmik aanniqsijuq → the polar bear cured your boy\n\n - (15) Angunahuktiit aarqijuq → the hunter cured → needs object?\n\n - (17) Qaijutit → \"you fell\"\n\n - (16) Ilinniaqtitsiji qukiqtait → hurt → someone hurt the dog?\n\n6. Derive verb and object:\n - \"takujanga\" = \"saw you\" → in past, agent, object\n → \"Amaruup angatkuit takujanga\" = the hunter saw you\n → \"angatkuit\" = \"came\" → but \"angatkuit\" is not a verb in the examples\n\nWait: in sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\"\n\nBut \"angatkuit\" is not in given entries. Check sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → the hunter shot a polar bear\n\n→ \"qukiqsijuq\" = \"a polar bear\"\n\n→ \"qukiqsijuq\" = \"a polar bear\"? What's the root?\n\nLook at 7: \"Nanuq qaijuq\" → \"the polar bear came\"\n\n→ \"qaijuq\" = \"came\"\n\nSo \"angatkuit\" → not in list?\n\nPossibly a typo or morphological variation?\n\nWait: sentence 13: \"Amaruup angatkuit takujanga\"\n\nNo \"angatkuit\" in list → possible typo?\n\nWait, sentence 7: \"Nanuq qaijuq\" → polar bear came\n\nBut \"angatkuit\" → perhaps a form of \"came\"?\n\nThen \"angatkuit\" = \"came\"\n\nBut in sentence 13: \"Amaruup angatkuit takujanga\"\n\n→ \"the hunter came and saw you\"? Or just \"the hunter saw you\"?\n\nBut \"takujanga\" → \"saw you\"\n\nPossibly \"angatkuit\" is a verb meaning \"came\", but in context, it's in a past object?\n\nWait: \"angatkuit takujanga\" → could be \"came and saw you\" or \"came to see you\"\n\nBut other forms: \"iluaqhaijivit\" → \"the doctor cured you\"\n\nPattern: In all cases, the verb is in -it form (past), and the object is marked by the verb stem or a noun.\n\nNow, sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → the shaman cured a doctor\n\n→ \"iluaqhaijimik\" = \"a doctor\"\n\n→ so \"iluaqhaiji\" + \"-mik\" = \"a doctor\"\n\nSimilarly, \"inuuhukturmik\" = \"your boy\"\n\n\"aanuqtuq\" → not present\n\n\"qukiqsijuq\" = \"a polar bear\"\n\nSo root of \"qukiqsijuq\" = \"qukiqtait\" → \"shot\"\n\nBut sentence 16: \"Ilinniaqtitsiji qukiqtait\" → \"hurt\" + \"shot\"\n\nBut \"hurt\" = \"ilinniaqtitsiji\"\n\n\"qukiqtait\" = \"shot\"\n\nSo \"hurt and shot\"?\n\nBut that may not be intended.\n\nWait: both are action verbs → could be compound?\n\nBut likely separate.\n\nNow review sentence 17: \"Qaijutit\" → suspected to be \"you fell\" → matches sentence 11: \"Ukiakhaqtutit\" → \"you fell\"\n\nSo \"qaijutit\" = \"you fell\"\n\nYes → likely \"qaijutit\" = \"you fell\"\n\n(17) → \"you fell\"\n\nNow sentence 15: \"Angunahuktiit aarqijuq\"\n\n→ \"Angunahuktiit\" = the hunter (subject)\n→ \"aarqijuq\" → likely \"cured\" + \"a bear\"? Or \"cured someone\"?\n\nSentence 4: \"iluaqhaijiup aarqijaatit\" → the doctor cured you\n\n→ \"aarqijaatit\" = \"cured you\"\n\n→ \"aarqijaat\" → cured\n\nThus \"aarqijuq\" → likely \"cured a bear?\" → but no object\n\nSuppose object is missing → \"the hunter cured\" — but who?\n\nPossibly the object is implied or missing?\n\nCompare sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy\n\n→ \"iluaqhaijivit\" = the doctor\n→ \"inuuhuktuit\" = your boy\n→ \"aarqijanga\" = cured\n\nSo \"aarqijaatit\" → cured you → perfective past\n\nThen \"aarqijuq\" → likely \"cured\" + a noun → object must be missing?\n\nBut in 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured [someone]\" → object missing?\n\nBut in translation, we have to infer — likely missing object = \"you\" or \"a person\"?\n\nBut in 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n→ \"Nanuit\" = the polar bear\n→ \"inuuhukturmik\" = your boy\n→ \"aanniqsijuq\" = \"cured\" → \"cured your boy\"\n\nThus \"aanniqsijuq\" = \"cured\", with object marked\n\nSimilarly, \"aarqijuq\" → misses object\n\nStill, based on sentence 8, \"aarqijanga\" = \"cured\" (intransitive or with object)\n\nIn (8), it's \"cured your boy\" → so \"aarqijanga\" includes object?\n\nIn (4): \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\"\n\nSo aarqijaatit = \"cured you\"\n\nSo \"aarqijaat\" = cured, with object in suffix\n\nThen \"aarqijuq\" → \"cured\" + no object → so potentially \"cured you\" → default object?\n\nBut in 15: \"Angunahuktiit aarqijuq\" → the hunter cured you?\n\nYes — likely.\n\nSimilarly, sentence 18: \"Angunahuktimik aarqisijutit\"\n\n→ \"angunahuktimik\" = your hunter?\nNo — \"Angunahuktimik\" → \"the hunter\" + possessive?\n\nPossibly: \"Angunahuktimik\" = \"a hunter who cured\"\n\nBut \"aarqisijutit\" = \"cured you\" → from \"aariqijaatit\" → cured you\n\nSo \"aarqisijutit\" = cured you\n\nThus sentence 18: \"the hunter cured you\" — with possession?\n\n\"Angunahuktimik\" → is this \"your hunter\"?\n\nBut no \"your\" → conflict\n\nWait — \"inuuhukturmik\" = \"your boy\"\n\n\"inuuhuktuit\" = \"your boy\" (nominal)\n\nSimilarly, \"angunahuktimik\" → \"a hunter of yours\"? Or \"your hunter\"?\n\nBut sentence 9: \"Angunahuktiup amaruq iputujanga\" → the hunter speared the wolf\n\nNo possessive\n\nBut sentence 18: \"Angunahuktimik aarqisijutit\"\n\n→ \"angunahuktimik\" → \"your hunter\"? Possibly\n\nBut \"you\" is not the subject — if \"your hunter cured you\", then it matches.\n\nSimilarly, 16: \"Ilinniaqtitsiji qukiqtait\"\n\n→ \"ilinniaqtitsiji\" = \"hurt\" → like \"you hurt the teacher\"\n→ \"qukiqtait\" = \"shot\"\n\nIs it \"you hurt and shot\"? Or compound?\n\nBut in sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher\n\n→ \"ilinniaqtitsijiit\" = hurt → \"your teacher\" is object\n\nSo \"ilinniaqtitsiji\" = \"hurt\"\n\nThus \"ilinniaqtitsiji qukiqtait\" → \"hurt\" + \"shot\" → likely intentional?\n\nBut only if both were actions.\n\nAlternatively, could be \"your teacher hurt the dog\" — but no.\n\n\"ilinniaqtitsiji\" is the verb \"hurt\", not \"your teacher\"\n\nNo subject — so likely missing subject?\n\nWait: in 16: \"Ilinniaqtitsiji qukiqtait\"\n\nCompare to (10): \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher\n\nSo stem \"ilinniaqtitsiji\" = \"hurt\"\n\nNo subject? But here, no subject → so possible \"you hurt the dog\"?\n\nBut \"qukiqtait\" = \"shot\"\n\nCould it be \"you hurt and shot\"?\n\nBut that seems odd.\n\nAlternatively, could it be a \"compound verb\"? In some languages, verbs compound.\n\nBut no parallel in example.\n\nAnother possibility: \"ilinniaqtitsiji\" is a verb, \"qukiqtait\" is a noun?\n\nNo — \"qukiqtait\" is likely a verb.\n\nLook: \"qukiqtait\" → in sentence 2: \"inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n\"qukiqtanga\" = \"shot\"\n\nSo \"qukiqtait\" → might be \"shot\" → root \"qukiqt\"\n\nSo \"qukiqtait\" = \"shot\"\n\nSo sentence 16: \"hurt\" + \"shot\" → not a single action.\n\nBut in absence of subject, perhaps \"you hurt and shot\"?\n\nBut that doesn’t match pattern.\n\nWait — sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\nCompare to sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher\n\nSo structure: subject + verb + object\n\nSentence 16: no subject — so possibly \"you hurt\" and \"shot\", but with linkage?\n\nPossibly the verb is \"to hurt\", object missing?\n\nBut no object.\n\nAlternative: misreading of affix?\n\n\"ilinniaqtitsiji\" → a verb root\n\nIn (10), it's in -it form with object.\n\nSo likely, in (16), it's a missing subject.\n\nOnly minimal predicate.\n\nBut sentence 17: \"Qaijutit\" → \"you fell\"\n\nMatches sentence 11: \"Ukiakhaqtutit\" → \"you fell\"\n\nSo \"qaijutit\" = \"you fell\"\n\nNow back to 13: \"Amaruup angatkuit takujanga\"\n\n→ \"Amaruup\" = the hunter\n→ \"angatkuit\" → verb? Is this \"came\"?\n(sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\")\n\nSo \"qaijuq\" = \"came\"\n\n\"angatkuit\" — possibly a variant?\n\nPossibly \"angatkuit\" = \"came\"\n\nThen \"angatkuit takujanga\" = \"came and saw you\"\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\"\n\nSo \"takujanga\" = \"saw you\"\n\nThus \"Amaruup angatkuit takujanga\" → \"the hunter came and saw you\"\n\nSo translation: the hunter came and saw you\n\n14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n→ \"Nanuit\" = the polar bear\n→ \"inuuhukturmik\" = your boy\n→ \"aanniqsijuq\" = \"cured\" → like \"cured your boy\"\n\nSo → \"the polar bear cured your boy\"\n\n15: \"Angunahuktiit aarqijuq\"\n\n→ \"Angunahuktiit\" = the hunter\n→ \"aarqijuq\" → cured → likely \"cured you\"\n\n→ \"the hunter cured you\"\n\n16: \"Ilinniaqtitsiji qukiqtait\"\n\n→ \"ilinniaqtitsiji\" = \"hurt\"\n→ \"qukiqtait\" = \"shot\"\n\nBut no subject, no object.\n\nHowever, in (10): \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher\n\nSo this might be \"you hurt the doctor\" or \"you hurt and shot\"?\n\nBut \"qukiqtait\" appears only in \"qukiqtanga\" or \"qukiqsijuq\"\n\n\"qukiqsijuq\" = \"a polar bear\"\n\nNo direct.\n\nCould \"qukiqtait\" = \"a dog\"?\n\nNo — \"qingmiq\" = dog.\n\nBest guess: perhaps \"you hurt and shot\"?\n\nBut no.\n\nPossibly typo — should be \"ilinniaqtitsijiup qukiqtait\" — \"the dog hurt and shot\"?\n\nBut not.\n\nAlternatively, might be \"you hurt the dog\"?\n\nBut \"qukiqtait\" is \"shot\", not \"the dog\".\n\nNo.\n\nAnother possibility: \"ilinniaqtitsiji\" is a participial form?\n\nUnlikely.\n\nGiven that no subject is specified, and only one verb, likely missing.\n\nBut in context of patterns, maybe it's \"you hurt the dog\"?\n\nBut no argument.\n\nWait: sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\"\n\nSo \"putujait\" = \"speared\"\n\n\"qukiqtait\" = \"shot\"\n\nSo both are verbs.\n\nSo perhaps 16 = \"you hurt and shot\" — with possible object implied?\n\nBut no object.\n\nAlternatively, could be \"you hurt the dog\"?\n\nBut \"qukiqtait\" is not \"the dog\".\n\nStill, we must assign a translation.\n\nGiven: in (10), the dog hurt the teacher → so \"ilinniaqtitsiji\" = \"hurt\" (transitive)\n\nSo in (16), \"ilinniaqtitsiji qukiqtait\" → likely \"you hurt the dog\" → no?\n\nBut \"qukiqtait\" is not \"the dog\".\n\nSo another thought: the verb is \"to hurt\", and \"qukiqtait\" is the object → \"you hurt a shot\"?\n\nNo.\n\nFinal: the most plausible is that it is a compound verb, and in absence of structure, it is \"you hurt and shot\".\n\nBut that seems forced.\n\nAlternatively, based on sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\nCompare to (10): subject + verb + object\n\nHere, no subject, no object → so likely incomplete.\n\nBut no other clue.\n\nWe may assume the subject is \"you\" — by analogy to sentence 17.\n\nSentence 17: \"Qaijutit\" → you fell\n\nSo 16: \"you hurt and shot\"?\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11837.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given sentences in Inuktitut with English translations, and we are to translate six new sentences (13–18) into English.\n\nStep-by-step, we analyze the examples for patterns in morphology, word order, and verb structure.\n\n---\n\n**Step 1: Identify consistent verb patterns**\n\nLook at verb stems and their affixes to determine the structure.\n\n| Sentence | Inuktitut | English |\n|--------|---------|--------|\n| 1 | Qingmivit takujaatit | Your dog saw you |\n| 2 | Inuuhuktuup iluaqhaiji qukiqtanga | The boy shot the doctor |\n| 3 | Aanniqtutit | You hurt yourself |\n| 4 | Iluaqhaijiup aarqijaatit | The doctor cured you |\n| 5 | Qingmiq iputujait | You speared the dog |\n| 6 | Angatkuq iluaqhaijimik aarqisijuq | The shaman cured a doctor |\n| 7 | Nanuq qaijuq | The polar bear came |\n| 8 | Iluaqhaijivit inuuhuktuit aarqijanga | Your doctor cured your boy |\n| 9 | Angunahuktiup amaruq iputujanga | The hunter speared the wolf |\n|10 | Qingmiup ilinniaqtitsijiit aanniqtanga | The dog hurt your teacher |\n|11 | Ukiakhaqtutit | You fell |\n|12 | Angunahukti nanurmik qukiqsijuq | The hunter shot a polar bear |\n\n---\n\n**Step 2: Break down verb forms**\n\nMany verbs are built with:\n\n- A **stems** (action)\n- A **suffix** indicating **aspect** or **voice**\n- **Possessive markers** (your, my, their, etc.)\n- **Object** particles or possessive chains\n\nLook at verb structure in terms of **subject + verb + object** construction.\n\nWe see the following verbs and their patterns:\n\n- **takujanga** → \"saw\" \n → \"takujaatit\" = \"saw you\" → \"takujanga\" = \"saw [someone]\" \n → In (1): *Qingmivit takujaatit* → \"Your dog saw you\" \n → So *takujanga* is base verb for \"saw\" → \"saw [someone]\"\n\n- **qukiqtanga** → \"shot\" \n → “The boy shot the doctor” → *inuuhuktuup iluaqhaiji qukiqtanga* \n → *qukiqtanga* = \"shot\" → crate + object \n → *iqukiqtanga* → \"shot\" \n → *qukiqsijuq* in (12) = \"shot a polar bear\"\n\n- **aarqisijuq** → \"cured\" \n → (4) “The doctor cured you” → *iluaqhaijiup aarqijaatit* → \"cured you\" \n → *aarqijaatit* → \"cured you\" \n → *aarqisijuq* in (6) = \"cured a doctor\"\n\n- **iputujait** → \"speared\" \n → (5) \"You speared the dog\" → *Qingmiq iputujait* \n → (9) \"The hunter speared the wolf\" → *Angunahuktiup amaruq iputujanga* \n → *iputujanga* = \"speared [someone]\"\n\n- **aanniqtanga** → \"hurt\" \n → (3) \"You hurt yourself\" → *aanniqtutit* → \"hurt\" (with reflexive) \n → (10) \"The dog hurt your teacher\" → *ilinniaqtitsijiit aanniqtanga* \n → *aanniqtanga* = \"hurt\"\n\n- **qaijuq** → \"came\" \n → (7) *Nanuq qaijuq* → \"The polar bear came\" \n → so *qaijuq* = \"came\"\n\n- **ukiakhaqtutit** → \"fell\" \n → (11) *Ukiakhaqtutit* → \"You fell\" \n → this reflexive/autonomous action\n\n---\n\n**Step 3: Identify affix patterns and possessive markers**\n\nCommon markers:\n\n- **-it** = 3rd person singular verb (past) \n → *takujait* → \"saw\" (subject + verb) \n → *aanniqtutit* → \"you hurt yourself\"\n\n- Possessive markers:\n - *your* = *inuuhuktu* / *iluaqhaiji* (boy/doctor) → likely *inuuhuktuit* → \"your boy\"\n\n- The phrase *inuuhuktuit* means \"your boy\"\n- *iluaqhaijivit* → \"your doctor\" → \"iluaqhaiji\" + *-vit* = possessive\n\n- *aanniqtanga* → \"hurt\" → used with object or reflexive\n\n- Object structure: usually noun + verb suffix\n- Verb stem + object marker suffix (like -a, -it, -anga)\n\nLet’s find minimal pairs to see patterns.\n\nCompare:\n\n- 1: Qingmivit takujaatit → \"Your dog saw you\" \n → Base: *Qingmivit* (your dog), *takujatit* → \"saw you\"\n\n- 9: Angunahuktiup amaruq iputujanga → \"The hunter speared the wolf\" \n → *Angunahuktiup* → \"The hunter\", *amaruq* → \"the wolf\", *iputujanga* → \"speared\"\n\nSo: \n**Subject + Object + Verb (with object-linked suffix)**\n\nBut in (1): Subject + Verb (with object)\n\nIn (4): *Iluaqhaijiup aarqijaatit* → \"The doctor cured you\" → Object is \"you\" → no separate noun\n\nSo object can be marked directly in verb.\n\nWait: \n- *takujanga* = \"saw\" \n- *iputujanga* = \"speared\" \n- *aarqisijuq* = \"cured\"\n\nSame pattern: verb stems with object-marking suffix.\n\nNow check object markers:\n\n- *takujanga* → saw [someone]? \n- *qukiqtanga* → shot [someone]? \n- *aarqisijuq* → cured [someone]? \n→ All have similar structure.\n\nAlso, in (8): *Iluaqhaijivit inuuhuktuit aarqijanga* → \"Your doctor cured your boy\" \n→ *iluaqhaijivit* = your doctor \n→ *inuuhuktuit* = your boy \n→ *aarqijanga* = cured\n\nSimilarly, in (10): *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" \n→ *Qingmiup* = the dog \n→ *ilinniaqtitsijiit* = your teacher \n→ *aanniqtanga* = hurt\n\nSo pattern: \n**[Subject] + [Object with possessive] + [Verb base]**\n\nBut verb itself contains the object marking.\n\nBut look at (9): *Angunahuktiup amaruq iputujanga* → \"The hunter speared the wolf\" \nNo possessive in object → object is \"the wolf\" → *amaruq*\n\nSo object can be noun phrase.\n\nNow, we have named stems:\n\n- *takuj* → saw \n- *qukiq* → shot \n- *aarqi* → cured \n- *iputuj* → speared \n- *aanniqt* → hurt \n- *qaiju* → came \n- *ukiakhaq* → fell\n\nNow, affixes:\n\n- *-vit* = possessive (your) → attaches to nouns \n → *inuuhuktuit* = your boy \n → *iluaqhaijivit* = your doctor \n → *ilinniaqtitsijiit* = your teacher (note: \"ilinniaqtitsijiit\" — seems like \"your teacher\", built from \"ilinniaqtitsiji\" + -it? Probably)\n\n- *-up* = marker for an agent (possibly plural or topic)? \n → (2): *Inuuhuktuup* → \"The boy\" — not possessive. \n → (9): *Angunahuktiup* → \"the hunter\" \n → (12): *Angunahukti nanurmik qukiqsijuq* → \"The hunter shot a polar bear\" \n → so *Angunahukti* = hunter, *up* may be applicative or topic marker\n\n→ Appears that *-up* marks the subject as a nominal phrase, perhaps in active voice.\n\nBut in (2), *Inuuhuktuup iluaqhaiji qukiqtanga* → \"The boy shot the doctor\" \n→ *Inuuhuktuup* = \"the boy\" → subject \n→ *iluaqhaiji* = doctor → object \n→ *qukiqtanga* = shot\n\nSo subject is marked with *-up* → agent\n\nBut in (1): *Qingmivit* → not *-up* → \"your dog\" → not marked as \"the dog\"?\n\nIs *-up* used for definite or topicalized subject?\n\nCompare:\n\n- (7): *Nanuq qaijuq* → \"The polar bear came\" → *Nanuq* → has no *-up* \n- (11): *Ukiakhaqtutit* → \"You fell\" → no subject with *-up*\n\n→ So *-up* may appear only when the subject is not possessed or is a formal agent.\n\nBut in (1), *Qingmivit* → \"your dog\" → not possessive — this seems a direct noun.\n\nBut *Your dog* vs. *The boy* — both are agents.\n\nNow, witness minimal pairs:\n\n**13. Amaruup angatkuit takujanga**\n\nBreak down:\n- *Amaruup* → likely \"the wolf\" or \"a wolf\" → matches (9) *amaruq* (wolf) → \"the wolf\" with *up*\n- *angatkuit* → verb stem? → *angatkuq* (in 6) → \"cured\" → so *angatkuit* = \"cured you\"?\n- But *takujanga* → \"saw\"\n\nSo \"the wolf cured you\"? \nBut *angatkuit* — is this *angatkuq* with *-it*?\n\nLook at (6): *Angatkuq iluaqhaijimik aarqisijuq* → \"The shaman cured a doctor\" \n→ *Angatkuq* = verb \"cured\" \n→ *iluaqhaijimik* = a doctor → object \n→ *aarqisijuq* = \"cured\" (object marked)\n\nSo verb stem + object marking\n\nNow *angatkuit* → if *angatkuq* is \"cured\", then *angatkuit* could be \"cured you\" or \"cured [someone]\"\n\nSimilarly, in (4): *iluaqhaijiup aarqijaatit* → \"cured you\" \n→ so *aarqijaatit* = cured you\n\nSo *aarqijaatit* = cured you → verb with object\n\nTherefore, in 13: *angatkuit takujanga* → *angatkuit* = cured? — but *takujanga* = saw\n\nSo does it mean \"The wolf saw you\"?\n\nBut *angatkuit* → likely verb stem, not object.\n\nWait — compare (1): *Qingmivit takujaatit* → \"your dog saw you\" → subject + verb + object\n\nSo in 13: *Amaruup* = subject \n→ *angatkuit* = ??? \nBut *angatkuit* is not a known verb in our dictionary.\n\nWe have:\n- *angatkuq* → cured \n- *angunahukti* → hunter\n\nSo where does *angatkuit* come from?\n\nCould it be a verb with a different meaning?\n\nCheck (14): *Nanuit inuuhukturmik aanniqsijuq*\n\n- *Nanuit* → \"the polar bear\" (from 7: *Nanuq qaijuq*) → likely *nanuit* is the polar bear (with *-it*?) \n- *inuuhukturmik* → \"your boy's\" or \"your boy\"? \n → (8): *inuuhuktuit* = your boy → so *inuuhukturmik* = “your boy's” or “your boy”? \n → *-mik* may be possessive (genitive or possessive) \n → *inuuhuktu* = boy → *inuuhukturmik* = a boy’s something? \n → *aanniqsijuq* = hurt? — *aanniqtanga* = hurt → *aanniqsijuq* = “hurt [someone]”\n\nSo likely *aanniqsijuq* = \"hurt a boy\"\n\nBut in (3): \"You hurt yourself\" → *aanniqtutit* → so *aanniqt* stem\n\n→ so *aanniqsijuq* = hurt [someone] — object\n\nThus: *Nanuit inuuhukturmik aanniqsijuq* → \"The polar bear hurt your boy\"\n\nSimilarly:\n\n(15): *Angunahuktiit aarqijuq*\n\n- *Angunahuktiit* → \"your hunter\" or \"the hunter\"? \n → (9): *Angunahuktiup* → hunter → so *-it* = possessive = \"your hunter\"? \n → *aarqijuq* → \"cured\" → *aarqi* stem\n\n→ So “your hunter cured” — but what?\n\n→ *aarqijuq* = cured\n\n→ So “your hunter cured” — what? → likely \"cured you\", but no object.\n\nWait — is there an implied object?\n\nCompare (4): \"The doctor cured you\" — object \"you\"\n\nBut here it's just *aarqijuq* → without object.\n\nSimilarly, (8): \"Your doctor cured your boy\" — object is specified: \"your boy\"\n\nSo in (15): *Angunahuktiit aarqijuq* → without object → likely means \"your hunter cured you\"\n\nBecause in (4): *iluaqhaijiup aarqijaatit* → doctor cured you → object \"you\"\n\nSo probably all these verbs with no object = \"cured you\" (if that’s the default)\n\nBut need confirmation.\n\n(16): *Ilinniaqtitsiji qukiqtait*\n\n- *Ilinniaqtitsiji* → \"your teacher\" (from (10): \"the dog hurt your teacher\") \n- *qukiqtait* → \"shot\" → verb stem\n\n→ so \"your teacher shot\" — who?\n\n→ object missing → likely implies \"shot someone\" — but verb is \"qukiqtait\" → shot\n\nBut in (2): \"The boy shot the doctor\" → subject + object + verb\n\nHere: subject is \"your teacher\", verb is \"qukiqtait\" → so likely \"your teacher shot [someone]\"\n\nBut object is missing — so default object?\n\nNo — in all cases, object comes before verb? Or after?\n\nLook at (2): \"The boy shot the doctor\" → subject-verb-object → *Inuuhuktuup iluaqhaiji qukiqtanga*\n\n→ So SVO\n\nSimilarly, (1): *Qingmivit takujaatit* → subject-verb-object\n\n(9): *Angunahuktiup amaruq iputujanga* → SVO\n\nSo pattern: Subject + Object + Verb\n\nWait — no: (4): *Iluaqhaijiup aarqijaatit* → \"The doctor cured you\" → object (you) comes after verb?\n\nWait — no: *iluaqhaijiup* = subject, *aarqijaatit* = verb with object\n\nSo structure: \nSubject (noun phrase) + Verb (base with object marking)\n\nIn (2): *Inuuhuktuup iluaqhaiji qukiqtanga* → subject + object + verb \n→ So object appears between subject and verb\n\nSimilarly, (1): *Qingmivit takujaatit* → very similar → subject + verb + object?\n\nBut *Qingmivit* is \"your dog\", then *takujaatit* = \"saw you\" → so object \"you\" is part of verb?\n\nYes — in (1): *takujaatit* = saw you → verb includes object\n\nIn (4): *aarqijaatit* = cured you → verb includes object\n\nIn (10): *ilinniaqtitsijiit aanniqtanga* → \"your teacher\" + \"hurt\" → *aanniqtanga* = hurt → so *aanniqtanga* alone = hurt [someone]?\n\nBut in (10), \"your teacher\" is subject, then object (teacher?) — no, the sentence is \"The dog hurt your teacher\" → so actually: the dog is subject, the teacher is object, verb \"hurt\"\n\nBut in (10): *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" → subject (dog) + object (your teacher) + verb (hurt)\n\nSo structure: subject + object + verb → S-O-V\n\nSimilarly, (2): \"The boy shot the doctor\" → S-O-V\n\n(9): \"The hunter speared the wolf\" → S-O-V\n\nSo yes — structure is **Subject + Object + Verb**\n\nIn verb, object is marked with suffix.\n\nBut in (1): \"Your dog saw you\" → *Qingmivit takujaatit* → subject then verb, with object embedded.\n\nSo verb form includes object.\n\nBut in sentences like (9): *Angunahuktiup amaruq iputuj", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11590.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 2, + "output": "Analyze the given Inuktitut sentences and their English translations to infer the morphological and syntactic patterns, focusing on verb stems, affixes, subjects, objects, and aspect.\n\nFirst, build a morphological alignment table.\n\nSentence 1: Qingmivit takujaatit → Your dog saw you \n- \"Qingmivit\" = your dog (possessive + noun stem) \n- \"takujaatit\" = saw (verb + past tense affix -it) \n→ Subject: \"your dog\" → \"Qingmi\" + possessive \"your\" + plural/possessive suffix \n\nSentence 2: Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor \n- \"Inuuhuktuup\" = the boy (subject) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (verb) \n→ \"qukiqtanga\" is verb \"qukiq-\" (to shoot) + past tense -ta + -nga (his/their) → but object is marked with \"-ji\" → object marking in verb? \nBut in 1: \"takujaatit\" — \"takuj\" (see) + \"a\" (with object) + \"a\" (past tense), so verb takes object marker?\n\nWait in 1: \"takujaatit\" \n\"takuj-\" (see) + \"a\" (object) + \"a\" (past tense)? But \"a\" appears in both \"takuj aat\" and \"takuj aatit\" — probably \"a\" is object marker.\n\nBut in 1: \"Qingmivit takujaatit\" — subject (your dog) + verb (saw you)\n\nIn 4: \"Iluaqhaijiup aarqijaatit\" → the doctor cured you \n→ \"aarqijaatit\" — \"aarqij-\" (cure) + \"a\" (object) + \"it\" (past)? \n\"aarqijaatit\" = cured you → object \"you\" → \"a\" + \"t\" (past)\n\nIn 5: \"Qingmiq iputujait\" → you speared the dog \n\"putuj\" = spear, \"ait\" = past tense → so \"iputujait\" = speared (past tense, no object marker?) \nBut 3: \"Aanniqtutit\" → you hurt yourself → verb + reflexive \n\"anniqt\" = hurt, \"ut\" = past → \"aanniqtutit\" → reflexive?\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n\"ilinniaqtitsijiit\" = hurt? \n\"ilinniaq\" = hurt → \"itsijiit\" = with object (your teacher)? \nPossibly the verb takes object with a possessive affix?\n\nNotice: \n- Word \"takuj\" appears in 1 and 4: \"takuj\" + object marker + past \n- \"aarqij\" appears in 4 and 6: \"aarqij\" + object marker + past \n- \"iputuj\" in 5 and 9: \"iputuj\" + past → 5: \"iputujait\" \n- \"qukiq\" in 2 and 12: 2: \"qukiqtanga\", 12: \"Angunahukti nanurmik qukiqsijuq\" → \"qukiqsijuq\" = shot\n\nNow, look at possessive markers:\n\nSentence 1: \"Qingmivit\" — \"Qingmi\" (dog) + \"v\" (your) → i.e., \"Qingmivit\" = your dog \nSentence 3: \"Aanniqtutit\" — \"you hurt yourself\" → \"aanniqtutit\" — \"a\" + \"anniqt\" → first person? \n\"Aanniqtutit\" → \"a\" (subject) + \"anniqt\" (hurt) + \"ut\" (past) + \"t\" (reflexive)? → \"a\" may be 1st person, and \"t\" in \"ut\" = past → reflect?\n\nSimilarly, 11: \"Ukiakhaqtutit\" → you fell → \"ukiakhaq\" + \"ut\" → verb + past \nSo \"ut\" = past tense\n\nNow, look at object marking:\n\nIn 1: \"takujaatit\" → \"takuj\" + \"a\" + \"a\" + \"it\"? \n\"takuj\" (see) + \"a\" (object) + \"a\" (1st person?) → no, \"takujaatit\" → you = object? \nBut \"Qingmivit takujaatit\" → your dog saw you → so object is \"you\"\n\nSo \"takuj\" + object marker \"a\" + past \"it\" → \"takujaatit\"\n\nSimilarly, in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → \"aarqijaatit\" → \"aarqij\" (cure) + \"a\" (object) + \"it\"\n\nIn 5: \"Qingmiq iputujait\" — no external object marker → \"iputujait\" = you speared the dog → object marked as \"the dog\" in noun phrase?\n\n\"Qingmiq\" = the dog (possessive form?) — \"Qingmi\" + \"q\" = \"dog\" in this context?\n\nPossibly the object is in noun phrase → verb with past tense only.\n\nIn 9: \"Angunahuktiup amaruq iputujanga\" → the hunter speared the wolf \n\"iputujanga\" → \"iputuj\" (spear) + \"a\" + \"nga\" → \"a\" (object) + \"nga\" (past)? \n\"anga\" → past? → \"iputujanga\" = spear(ed) the wolf → object marked with \"a\", and past tense?\n\nCompare: \n- \"takujaatit\" → verb root + object marker \"a\" + past \"it\" \n- \"aarqijaatit\" → same \n- \"iputujait\" → no object marker → must be object in noun phrase \n- \"iputujanga\" → \"a\" + \"nga\" → object marker, different past suffix?\n\nWait — compare 5 and 9:\n\n5: \"Qingmiq iputujait\" → \"putujait\" → \"a\" not present → object is \"the dog\" in noun phrase \n9: \"Angunahuktiup amaruq iputujanga\" → \"iputujanga\" → has \"a\" → object is \"the wolf\"\n\nSo object is marked in verb with affix \"a\" only if not in noun phrase?\n\nBut in 4: \"iluaqhaijiup aarqijaatit\" → object \"the doctor\" is in noun phrase, verb takes \"a\" \n→ verb has object marker \"a\" regardless?\n\nNo — in 4: \"iluaqhaijiup\" = the doctor (object) → noun phrase → verb is \"aarqijaatit\" → has \"a\" → so verb includes object marker?\n\nBut in 5: \"Qingmiq iputujait\" → no \"a\" → object not marked in verb → object is \"the dog\" which is in noun phrase?\n\nSo the verb root is marked with object suffix only when the object appears in the verb? Unlikely.\n\nAlternatively, perhaps \"a\" is a general object marker, attached to verb.\n\nIn 4: \"aarqijaatit\" → object \"you\" — marked with \"a\"? \nBut \"iluaqhaiji\" → the doctor → object → so why is there \"a\" in verb?\n\nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"qukiqtanga\" → no \"a\" → object is \"doctor\", so no object marker in verb?\n\nBut in 4: \"aarqijaatit\" → \"a\" present → \"iluaqhaijiup\" is object → same structure as 2?\n\nContradiction.\n\nWait: in 2: \"qukiqtanga\" → so verb has no object marker \nIn 4: \"aarqijaatit\" → has \"a\" → \"a\" appears in verb\n\nBut in 2: object is \"iluaqhaiji\" → marked with \"-ji\" → so object marker in noun? \nIn 4: \"iluaqhaijiup\" — \"up\" is poss? \"iluaqhaijiup\" = \"the doctor\" → same?\n\nBut in 4: verb \"aarqijaatit\" → has \"a\"\n\nSimilarly, in 1: \"takuj aatit\" → verb has \"a\" → object \"you\"\n\nIn 5: no \"a\" → verb = \"iputujait\"\n\nSo only when the object is in the object position of a clause, it may be marked in verb via \"a\"?\n\nPossibly, there is an object affix \"a\" in the verb, and the object is directly marked only in some cases.\n\nBut in 3: \"Aanniqtutit\" → no object — reflexive? \n\"anniqtut\" → hurt → \"tut\" = past → reflexive? \nLanguage has reflexive used when subject and object are same.\n\nNow, look at possessive prefixes:\n\n1. Qingmivit → \"v\" = your → 2nd person possessive? \n3. \"Aanniqtutit\" → \"a\" = subject → 1st person \n5. \"Qingmiq\" → \"q\" = the dog? → 'q' = definite article? \n6. \"Angatkuq iluaqhaijimik aarqisijuq\" → \"iluaqhaijimik\" → \"mik\" → object marker? → \"mik\" = object → \"iluaqhaijimik\" = the doctor (object) → verb \"aarqisijuq\" = cured\n\n\"aarqisijuq\" → \"aarqisij\" → cured + \"uq\" → past?\n\nIn 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → the shaman cured a doctor → so \"iluaqhaijimik\" is object → marked with \"mik\" → object suffix?\n\nBut in 4: \"iluaqhaijiup aarqijaatit\" → \"up\" not \"mik\" → but both have object?\n\nPossibly different object markers.\n\nCompare:\n\n- 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → object: \"iluaqhaiji\" → marked with \"ji\" \n- 4: \"iluaqhaijiup aarqijaatit\" → object: \"iluaqhaijiup\" → \"up\" — possessive? \n- 6: \"iluaqhaijimik\" → \"mik\" — object suffix \n- 9: \"angunahuktiup amaruq iputujanga\" → object: \"amaruq\" → marked with \"q\" → \"amaruq\" → \"q\" = possessive?\n\nWait: in 9: \"angunahuktiup amaruq iputujanga\" → \"amaruq\" = the wolf? \n\"amaruq\" → \"amar\" + \"uq\" → could be noun + definite?\n\nIn 5: \"Qingmiq iputujait\" → \"Qingmiq\" = the dog — definite article \"q\"\n\nSo \"q\" = definite article or poss?\n\nPossibly \"q\" and \"up\" and \"mik\" and \"ji\" are all markers for object or poss.\n\nBut in 1: \"Qingmivit\" → \"v\" → your → possessive \nIn 2: no possessive → \"Inuuhuktuup\" = the boy — \"tu\" + possessive?\n\n\"tu\" = the? → \"inuuhuktuup\" → \"inuuhuk\" + \"tu\" + \"up\"? \n\"tu\" = definite → \"up\" = possessive? \n\nIn 3: \"Aanniqtutit\" → \"a\" = subject → 1st person → possessive? \n\nIn 4: \"iluaqhaijiup\" → \"up\" → possessive → \"doctor\" — so \"iluaqhaijiup\" = your doctor?\n\nBut translation says \"the doctor cured you\" — not \"your doctor\"\n\nContradiction? \n\n\"iluaqhaijiup\" — \"iluaqhaiji\" = doctor + \"up\" = possessive? → your doctor? \nBut translation says \"the doctor cured you\"\n\nBut in 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n→ \"iluaqhaijivit\" = your doctor → \"vit\" = possessive? \n→ \"inuuhuktuit\" = your boy → \"uit\" = possessive?\n\nSo possessive form is marked by suffixes:\n\n- \"v\" → your (e.g. 1: Qingmivit) \n- \"up\" → your (e.g. 4 and 8) \n- \"uit\" → your → in 8: inuuhuktuit \n- \"mik\" → object (in 6) \n- \"ji\" → object (in 2) \n- \"q\" → definite article or object noun?\n\nBut in 4: \"iluaqhaijiup\" = your doctor? But translation says \"the doctor\" — unless \"up\" is just marker for the object?\n\nBut in 8: \"iluaqhaijivit\" = your doctor → so \"vit\" = possessive → confirms possessive markers.\n\nNow, verb morphology:\n\nAll verbs take a past tense suffix, and sometimes an object marker.\n\nNote:\n\n- 1: takujaatit → \"takuj\" + \"a\" + \"at\" + \"it\"? \n\"takuj aat it\" → object marker \"a\" → object is \"you\"\n\nIn 4: \"aarqijaatit\" → \"aarqij\" + \"a\" + \"at\" + \"it\" → object \"you\"\n\nIn 5: \"iputujait\" → no \"a\" → verb only has \"ait\"\n\nIn 9: \"iputujanga\" → \"a\" + \"nganga\"? → \"a\" object marker? \"iputujanga\" = speared the wolf → object marked\n\nIn 12: \"Angunahukti nanurmik qukiqsijuq\" → \"qukiqsijuq\" → \"qukiqsij\" + \"uq\"? → \"uq\" = past?\n\n\"qukiqsijuq\" = shot → \"qukiq\" base + \"sij\" (object?) + \"uq\" (past)\n\nBut in 2: \"qukiqtanga\" = shot → no object marker?\n\nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → object \"doctor\" — not marked in verb → verb has no \"a\" → only \"tanga\" = past?\n\nIn 9: \"iputujanga\" → has \"a\" → object marked\n\nIn 6: \"aarqisijuq\" → \"a\" in \"sijuq\"? \"sij\" → object? \"a\" → object?\n\nPossibly the object marker is always in the verb when object is present.\n\nBut in 2, object is present — no \"a\" in verb.\n\nIn 2: \"qukiqtanga\" — no \"a\"\n\nIn 5: \"iputujait\" — no \"a\" — object is \"the dog\" in noun phrase?\n\nIn 9: \"iputujanga\" — has \"a\" — object is \"the wolf\" in noun phrase?\n\nInconsistent.\n\nWait: sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n\"ilinniaqtitsijiit\" = hurt → verb \n\"aanniqtanga\" = hurt (past)? \n\"ilinniaqtitsijiit\" → \"ilinniaq\" + \"tsijiit\" → \"tsiji\" = object marker? \n\"tsiji\" → object → so object in verb?\n\nTranslated: \"the dog hurt your teacher\" — object is \"your teacher\"\n\nSo in 10: \"ilinniaqtitsijiit\" → verb with object marker \"tsiji\" → object \"your teacher\"\n\nSimilarly, in 4: \"aarqijaatit\" → \"a\" — object \"you\"\n\nIn 6: \"aarqisijuq\" → \"sijuq\" → \"sij\" — object marker?\n\nIn 9: \"iputujanga\" → \"a\" — object marker?\n\nSo object marker is attached to verb stem.\n\nTypes of object markers:\n\n- \"a\" — used in 1,4,8? \n- \"ji\" — used in 2 (iluaqhaiji) — but not in verb \n- \"mik\" — in 6: iluaqhaijimik → object \n- \"sij\" — in 6: aarqisijuq → \"sij\"? \n- \"tsiji\" — in 10: ilinniaqtitsijiit → \"tsiji\"\n\nSo different markers: \n- \"a\", \"mik\", \"sij\", \"tsiji\" serve as object markers in verb\n\nBut in 1: \"takujaatit\" → has \"a\" \nIn 4: \"aarqijaatit\" → \"a\" \nIn 6: \"aarqisijuq\" → likely has \"sij\" or \"ij\"? \n\"aarqisijuq\" → \"sij\" → object \nIn 10: \"ilinniaqtitsijiit\" → \"tsiji\" → object\n\nSo object marker type depends on verb root?\n\nNow, past tense suffixes:\n\n- \"it\" — 1,3,4,5,8 → \"it\" \n- \"nganga\" — 9 → \"anga\" \n- \"tanga\" — 2 → \"tanga\" \n- \"uq\" — 6,12 → \"uq\"\n\nSo differences in past tense suffix:\n\n- \"it\" — common \n- \"tanga\" — in ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10767.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "solver_checklist", + "sample_index": 3, + "output": "We are given a set of Inuktitut sentences with English translations. Our task is to translate six new sentences into English, based on identifying patterns in the provided examples.\n\nStep 1: Identify core verb patterns and their semantic roles.\n\nLook at the verbs and their inflections:\n\n- \"takujaatit\" → \"saw\" (1), \"takujanga\" → \"saw\" (13) → past tense, third person, object marked?\n- \"iluaqhaiji\" → \"shot\" (2), \"qukiqtanga\" → \"cured\" (4), \"qukiqsijuq\" → \"shot\" (12)\n- \"aanniqtanga\" → \"hurt\" (3,10), \"aanniqsijuq\" → \"hurt\" (14)\n- \"aarqijaatit\" → \"cured\" (4), \"aarqijanga\" → \"cured\" (8), \"aarqisijuq\" → (6), \"aarqisijutit\" → (18)\n- \"angatkuq\" → \"came\" (7), \"angatkuit\" → (13)\n- \"inuuhuktuup\" → \"boy\" (2), \"inuuhuktuit\" → \"boy\" (8), \"inuuhukturmik\" → \"boy\" (14)\n- \"nanuq\" → \"bear\" (7), \"nanurtik\" → \"bear\" (12), \"nanuit\" → (14)\n- \"qingmivit\" → \"dog saw\" (1), \"qingmiq\" → (5), \"qingmiup\" → (5)\n- \"iputujait\" → \"spear\" (5), \"iputujanga\" → (10), \"iputujanga\" → (9)\n\nAffixation patterns:\n\n- Subject + verb + object?\n- Conjugation with object marker in verb: often involves suffixes like -it, -anga, -janga, -sijuq\n\nExamine verb stems:\n\n| Stem | Meaning |\n|------|--------|\n| takujaat | to see |\n| iluaqhaij | to shoot |\n| aanniqt | to hurt |\n| aarqij | to cure |\n| angatkuq | to come |\n| inuuhuktu | boy |\n| qingmi | dog |\n| iputuj | to spear |\n| qaijuq | to fall |\n\nTense and aspect:\n\n- -it: past tense, marked on verb (S-v-ation)\n- -anga: past tense, often with object or person\n- -up: present or unmarked\n- -mik: genitive or nominalized\n- -it (ending) indicates past tense\n\nNow, look for minimal pairs:\n\nExample 1: Qingmivit takujaatit → \"Your dog saw you\"\n- Subject: Qingmivit (dog) → \"your dog\"\n- Verb: takujaatit → \"saw\"\n- Object: \"you\" → implied, but possibly marked?\n\nExample 4: Iluaqhaijiup aarqijaatit → \"The doctor cured you\"\n- Subject: Iluaqhaijiup (doctor)\n- Verb: aarqijaatit → \"cured\"\n- Object: \"you\"\n\nExample 5: Qingmiq iputujait → \"You speared the dog\"\n- \"You\" is subject → \"qingmiq\" → \"dog\" (but \"iputujait\" = \"spear\")\n- So \"You speared the dog\" → verb \"iputujait\" = \"spear\", object \"dog\"\n\nWait: \"qingmiq\" → “the dog”? But in (1), “qingmivit” = “your dog” → \"vit\" = possessive?\n\nPossessive markers:\n- -vit → \"your\"\n- -up → might be object or form of noun?\n\nWait: (1): Qingmivit takujaatit → \"Your dog saw you\"\n→ So \"qingmivit\" = \"your dog\"\n\nSo:\n- \"qingmi\" = dog\n- \"vit\" = your → possessive\n\nSimilarly:\n(5): Qingmiq iputujait → \"You speared the dog\"\n→ Perhaps \"qingmiq\" = \"the dog\"\n\nBut \"q\" instead of \"v\"? Why?\n\nPossibility: \"q\" = accusative or object marker?\n\nCheck (10): Qingmiup ilinniaqtitsijiit aanniqtanga → \"The dog hurt your teacher\"\n→ \"qingmiup\" → \"the dog\"?\n\n\"up\" might be a possessive or article?\n\nAlternatively, look at object markers.\n\nFrom (2): Inuuhuktuup iluaqhaiji qukiqtanga → \"The boy shot the doctor\"\n→ iluaqhaiji = doctor → object\n→ iluaqhaiji = doctor → must be a noun, but is it handled by suffix?\n\n(4): Iluaqhaijiup aarqijaatit → \"The doctor cured you\"\n→ \"iluaqhaijiup\" → \"the doctor\"\n\nSo \"up\" = definite article or nominalizer?\n\nSimilarly, (1): Qingmivit → \"your dog\"\n\nPossibility: all nouns have possessive or article suffix attached to stem.\n\nNow verb patterns:\n\n- \"takujanga\" in (13): Amaruup angatkuit takujanga\n→ \"Amaruup\" = \"the hunter\"? (since (9): Angunahukti nanurmik qukiqsijuq → the hunter shot a polar bear)\n\nSo:\n- \"Amaruup\" → likely means \"the hunter\"\n- \"angatkuit\" → \"came\" (from (7): Angatkuq → came)\n- \"takujanga\" → \"saw\"\n\nSo → \"The hunter came and saw\"\n\nBut is it \"came and saw\" or \"came and saw you\"?\n\nNo object here.\n\nWait: (13): Amaruup angatkuit takujanga → no object → likely \"the hunter came and saw\" (someone implied)\n\nBut in (1): \"your dog saw you\" — object is marked.\n\nBut here — no object — no marker.\n\nSo perhaps \"takujanga\" = saw (without an explicit object)\n\nSo → \"The hunter came and saw\"\n\nNow (14): Nanuit inuuhukturmik aanniqsijuq\n\nBreak down:\n- \"Nanuit\" = \"the polar bear\"\n- \"inuuhukturmik\" = \"boy\" (from (2) and (8))\n- \"aanniqsijuq\" = \"hurt\" (from (3) and (10))\n\nSo → \"The polar bear hurt your boy\"\n\n\"mik\" → definite or genitive?\n\n(12): Angunahukti nanurmik qukiqsijuq → \"The hunter shot a polar bear\"\n→ \"nanurmik\" = \"a polar bear\"? → uses \"mik\", which can be possessive or genitive?\n\nSimilarly, (6): Angatkuq iluaqhaijimik aarqisijuq → \"The shaman cured a doctor\"\n→ \"iluaqhaijimik\" = \"a doctor\"\n\nSo \"mik\" = \"a\" (definite article or indefinite)\n\nSo → \"a doctor\" → \"iluaqhaijimik\"\n\nSimilarly, \"inuuhukturmik\" = \"your boy\"\n\nSo → \"The polar bear hurt your boy\"\n\n(15): Angunahuktiit aarqijuq\n\n- \"Angunahuktiit\" → \"the hunter\" (pl.?), \"it\" = past tense\n- \"aarqijuq\" → \"cured\"\n\nSo → \"The hunter cured\"\n\nBut no object?\n\nWait — (8): Iluaqhaijivit inuuhuktuit aarqijanga → \"Your doctor cured your boy\"\n→ \"aarqijanga\" = cured\n\nSo \"aarqijaatit\" = cured → \"aarqij\" root\n\nSimilarly, (6): \"aarqisijuq\" = cured\n\nSo \"aarqijuq\" = cured?\n\nSo \"Angunahuktiit aarqijuq\" = \"The hunter cured\"\n\nBut with whom? No object — so likely the meaning is \"The hunter cured (someone)\" — but context may imply.\n\nBut no object — must be inferred from pattern.\n\nFrom (4): Iluaqhaijiup aarqijaatit → doctor cured you\n\nSo verbs with \"aarqi\" + suffix → cure\n\n(15): Angunahuktiit aarqijuq → \"The hunter cured [someone]\"\n\nBut what’s the object? It's missing — perhaps the object is implied.\n\nBut is there a general structure?\n\nWe have a pattern:\n\n[Subject] + [verb stem] + [object marked by possessive or suffix]\n\nLook at (16): Ilinniaqtitsiji qukiqtait\n\n- \"ilinniaqtitsiji\" → \"your teacher\" (from (10): Qingmiup ilinniaqtitsijiit aanniqtanga → \"The dog hurt your teacher\")\n→ \"ilinniaqtitsijiit\" → \"your teacher\"\n→ \"it\" = past tense → so \"ilinniaqtitsiji\" = \"your teacher\"\n\nBut \"qukiqtait\" → \"shot\" (from (2), (12))\n\nSo → \"Your teacher shot\"\n\nBut object missing?\n\n\"qukiqtait\" — from (12): Angunahukti nanurmik qukiqsijuq → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"shot a polar bear\"\n\nSo \"qukiqtait\" → \"shot\" — likely \"a [something]\"?\n\nBut no object.\n\nSo (16): Ilinniaqtitsiji qukiqtait → \"Your teacher shot\"\n\nLikely — \"shot\" someone — implied.\n\nBut what about (17): Qaijutit → \"You fell\"\n\n(11): Ukiakhaqtutit → \"You fell\"\n\nSo \"qaijutit\" = \"you fell\"\n\nSo → (17): Qaijutit → \"You fell\"\n\n(18): Angunahuktimik aarqisijutit\n\n- \"Angunahuktimik\" → \"the hunter\" + \"mik\" → likely \"a hunter\"? or \"the hunter\"\n- \"aarqisijutit\" → \"cured\" (from (6), (8))\n\n(6): Angatkuq iluaqhaijimik aarqisijuq → \"The shaman cured a doctor\" → \"aarqisijuq\" = cured\n\nSo \"aarqisijutit\" → past tense \"cured\"\n\nNo object → so → \"A hunter cured\" → (maybe a doctor?)\n\nBut no object — so must be \"a hunter cured (someone)\"\n\nBut probably just \"The hunter cured\"\n\nBut with object missing?\n\nWait — \"mik\" → indefinite article → \"a\"\n\nSo \"Angunahuktimik\" → \"a hunter\"?\n\nBut (9): Angunahukti nanurmik qukiqsijuq → \"The hunter shot a polar bear\" — \"the\"\n\nSo \"the\" is used.\n\nBut in (18): Angunahuktimik → possibly \"a hunter\"\n\nBut in context, likely just \"the hunter\", and \"mik\" may be a genitive or possessive.\n\nAlternatively, \"mik\" = \"a\"\n\nBut in (14): \"inuuhukturmik\" → \"your boy\" → with \"mik\" after possessive?\n\n\"mik\" is used with noun stems.\n\nBut (12): Angunahukti nanurmik qukiqsijuq → \"the hunter shot a polar bear\"\n\n→ \"nanurmik\" — \"a polar bear\"? Like \"a bear\"\n\nSo → \"mik\" indicates \"a\" (indefinite)\n\nSimilarly, \"inuuhukturmik\" = \"your boy\" — \"mik\" = \"a\" or possessive?\n\nWait — (8): Iluaqhaijivit inuuhuktuit aarqijanga → \"Your doctor cured your boy\" → so \"inuuhuktuit\" = \"your boy\"\n\nSo \"uit\" = possessive marker?\n\nPossessive markers:\n\n- \"vit\" = your (e.g., Qingmivit → \"your dog\")\n- \"uit\" = your? (e.g., inuuhuktuit → \"your boy\")\n- \"up\" = the? (e.g., iluaqhaijiup → \"the doctor\")\n\nSo:\n- Possessive: vit, uit, uit\n- Definite: up, (possible)\n- Indefinite: mik\n\nSo in (14): Nanuit inuuhukturmik aanniqsijuq → \"Nanuit\" = \"the polar bear\", \"inuuhukturmik\" = \"your boy\", \"aanniqsijuq\" = \"hurt\"\n\nSo → \"The polar bear hurt your boy\"\n\n(15): Angunahuktiit aarqijuq → \"The hunter cured\"\n\n(16): Ilinniaqtitsiji qukiqtait → \"Your teacher shot\"\n\n(17): Qaijutit → \"You fell\"\n\n(18): Angunahuktimik aarqisijutit → \"a hunter cured\"\n\nBut does \"a\" or \"the\" matter?\n\nIn (6): Angatkuq iluaqhaijimik aarqisijuq → \"The shaman cured a doctor\" → uses \"mik\" = \"a\"\n\nSo \"mik\" = \"a\"\n\nSimilarly, (18): Angunahuktimik → \"a hunter\"\n\n\"aarqisijutit\" → \"cured\" (past tense)\n\nBut no object — so likely \"a hunter cured\" — someone?\n\nBut in context, such sentences are often complete — object missing but implied or generic.\n\nBut let's go sentence by sentence:\n\n13. Amaruup angatkuit takujanga \n\"Amaruup\" = \"the hunter\" (from (9) Angunahukti nanurmik qukiqsijuq → \"the hunter shot a polar bear\")\n\"angatkuit\" = \"came\" (from (7) Angatkuq → came)\n\"takujanga\" = \"saw\" (from (1) takujaatit → saw)\n\nSo → \"The hunter came and saw\"\n\n(No object)\n\n14. Nanuit inuuhukturmik aanniqsijuq \n\"Nanuit\" = \"the polar bear\" \n\"inuuhukturmik\" → \"your boy\" \n\"aanniqsijuq\" → \"hurt\" \n→ \"The polar bear hurt your boy\"\n\n15. Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (past tense) \n\"aarqijuq\" → \"cured\" \n→ \"The hunter cured\"\n\n16. Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" → \"your teacher\" (from (10): Qingmiup ilinniaqtitsijiit aanniqtanga → \"the dog hurt your teacher\") \n\"qukiqtait\" → \"shot\" \n→ \"Your teacher shot\"\n\n17. Qaijutit \n\"Qaijutit\" → from (11) Ukiakhaqtutit → \"you fell\" \n→ \"You fell\"\n\n18. Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"a hunter\" (since \"mik\" = indefinite) \n\"aarqisijutit\" → \"cured\" \n→ \"A hunter cured\"\n\nBut is it \"a hunter cured\" or \"the hunter cured\"?\n\nIn (9): Angunahukti → \"the hunter\" \nIn (18): Angunahuktimik → with \"mik\" → likely \"a hunter\"\n\nIn (6): Angatkuq iluaqhaijimik aarqisijuq → \"the shaman cured a doctor\" → \"mik\" after noun, so \"a doctor\"\n\nSo \"mik\" = indefinite article \"a\"\n\nTherefore, \"Angunahuktimik\" = \"a hunter\"\n\n\"aarqisijutit\" = \"cured\"\n\n→ \"A hunter cured\"\n\nBut can \"a\" be omitted in such formulations? Probably not — the pattern requires it.\n\nFinal translations:\n\n13. The hunter came and saw \n14. The polar bear hurt your boy \n15. The hunter cured \n16. Your teacher shot \n17. You fell \n18. A hunter cured\n\nBut (15) — \"the hunter cured\" — is that complete?\n\nYes — in (8): Iluaqhaijivit inuuhuktuit aarqijanga → \"Your doctor cured your boy\" — so \"cured\" has object.\n\nBut here, no object — so likely generic.\n\nSimilarly, (18) → \"a hunter cured\" — no object — so allowed.\n\nSo we conclude:\n\na.1 / 13.: The hunter came and saw \na.2 / 14.: The polar bear hurt your boy \na.3 / 15.: The hunter cured \na.4 / 16.: Your teacher shot \na.5 / 17.: You fell \na.6 / 18.: A hunter cured\n\n\\boxed{a.1: The hunter came and saw; a.2: The polar bear hurt your boy; a.3: The hunter cured; a.4: Your teacher shot; a.5: You fell; a.6: A hunter cured}", + "generated_tokens": 3899, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: The hunter came and saw; a.2: The polar bear hurt your boy; a.3: The hunter cured; a.4: Your teacher shot; a.5: You fell; a.6: A hunter cured", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 10749.0, + "ioling_final_answer_chars": 146.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are to write out in Nahuatl the numbers 42 and 494, based on the given equations from Nahuatl and Arammba, using linguistic patterns derived from the provided examples.\n\nStep 1: Identify arithmetic patterns and components.\n\nWe look for known number decompositions and operations in the examples.\n\nFirst, from equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nThis appears to be a multiplication: \n\"mahtlactli-on-cë\" × \"mahtlactli\" → \"mäcuïl-pöhualli-om-mahtlactli\"\n\nLet’s assume:\n- \"mahtlactli\" = 20\n- \"mahtlactli-on-cë\" = 20 + 1 = 21 \n(“on-cë” may mean “plus one” or “with one”)\n\nThen: \n21 × 20 = 420 → but the result is \"mäcuïl-pöhualli-om-mahtlactli\"\n\nWait — but 21 × 20 = 420, not 42.\n\nBut 42 = 20 + 2. So we need a decomposition of 42 as 20 + 2.\n\nWe also see in equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nBreak this: \n\"yë-pöhualli-on-chicöme\" + \"mahtlactli-on-nähui\" = \"näuh-pöhualli-on-cë\"\n\nLet’s hypothesize that \"pöhualli\" is 20, \"cë\" is 1.\n\nFrom (4): mäcuïlli + öme = chicöme \nmäcuïlli + öme = chicöme\n\n\"mäcuïlli\" is likely 11 (known in Nahuatl: 11 = “mäcuïlli”) \n\"öme\" = 1 \nSo 11 + 1 = 12? But result is “chicöme” — a compound meaning “12”?\n\nAlternatively, is “öme” a number?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \n\"cem-pöhualli\" × \"öme\" = \"öm-pöhualli\"\n\nThis structure is unusual. Try if “cem-pöhualli” is 2 × 20 = 40, “öme” = 1 → result is “öm-pöhualli” — could be 40?\n\nBut “öm-pöhualli” = 40? Then “cem-pöhualli” = 40? No: if 40 × 1 = 40 → ok.\n\nBut “cem” likely means “2” (as in 20 is “pöhualli”), so “cem-pöhualli” = 20 + 20 = 40? That would make sense.\n\nSo: \n“cem-pöhualli” = 40 \n“öme” = 1 \n40 × 1 = 40 → output “öm-pöhualli” = 40 → consistent.\n\nSo multiplication: a × b = c.\n\nThus, “öme” = 1.\n\nAlso, from (4): mäcuïlli + öme = chicöme \nmäcuïlli = 11 → 11 + 1 = 12 → \"chicöme\" = 12\n\nSo: 11 + 1 = 12 \n12 = \"chicöme\"\n\nNow, back to equation (1): \n\"mahtlactli-on-cë\" × \"mahtlactli\" = mäcuïl-pöhualli-om-mahtlactli\n\nLet’s assume:\n- \"mahtlactli\" = 20\n- \"on-cë\" = +1 → so \"mahtlactli-on-cë\" = 21\n- 21 × 20 = 420\n\nRight-hand side: mäcuïl-pöhualli-om-mahtlactli\n\nWe know mäcuïlli = 11, so mäcuïl = 11? Or is it mäcuïl-pöhualli?\n\nPossibly \"mäcuïl-pöhualli\" = 11 × 20 = 220\n\nThen \"mäcuïl-pöhualli-om-mahtlactli\" = 220 + 20 = 240? But 21×20=420 — mismatch.\n\nAlternative: is there a structure for 42?\n\nWe are to write 42 and 494.\n\nTry equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may be a number composed of a base and additions.\n\nBut without direct anchor, we may rely on known bases.\n\nFrom Arammba, equation (10): \nyenówe × yenówe tàxwo = fete yenówe tàxwo\n\n\"yenówe\" × \"yenówe tàxwo\" = \"fete yenówe tàxwo\"\n\n\"tàxwo\" may mean \"plus\" or \"with\" — like adding to a total.\n\nSo: a × (a + something) = result.\n\nPossibly \"yenówe\" = 2 → 2 × (2 + x) = fete 2 + x?\n\nBut result is “fete yenówe tàxwo” → may mean 2 + x?\n\nNot clear.\n\nBut note equation (12): \nnimbo + yànparo tàxwo = yenówe tàxwo \n\"nimbo\" + \"yànparo\" + \"tàxwo\" → \"yenówe tàxwo\"\n\nSo again, \"yànparo tàxwo\" may mean \"yànparo + one\" or \"yànparo + something\"\n\nEquation (11): nimbo × fete = tarumba \nnimbo × fete = tarumba \nCould be multiplication.\n\nBack to Nahuatl.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n\"mahtlactli-om-ëyi\" = 20 + x? \"om\" may mean \"plus\"\n\n\"ëyi\" = some number\n\nLeft: (20 + x) × y = result\n\nRight: cem-pöhualli-on-caxtölli-on-nähui\n\n“cem-pöhualli” = 40 (2×20) \nSo “cem-pöhualli-on-caxtölli-on-nähui” = 40 + ? + ?\n\nPossibly “on-caxtölli” = 10, “on-nähui” = 1\n\nSo this result = 40 + 10 + 1 = 51?\n\nThen (20 + x) × y = 51\n\nPossible: if (20 + x) = 17, y = 3 → 17×3 = 51\n\nBut 17×3 = 51 — possible.\n\nBut not helping much.\n\nFrom equation (6): mäcuïlli × ëyi = caxtölli \nmäcuïlli = 11 → 11 × ëyi = caxtölli\n\nSo caxtölli = 11 × ëyi\n\nIf ëyi = 1 → 11, so caxtölli = 11?\n\nBut “caxtölli” may be 11.\n\nThen in (5): (20 + x) × y = 40 + 10 + 1 = 51\n\nIf y = 3 → ëyi = 3 → caxtölli = 33\n\nSo \"caxtölli\" = 33?\n\nPossibly.\n\nNow, back to (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nTry to assign:\n- \"mahtlactli\" = 20\n- \"on-cë\" = +1 → so left = 21 × 20 = 420\n\nRight: mäcuïl-pöhualli-om-mahtlactli \nBreak as: “mäcuïl-pöhualli” + “om” + “mahtlactli”\n\nIf “mäcuïl-pöhualli” = 11 × 20 = 220 \nThen +20 → 240 — still not 420.\n\nAlternative: maybe “mäcuïl-pöhualli” = 220? No.\n\nWait — could multiplication be of numbers like 2×21?\n\nWhat if the structure is: (a) × (b) = (a×b)\n\nWe need to see if there's a known number for 42.\n\nLook at equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n\"yë-tzontli\" — may be 10 or 11?\n\n\"tzontli\" = 10? Known in some traditions.\n\n\"on-pöhualli\" = 20?\n\n\"on-caxtölli\" = 10?\n\n\"on-cë\" = 1?\n\nSo: 10 + (20 + 10 + 1) = 41?\n\nThen equals \"ndamno\" — which may be 42?\n\nPossibly.\n\nSo: \n\"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\" = 10 + 20 + 10 + 1 = 41\n\nBut result is \"ndamno\" = 42?\n\nClose.\n\nAlternatively, could \"yë-tzontli\" = 11?\n\nThen 11 + 20 + 10 + 1 = 42 → yes!\n\nSo 11 + 20 + 10 + 1 = 42.\n\nTherefore, \"yë-tzontli\" = 11 \n\"pöhualli\" = 20 \n\"caxtölli\" = 10 \n\"on-cë\" = 1\n\nSo each additive component is a known number:\n\n- 11 = yë-tzontli \n- 20 = pöhualli \n- 10 = caxtölli \n- 1 = cë\n\nThus, 42 = yë-tzontli + pöhualli + caxtölli + cë\n\nNow, in expression: \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n“on” likely means \"plus\" or \"added to\"\n\nSo \"A-on-B\" = A + B?\n\nBut “on” seems to attach to number.\n\nSo \"yë-tzontli-on-näuh-pöhualli\" = yë-tzontli + pöhualli \nThen + caxtölli → then + cë\n\nSo the structure is additive: a + b + c + d\n\nSo 42 = 11 + 20 + 10 + 1\n\nNow, for the number 494.\n\nWe need to decompose 494.\n\n494 = 400 + 90 + 4\n\nOr, better: 400 = 4 × 100 → but no 100?\n\nIn Nahuatl, numbers are often based on 20.\n\n20 × 20 = 400 \n20 × 20 = 400 \nThen 90 = 4 × 20 + 10 \n4 × 20 = 80 → 80 + 10 = 90 \nThen 4 = 1 × 4? Not clear.\n\nBut known structure:\n\n\"pöhualli\" = 20 \n\"tzontli\" = 10 \n\"näuh\" = 1?\n\nBut in (13), 11 + 20 + 10 + 1 = 42\n\nSo is 42 = yë-tzontli + pöhualli + caxtölli + cë\n\nWith:\n- yë-tzontli = 11\n- pöhualli = 20\n- caxtölli = 10\n- cë = 1\n\nSo general additive composition.\n\nNow, 494:\n\nFirst, break 494 in base 20.\n\n494 ÷ 20 = 24.7 → 24 × 20 = 480 \n494 - 480 = 14\n\nSo 494 = 24 × 20 + 14\n\nNow, 24 = 1 × 20 + 4 → but better: 24 = 20 + 4\n\nSo 494 = (20 + 4) × 20 + 14\n\n= 20×20 + 4×20 + 14\n\n= 400 + 80 + 14 \n80 = 4×20 \n14 = 10 + 4\n\nNow, we can build this with known morphemes.\n\nWe have:\n- \"pöhualli\" = 20\n- \"tzontli\" = 10 (assumed from prior pattern)\n- \"cë\" = 1\n- \"caxtölli\" = 10\n- \"yë-tzontli\" = 11\n\nWe need to build 494 = 400 + 80 + 14\n\n= (20 × 20) + (4 × 20) + (10 + 4)\n\nNow, in Nahuatl, “mahtlactli” = 20 → likely “pöhualli” used in multiple bases.\n\nAlso, from equation (2): cem-pöhualli × öme = öm-pöhualli \n\"cem-pöhualli\" = 40 → 2×20 \nSo multiplication by 1 → result 40 → so \"öme\" = 1\n\nSo, multiplication of numbers using known components.\n\nHow to write 20 × 20?\n\nWe know in (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nNot matching.\n\nBut perhaps \"mahtlactli\" × \"mahtlactli\" = something?\n\nNot given.\n\nBut we know that multiplication of a number by 20 may be expressed via a compound.\n\nFrom (6): mäcuïlli × ëyi = caxtölli \n\"mäcuïlli\" = 11 → 11 × x = caxtölli\n\nWe don’t know x.\n\nBut from (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe earlier tried to assign.\n\nBut crucially, from (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n\"cen-tzontli\" = 100? (as in “cen” = 100, “tzontli” = 10)\n\nPossibly:\n\n“cen” = 100 \n“tzontli” = 10 \n“cem-pöhualli” = 40 \n“mahtlactli” = 20 \n“öme” = 1\n\nSo: 100 + 10 + 40 + 20 + 1 = 171\n\nBut result is \"yànparo tarumba\"\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo \"cen-tzontli\" = 100 + 10 = 110 → equals \"tarumba tambaroy fete asàr\"\n\nSo “tarumba” = 110?\n\nBut from (11): nimbo × fete = tarumba → so if \"nimbo\" = 10, \"fete\" = 11 → 110?\n\nThen \"nimbo\" = 10, \"fete\" = 11 → so \"tarumba\" = 110\n\nSo \"cen-tzontli\" = 110 → consistent\n\nTherefore:\n\n- cen = 100 \n- tzontli = 10 \n- pöhualli = 20 \n- cë = 1 \n- caxtölli = 10 \n- öme = 1 \n- mäcuïlli = 11 \n- yë-tzontli = 11\n\nThus, in (13): yë-tzontli + pöhualli + caxtölli + cë = 11 + 20 + 10 + 1 = 42 → matches\n\nSo now, for 494:\n\n494 = 400 + 80 + 14\n\n= 20 × 20 + 4 × 20 + 14\n\n= 20 × 20 + 4 × 20 + 10 + 4\n\nNow, how to write:\n\n- 20 × 20: need a compound \n- 4 × 20: 4 × 20 \n- 10: tzontli \n- 4: ? → 4 = 10 - 6? No — we have no 4\n\nBut 4 = 11 - 7? Not direct.\n\nWe have \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8529.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 42 and 494 in Nahuatl, based on the patterns observed.\n\nStep 1: Analyze the Nahuatl equations to extract number system patterns.\n\nLook at the equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) gives a result involving \"mäcuïl-pöhualli-om-mahtlactli\"\n\n(2) cem-pöhualli × öme = öm-pöhualli \n→ (B × C) = D\n\n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ (E + F) = G\n\n(4) mäcuïlli + öme = chicöme \n→ (H + I) = J\n\n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (K × L) = M\n\n(6) mäcuïlli × ëyi = caxtölli \n→ (H × L) = N\n\nFocus on multiplicative and additive operations.\n\nFrom (4): mäcuïlli + öme = chicöme \n→ suggests that \"öme\" is a unit, \"mäcuïlli\" is a number, and \"chicöme\" is a derived value.\n\nFrom (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ \"mahtlactli\" appears in both terms and in result. But what is \"mahtlactli\"? Possibly a base unit.\n\nLet us assume that \"mahtlactli\" = 1. Then (1) says: \n(1 × 1) = mäcuïl-pöhualli-om-mahtlactli → that suggests that 1 × 1 = some compound.\n\nBut (1) is multiplication of two \"mahtlactli\", which may not be 1, but perhaps \"mahtlactli\" itself is a numeral. Let’s instead look at (4), which shows addition: \nmäcuïlli + öme = chicöme \n→ mäcuïlli + öme = chicöme\n\nThis resembles addition: if öme = 1, then mäcuïlli = chicöme – 1.\n\nSimilarly, (6): mäcuïlli × ëyi = caxtölli \n→ suggests that mäcuïlli × ëyi = caxtölli\n\nCompare to (2): cem-pöhualli × öme = öm-pöhualli \n→ if öme = 1, then cem-pöhualli × 1 = öm-pöhualli → so cem-pöhualli = öm-pöhualli → implies multiplication by 1 is identity.\n\nBut this seems inconsistent unless öme = 1.\n\nLet’s suppose that öme = 1.\n\nThen (4): mäcuïlli + 1 = chicöme → so mäcuïlli = chicöme – 1 \n→ so \"chicöme\" may be a number one more than mäcuïlli\n\nSimilarly, (6): mäcuïlli × ëyi = caxtölli \n→ a multiplication rule\n\nNow, look at equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (mahtlactli-om-ëyi) × ëyi = compound\n\nIf we assume that \"mahtlactli-om-ëyi\" is like (a × b), or perhaps a × (b), then result is a composite.\n\nWe see in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ addition of two terms.\n\nNow look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nNote that on-cë appears in (1), (3), (13). In (1), we had \"mahtlactli-on-cë\", so \"on-cë\" is part of a compound. In (3): \"näuh-pöhualli-on-cë\"\n\nAlso (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \nWe have \"cen-tzontli\" and other terms.\n\nBut big clue is in (15): \ncen-tzontli = tarumba tambaroy fete asàr \n\n→ so cen-tzontli = a compound of three items: tarumba, tambaroy, fete, asàr\n\nSimilarly (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSo “cen-” is a prefix, and attached to a numeral (tzontli, xiquipilli) gives a full number.\n\nNow, compare to (15): \n“cen-tzontli” = tarumba tambaroy fete asàr → so “tarumba” is part of the number.\n\nIn Arammba (11): nimbo × fete = tarumba \n→ so tarumba = nimbo × fete\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ implies (Y × Y) = F × Y → then Y × Y = F × Y → so Y = F → unless multiplicative identity, this suggests Y = F → so fete = yenówe?\n\nFrom (10): (yenówe) × (yenówe tàxwo) = fete (yenówe tàxwo) \n→ so (A × B) = C × B → implies A = C → so yenówe = fete\n\n→ So fete = yenówe\n\nThen (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + yànparo tàxwo = yenówe tàxwo\n\nFrom (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ yànparo tàxwo + fete-asàr tàxwo = yànparo fete \n→ suggests that “asàr” is a unit, and “tàxwo” may be a modifier.\n\nBut from (12): nimbo + yànparo tàxwo = yenówe tàxwo \nand fete = yenówe → so nimbo + yànparo tàxwo = fete tàxwo\n\n→ so nimbo + A = fete × A → only possible if nimbo = fete × A – A → nimbo = A (fete – 1)\n\nBut fete = yenówe → so nimbo = A (yenówe – 1)\n\nWhich suggests a form like “base × (unit – 1)”\n\nBut this is not necessary for the actual target.\n\nKey: In Nahuatl, numbers are formed via multiplication and addition of base units.\n\nFrom the Nahuatl equations:\n\n(4): mäcuïlli + öme = chicöme → likely means 1 × öme = 1 → so öme = 1\n\n(6): mäcuïlli × ëyi = caxtölli → so multiplication\n\n(1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli → a square\n\nNow, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nNote: “yë-tzontli” → likely a numeral, and “on” is a preposition.\n\nWe see \"on-cë\" in multiple forms — perhaps “cë” is 1 or a unit.\n\nAlso, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nBut from (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1, then cem-pöhualli = öm-pöhualli → so component units.\n\nNow observe: (14) has \"cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\"\n\nCompare expression in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nAnd in (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo “cen-tzontli” is a single number, broken into components.\n\nIn Arammba, “tarumba” = nimbo × fete (from 11)\n\nIn Nahuatl, “tarumba” appears in 15.\n\nAlso, in (13), we have a compound: yë-tzontli-on-... = ndamno\n\nPerhaps “tzontli” is a base numeral.\n\nTry to interpret 42.\n\n42 = 6 × 7 \nor 7 × 6 \nor 40 + 2 \nor 3 × 14, etc.\n\nIn Nahuatl, the number system may be base-20.\n\nNote: in many Nahuatl texts, numbers are expressed in vigesimal.\n\nWe see the word \"mahtlactli\" — known to be \"20\" in Nahuatl.\n\nIndeed, \"mahtlactli\" = 20.\n\nThen from (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ 20 × 20 = 400 → so result is 400\n\nBut what is \"mäcuïl-pöhualli-om-mahtlactli\"?\n\n\"pöhualli\" may be 1 or a unit, and \"om\" might mean \"of\".\n\nNote that in (4): mäcuïlli + öme = chicöme \nIf \"öme\" = 1, and \"mäcuïlli\" = 19 (since 19 + 1 = 20), then \"chicöme\" = 20.\n\nBut mäcuïlli → may be 19.\n\nIn fact, 19 is often called \"cicöme\" or similar.\n\nBut in (4): mäcuïlli + öme = chicöme → so if öme = 1, then mäcuïlli = chicöme – 1 → so chicöme = mäcuïlli + 1\n\nSo if mäcuïlli = 19, then chicöme = 20.\n\nSimilarly, mäcuïlli × ëyi = caxtölli \n→ if ëyi = 1, then caxtölli = 19\n\nBut if ëyi = 1 → then 19 × 1 = 19 → so caxtölli = 19\n\nNow look at (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n\"mahtlactli-om-ëyi\" → 20 – 1 = 19? Or 20 + (–1)? → possible as 19.\n\nThen 19 × 1 = 19 → so cem-pöhualli-on-caxtölli-on-nähui = 19\n\nSo perhaps \"cem-pöhualli\" is 1, \"caxtölli\" = 19, \"nähui\" = 1? But 1 × 19 = 19 → so may be 19.\n\nBut the product is 19 → so (19) × (1) = 19.\n\nThus, structure: (20 – 1) × 1 = 19\n\nNow, equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ (A + B) = C\n\n\"yë-pöhualli-on-chicöme\" → may be like 1 × (chicöme) → so if chicöme = 20, then 1 × 20 = 20\n\n\"mahtlactli-on-nähui\" → 20 × 1 = 20\n\nThen sum = 40? → right side: näuh-pöhualli-on-cë → perhaps 40?\n\nBut 20 + 20 = 40 → likely.\n\nThus, addition of two 20s gives 40.\n\nNow, what is 20? It is “mahtlactli”\n\nSo addition: mahtlactli + mahtlactli = 40\n\nSimilarly, multiplication: mahtlactli × mahtlactli = 400\n\nNow, what is 1? It is “öme”\n\nSo general system:\n\n- 1 = öme \n- 20 = mahtlactli \n- 19 = mäcuïlli (since mäcuïlli + 1 = 20)\n\nThus, numbers are built via:\n\n- addition: X + Y \n- multiplication: X × Y\n\nWe can now attempt to write 42.\n\n42 = 20 + 20 + 2 \nBut 2 = ? → if 2 is available.\n\nWe have \"öme\" = 1 → so perhaps we can build other numbers.\n\nFrom (6): mäcuïlli × ëyi = caxtölli → so 19 × ëyi = caxtölli\n\nIf ëyi = 1 → 19 × 1 = 19 → caxtölli = 19 \nIf ëyi = 2 → 19 × 2 = 38 → caxtölli = 38? \n\nBut in (3), we have addition: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “yë-pöhualli” is 1, “chicöme” = 20 → so 1 × 20 = 20\n\n“mahtlactli-on-nähui” = 20 × 1 = 20 → sum = 40\n\nSo 20 + 20 = 40\n\nNow, what about 2? Need a way to build 2.\n\nWe see in (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1 → then cem-pöhualli = öm-pöhualli → so 1 × 1 = 1 → consistent.\n\nBut no direct 2.\n\nFrom (4): mäcuïlli + öme = chicöme → 19 + 1 = 20\n\nSo only base units: 1 and 20\n\nBut we need 2.\n\nHow to build 2?\n\nFrom (4) and (6), we have:\n\nmäcuïlli (19) + öme (1) = 20\n\nSo 19 + 1 = 20 → so 20 = 19 + 1\n\nThus, 20 = 19 + 1\n\nBut we can compose larger numbers.\n\nNow, what is 42?\n\n42 = 20 + 20 + 2 \n= 20 + 20 + (1 + 1)\n\nBut 1 = öme\n\nSo 42 = 20 + 20 + öme + öme\n\nBut in Nahuatl, how is addition expressed?\n\nLook at (3): A + B = C → so “yë-pöhualli-on-chicöme + mahtlactli-on-nähui” → written as a compound.\n\nBut in (3), it's written as: \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo the sum is written as a compound with “on” structure.\n\nSo addition: X + Y → written as (X-on-Y) or something.\n\nBut the left side is a sum, and right side is a compound.\n\nBut we see in (14): cen-tzontli = tarumba tambaroy fete asàr\n\nSo a single number is broken into multiple parts.\n\nSimilarly, in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSo the number is built as a chain: \"yë-tzontli-on-...-on-...\"\n\nSo likely, numbers are formed as:\n\n[base] on [component] on [component] ...\n\nEach component may represent a value in the number system.\n\nSo 42 = 20 + 20 + 2 \n= 20 × 2 + 2\n\nBut 2 = 1 + 1\n\nSo 42 = 20 × 2 + 2 = 20 × (1 + 1) + (1 + 1)\n\nNow, can we build 2 via addition?\n\nYes: 1 + 1 = 2 → so “öme + öme”\n\nThen 20 × 2 → 20 × (öme + öme)\n\nSo 42 = 20 × (öme + öme) + (öme + öme)\n\nNow, how is multiplication expressed?\n\nIn (1): mahtlactli × mahtlactli → “mahtlactli-on-cë” × mahtlactli → result = mäcuïl-pöhualli-om-maht", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9607.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are given a set of equations in Nahuatl and Arammba, and asked to write out the Nahuatl expressions for 42 and 494.\n\nWe must use the examples to infer the linguistic pattern—specifically the number system and operations.\n\n---\n\n**Step 1: Identify arithmetic patterns in the equations**\n\nLook at the examples:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ A × A = B \nNote: \"mahtlactli\" appears on both sides, and \"cë\" and \"pöhualli\" are used.\n\n(2) cem-pöhualli × öme = öm-pöhualli \n→ This is multiplication: a × b = c\n\n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Addition: a + b = c\n\n(4) mäcuïlli + öme = chicöme \n→ Addition: a + b = c\n\n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ A × B = C\n\n(6) mäcuïlli × ëyi = caxtölli \n→ A × B = C \n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ a + a = a × b → suggests that addition and multiplication are related, perhaps with identities\n\n(8) ngámbi + asàr = tambaroy \n→ addition\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ addition: a + b = c, and \"tàxwo\" seems a marking or operator\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ multiplication with a marking\n\n(11) nimbo × fete = tarumba \n→ multiplication\n\n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ addition\n\nNow, observe (13) and (14), which link expressions and give translations:\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nLet’s deduce the core number system.\n\n---\n\nFrom (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nNote that in (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nThis suggests multiplication results in compound expressions.\n\nCompare to (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n→ It seems that “mahtlactli” may represent 1, and multiplication is concatenated.\n\nBut note: the left side has “mahtlactli-on-cë” × “mahtlactli” → result has “pöhualli” and “mahtlactli”\n\nWe see “pöhualli” appears often in products.\n\nAnother idea: the expressions may encode base-20 (vigesimal) system.\n\nTry to decode the target numbers: 42 and 494.\n\n42 = 2 × 21 = 2 × (20 + 1) = 2×20 + 2×1 → 2×20 + 2×1 = 40 + 2 → 42 \n494 = 20×24 + 14 → 24×20 = 480, 494 - 480 = 14 → 24×20 + 14\n\nBut 24 = 20 + 4 → 494 = (20+4)×20 + 14 = 20×20 + 4×20 + 14\n\nAlternatively, 494 = 20×24 + 14 → so we can think in base 20.\n\nWe must find morphemes for 1, 2, 10, 20, etc.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nThis looks like a × b = c — perhaps “cem-pöhualli” is 20? “öme” is 1?\n\nLet’s suppose:\n- “öme” = 1\n- “cem-pöhualli” = 20\n\nThen (2): 20 × 1 = 1 → no, that doesn’t work.\n\nWait — (2): cem-pöhualli × öme = öm-pöhualli → implies multiplication gives öm-pöhualli, which may be 20?\n\nBut 20×1 = 20 → possible.\n\nSo if “öme” = 1, and “cem-pöhualli” = 20 → 20 × 1 = 20 → so öm-pöhualli = 20\n\nBut this would mean multiplication gives same number? That's not helpful.\n\nAlternatively, maybe “cem-pöhualli” = 2, “öme” = 1 → 2×1 = 2?\n\nBut result is öm-pöhualli → if cem-pöhualli and öm-pöhualli are different forms, maybe it's a different 2? Not likely.\n\nLook at (4): mäcuïlli + öme = chicöme \n→ Addition: a + b = c\n\nSuppose “öme” = 1, “mäcuïlli” = 10 → 10 + 1 = 11 → “chicöme” = 11\n\n(1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ if mahtlactli = 1 → then 1 × 1 = 1 → but result has mäcuïl-pöhualli-om-mahtlactli → clearly more than 1\n\nSo maybe mahtlactli = 20?\n\nTry: mahtlactli = 20 → 20 × 20 = ? → result is mäcuïl-pöhualli-om-mahtlactli\n\nThat's 20×20 = 400 → 400 in base 20.\n\nNow, 20×20 = 400 → 400 ÷ 20 = 20 → 20×20 → so 20×20 = 20×20 → but the expression is complex.\n\nNote: in (1), left: mahtlactli-on-cë × mahtlactli → perhaps “mahtlactli-on-cë” is 1, and “mahtlactli” is 1 → 1×1 = 1\n\nBut result is mäcuïl-pöhualli-om-mahtlactli — clearly not 1.\n\nAlternative: maybe “cë” is a marker for a count or multiplier.\n\nAnother clue: in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nThis is addition: a + b = c\n\nSuppose:\n- “yë-pöhualli-on-chicöme” = 10 + something\n- “mahtlactli-on-nähui” = 1×something\n- Result = 10+something\n\nBut difficulties.\n\nLook at (15): cen-tzontli = tarumba tambaroy fete asàr\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWait — (14) has “cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → and equals yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo possibly, “cen-tzontli” is a number, and (14) is that number × something?\n\nBut (14) has “cen-tzontli-on-...” → “on” may mean “plus” or “times”?\n\nIn (1): mahtlactli-on-cë × mahtlactli = ... → “on” may mean multiplication.\n\nSimilarly, (3): yë-pöhualli-on-chicöme + ... — “on” may be multiplication or addition.\n\nBut (3) uses “+” sign, others use “on”.\n\nIn (3): \"+\" signs are used in text, so likely “on” = “multiplied by” or “added to”.\n\nBut in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = ... → so “on” appears only in one term.\n\nBut in (1): mahtlactli-on-cë × mahtlactli → “on” may be a genitive or multiplication marker.\n\nLet’s suppose that “A-on-B” means A times B.\n\nThen (1): (mahtlactli-on-cë) × mahtlactli = result \n→ (1 × cë) × 1 = result? → doesn’t make sense.\n\nAlternatively, “A-on-B” means A plus B?\n\nIn (3): yë-pöhualli-on-chicöme + ... → has “+” so “on” is not addition.\n\nBut in (3), “on” is used only once: in “on-chicöme” — and the rest is added.\n\nPerhaps the “on” is just a compound marker.\n\nAnother idea: Nahuatl uses a vigesimal (base 20) system.\n\nWe have:\n\nFrom (4): mäcuïlli + öme = chicöme \n→ 10 + 1 = 11 → so “öme” = 1, “mäcuïlli” = 10 → “chicöme” = 11\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \n→ suppose “cem-pöhualli” = 20, “öme” = 1 → 20×1 = 20 → result is “öm-pöhualli” → so 20×1 = 20\n\nSo “cem-pöhualli” = 20, “öm-pöhualli” = 20 → probably same value.\n\nBut it has different forms → maybe not.\n\nFrom (6): mäcuïlli × ëyi = caxtölli \n→ 10 × ? = caxtölli\n\nWe might guess that “ëyi” = 2 → 10×2 = 20 → caxtölli = 20?\n\nBut then (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nLet’s assume:\n- mahtlactli = 1\n- ëyi = 2\n- so mahtlactli-om-ëyi = 1×2 = 2\nThen 2 × 2 = 4 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nNow, if cem-pöhualli = 20, caxtölli = 20 → then 20 on 20 on nähui → perhaps 40 + 20 = 60? Not 4.\n\nAlternatively, perhaps “on” is a multiplicative operation.\n\nSo “A-on-B” means A × B\n\nThen:\n(1): (mahtlactli-on-cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (1 × cë) × 1 = 1 × cë = ? = mäcuïl-pöhualli-om-mahtlactli\n\nNot clear.\n\nFrom (6): mäcuïlli × ëyi = caxtölli \n→ 10 × 2 = 20 → caxtölli = 20\n\nFrom (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (1×2) × 2 = 4 → so result = 4\n\nNow, what is 4 in the expression?\n\nResult: cem-pöhualli-on-caxtölli-on-nähui → might represent 20 + 20 + 1? = 41? Not 4.\n\nAlternatively, maybe “on” means “plus”\n\nThen (5): (1×2) + 2 = 4 → expressed as cem-pöhualli-on-caxtölli-on-nähui → 20 + 20 + 1 = 41 — too big.\n\nNo.\n\nPerhaps the \"on\" is just a compound form.\n\nNow look at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe know from (4): mäcuïlli + öme = chicöme → 10+1=11\n\nAlso (6): mäcuïlli × ëyi = caxtölli → 10×2=20\n\nSo caxtölli = 20\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli → 20×1 = 20 → so öm-pöhualli = 20\n\nSo cem-pöhualli = 20\n\nThen “pöhualli” is associated with 20.\n\nNow, (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose mahtlactli = 1, so (1 × cë) × 1 = 1 × cë = 1 × cë\n\nResult: mäcuïl-pöhualli-om-mahtlactli → which could be 10 + 20 + 1 = 31?\n\nIf cë = 10 → 1×10 = 10 → 10 + 20 + 1 = 31 → but 1×10 = 10 → not 31.\n\nAlternatively, maybe “mahtlactli-on-cë” = 1 × 10 = 10 → 10 × 1 = 10 → result is mäcuïl-pöhualli-om-mahtlactli = 10 + 20 + 1 = 31 → not 10.\n\nNo.\n\nAnother idea: use the Arammba side for comparison.\n\nArammba:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ 2 + 2 = 2 × something → implies that 2×something = 4 → so 2×yànparo = 4 → yànparo = 2\n\n(8) ngámbi + asàr = tambaroy → 2 + ? = ?\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ 2 + ? = 2 (if tàxwo is a mark) → not likely.\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (a) × (a) = b → so a×a = b\n\n(11) nimbo × fete = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo\n\nFrom (7): 2 + 2 = 2 × yànparo → so yànparo = 2\n\nSo in Arammba:\n- ngámbi = 2\n- yànparo = 2\n\n(8) 2 + asàr = tambaroy → so asàr = ?\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ a × a = b → if a=2, 2×2=4 → result b = fete 2 → so fete 2 = 4\n\nSo fete 2 = 4\n\n(11) nimbo × fete = tarumba → nimbo × 4 = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe → 2\n\nSo 2 = 2 → only if nimbo = 0 → not likely.\n\n(12): nimbo + 2 = 2 → so nimbo = 0? Then (11): 0×4 = 0 = tarumba → possible.\n\nSo nimbo = 0\n\nThen (11): 0×fete = 0 = tarumba → tarumba = 0\n\nBut (15): cen-tzontli = tarumba tambaroy fete asàr → so 0 + ? + ? + ? = ? → this suggests \"cen-tzontli\" is 0 or 1?\n\nNo.\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo → 0,0,2 → so perhaps cen-xiquipilli = something with 0,0,2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9224.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "We are given several equations in Nahuatl and Arammba, and we are to derive how to write **42** and **494** in Nahuatl.\n\nWe are told to:\n- Use explicit alignment\n- Identify reusable morphemes, affixes, operations\n- Derive arithmetic decomposition first, then map into Nahuatl\n- Verify via examples\n\n---\n\n### Step 1: Understand the arithmetic patterns in Nahuatl\n\nWe are not given a direct numeral system, so we infer from equations.\n\n#### Equation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nLet’s break this down.\n\n- Left: `mahtlactli-on-cë × mahtlactli`\n- Right: `mäcuïl-pöhualli-om-mahtlactli`\n\n\"mahtlactli\" likely means \"100\" or \"10\", or unit for multiplication.\n\n\"on-cë\" may be a marker or suffix.\n\nLet’s suppose \"mahtlactli\" = 10. Then:\n- 10 × 10 = 100 → right-hand side should be 100.\n\nTry assigning: \nLet `mahtlactli = 10` \nThen left: `10 × 10 = 100` \nRight: `mäcuïl-pöhualli-om-mahtlactli`\n\nNow, see equation (4): \n`mäcuïlli + öme = chicöme` \nThis suggests addition: mäcuïlli + öme = chicöme → possibly 100 + 1 = 101?\n\nBut `öme` may be 1.\n\nSo: \n- `öme = 1` \n- `mäcuïlli = 100` → so `mäcuïl-` is likely 100 \n- `chicöme = 101`\n\nThen from (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nTry translating the whole thing. \nLeft: `mahtlactli-on-cë × mahtlactli` → 10 × 10 = 100 \nRight: `mäcuïl-pöhualli-om-mahtlactli` → 100 + 10 = 110? \nBut 10 × 10 = 100, not 110.\n\nAlternative: perhaps `mahtlactli-on-cë` is 10 + 1 = 11?\n\nTry: `(10 + 1) × 10 = 110` \nRight: `mäcuïl-pöhualli-om-mahtlactli` → if `mäcuïl` = 100, `pöhualli` = 10 → 100 + 10 = 110 → matches!\n\nSo: \n`mahtlactli` = 10 \n`öme` = 1 \n`mahtlactli-on-cë` = 10 + 1 = 11 \n`mäcuïl` = 100 \n`pöhualli` = 10 \n\nSo we now have:\n- 10 = mahtlactli \n- 1 = öme \n- 100 = mäcuïl \n- 10 = pöhualli \n- 11 × 10 = 110 → 100 + 10 → mäcuïl-pöhualli-om-mahtlactli\n\n(“om” may be “plus” or “and”)\n\nCheck equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nTry to interpret:\n\n- `yë-pöhualli-on-chicöme`: probably `yë` = 1, `pöhualli` = 10, `chicöme` = 101 → 1 × 101 = 101? \n- `mahtlactli-on-nähui`: 10 + something? \n- Sum → `näuh-pöhualli-on-cë`\n\nTry assigning values.\n\nWe already have:\n- `öme = 1` \n- `mäcuïlli = 100` → so `chicöme = 100 + 1 = 101`? \n- `pöhualli = 10`\n\nSo `yë-pöhualli-on-chicöme` = `1 × 101` = 101 \n`mahtlactli-on-nähui` = 10 + n? \nSum = 101 + 10 + n → total = 111 + n\n\nResult is `näuh-pöhualli-on-cë` \n`näuh-pöhualli-on-cë` → is it 111? 111 = 100 + 10 + 1 → 111\n\nSo if n = 1 → `mahtlactli-on-nähui = 11`\n\nSo `nähui = 1` → then `mahtlactli-on-nähui = 11`\n\nSo consistent.\n\nThus:\n- 1 = öme = nähui \n- 10 = mahtlactli = pöhualli \n- 100 = mäcuïl = mäcuïlli\n\nNow (5): \n`mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nLet’s decode:\nLeft: `(10 + x) × x` → equals something \nRight: `cem-pöhualli-on-caxtölli-on-nähui`\n\nWe know from (2): \n`cem-pöhualli × öme = öm-pöhualli` \nTry: \n`cem-pöhualli × 1 = öm-pöhualli`\n\nSo if `öme = 1`, then `cem-pöhualli = öm-pöhualli`\n\nAssume `cem-pöhualli = öm-pöhualli = x` → so same value.\n\nNow, (5): `(10 + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nRight: `cem-pöhualli` = x \n`caxtölli` = ? \n`on` = connector\n\nTry to guess with numbers.\n\nTry ëyi = 1 → (10+1) × 1 = 11 → result is `cem-pöhualli-on-caxtölli-on-nähui` → 11\n\nWhich is 10 + 1\n\nSo does this mean: `x = 10 + 1`?\n\nWe have: `cem-pöhualli = x = 10+1 = 11` → which is same as `öm-pöhualli` → so 11\n\nBut earlier, `öm-pöhualli` = 11 → yes.\n\nThen `caxtölli` must be zero or 0?\n\nThen `cem-pöhualli-on-caxtölli-on-nähui = 11 + 0 + 1 = 12?` → not matching.\n\nWait: \"on\" may be additive.\n\nSo if (10+1)×1 = 11 → 11 → written as cem-pöhualli-on-caxtölli-on-nähui?\n\nBut if it's 11, and cem-pöhualli = 11, then what are the others?\n\nSo perhaps only cem-pöhualli = 11, and the rest are zero or placeholders?\n\nBut (6): `mäcuïlli × ëyi = caxtölli` \nmäcuïlli = 100 → 100 × 1 = 100 → caxtölli = 100\n\nThus: (6) suggests caxtölli = 100\n\nThen (5) result: `cem-pöhualli-on-caxtölli-on-nähui` → 11 + 100 + 1 = 112?\n\nBut left: (10+1)×1 = 11 → not 112.\n\nContradiction.\n\nSo perhaps ëyi ≠ 1.\n\nTry ëyi = 2 → (10 + 2) × 2 = 12 × 2 = 24\n\nSo result = 24\n\nRight: cem-pöhualli-on-caxtölli-on-nähui \nWe know from (6): mäcuïlli × ëyi = caxtölli → 100 × 2 = 200\n\nSo caxtölli = 200\n\nThen cem-pöhualli = ? and on-nähui = ?\n\nIf result = 24, and caxtölli = 200 → too large → impossible.\n\nSo contradiction.\n\nWait — unless multiplication is not base 10, or the system uses base 20.\n\nIn Nahuatl, numerals are typically base-20.\n\nTry base-20.\n\nTry assigning:\n\n- 1 = öme \n- 20 = mahtlactli \nThen 10 × 10 = 100 → 100 in base 20 = 2×20 + 20 = 2×20 + 20? No, 20² = 400.\n\nWait: 20 × 20 = 400 → not 100.\n\nBut Nahuatl is base-20, so numbers like “20” = “one twenties”, “40” = “two twenties”, etc.\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nIf mahtlactli = 20 → 20 × 20 = 400 \nRight: mäcuïl-pöhualli-om-mahtlactli → mäcuïl = 100? (in base 20: 100 = 5×20 = 100)\n\nWait: 20 × 20 = 400 \nIn base 20: 400 = 20² → 1×20² = 400 → written as \"1\" for 400?\n\nBut we don’t have “one hundred” in that form.\n\nBack.\n\nFrom equation (4): \nmäcuïlli + öme = chicöme \nSuppose öme = 1 \nIf mäcuïlli = 100 → 100 + 1 = 101 → chicöme = 101\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli \nSo cem-pöhualli × 1 = öm-pöhualli → so cem-pöhualli = öm-pöhualli\n\nThis suggests that “cem-pöhualli” and “öm-pöhualli” are the same value.\n\nNow (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSuppose ëyi = 1 → then (mahtlactli + 1) × 1 = mahtlactli + 1\n\nRight: cem-pöhualli-on-caxtölli-on-nähui → if cem-pöhualli = 11, and caxtölli = 100, and nähui = 1 → total = 11+100+1 = 112\n\nLeft = 11 → not match.\n\nIf ëyi = 2 → (mahtlactli + 2) × 2 = 2×(x+2), x=mahtlactli\n\nTry to guess that mahtlactli = 20\n\nThen (20+2)×2 = 44\n\nRight: cem-pöhualli-on-caxtölli-on-nähui\n\nFrom (6): mäcuïlli × ëyi = caxtölli → 100 × 2 = 200 → so caxtölli = 200\n\nSo result is cem-pöhualli + 200 + 1 → if nähui=1\n\nSo total = cem-pöhualli + 201\n\nSet equal to 44 → cem-pöhualli = 44 - 201 = -157 → invalid.\n\nSo no.\n\nAlternative: the multiplicative system may represent multiplication differently.\n\nLook at (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nWe have:\n- pöhualli = 10\n- chicöme = 100 + 1 = 101\n- yë = 1 → so 1 × 101 = 101\n- mahtlactli = 10 → mahtlactli-on-nähui = 10 + n\n- sum = 101 + 10 + n = 111 + n\n- result: näuh-pöhualli-on-cë → näuh-pöhualli = 110? (10×11), on-cë = 1 → 111\n\nSo 111 + n = 111 → n = 0 → so nähui = 0? But earlier we had nähui = 1\n\nContradiction.\n\nAlternatively, “on” may be compound base.\n\nLet’s try to find known number in Nahuatl:\n\n42 in base 20: \n42 ÷ 20 = 2 remainder 2 → so 2×20 + 2 → “two twenties and two”\n\n494: \n494 ÷ 20 = 24 remainder 14 → 24×20 = 480, 494 - 480 = 14 → 24×20 + 14 → “twenty-four twenties and fourteen”\n\nSo likely, in Nahuatl, numbers are formed with:\n- units (1-19)\n- tens (20, 40, 60, ..., 180)\n- hundreds (200, 400, etc.)\n\nNow, look at (4): mäcuïlli + öme = chicöme \nIf öme = 1, mäcuïlli = 100 → chicöme = 101 → so mäcuïlli = 100 → could be 5×20\n\nSo 5×20 = 100\n\nSo mäcuïl = 5×20\n\nSimilarly, pöhualli = 1×20\n\nThen 10 = 1×20\n\nSo if mahtlactli = 20\n\nThen (1): (mahtlactli-on-cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n\"mahtlactli-on-cë\" = 20 + 1 = 21 \n21 × 20 = 420\n\nRight: mäcuïl-pöhualli-om-mahtlactli \nmäcuïl = 100 → 5×20 \npöhualli = 20 \nmahtlactli = 20\n\nSo 100 + 20 + 20 = 140 → not 420\n\nNo.\n\nTry (1): (mahtlactli-on-cë) × mahtlactli = 420 → 21×20=420\n\nRight: mäcuïl-pöhualli-om-mahtlactli\n\nIf mäcuïl = 20, pöhualli = 20, mahtlactli = 20 → 20+20+20=60 → no.\n\nTry mäcuïl = 20 → so 20×20 = 400\n\n400 + 20 = 420 → if pöhualli = 20\n\nThen: 400 + 20 = 420 → matches with (mahtlactli-on-cë) × mahtlactli = 420\n\nSo if mahtlactli = 20 → then mahtlactli-on-cë = 20 + 1 = 21 → 21×20 = 420 \nRight: mäcuïl-pöhualli-om-mahtlactli → 20 + 20 + 20 = 60? Only if mäcuïl = 20\n\nBut 20+20+20=60 → not 420\n\nUnless \"mäcuïl\" stands for 20×20 = 400\n\nSo mäcuïl = 400 → 20×20\n\nThen mäcuïl-pöhualli-om-mahtlactli = 400 + 20 + 20 = 440 → not 420\n\n5×20=100 → 4×20=80 → 3×20=60\n\nTry: 420 = 21×20\n\nSo could be 2×200 + 2×20 = 440 → too big", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8236.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "solver_checklist", + "sample_index": 0, + "output": "We are given several equations in Nahuatl and Arammba, and we must determine how to express **43** and **569** in Arammba.\n\nWe are to solve only part (c): write 43 and 569 in Arammba.\n\n---\n\n### Step 1: Identify relevant equations\n\nWe look for equations involving arithmetic operations and numerals, especially multiplication, addition, or known number patterns.\n\n#### Nahuatl equations:\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ multiplication: mahtlactli × mahtlactli → mäcuïl-pöhualli-om-mahtlactli\n\n(2) cem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × öme = öm-pöhualli\n\n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ addition\n\n(4) mäcuïlli + öme = chicöme \n→ addition\n\n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ multiplication\n\n(6) mäcuïlli × ëyi = caxtölli \n→ multiplication\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo\n\n---\n\n### Step 2: Extract number patterns and known values\n\nLet’s look for known values in the Nahuatl data that might correspond to numbers.\n\nWe see the following compound numbers:\n\n- mahtlactli = ? \n- cem-pöhualli = ? \n- öme = ? \n- mäcuïl-pöhualli-om-mahtlactli = ?\n\nBut the key may lie in equations that suggest known number values.\n\n#### Equation (1): \nmahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nSuppose mahtlactli = 1 → then 1×1 = 1, but the result is a compound form.\n\nAlternatively, perhaps mahtlactli = 10?\n\nSuppose mahtlactli = 10 → 10×10 = 100 → result: mäcuïl-pöhualli-om-mahtlactli\n\nBut “mäcuïl-pöhualli” is a familiar form — appears in (1) and (4).\n\nEquation (4): mäcuïlli + öme = chicöme\n\nThis suggests mäcuïlli + öme = chicöme\n\nWe might guess that mäcuïlli = 1, öme = 2 → chicöme = 3? \nOr mäcuïlli = 2, öme = 1 → chicöme = 3?\n\nAlternatively, from (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nSuppose mahtlactli = 20 → 20×20 = 400 → then result is 400?\n\nBut note: in (13), we have a long compound: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nAnd (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe see that in (15): cen-tzontli = tarumba tambaroy fete asàr \n→ suggests that \"cen-tzontli\" is a compound number, and equals a sum of roots: tarumba + tambaroy + fete + asàr\n\nBut in (11): nimbo × fete = tarumba \n→ suggests multiplication \n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ addition\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (yenówe) × (yenówe tàxwo) = (fete) (yenówe tàxwo)\n\nLikely: (a × b) = c, where c = fete × b → suggests a = fete?\n\nSo yenówe × (yenówe tàxwo) = fete × (yenówe tàxwo)\n\nAssuming the last part is shared (yànparo tàxwo), then:\n\nyenówe × X = fete × X → only possible if yenówe = fete.\n\nSo fete = yenówe.\n\nThen from (10): yenówe × (yenówe tàxwo) = fete × (yenówe tàxwo) → yes, checks out.\n\nNow from (11): nimbo × fete = tarumba \n→ nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + yànparo tàxwo = yenówe tàxwo\n\nNow from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut we see from (8): ngámbi + asàr = tambaroy \n→ so asàr = tambaroy - ngámbi\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ ngámbi × 2 = ngámbi × yànparo → only possible if yànparo = 2\n\nSo yànparo = 2\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2×t = yànparo×t → but yànparo = 2, so yànparo tàxwo = 2×t\n\nSo: nimbo + 2t = 2t → nimbo = 0 → contradiction?\n\nWait — no.\n\n\"tàxwo\" is likely a marker of repetition or multiplication — perhaps \"x\".\n\nSo: \"yànparo tàxwo\" = yànparo × something.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2×ngámbi = ngámbi × yànparo → so yànparo = 2\n\nSo yànparo = 2\n\nEquation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 × t) + (fete × asàr) = 2 × fete\n\nThat seems odd unless t = 0 or something.\n\nWait — perhaps \"fete asàr tàxwo\" = fete × asàr\n\nSo (2 × t) + (fete × asàr) = 2 × fete\n\nBut fete = yenówe\n\nWe have from (10): yenówe × (yenówe tàxwo) = fete × (yenówe tàxwo) → yenówe = fete\n\nSo fete = yenówe\n\nNow, equation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 × t) + (fete × asàr) = 2 × fete\n\nSo: 2t + fete × asàr = 2fete\n\nThen: 2t + fete × asàr = 2fete \n→ 2t = 2fete − fete × asàr = fete (2 − asàr)\n\nWe can solve for t if we know fete and asàr.\n\nNow, from (8): ngámbi + asàr = tambaroy\n\nAnd from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nWe are told that \"cen-tzontli\" is a number.\n\nSimilarly, \"cen-xiquipilli\" appears in (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThis might be a large number.\n\nNow, from (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis suggests a compound: cen-tzontli + cem-pöhualli + mahtlactli + öme → yànparo tarumba\n\nWait — it's written as: cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThe \"on\" and \"om\" suggest combination — perhaps relational or addition.\n\nNow, from (15): cen-tzontli = tarumba tambaroy fete asàr \n→ so cen-tzontli is the sum of those components.\n\nBut from (14), cen-tzontli is combined with other terms to give yànparo tarumba.\n\nIf tarumba = nimbo × fete, and yànparo = 2, then perhaps yànparo tarumba = 2 × tarumba?\n\nBut only if the structure implies multiplication.\n\nAlternatively, perhaps \"yànparo tarumba\" = 2 × tarumba\n\nBut let’s consider specific values.\n\nTry to assign numbers.\n\nAssume:\n\n- yànparo = 2 (from (7): ngámbi + ngámbi = ngámbi × yànparo → yànparo = 2)\n\n- fete = yenówe (from (10))\n\n- from (11): nimbo × fete = tarumba → tarumba = nimbo × fete\n\n- from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nNow from (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThis suggests that \"cen-xiquipilli\" is a number built from those parts.\n\nBut we don't know the values.\n\nNow from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis seems like a large number.\n\nBut we are to solve 43 and 569 in Arammba.\n\nSo we need to find a way to decompose 43 and 569 using known patterns.\n\nLet us look at known number facts in Nahuatl.\n\nIn Nahuatl, the number 20 is a base. 20 × 2 = 40, 20 × 2 + 3 = 43. \nSimilarly, 20 × 2 = 40 → 43 = 40 + 3\n\nIn fact, in many Mesoamerican systems, numbers are based on 20.\n\nIn (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nSuppose mahtlactli = 20 → 20×20 = 400 → then 400 → mäcuïl-pöhualli-om-mahtlactli\n\nNow mäcuïl-pöhualli might be 400?\n\nmäcuïl = \"bowl\", pöhualli = \"calendar\"\n\nBut more importantly, in (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 1, öme = 2 → chicöme = 3? \nOr if mäcuïlli = 20, öme = 1 → chicöme = 21?\n\nBut let's go to equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ possibly addition involving units.\n\nBack to (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSuppose ëyi = cem-pöhualli-om-... ?\n\nBut we may not need all of that.\n\nNow look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe see this has: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë → possibly a number.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSuppose cen-tzontli is a number, say X, and it is combined with other terms to give yànparo tarumba.\n\nBut from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSo substituting into (14): \n[cen-tzontli] + [cem-pöhualli] + [mahtlactli] + [öme] = yànparo tarumba\n\nBut cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSo:\n\n(tarumba + tambaroy + fete + asàr) + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nNow group:\n\ntarumba + tambaroy + fete + asàr + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nSubtract tarumba from both sides:\n\ntambaroy + fete + asàr + cem-pöhualli + mahtlactli + öme = (yànparo − 1) tarumba\n\nBut yànparo = 2 → yànparo − 1 = 1\n\nSo:\n\ntambaroy + fete + asàr + cem-pöhualli + mahtlactli + öme = tarumba\n\nBut from (11): nimbo × fete = tarumba → so tarumba = nimbo × fete\n\nSo:\n\ntambaroy + fete + asàr + cem-pöhualli + mahtlactli + öme = nimbo × fete\n\nNow, from (8): ngámbi + asàr = tambaroy → so tambaroy = ngámbi + asàr\n\nSo:\n\n(ngámbi + asàr) + fete + asàr + cem-pöhualli + mahtlactli + öme = nimbo × fete\n\n→ ngámbi + 2asàr + fete + cem-pöhualli + mahtlactli + öme = nimbo × fete\n\nThis is getting complex.\n\nBut now consider the possibility that the number system in Arammba uses a base-10 or mixed system.\n\nWe need to express 43 and 569.\n\nNote that 43 = 40 + 3 → 20×2 + 3 \n569 = 500 + 60 + 9 → 20×25 + 10×6 + 9\n\nBut Arammba might have a base-20 system.\n\nWe need to find a number that appears in the data for known counts.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo → so yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy\n\nSuppose ngámbi = 1 → then asàr = tambaroy − 1\n\nBut not helpful.\n\nFrom (10): yenówe × (yenówe tàxwo) = fete × (yenówe tàxwo) → so yenówe = fete\n\nFrom (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × fete\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nNow, is there any equation where we can get a known value?\n\nLook at (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 × t) + (fete × asàr) = 2 × fete\n\nAssume fete = 1 → then (2t) + (1 × asàr) = 2\n\n→ 2t + asàr = 2 → possible if t = 0, asàr = 2 → then tambaroy = ngámbi + 2\n\nBut no values.\n\nAlternatively, suppose fete = 3 → then 2t + 3asàr = 6\n\nPossible solutions: t = 0, asàr = 2 → 6 → 2×0 + 3×2 = 6 → ok\n\nThen fete = 3\n\nThen from (11): nimbo × 3 = tarumba → tarumba = 3 × nimbo\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 3nimbo + (ngámbi + asàr) + 3 + asàr = 3nimbo + ngámbi + 2asàr + 3\n\nWe don’t know values.\n\nBut now consider that in Nahuatl, \"mahtlactli\" may be 20.\n\nIn (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9893.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given systems of equations in Nahuatl and Arammba, and asked to translate the numbers **43** and **569** into Arammba.\n\nWe must deduce the structure of the numeral system in Arammba using the equations provided.\n\n---\n\n### Step 1: Analyze the equations for patterns of arithmetic and structure.\n\nStart with Nahuatl and Arammba pairs to find numerical and morphological correspondences.\n\n---\n\nIn **(1)**: \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLet’s assign: \n- mahtlactli = 1 \n- cë = \"on\" (a directional/possession marker) \n- So: 1 × 1 = ??? → leads to mäcuïl-pöhualli-om-mahtlactli\n\nBut compare to (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n\nThis looks like a sum of two units.\n\nLook at (4): \nmäcuïlli + öme = chicöme → suggests 1 + 1 = 2? → perhaps mäcuïlli is 1, öme is 1 → chicöme = 2\n\nBut in (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nLet’s suppose:\n- mahtlactli = 1\n- ëyi = x \n→ 1 × x = cem-pöhualli-on-caxtölli-on-nähui \n\nAlso (6): \nmäcuïlli × ëyi = caxtölli \nSo: 1 × x = caxtölli → so caxtölli = x? \n≠ cem-pöhualli-on-caxtölli-on-nähui → so x is greater than just caxtölli.\n\nMaybe “×” means multiplication, and affixes represent components.\n\nBut focus on the Arammba side.\n\n---\n\n### Step 2: Study Arammba arithmetic\n\nEquation (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 ngámbi = ngámbi × yànparo\n\nThis implies that **2 = yànparo**? \nBecause if we assume ngámbi is a unit (e.g., 1), then: \n1 + 1 = 1 × yànparo → 2 = yànparo\n\nSo **yànparo = 2**\n\nEquation (8): ngámbi + asàr = tambaroy \n→ 1 + asàr = tambaroy \nSo asàr = tambaroy - 1\n\nEquation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nLet’s parse: \n\"yànparo tàxwo\" → possibly \"2 + ?\" \n\"asàr tàxwo\" → \"asàr + ?\"\n\nBut the result is just \"yànparo fete\" → i.e., \"2 fete\"\n\nSo: (2 + ?) + (? + asàr) = 2 fete?\n\nStrange.\n\nWait: perhaps \"tàxwo\" is a marker that means \"added\", or \"together\".\n\nMaybe \"A + B tàxwo\" = \"A + B\" (sum)\n\nSo: yànparo tàxwo + fete asàr tàxwo = (yànparo) + (fete asàr)\n\nAnd this equals yànparo fete → so (yànparo) + (fete asàr) = yànparo fete\n\nTherefore: fete asàr = fete → so asàr = 0? Contradiction.\n\nAlternatively, \"fete asàr\" is a unit.\n\nEquation (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (yànparo) + (fete asàr) = yànparo fete\n\nThis suggests that adding (yànparo) and (fete asàr) gives (yànparo) + (fete)\n\nSo: fete asàr = fete → asàr = 1? \nThen fete asàr = fete × 1? \nBut fete asàr seems to be a compound word.\n\nAlternatively, suppose \"fete\" is a unit, and \"asàr\" is a value.\n\nBut from (8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = tambaroy - 1\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo: y × y = fete y → so y² = fete y → so y = fete?\n\nThus: **yenówe = fete**\n\nBecause y² = fete × y → y² - fete × y = 0 → y(y - fete) = 0 → so y = fete\n\nSo yenówe = fete\n\nThen (8): 1 + asàr = tambaroy \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → confirmed.\n\nNow (11): nimbo × fete = tarumba → since fete = yenówe → nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe → yànparo = 2 → so yenówe = nimbo + 2\n\nBut from (10), yenówe = fete → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba \n→ nimbo × (nimbo + 2) = tarumba\n\nSo tarumba = nimbo(nimbo + 2)\n\nNow, also from (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nCen-tzontli is a compound.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nBut this is too complex.\n\nBack to arithmetic.\n\nWe have:\n- yànparo = 2\n- fete = yenówe\n- yenówe = nimbo + 2\n- fete = nimbo + 2\n- tarumba = nimbo × (nimbo + 2)\n\nNow, (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = tarumba + tambaroy + fete + asàr?\n\nBut \"tambaroy\" from (8) is ngámbi + asàr = 1 + asàr\n\nSo tambaroy = 1 + asàr\n\nThus: \ntarumba = nimbo × (nimbo + 2) \ntambaroy = 1 + asàr \nfete = nimbo + 2 \nasàr = ? \n\nBut we only know one equation for asàr.\n\nNo direct link — so perhaps the numbers are built from components.\n\nNow look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis seems to be a large number.\n\nIn (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\ncen-tzontli-on-cem-... → similar to earlier equations.\n\nNotice the analogies:\n\nIn Nahuatl: \n(2): cem-pöhualli × öme = öm-pöhualli → likely 2 × 1 = 2 → cem-pöhualli = 2, öme = 1 → so 2×1 = 2\n\nAlso (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli → 1×1 = ? → so 1×1 = 1 with some affix → likely mäcuïl-pöhualli = 2?\n\nWait: mäcuïl-pöhualli → perhaps 2?\n\nThen (1): 1×1 = 2? → no.\n\nWait: “mahtlactli-on-cë × mahtlactli” = “mäcuïl-pöhualli-om-mahtlactli”\n\nSo: 1 × 1 = 2? → 1×1=1 → not 2.\n\nAlternatively, “on” may be a modifier.\n\nBut in (4): mäcuïlli + öme = chicöme → if mäcuïlli = 1, öme = 1 → 1 + 1 = 2 → so chicöme = 2\n\nSimilarly, (6): mäcuïlli × ëyi = caxtölli → 1 × x = caxtölli → x = caxtölli\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nSo (1 × ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ ëyi² = cem-pöhualli-on-caxtölli-on-nähui\n\nFrom (6): ëyi × 1 = caxtölli → ëyi = caxtölli\n\nSo ëyi² = caxtölli × caxtölli → = cem-pöhualli-on-caxtölli-on-nähui\n\nSo cem-pöhualli-on-caxtölli-on-nähui = (caxtölli)²\n\nThus, in Nahuatl:\n- 1 × 1 = 1 (with affixes) \n- 1 + 1 = 2 \n- x × x = x² = some compound\n\nSimilarly, in Arammba, from (10): \nyenówe × yenówe tàxwo = fete yenówe tàxwo \n→ y × y = fete × y → y(y - fete) = 0 → y = fete \nSo yenówe = fete\n\nThen from (12): nimbo + yànparo = yenówe \n→ nimbo + 2 = yenówe = fete → so nimbo = fete - 2\n\nNow from (11): nimbo × fete = tarumba \n→ (fete - 2) × fete = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nAssume that “tambaroy” = ngámbi + asàr = 1 + asàr \nSo asàr = tambaroy - 1\n\nThen:\ncen-tzontli = (fete-2)fete + (1 + asàr) + fete + asàr \n= (fete² - 2fete) + (1 + asàr) + fete + asàr \n= fete² - 2fete + 1 + asàr + fete + asàr \n= fete² - fete + 1 + 2asàr\n\nNow, in (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nNot directly useful.\n\nLook now at the total in (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli → likely 2 × 1 = 2 → so cem-pöhualli = 2, öme = 1\n\nAssume:\n- öme = 1\n- cem-pöhualli = 2\n\nThen in (14): \ncen-tzontli-on-2-om-1-om-1 = 2 × tarumba\n\nSo cen-tzontli + (2 om 1 om 1) = 2 × tarumba\n\nBut what does “om” mean?\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n“om” is a connector, like “and” or in a list.\n\nSo perhaps “om” = addition or list of components.\n\nThen in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme \n→ cen-tzontli + (2 + 1 + 1) = cen-tzontli + 4\n\nAnd this equals yànparo tarumba = 2 × tarumba\n\nSo:\ncen-tzontli + 4 = 2 × tarumba\n\nBut earlier, cen-tzontli = fete² - fete + 1 + 2asàr\n\nSo:\nfete² - fete + 1 + 2asàr + 4 = 2 × tarumba \n→ fete² - fete + 5 + 2asàr = 2 × tarumba\n\nRecall from (11): tarumba = (fete - 2) × fete = fete² - 2fete\n\nSo substitute:\nLHS: fete² - fete + 5 + 2asàr \nRHS: 2(fete² - 2fete) = 2fete² - 4fete\n\nSet equal:\nfete² - fete + 5 + 2asàr = 2fete² - 4fete \n→ 0 = fete² - 3fete - 5 - 2asàr\n\n→ fete² - 3fete - 5 = 2asàr\n\n→ asàr = (fete² - 3fete - 5)/2\n\nNow asàr must be a positive integer (since it's a numeral). Try small integer values of fete.\n\nTry fete = 5: \nasàr = (25 - 15 - 5)/2 = 5/2 → not integer\n\nfete = 6: (36 - 18 - 5)/2 = 13/2 → no\n\nfete = 7: (49 - 21 - 5)/2 = 23/2 → no\n\nfete = 4: (16 - 12 - 5)/2 = -1/2 → no\n\nfete = 3: (9 - 9 - 5)/2 = -5/2 → no\n\nfete = 8: (64 - 24 - 5)/2 = 35/2 → no\n\nfete = 9: (81 - 27 - 5)/2 = 49/2 → no\n\nNo integer solution? That suggests mistake.\n\nAlternative: perhaps “on” and “om” are not additive but represent multiplication.\n\nBut in (7): ngámbi + ngámbi = ngámbi × yànparo → 2 = yànparo → good.\n\nIn (10): y × y = fete × y → y = fete → good.\n\nIn (12): nimbo + 2 = fete → nimbo = fete - 2\n\nIn (11): nimbo × fete = tarumba → (fete - 2) × fete = tarumba\n\nNow equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nPossibly cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut tampbaroy = ngámbi + asàr = 1 + asàr\n\nSo cen-tzontli = tarumba + (1 + asàr) + fete + asàr = tarumba + fete + 1 + 2asàr\n\nNow from (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe assume cem-pöhualli = 2, mahtlactli = 1, öme = 1\n\nSo \"on-cem-pöhualli-om-mahtlactli-om-öme\" = (2 + 1 + 1) = 4? Or list?\n\n\"on\" may be part of the base.\n\nBut \"cen-tzontli-on-...\" may mean cen-tzontli plus the compound.\n\nSo cen-tzontli + 4 = 2 × tarumba\n\nSo:\ncen-tzontli + 4 = 2(fete² - 2fete)\n\nBut cen-tzontli = fete² - 2fete + fete + 1 + 2asàr = fete² - fete + 1 + 2asàr\n\nSo:\n(fete² - fete + 1 + 2asàr) + 4 = 2fete² - 4fete \n→ fete² - fete + 5 + 2asàr = 2fete² - 4fete \n→ 0 = fete² - 3fete - 5 - 2asàr \n→ 2asàr = -fete² + 3fete + 5\n\nTry integer values:\n\nfete = 1: 2asàr = -1 + 3 + 5 = 7 → asàr = 3.5 → no \nfete = 2: -4 + 6 + 5 = 7 → 3.5 \nfete = 3: -9 + 9 + 5 = 5 → asàr = 2.5 \nfete = 4", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9016.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "solver_checklist", + "sample_index": 2, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to translate the numbers **43** and **569** into Arammba.\n\nWe must find a pattern in the equations that allows us to derive how numbers are formed in Arammba — particularly how arithmetic operations and number decompositions are expressed.\n\n---\n\n### Step 1: Identify number patterns in Nahuatl\n\nLook for number formations or arithmetic operations.\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nThis may represent 2×2 = 4? But no clear direct number. \n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n→ (X × Y) = Z — possibly multiplication or specific number? \n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Addition? Possibly: A + B = C \n\nEquation (4): \nmäcuïlli + öme = chicöme \n→ A + B = C — could be a base addition: 2 + 1 = 3? \n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ A × B = C — likely a multiplication rule \n\nEquation (6): \nmäcuïlli × ëyi = caxtölli \n→ multiplication: A × B = C \n\nNote: mäcuïlli likely means 2 (from equation 4), and ëyi could be 1. Then mäcuïlli × ëyi = caxtölli → 2×1 = 2? \nBut caxtölli appears in (5) with larger result. So maybe not.\n\nNow examine equations (13) and (14) — which link to the final question.\n\nEquation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n→ likely a number expression involving nested structure.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n→ multiplication or addition?\n\nEquation (15): \ncen-tzontli = tarumba tambaroy fete asàr \n→ “cen-tzontli” = sum of three components: tarumba, tambaroy, asàr\n\nEquation (16): \ncen-xiquipilli = weremeke tarumba nimbo yànparo \n→ “cen-xiquipilli” = sum of four components\n\nNow note: \nIn (15), cen-tzontli = tarumba + tambaroy + fete + asàr \nIn (16), cen-xiquipilli = weremeke + tarumba + nimbo + yànparo\n\nBut only in (15) and (16) are we seeing compound numbers formed as sums.\n\nNow observe:\n\nIn (8): ngámbi + asàr = tambaroy \n→ a sum: A + B = C\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (A + B) = C — possibly shared units? \"tàxwo\" may mean \"and\" or \"plus\"\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ A × B = C — here, multiplication?\n\nIn (11): nimbo × fete = tarumba \n→ multiplication: A × B = C \n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ A + B = C \n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo — suggests a sum of two things equals a compound term.\n\nNow from (11): nimbo × fete = tarumba \n→ maybe nimbo = 3, fete = 2 → 3×2 = 6 → tarumba = 6 \nBut in (15), tarumba is a component of cen-tzontli.\n\nAlso, in (15): cen-tzontli = tarumba + tambaroy + fete + asàr \n\nBut from (8): ngámbi + asàr = tambaroy — so asàr is one of the terms.\n\nNow, perhaps ngámbi = 1?\n\nTry assigning numbers.\n\nTry: \nAssume ngámbi = 1 (base unit)\n\nThen (8): 1 + asàr = tambaroy \nSo tambaroy = 1 + asàr\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ likely addition\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (A × A) = B — possibly a square?\n\nSuppose yenówe = 2, then yenówe × yenówe tàxwo = 4 → fete 2 tàxwo → so fete = 2?\n\nThen (11): nimbo × fete = tarumba → nimbo × 2 = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo = 2 tàxwo\n\nTry nimbo = 3 → 3×2 = 6 → tarumba = 6 → possible.\n\nThen (12): 3 + yànparo tàxwo = 2 tàxwo → so yànparo tàxwo = -1? Impossible.\n\nSo must revise.\n\nAlternate: maybe \"tàxwo\" is a marker for \"plus\" or \"with\", not a number.\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (A + B) = C — so maybe \"fete asàr\" is a unit, and \"tàxwo\" is a connector.\n\nSo likely: \nx + y = z → where x and y are components, and \"tàxwo\" denotes addition.\n\nSo (8): ngámbi + asàr = tambaroy — addition \n(9): yànparo + fete asàr = yànparo fete — meaning: yànparo and (fete asàr) = yànparo fete — so fete asàr is a compound unit?\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ A × B = C — B is \"yenówe tàxwo\" — perhaps a modified version of A?\n\nSuppose \"yenówe tàxwo\" is (yenówe) + something?\n\nBut result is \"fete yenówe tàxwo\" — so perhaps multiplication is not literal.\n\nBut (11): nimbo × fete = tarumba \nSo multiplication is defined.\n\nNow, in (15): cen-tzontli = tarumba + tambaroy + fete + asàr \nWe need to find what cen-tzontli means.\n\nSimilarly, (16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo\n\nNow what about numbers?\n\nWe are to write 43 and 569 in Arammba.\n\nSo we must find a number system.\n\nTry to map:\n\nFrom the structure, perhaps there's a way to build numbers via multiplication and addition.\n\nLook at (2): cem-pöhualli × öme = öm-pöhualli — could be 1×2 = 2? Or 2×1 = 2?\n\nFrom (4): mäcuïlli + öme = chicöme — possible 2 + 1 = 3?\n\nFrom (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui — likely (2×1) = something?\n\nBut output includes cem-pöhualli and caxtölli — cem-pöhualli might be 1, caxtölli might be 2?\n\nWe don’t have enough direct mappings.\n\nBut now, in (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nPossibly a composite number.\n\nSuppose \"yë-tzontli\" is 1, \"näuh-pöhualli\" is 2, \"caxtölli\" is 3, \"cë\" is 4? But seems arbitrary.\n\nBut in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis looks like: (cen-tzontli) + (cem-pöhualli) + (mahtlactli) + (öme) = result?\n\nBut right-hand side is yànparo tarumba — not necessarily a sum.\n\nAlternatively, perhaps “on” or “om” indicates multiplicative operations.\n\n“on” may mean “times” or “with”.\n\nFor example, in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n“on” might denote multiplication.\n\nSo perhaps “A-on-B” = A × B?\n\nCheck: \n(1): mahtlactli-on-cë × mahtlactli = result \nSo (A-on-B) × C = D? Not clear.\n\nBut (1) = (mahtlactli × cë) × mahtlactli? But why is it written as “on”?\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nHere, “on” might be used for multiplication or combination.\n\nBut also has \"+\" and \"=\".\n\nNow consider that in (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nEach of these is a known term from equations:\n\nFrom (8): tambaroy = ngámbi + asàr\n\nSo if ngámbi = 1, and asàr = x, then tambaroy = 1 + x\n\nFrom (15): cen-tzontli = tarumba + (1 + x) + fete + x \n→ = tarumba + fete + 1 + 2x\n\nFrom (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × fete\n\nNow we want to assign values.\n\nTry to find minimal values.\n\nAssume base units:\n\nLet:\n- ngámbi = 1 \n- asàr = 1 → then from (8): tambaroy = 1 + 1 = 2 \nFrom (11): nimbo × fete = tarumba \nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nSuppose fete = 2 → then tarumba = nimbo × 2\n\nTry nimbo = 3 → tarumba = 6\n\nThen (15): cen-tzontli = 6 + 2 + 2 + 1 = 11 \nSo cen-tzontli = 11\n\nBut is that consistent?\n\nIn (16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo \n= weremeke + 6 + 3 + yànparo\n\nNo value yet.\n\nWe don’t have a direct term for weremeke.\n\nBut perhaps we can find a multiplier.\n\nNow, from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nAssume yenówe = 2\n\nThen left: 2 × (2 tàxwo) = 4? \nRight: fete 2 tàxwo → fete = 2 → matches!\n\nSo fete = 2\n\nSo consistent.\n\nNow (12): nimbo + yànparo tàxwo = yenówe tàxwo = 2 tàxwo\n\nSo nimbo + yànparo tàxwo = 2 tàxwo\n\nNow nimbo = 3 → 3 + yànparo tàxwo = 2 tàxwo → impossible.\n\nSo nimbo must be ≤ 2.\n\nTry nimbo = 2 → then tarumba = 2 × fete = 4\n\nNow (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 4 + 2 + 2 + 1 = 9\n\n(12): 2 + yànparo tàxwo = 2 tàxwo → so yànparo tàxwo = 0? Not likely.\n\nTry nimbo = 1 → then tarumba = 1 × 2 = 2\n\nThen (15): 2 + 2 + 2 + 1 = 7\n\n(12): 1 + yànparo tàxwo = 2 tàxwo → so yànparo tàxwo = 1 → so yànparo = 1?\n\nPossible.\n\nNow can we get larger numbers?\n\nBut we need to build 43 and 569.\n\nNow look at (7): ngámbi + ngámbi = ngámbi × yànparo \n1 + 1 = 1 × yànparo → 2 = yànparo → so yànparo = 2\n\nOh! We missed that.\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \nSo 1 + 1 = 1 × yànparo → 2 = yànparo\n\nSo yànparo = 2\n\nNow (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (2) = (yenówe) (with tàxwo)\n\nBut result is \"yenówe tàxwo\"\n\nSo nimbo + 2 = yenówe\n\nBut from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo = 2 yenówe tàxwo\n\nSo if yenówe = 3, then left: 3 × 3 = 9 → right: 2 × 3 = 6 → not equal.\n\nIf yenówe = 1 → 1×1 = 1 → right: 2×1=2 → no.\n\nIf yenówe = 2 → left: 2×2 = 4 → right: 2×2 = 4 → YES\n\nSo yenówe = 2\n\nThen from (12): nimbo + 2 = 2 → nimbo = 0? Invalid.\n\nContradiction.\n\nSo earlier assumption fails.\n\nGo back.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nSo 2 = 1 × yànparo → yànparo = 2\n\nSo yànparo = 2\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nLet x = yenówe \nThen left: x × (x tàxwo) — does \"tàxwo\" mean \"and\" or a unit?\n\nIf it means scalar or addition, then (x × x) = fete × x → x² = fete × x → x = fete, assuming x ≠ 0\n\nSo x = fete\n\nThus fete = x = yenówe\n\nSo fete has the same value as yenówe\n\nFrom (11): nimbo × fete = tarumba → nimbo × x = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = x (since yànparo = 2)\n\nSo nimbo = x - 2\n\nThen tarumba = (x - 2) × x\n\nFrom (8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy \n→ asàr = tambaroy - 1\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr \n= (x(x-2)) + (tambaroy) + x + (tambaroy - 1) \n= x² - 2x + tambaroy + x + tambaroy - 1 \n= x² - x + 2 tambaroy - 1\n\nWe don't have a value for tambaroy.\n\nBut we don't need it yet.\n\nNow, this expression is a function of x.\n\nWe need to find which x makes sense with the others.\n\nx = fete = yenówe\n\nx ≥ 2 (since nimbo = x-2 ≥ 0 → x ≥ 2)\n\nTry x=2 → nimbo = 0 → invalid (no zero)\n\nx=3 → nimbo = 1\n\ntarumba = 1×3 = 3\n\ntambaroy = ? → undefined\n\n(15): cen-tzontli = 3² - 3 + 2(tambaroy) -1 = 9-3 + 2t -1 = 5 + 2t\n\nNo value.\n\nBut perhaps the real pattern is that Arammba uses a base-10 number system with compound expressions.\n\nNow look at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may represent a number like 10×10 + 9×10 + 10 + 1 → or more likely, it's a compound of place values.\n\nPerhaps each unit has a value:\n\nSuppose:\n- yë-tzontli = 1\n- näuh-pöhualli = 10\n- caxtölli = 100\n- cë = 1000\n\nThen: 1×1000 + 10×100 + 1", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10166.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "solver_checklist", + "sample_index": 3, + "output": "First, identify the numerical patterns in the given equations.\n\nWe are to write 43 and 569 in Arammba.\n\nStart by analyzing the arithmetic and structure in the examples.\n\nLook at equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ This appears to be a multiplication operation. The left side is “A × A”, and the product is (some function of A). \nBut the right side is complex; likely, multiplication is represented via a compound with “pöhualli” and other affixes.\n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × öme → öm-pöhualli \nThis is suspiciously simple: one term multiplied by another yields a similar form but with a shift in affix.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Addition: left-hand side has two addends; result has “näuh-pöhualli-on-cë” \nMatches with (4): mäcuïlli + öme = chicöme → sum of two numbers yields a compound.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ multiplication: (A × B) → some long product \nEquation (6): mäcuïlli × ëyi = caxtölli → simpler, direct multiplication\n\nSo, multiplication seems to use a pattern involving affixes like -pöhualli, -cem, -caxtölli, etc.\n\nNow, in Arammba, look at the examples:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ Addition of two ngámbi gives same as multiplication of ngámbi × yànparo \nSo: 2 × A = A × B → suggests that A + A = A × B \nThus, 2A = A × B → so B is a multiplier associated with doubling.\n\nThen (8) ngámbi + asàr = tambaroy \n→ 2 = A + B → not clear. But (7) and (8) suggest that addition and multiplication are distinct, and may involve compound terms.\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ Addition with \"tàxwo\" affix → the result drops the \"tàxwo\" and combines.\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ Multiplication: A × (A tàxwo) → gives (fete A tàxwo) \nSo: A × (A with suffix) = (fete + A with suffix)\n\nThis suggests a multiplication operation where one factor is modified with -tàxwo (a marking), and the product has a \"fete\" prefix.\n\n(11) nimbo × fete = tarumba \n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n\nNow, equations (13) and (14) are compound:\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nWe have a multi-component expression, likely a number indicator.\n\n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nImportant: (15) cen-tzontli = tarumba tambaroy fete asàr \n→ “cen-tzontli” is a number? But right side has tarumba, tambaroy, fete, asàr — which appear in (8), (11), (10), (12)\n\nNote: From (8): ngámbi + asàr = tambaroy → so tambaroy may be 2? (as asàr is a numerical unit)\n\nFrom (11): nimbo × fete = tarumba → so tarumba is product of nimbo and fete → perhaps nimbo = 1, fete = 2 → tarumba = 2?\n\nWait: (12): nimbo + yànparo tàxwo = yenówe tàxwo \nBut (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo if we suppose that yenówe = 1 (unit), then yenówe tàxwo = 1 with appendix.\n\nFrom (10): 1 × (1 tàxwo) = fete (1 tàxwo) \n→ So 1 × (1 tàxwo) = fete (1 tàxwo) → implies fete = 1?\n\nBut (11): nimbo × fete = tarumba → so if fete = 1, then tarumba = nimbo\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ If nimbo = 1, then 1 + (yànparo tàxwo) = yenówe tàxwo \n→ This would mean yànparo tàxwo = 0? Not likely.\n\nAlternatively, consider that “yànparo tàxwo” is a marking of some number with a multiplicative suffix.\n\nBack to (7): ngámbi + ngámbi = ngámbi × yànparo \n→ So 2 ngámbi = ngámbi × yànparo \nThus, 2A = A × B → implies B = 2\n\nConclusion: yànparo = 2\n\nSimilarly, from (8): ngámbi + asàr = tambaroy \n→ So 1A + 1B = C → perhaps A = 1, B = 1 → A + B = 2\n\nSo tambaroy = 2\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ So A × A = (fete A) \nThus, 1 × 1 = fete 1 → implies fete = 1?\n\nBut from (11): nimbo × fete = tarumba → nimbo × 1 = tarumba → tarumba = nimbo\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \nNow yànparo = 2 → yànparo tàxwo = 2 with suffix \nSo nimbo + 2 = 1? → doesn’t work.\n\nWait: perhaps the “yànparo tàxwo” is a number larger than 1.\n\nAnother idea: use the example (13) and (14) to extract number values.\n\nLook at (15): cen-tzontli = tarumba tambaroy fete asàr \n→ “cen-tzontli” is a number, and equals “tarumba tambaroy fete asàr”\n\nFrom earlier: \n- tambaroy appears in (8): ngámbi + asàr = tambaroy → so tambaroy = 2 \n- tarumba appears in (11): nimbo × fete = tarumba → so tarumba is a product \n- fete in (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = 1 (since 1×1 = fete1) \n→ So tarumba = nimbo × 1 → tarumba = nimbo\n\nSo in (15): cen-tzontli = tarumba fete asàr = nimbo × 1 × asàr\n\nAsar appears in (8): ngámbi + asàr = tambaroy = 2 → so if ngámbi = 1, then asàr = 1\n\nSo asàr = 1\n\nThus: cen-tzontli = nimbo × 1 × 1 = nimbo\n\nSo cen-tzontli = nimbo\n\nSimilarly, from (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nBut we already have tarumba = nimbo, and yànparo = 2\n\nSo: cen-xiquipilli = weremeke (nimbo) (nimbo) (2)\n\nBut in (15): cen-tzontli = nimbo\n\nSo cen-tzontli = nimbo\n\nLikely, cen-tzontli = 1, since it is the only number with equality to a product.\n\nWait: if cen-tzontli = nimbo, and nimbo is a number, then cen-tzontli is a number.\n\nBut cen-tzontli is also written in other equations.\n\nAnother possibility: the affixes represent components of a number.\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\n\"tzontli\" may be a base unit (like \"1\"). \nIn (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nWe can try to interpret \"cen-tzontli\" as a tens or hundreds place?\n\nNote: (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf tarumba = nimbo, fete = 1, asàr = 1, and tambaroy = 2, then:\n\ncen-tzontli = nimbo × 1 × 1 = nimbo\n\nSo cen-tzontli = nimbo\n\nSo nimbo = some value, say 5?\n\nBut we need to know the value of the number 43 and 569.\n\nLet’s try to reconstruct the system.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nSo 2 ngámbi = ngámbi × yànparo → yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \nAssume ngámbi = 1, so asàr = 1 → tambaroy = 2\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo 1 × (1) = fete (1) → implies fete = 1\n\nFrom (11): nimbo × fete = tarumba → nimbo × 1 = tarumba → tarumba = nimbo\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \nyànparo = 2 → yànparo tàxwo = 2 with marker → so nimbo + 2 = 1 → impossible\n\nContradiction.\n\nAlternative: the \"yànparo tàxwo\" is not a literal number, but a compound.\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ So (A + B) → gives A fete \nThis looks like a combination: two addends with suffix = result with different structure\n\nSo perhaps suffix \"tàxwo\" marks a number in a different base or set.\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo 1 × (1 with tàxwo) = fete (1 with tàxwo) → if 1×1 = 1, then we get fete 1 → so fete = 1\n\nThus fete = 1\n\n(11): nimbo × 1 = tarumba → tarumba = nimbo\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nNow try to assign values.\n\nSuppose units:\n\n- ngámbi = 1\n- asàr = 1\n- yànparo = 2\n- fete = 1\n- tarumba = nimbo\n- yenówe = 1\n\nThen (12): nimbo + (2) = 1 → only if nimbo = -1 → invalid\n\nSo the suffix \"tàxwo\" cannot mean \"value\", may instead mark a different place value or operation.\n\nAlternative: the arithmetics in Arammba use a place-value system with affixes.\n\nLook at (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nThis is addition: left side has two terms, each with “tàxwo”; result is without “tàxwo”, and with “fete”\n\nSo perhaps “x tàxwo” represents a subunit, and addition produces a compound without suffix, but with new affix.\n\nSo to perform addition of two numbers with \"tàxwo\" suffix, the result is a new number with a different affix (fete) and without suffix.\n\nSo addition is not just sum, but requires a transformation.\n\nSimilarly, multiplication in (10): A × A tàxwo = fete A tàxwo \nSo A × (A with marker) = (fete + A with marker)\n\nIf A = 1, then 1 × (1 tàxwo) = fete (1 tàxwo) → so fete = 1\n\nSo again, fete = 1\n\nNow from (11): nimbo × fete = tarumba → nimbo × 1 = tarumba → tarumba = nimbo\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \nSuppose that \"yànparo tàxwo\" means \"2 in a subunit\", and \"yenówe tàxwo\" is a number.\n\nSuppose that \"yànparo\" = 2, and \"yànparo tàxwo\" = 2 in a special place.\n\nSo nimbo + 2 = ? and equals yenówe tàxwo\n\nBut if we assume that yenówe tàxwo is a number, and no value assigned, it may represent 1 or 2.\n\nOnly consistent with if nimbo = 1 and yànparo = 1, but (7) says ngámbi + ngámbi = ngámbi × yànparo → so if ngámbi = 1, then 2 = 1 × yànparo → yànparo = 2\n\nSo yànparo = 2\n\nThen (12): nimbo + 2 = yenówe tàxwo\n\nIf we assume yenówe is 1, then yenówe tàxwo = 1 with suffix → may mean 1\n\nSo nimbo + 2 = 1 → impossible.\n\nThus, the suffix \"tàxwo\" may not be adding a number, but marking a different operation.\n\nPerhaps multiplication is not of values, but of structures.\n\nAnother idea: in (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 = 1 × yànparo → yànparo = 2\n\nIn (8): ngámbi + asàr = tambaroy → 1 + 1 = tambaroy → tambaroy = 2\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr \n→ if tambaroy = 2, fete = 1, asàr = 1, tarumba = nimbo, then:\n\ncen-tzontli = nimbo × 2 × 1 × 1 = 2 × nimbo\n\nBut from (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nAlso, (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno → likely a number\n\nNow, look at equation (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nSuppose that \"cen\" is a base unit like 10.\n\nSo cen-tzontli = 10 × tzontli\n\nAnd tzontli is a unit.\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf we suppose that \"tambaroy\" = 2, \"fete\" = 1, \"asàr\" = 1, then:\n\ncen-tzontli = tarumba × 2 × 1 × 1 = 2 × tarumba\n\nBut tarumba = nimbo\n\nSo cen-tzontli = 2 × nimbo\n\nBut cen-tzontli = 10 × tzontli\n\nSo 10 × tzontli = 2 × nimbo\n\nSo nimbo = 5 × tzontli\n\nNow (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\ncen-xiquipilli = 10 × xiquipilli\n\n= weremeke (nimbo) (nimbo) (2)\n\nSo if each of (nimbo, nimbo, 2) is a component, then likely this is a number built from parts.\n\nSuppose the number is 10 × xiquipilli = weremeke (5×tzontli) (5×tzontli) (2)\n\nBut we need to represent 43 and 569.\n\n43 = 40 + 3 = 4×10 + 3\n\n569 = 500 + 60 + 9 = 5×100 + 6×10 + 9\n\nWe need to find a way to build numbers with units like \"tzontli\", \"xiquipilli\", etc.\n\nFrom (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n\"yë\" may be a modifier.\n\n\"tzontli\" might be 1.\n\n\"pöhualli\" might be 20 or 12.\n\nIn Nahu", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10608.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 0, + "output": "Step 1: Analyze the given examples to identify consistent morphological and syntactic patterns.\n\nLook at the verbs and their affixes to determine the core structure.\n\nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu \n→ \"We bought the camels for the neighbours.\" \n\"kanarriːcciːg\" = bought (verb) \n\"kamiːg\" = the camels (object) \n\"jaːnticcirsu\" = for the neighbours (prepositional phrase with \"jaːnti\" = neighbours)\n\nExample 2: tirt kadeːg allesu \n→ \"The owner repaired the dress.\" \n\"tirt\" = the owner (subject) \n\"kadeːg\" = repaired (verb) \n\"allesi\" = the dress (object)\n\nExample 3: jahali waliːg darbadki biticcirra \n→ \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men (subject) \n\"waliːg\" = will (future auxiliary) \n\"darbadki\" = give (verb) \n\"biticcirra\" = the chicken (object) \n→ \"to the dogs\" is missing. But \"biticcirra\" = chicken, not dogs. So \"to the dogs\" must be part of a prepositional phrase.\n\nWait: \"darbadki\" likely means \"give\", and \"biticcirra\" = chicken. So \"to the dogs\" is a separate clause. But no direct \"to the dogs\" word. Later we see \"elirsu\" and \"deːccirsa\" which resemble \"to the X\".\n\nExample 4: man jahalgi kadeːcciːg maːgtirsu \n→ \"He stole the dresses for the young man.\" \n\"man\" = he \n\"jahalgi\" = stole (past) \n\"kadeːcciːg\" = the dresses (object) \n\"maːgtirsu\" = for the young man\n\nNote: \"maːgtirsu\" = for the young man → \"maːg\" = young man, \"ti\" = for, \"rsu\" = the?\n\nExample 5: ay beyyeːcciːg ajaːnirri \n→ \"I am buying the necklaces.\" \n\"ay\" = I \n\"beyyeːcciːg\" = buying (present) \n\"ajaːnirri\" = the necklaces\n\nSimilarly: \nExample 6: wal aygi baːbiːg eldeːnsu \n→ \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (past) \n\"baːbiːg\" = the doors \n\"eldeːnsu\" = for me\n\nSo pattern: \n- Subject: e.g., ar, tirt, jahali, man, ay, wal \n- Verb: e.g., kanarriːcciːg, kadeːg, darbadki, kadeːcciːg, beyyeːcciːg, aygi, baːbiːg \n- Object: e.g., kamiːg, allesu, biticcirra, maːgtirsu, ajaːnirri, eldeːnsu \n- Preposition: \"for\" appears with \"jaːnticcirsu\", \"maːgtirsu\", \"eldeːnsu\", \"alletirsi\" → likely \"for\" is a prepositional phrase with a noun\n\nPossibility: The structure is: \n[Subject] [verb] [object] [for [demonstrative or noun]] \n\nBut in 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → \"eldeːnsu\" = for me \nIn 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → \"maːgtirsu\" = for the young man\n\nThus, \"for\" is a separate element, likely with a possessive/demonstrative.\n\nCheck: \nExample 8: iːdi magaski kamiːg tirsa \n→ \"The men gave the camels to the thief.\" \n\"iːdi\" = the men \n\"magaski\" = gave \n\"kamiːg\" = the camels \n\"tirsa\" = to the thief\n\nAh! So \"tirsa\" = to the thief\n\nSimilarly, Example 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs\" → to the dogs?\n\nBut no \"to\" word. Wait – in 8, \"tirsa\" = to the thief\n\nIn 1: \"jaːnticcirsu\" → for the neighbours\n\nIn 4: maːgtirsu → for the young man\n\nSo we have two prepositional constructions:\n\n- \"jaːnticcirsu\" → for the neighbours \n- \"maːgtirsu\" → for the young man \n- \"eldeːnsu\" → for me \n- \"tirsa\" → to the thief \n\nSo: \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours \n- \"maːgtirsu\" = for the young man \n- \"eldeːnsu\" = for me \n\nBut in example 3: no \"to\" phrase → perhaps the object is already \"the chicken\", and \"to the dogs\" is not stated.\n\nWait: the translation says: \"The young men will give the chicken to the dogs.\" → so \"to the dogs\" must be present.\n\nBut no such word appears. So perhaps the verb takes a prepositional phrase of \"to\" or \"for\".\n\nCompare to example 13: hanu tirtiːg elirsu → \"I will strike the donkey\" (from 9: ay hanuːg bijomri) → we have \"hanu\" = strike?\n\nExample 9: ay hanuːg bijomri → I will strike the donkey \n→ \"hanuːg\" = will strike \n\"bijomri\" = the donkey\n\nSo \"hanu\" is the verb root, \"hanuːg\" = will strike? (affective morpheme)\n\nBack to verb roots:\n\n- kanarriːcciːg = to buy \n- kadeːg = to repair \n- darbadki = to give \n- kadeːcciːg = to steal \n- beyyeːcciːg = to buy \n- baːbiːg = to find \n- magas = to give \n- hanu = to strike\n\nAll verbs seem to have a root and a suffix indicating tense/aspect.\n\nSpecifically:\n\n- \"kanarriːcciːg\" → \"kanarri\" + \"ciːg\" → buy \n- \"kadeːg\" → repair \n- \"darbadki\" → give \n- \"kadeːcciːg\" → steal \n- \"beyyeːcciːg\" → buy \n- \"baːbiːg\" → find \n- \"magas\" → give \n- \"hanuːg\" → will strike\n\nFurther: \n\"kanarriːcciːg\" vs. \"kanarriːg\" → in 1, \"kanarriːcciːg\" with \"ciːg\" \nIn 10: sarkaːyi aygi beyyeːcciːg adeːnda → \"The cowards are giving me the necklaces\" \n\"aygi\" = are giving → present progressive \n\"beyyeːcciːg\" = giving \n\"adeːnda\" = me? or to me?\n\n\"adeːnda\" = me? → in 6: \"eldeːnsu\" = for me\n\nSo likely \"adeːnda\" = to me\n\nSimilarly, \"maːgtirsu\" = for the young man \n\"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief\n\nSo prepositions:\n\n- \"to\" = \"tirsa\" \n- \"for\" = \"jaːnticcirsu\", \"maːgtirsu\", \"eldeːnsu\", \"adeːnda\"\n\nNow, for objects:\n\n- \"kamiːg\" = the camels \n- \"allesi\" = the dress \n- \"biticcirra\" = the chicken \n- \"maːgtirsu\" → \"for the young man\" \n- \"ajaːnirri\" = the necklaces \n- \"baːbiːg\" = the doors \n- \"bijomri\" = the donkey\n\nSo object markers: \"kamiːg\", \"allesi\", \"biticcirra\", \"ajaːnirri\", \"baːbiːg\", \"bijomri\"\n\nNow look at the new sentences.\n\n11. magasi argi ajomirra \n\"magasi\" = ? → magas = give → \"magasi\" = give? \n\"argi\" = ? \n\"ajomirra\" = ? → similar to \"bijomri\" = donkey → \"ajomirra\" = the donkey?\n\nSo: \"magasi\" = give? \n\"argi\" = ? → possible tense or auxiliary? \nIn example 3: \"waliːg\" = will → future \nIn 5: \"ay beyyeːcciːg\" = I am buying → present continuous \n\n\"magasi\" likely = give (from \"magas\") \n\nThen \"argi\" – possible future auxiliary? \n\nCompare to example 3: \"jahali waliːg darbadki\" → \"will give\" \n\n\"argi\" not used before.\n\nBut \"waliːg\" is future auxiliary.\n\n\"magasi\" = give? with \"argi\" → perhaps \"argi\" is future? \n\nBut no parallel. \n\nAlternative: \"argi\" might be \"to\" or \"for\"? \n\nBut \"ajomirra\" = the donkey → object? \n\nSo: \"magasi argi ajomirra\" → give to the donkey?\n\nBut in example 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to the thief\n\n\"tirsa\" = to the thief → so \"to\" in prepositional phrase\n\nSimilarly, \"argi\" might be \"to\"?\n\nBut \"tirsa\" has \"ti\", \"r\", \"s\", \"u\" → might be a form.\n\nTry: \n\"magasi\" = give \n\"argi\" = to \n\"ajomirra\" = the donkey → object\n\nSo: \"give to the donkey\" → but subject missing?\n\nIn all cases, subject is missing in 11.\n\nBut in 11, no subject → so perhaps imperative or general?\n\nBut grammar likely has subject.\n\nBut in 10: sarkaːyi aygi beyyeːcciːg adeːnda → subject \"sarkaːyi\" = the cowards\n\nSo in 11, \"magasi argi ajomirra\" → maybe subject is implied?\n\nBut translations must be complete.\n\nNote: in 3, \"jahali waliːg darbadki biticcirra\" → \"will give the chicken\"\n\nSo verb + object = give + object\n\nSimilarly, 11: \"magasi argi ajomirra\" → \"give to the donkey\"\n\nBut need subject? → perhaps the verb \"magasi\" is not \"give\"? Maybe it's \"to give\"?\n\nWait: \"magas\" = give → \"magasi\" = give?\n\nNo other verb form.\n\nPerhaps \"argi\" is auxiliary? Like \"will\" or \"to\"?\n\nBut \"waliːg\" = will → in 3\n\nIs \"argi\" a tense? Probably not.\n\nBest to assume: “magasi” = give, “argi” = to, “ajomirra” = the donkey → “give to the donkey”\n\nBut sentence lacks subject.\n\nMaybe it's a construction like “Give to the donkey” (imperative or general).\n\nBut in all other examples, there is a subject.\n\nBut perhaps this is just a core verbal construction.\n\nNow 12. ay kanarriːg baːbki alletirsi \n\"ay\" = I \n\"kanarriːg\" = buy (stem) \n\"baːbki\" = for? \n\"alletirsi\" = ? → compare to \"jaːnticcirsu\" = for the neighbours → \"alletirsi\" → \"al\" + \"letirsi\"?\n\n\"al\" = the? \"letirsi\" = neighbours?\n\n\"jaːnticcirsu\" = for the neighbours → \"jaːnti\" = neighbours\n\n\"alletirsi\" → likely \"the neighbours\" → so \"alletirsi\" = the neighbours?\n\nBut in 1: \"jaːnticcirsu\" = for the neighbours\n\nSo \"baːbki\" = for? → then \"al\" = the?\n\n\"baːbki\" + \"alletirsi\" = for the neighbours?\n\nYes — \"baːbki alletirsi\" = for the neighbours\n\nSo \"ay kanarriːg baːbki alletirsi\" → \"I buy for the neighbours\"\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours\"\n\nSo \"kanarriːg\" = buy, \"baːbki\" = for, \"alletirsi\" = the neighbours\n\nYes → so “I buy for the neighbours”\n\n13. hanu tirtiːg elirsu \n\"hanu\" = strike \n\"tirtiːg\" = ? → \"tirt\" = owner → \"tirtiːg\" = to the owner? \n\"elirsu\" = ? → \"tirsa\" = to the thief → \"elirsu\" = to the owner?\n\n\"elirsu\" → likely \"to the owner\" → because \"tirt\" = owner\n\nSo \"hanu tirtiːg elirsu\" → \"I strike to the owner\"?\n\nBut \"hanu\" = strike, so \"I strike the owner\"? \nBut verb form: \"hanu\" alone means \"strike\" → if object is \"the owner\", then \"hanu elirsu\" = strike the owner\n\nBut here: \"hanu tirtiːg elirsu\" → \"tirtiːg\" = ? \n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"men gave camels to the thief\" → \"tirsa\" = to thief → \"tir\" = thief, \"s\" = to?\n\nSo \"tirt\" = owner → \"tirtiːg\" = to the owner?\n\nYes → \"tirtiːg\" = to the owner\n\nAnd \"elirsu\" = to the owner? — no, \"elirsu\" = to the owner?\n\nBut \"tir\" = thief → \"el\" = owner?\n\nPossibility: \"tir\" = thief → \"el\" = owner?\n\nIn \"tirsa\" = to thief → \"tir\" = thief \n\"elirsu\" → \"el\" = owner? → \"el\" + \"irsu\" → to the owner?\n\nYes → likely \"elirsu\" = to the owner\n\nSo \"hanu tirtiːg elirsu\" → \"I strike to the owner\" — but two prepositional phrases?\n\nUnlikely. Probably \"hanu\" + \"tirtiːg\" + \"elirsu\" → \"I strike the owner\"?\n\nBut \"tirtiːg\" = to the owner → if \"elirsu\" = to the owner → redundant.\n\nPerhaps \"tirtiːg\" = to the owner, \"elirsu\" = the owner?\n\nNo. Or perhaps \"elirsu\" = the owner.\n\nIn example 1: \"jaːnticcirsu\" → for the neighbours \nWe don't have a noun like \"owner\" but \"tirt\" = owner.\n\nSo likely \"elirsu\" = the owner\n\n\"tirtiːg\" = to the owner\n\nSo the sentence is \"I strike to the owner\" — awkward.\n\nAlternatively, \"hanu\" modifies object.\n\nBut \"hanu\" is transitive — \"I strike [someone]\"\n\nSo \"hanu tirtiːg elirsu\" → \"I strike [to the owner] the owner\"? No.\n\nBetter: \"tirtiːg\" = to the owner → so it's \"I strike to the owner\" — but said in active voice, not idiomatic.\n\nWait — in example 9: ay hanuːg bijomri → I will strike the donkey → \"hanu\" + object → \"the donkey\"\n\nSo \"hanu\" is transitive: \"strike X\"\n\nSo \"hanu tirtiːg elirsu\" → likely \"I strike [to the owner] [the owner]\" — not possible.\n\nPerhaps \"tirtiːg\" is object → \"tirt\" = owner → \"tirtiːg\" = the owner → so \"I strike the owner\"\n\nThen \"elirsu\" is redundant?\n\nBut \"elirsu\" could be a different noun.\n\n\"elirsu\" — in example 9: \"bijomri\" = the donkey → likely \"el\" = owner, \"irsu\" = the?\n\n\"elirsu\" = the owner\n\nSo \"hanu tirtiːg elirsu\" → \"I strike to the owner\" — not natural.\n\nAlternatively, \"tirtiːg\" is a different form — perhaps future?\n\nNo.\n\nAnother possibility: \"hanu\" = strike, \"tirtiːg\" = will (like waliːg), \"elirsu\" = the owner\n\nSo \"I will strike the owner\"\n\nYes — \"tirtiːg\" could be future auxiliary — like \"waliːg\"\n\nIn example 3: \"waliːg\" = will\n\nIn 11: \"argi\" could be future?\n\nBut \"tirtiːg\" — not \"waliːg\"\n\nBut \"waliːg\" appears only once.\n\n\"tirtiːg\" — could be \"to\" + \"tirt\"?\n\nBut no.\n\nPossibility: \"tirtiːg\" = to the owner (prepositional phrase)\n\n\"elirsu\" = the owner (noun)\n\nSo redundant.\n\nUnless “elirsu” is the", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11207.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 1, + "output": "Step 1: Identify recurring verb patterns and core elements in the examples.\n\nLook at the verb stems and their objects:\n- Example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n → \"kanarriːcciːg\" = buy; object \"kamiːg\" = camels; prepositional phrase \"for the neighbours\" = \"jaːnticcirsu\"\n\n- Example 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n → \"tirt\" = repair; object \"kadeːg\" = dress\n\n- Example 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n → \"darbadki\" = give; object \"biticcirra\" = chicken; to \"the dogs\"\n\n- Example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n → \"kadeːcciːg\" = steal; object \"kadeːcciːg\" (reiterated) = dresses; prepositional phrase \"for the young man\"\n\n- Example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n → \"beyyeːcciːg\" = buying; object \"ajaːnirri\" = necklaces\n\n- Example 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n → \"baːbiːg\" = find; object \"eldeːnsu\" = doors; \"for me\" → \"aygi\" = for me\n\n- Example 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n → \"ticcirsu\" = give; object \"waliːg\" = dogs; indirect object \"you (pl.)\"\n\n- Example 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n → \"tirsa\" = give; object \"kamiːg\" = camels; to \"the thief\"\n\n- Example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n → \"hanuːg\" = strike; object \"bijomri\" = donkey\n\n- Example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n → \"aygi\" = for me; \"beyyeːcciːg\" = buying/giving; object \"adeːnda\" = necklaces\n\nKey pattern: \n- Verbs are often transitive and take direct object (NOM) and optionally a prepositional phrase (e.g., \"for X\").\n- The prepositional phrase is formed with a particle (e.g., \"jaːnticcirsu\" = for the neighbours).\n- Subject is often marked by a pronoun or noun phrase, e.g., \"ay\" = I, \"man\" = he, \"wal\" = the dog, \"jahali\" = young men.\n\nStep 2: Identify affixes and fixed phrases.\n\n- \"kanarriːg\" → buy; \"kanarriːcciːg\" → buy (with object suffix or agent?)\n- \"beyyeːcciːg\" → buying\n- \"tirt\" → repair\n- \"darbadki\" → give\n- \"kadeːcciːg\" → steal\n- \"baːbiːg\" → find\n- \"tirsa\" → give\n- \"hanuːg\" → strike\n\nObserve object marking:\n- \"kamiːg\" = camels (pronoun object form?)\n- \"kadeːg\" = dress\n- \"biticcirra\" = chicken\n- \"maːgtirsu\" = young man\n- \"ajaːnirri\" = necklaces\n- \"eldeːnsu\" = doors\n- \"waliːg\" = dogs\n- \"bijomri\" = donkey\n- \"adeːnda\" = necklaces\n\nNow check for prepositional particles:\n- \"jaːnticcirsu\" = for the neighbours\n- \"aygi\" = for me\n- \"tirsa\" = give to (indirect object)\n- \"deːccirsa\" → possibly means \"to\" or \"for\" in examples\n\nExample 14: \"tirti argi kamgi deːccirsa\" → \"tirti\" = repair; \"argi\" = ??; \"kamgi\" = camels; \"deːccirsa\" → likely = for?\n\n\"tirti\" = repair? From \"tirt\" → \"tirti\" = root with thematic affix?\n\nLook for morphological patterns:\n\nUse minimal pairs:\n- Example 1: \"kanarriːcciːg kamiːg jaːnticcirsu\" → buy camels for neighbours\n- Example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → he stole dresses for young man\n- Example 6: \"wal aygi baːbiːg eldeːnsu\" → dog found doors for me\n\nSo \"aygi\" consistently means \"for me\"\n\nSimilarly, \"jaːnticcirsu\" = for the neighbours \n\"maːgtirsu\" = for the young man \n\"eldeːnsu\" = doors \n\"adeːnda\" = necklaces\n\nSo prepositions:\n- \"jaːnticcirsu\" → for the X (specific group)\n- \"aygi\" → for me\n- \"deːccirsa\" → likely \"for\" or \"to\" → in example 14: \"tirti argi kamgi deːccirsa\"\n\nNow analyze each target sentence:\n\n11. magasi argi ajomirra \n\"magasi\" → likely from \"magas\" (thief) + suffix → \"magasi\" = the thief? \n\"argi\" → possibly \"to\" or \"for\"? \n\"ajomirra\" → likely \"donkey\" (from \"bijomri\") → so \"ajomirra\" = donkey? \nBut in 9: \"hanuːg bijomri\" = I will strike the donkey → so \"bijomri\" = donkey \nThus \"ajomirra\" = donkey \nSo \"magasi argi ajomirra\" → the thief will strike the donkey? \n\nBut \"hanuːg\" = strike, \"magasi\" = thief, \"argi\" = to?\n\n\"magasi\" could be a noun — \"the thief\" \n\"argi\" → like \"hanu\" (strike) → but \"hanu\" is verb \n\"argi\" → likely \"to\", \"for\", or \"give\"?\n\nCompare with 9: \"hanuːg bijomri\" → I will strike donkey \nNo \"argi\" → so \"argi\" is not \"strike\" \n\nBut in example 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" \n→ \"tirsa\" = give to \n→ So \"tirsa\" = to (someone)\n\nPossibly \"argi\" = to?\n\nIn 11: \"magasi argi ajomirra\" → the thief to the donkey? That doesn't fit.\n\nMaybe \"argi\" is a verb?\n\nBut \"hanu\" is verb, \"tirt\" is verb, \"beyyeːcciːg\" is verb.\n\n\"argi\" not in examples as verb.\n\nPossibility: \"argi\" = for?\n\nCompare with 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me the necklaces \n\"aygi\" = for me\n\nSo \"argi\" = for?\n\nPossibly.\n\nSo \"magasi argi ajomirra\" = the thief is giving (for) the donkey?\n\nBut \"give\" verb is \"darbadki\" or \"tirsa\"\n\n\"magasi\" = the thief → subject? \n\"argi\" = for? \n\"ajomirra\" = donkey → object?\n\nBut \"give\" missing.\n\nPerhaps \"argi\" is an object marker?\n\nNo — in 3: \"jahali waliːg darbadki biticcirra\" → young men give chicken to dogs → \"biticcirra\" is object, \"to dogs\" is phrasal.\n\nSo in 11: \"magasi argi ajomirra\" → thief gives donkey?\n\nBut no verb.\n\nUnless \"argi\" is a verb?\n\nBut no verb fits.\n\nAlternative: \"magasi\" = verb? No — \"magas\" is noun (thief)\n\nBetter to test verb structure.\n\nRe-express all verbs:\n\n| Example | Verb | Object | Purpose Phrase |\n|--------|------|--------|----------------|\n| 1 | kanarriːcciːg | kamiːg | jaːnticcirsu |\n| 2 | tirt | kadeːg | (none) |\n| 3 | darbadki | biticcirra | (to dogs) |\n| 4 | kadeːcciːg | maːgtirsu | (for young man) |\n| 5 | beyyeːcciːg | ajaːnirri | (none) |\n| 6 | baːbiːg | eldeːnsu | aygi |\n| 7 | ticcirsu | waliːg | (to you) |\n| 8 | tirsa | kamiːg | to thief |\n| 9 | hanuːg | bijomri | (none) |\n|10 | beyyeːcciːg | adeːnda | aygi |\n\nSo verbs are transitive: [subject] [verb] [object] [optional prepositional phrase]\n\nPrepositional phrase:\n- \"jaːnticcirsu\" = for the neighbours\n- \"aygi\" = for me\n- \"tirsa\" → give to → may be verb, not prepositional\n\nBut in 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repair → likely verb \n\"argi\" = ? \n\"kamgi\" = camels → object \n\"deːccirsa\" = for?\n\nSo likely \"argi\" is a preposition: for\n\nSimilarly, in 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = strike → verb? \n\"tirtiːg\" = repair? → \"tirti\" = repair → \"tirtiːg\" = repair (past?) \n\"elirsu\" = doors?\n\nSo \"hanu tirtiːg elirsu\" → I strike the repair of doors? No.\n\n\"hanu\" = strike \n\"tirtiːg\" = ? \n\"elirsu\" = doors\n\nBut \"tirtiːg\" is not in examples.\n\nPossibility: \"tirtiːg\" = verb with object?\n\nBut example 6: \"wal aygi baːbiːg eldeːnsu\" — dog found doors for me\n\n\"tirtiːg\" is not found.\n\nWait: example 2: \"tirt kadeːg allesu\" → repair dress\n\nSo \"tirt\" = repair\n\n\"tirti\" = repair (same form?)\n\n\"tirtiːg\" → perhaps \"tirti\" + \"g\" = past tense or something?\n\nNo clear tense.\n\nBut in 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike \n\"tirtiːg\" = repair? \n\"elirsu\" = doors?\n\nSo \"I strike the repair of doors\"? That doesn’t make sense.\n\nPossibility: typo or misalignment.\n\nAlternative: \"tirtiːg\" = \"repair\" and \"elirsu\" = doors → so \"I repair the doors\"?\n\nBut \"hanu\" = strike, not repair.\n\nUnless \"hanu\" is \"I will\" or future?\n\nExample 9: \"ay hanuːg bijomri\" → I will strike the donkey → \"hanuːg\" = future tense of strike\n\nSo \"hanu\" = future\n\nThus in 13: \"hanu tirtiːg elirsu\" → I will repair the doors?\n\n\"tirtiːg\" = repair (with object) → so verb \"tirt\" → \"tirti\" = repair in form?\n\nYes — if \"tirti\" = repair (present), then \"tirtiːg\" = repair?\n\nPossibly, but no object all.\n\nIn example 2: \"tirt kadeːg allesu\" → subject \"the owner\", object \"dress\"\n\nSo \"tirt\" = repair\n\n\"tirti\" = repair (same verb)\n\nSo \"tirtiːg\" → likely \"repair\" (with object)\n\nSo \"hanu tirtiːg elirsu\" → I will repair the doors.\n\nThat makes sense.\n\nSimilarly, 14: \"tirti argi kamgi deːccirsa\" → repair (for?) camels for whom?\n\n\"argi\" → likely \"for\", \"deːccirsa\" = for?\n\nWe have only one \"deːccirsa\" → in 14, possibly \"for\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → men gave camels to thief → \"tirsa\" = to thief\n\n\"tirsa\" = to whom? → indirect object\n\nBut in 8, \"tirsa\" = to\n\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → for me\n\nSo two prepositions:\n- \"aygi\" = for me\n- \"jaːnticcirsu\" = for the neighbours\n- \"deːccirsa\" = for?\n\nIs \"deːccirsa\" = for?\n\nIn 14: \"tirti argi kamgi deːccirsa\" → \"repair camels for X\"\n\n\"argi\" may be a typo or misreading — check original.\n\nOriginal: \"tirti argi kamgi deːccirsa\"\n\nPossibly \"argi\" = \"to\", \"deːccirsa\" = \"for\"?\n\nBut no.\n\nPossibility: \"argi\" is root verb?\n\nBut no verb for \"repair\".\n\nAlternative: \"tirti\" = repair, \"kamgi\" = camels → object, \"deːccirsa\" = for?\n\nThen \"argi\" → could be error or redundant?\n\nWait — in 11: \"magasi argi ajomirra\"\n\n\"magasi\" = the thief? (from \"magas\" = thief)\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\"\n\n\"magaski\" = to the thief → so \"magas\" = thief\n\nSo \"magasi\" = the thief\n\n\"argi\" → could be \"to\" or \"gives\"\n\nBut no verb.\n\nUnless \"argi\" is a verb meaning \"give\"?\n\nBut \"darbadki\" = give.\n\nExample 3: \"jahali waliːg darbadki biticcirra\" = young men give chicken to dogs\n\nNo \"argi\"\n\nWait — in 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me the necklaces\n\n\"aygi\" = for me\n\n\"beyyeːcciːg\" = give\n\n\"adeːnda\" = necklaces\n\nSo \"beyyeːcciːg\" = give\n\nThus verb \"beyyeːcciːg\" = give\n\nSo in 11: \"magasi argi ajomirra\" → the thief gives the donkey?\n\nBut \"argi\" is not \"give\"\n\nPerhaps \"argi\" is a typo for \"beyyeːcciːg\"?\n\nNo — different.\n\n\"argi\" not in verbs.\n\nAnother idea: \"argi\" = to whom?\n\nLike \"tirsa\" = to\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief\n\nSo \"tirsa\" = to\n\nIn 14: \"tirti argi kamgi deːccirsa\" → repair [to] camels [for]?\n\n\"argi\" = to (preposition)\n\n\"deːccirsa\" = for?\n\nBut \"deːccirsa\" = for?\n\nIn 14: \"tirti argi kamgi deːccirsa\" → repair to camels for?\n\nNo — \"kamgi\" = camels → object\n\nSo \"tirti\" = repair, \"kamgi\" = object, \"argi\" = to someone, \"deːccirsa\" = for someone?\n\nToo many.\n\nPossibility: \"deːccirsa\" = for\n\n\"argi\" = to\n\nBut in 14, if \"tirti\" = repair, \"kamgi\" = camels, \"argi\" = to, \"deːccirsa\" = for — but \"to\" and \"for\" both?\n\nUnlikely.\n\nPerhaps \"argi\" = \"for\", and \"deːccirsa\" = redundant or error?\n\nBut in example 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces\n\nNo purpose phrase\n\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → dog found doors for me → \"aygi\" = for me\n\nSo \"aygi\" = for me\n\n\"jaːnticcirsu\" = for the neighbours\n\nThus, want to find what \"argi\" is.\n\nTry to see in which examples \"argi\" appears — only in 11 and 14.\n\n11: \"magasi argi ajomirra\" \n14: \"tirti argi kamgi deːccirsa\"\n\nIn 14: \"kamgi\" = camels → object \n\"deːccirsa\" = for? \n\nSo \"argi\" may be \"to\"\n\nSimilarly, in ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10707.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build an alignment table from the examples to identify consistent patterns in verb stems, objects, subjects, and affixes.\n\nKey observations:\n\n- All verbs are transitive and involve giving, buying, stealing, repairing, striking, or finding.\n- The verb stems often appear in the form: [agent] [verb-stem] [object] [prepositional/locative element].\n- Affixes mark subject, object, aspect, and direction.\n- The structure often follows: Subject + Object + [for/into/to] + [target] or [action].\n\nLook at verb patterns:\n\nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu. \n→ \"We bought the camels for the neighbours.\" \n\"kanarriːcciːg\" = bought (past), \"kamiːg\" = the camels, \"jaːnticcirsu\" = for the neighbours.\n\nExample 2: tirt kadeːg allesu. \n→ \"The owner repaired the dress.\" \n\"tirt\" = the owner, \"kadeːg\" = repaired, \"allesi\" = the dress.\n\nExample 3: jahali waliːg darbadki biticcirra. \n→ \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men, \"waliːg\" = will, \"darbadki\" = give, \"biticcirra\" = the chicken, \"tirsa\" = to the dogs.\n\nExample 4: man jahalgi kadeːcciːg maːgtirsu. \n→ \"He stole the dresses for the young man.\" \n\"man\" = he, \"jahalgi\" = stole, \"kadeːcciːg\" = the dresses, \"maːgtirsu\" = for the young man.\n\nExample 5: ay beyyeːcciːg ajaːnirri. \n→ \"I am buying the necklaces.\" \n\"ay\" = I, \"beyyeːcciːg\" = buying, \"ajaːnirri\" = the necklaces.\n\nExample 6: wal aygi baːbiːg eldeːnsu. \n→ \"The dog found the doors for me.\" \n\"wal\" = the dog, \"aygi\" = found, \"baːbiːg\" = the doors, \"eldeːnsu\" = for me.\n\nExample 7: magas ikki waliːg ticcirsu. \n→ \"The thief gave you (pl.) the dogs.\" \n\"magas\" = thief, \"ikki\" = you (pl.), \"ticcirsu\" = gave, \"waliːg\" = you (pl.)? Wait — “ikki waliːg” → you (pl.). “ticcirsu” = give.\n\nActually, “ticcirsu” = give, so “gave” is the verb.\n\nExample 8: iːdi magaski kamiːg tirsa. \n→ \"The men gave the camels to the thief.\" \n\"iːdi\" = the men, \"magaski\" = to the thief, \"kamiːg\" = the camels, \"tirsa\" = to the thief.\n\nWait — “magaski” = to the thief → so object is \"the camels\", recipient is \"the thief\" via affix.\n\nIn 8: iːdi (subject) + magaski (to thief) + kamiːg (object) + tirsa (give) → But \"tirsa\" is likely the verb? Seems redundant.\n\nWait: “iːdi magaski kamiːg tirsa” → The men gave the camels to the thief. \nSo verb is \"tirsa\" = gave. “magaski” = to the thief → prepositional phrase.\n\nSo verb is “tirsa” = to give.\n\nIn 2: “tirt” + kadeːg + allesu → “the owner repaired the dress.” “tirt” is subject, “kadeːg” is verb, “allesi” object.\n\nIn 6: “wal” + aygi + baːbiːg + eldeːnsu → dog found doors for me → “eldeːnsu” = for me.\n\nIn 4: man jahalgi kadeːcciːg maːgtirsu → he stole dresses for young man → “maːgtirsu” = for young man.\n\nSo “maːgtirsu” = for young man.\n\nSimilarly, “jaːnticcirsu” = for neighbours.\n\n“eldeːnsu” = for me.\n\n“allesi” = the dress.\n\n“kamiːg” = the camels.\n\n“waliːg” = will (future)\n\n“aygi” = found\n\n“beyyeːcciːg” = buying\n\n“tirsa” = give (verb)\n\n“ticcirsu” = give (verb)\n\nSo verb stems for key actions:\n\n- buy: beyyeːcciːg → \"buy\"\n- give: ticcirsu / tirsa (past, form varies)\n- repair: kadeːg\n- find: baːbiːg\n- strike: hanuːg\n\nNote: “hanuːg” in 9 → \"I will strike the donkey\" → \"hanuːg bijomri\" → \"strike the donkey\"\n\nSo “hanuːg” = strike (verb)\n\n“bijaːndi” = strike (future?) → in 15: “ay darbadki bijaːndi” → \"I will give the chicken to the dog?\" Wait.\n\nWait: 15 is “ay darbadki bijaːndi” → in guidance, it says “the young men will give the chicken to the dogs” — no, that's 3.\n\nActually, 15: ay darbadki bijaːndi → “I will give the chicken to the dogs”?\n\nBut 3: jahali waliːg darbadki biticcirra → “The young men will give the chicken to the dogs.”\n\nSo “darbadki” = give, “bijaːndi” = to the dogs?\n\nBut “bijaːndi” not in 3.\n\n3: “biticcirra” = the chicken, “tirsa” = to the dogs.\n\n“tirsa” = to the dogs.\n\nSo “tirsa” = to the dogs.\n\nIn 15: ay darbadki bijaːndi → \"I will give the chicken to the dogs\" → so “bijaːndi” = to the dogs?\n\nBut in 3, it's “tirsa” = to the dogs.\n\nWait — in 3: jahali waliːg darbadki biticcirra → “will give the chicken to the dogs.” So object = chicken, recipient = dogs → uses \"tirsa\"?\n\nBut the sentence says “to the dogs”, and uses “tirsa” → so “tirsa” = to the dogs?\n\nIn 8: iːdi magaski kamiːg tirsa → men gave camels to thief → “magaski” = to thief.\n\nSo “magaski” = to thief, “tirsa” = give.\n\nIn 6: wal aygi baːbiːg eldeːnsu → dog found doors for me → “eldeːnsu” = for me.\n\nSo for/with expressions:\n\n- jaːnticcirsu → for the neighbours\n- maːgtirsu → for the young man\n- eldeːnsu → for me\n- tirsa → to the dogs / to the thief\n- magaski → to the thief\n\nWait — in 8: “magaski kamiːg tirsa” → “to the thief” + “gave” → so “magaski” = to the thief, “tirsa” = verb.\n\nIn 6: “eldeːnsu” = for me → instead of “tirsa”.\n\nSo different prepositional markers.\n\nSo verbs:\n\n- kadeːg → repair\n- beyyeːcciːg → buy\n- darbadki → give\n- hanuːg → strike\n- aygi → find\n- tirsa → give (verb)\n- ticcirsu → give (verb)\n\nBut “tirsa” and “ticcirsu” both mean give?\n\nExample 7: magas ikki waliːg ticcirsu → thief gave you dogs → so “ticcirsu” = gave, “ikki” = to you (pl.)\n\nExample 8: iːdi magaski kamiːg tirsa → men gave camels to thief → “tirsa” = gave.\n\nSo both “tirsa” and “ticcirsu” = give, but different verb forms?\n\nWait, but “waliːg” = will → future tense.\n\nIn 3: jahali waliːg darbadki biticcirra → “will give”\n\nSo “darbadki” is the verb “give” → used in future in 3.\n\nIn 7: magas ikki waliːg ticcirsu → “gave” → past?\n\nBut “waliːg” = future → so “ticcirsu” = gave (future)?\n\nBut it's odd.\n\nPerhaps “tirsa” and “ticcirsu” are both give, possibly with different aspect.\n\nBut in 7: “magas ikki waliːg ticcirsu” → thief will give you the dogs → so future.\n\nIn 8: “iːdi magaski kamiːg tirsa” → men gave camels to thief → past.\n\nSo “tirsa” = past give, “ticcirsu” = future give?\n\nIn 3: jahali waliːg darbadki biticcirra → future give.\n\nBut “darbadki” = give.\n\nSo multiple forms for \"give\".\n\nThus, the verb for “give” has several forms:\n\n- darbadki → give (used in future with waliːg)\n- ticcirsu / tirsa → give, with different aspect or tense markers.\n\nActually, in 8: “tirsa” = gave (past), in 7: “ticcirsu” = will give (future) → so the verb changes with tense.\n\nBut “waliːg” is marked on clause for future.\n\nSo likely the intransitive or base verb is “tirsa” or “ticcirsu”.\n\nNow, look at object markers:\n\n- kamiːg → the camels\n- kadeːg → the dress\n- biticcirra → the chicken\n- baːbiːg → the doors\n- maːgtirsu → for the young man\n- ajaːnirri → the necklaces\n\nSo object is marked directly: “kamiːg”, “kadeːg”, etc.\n\nPrepositional phrases for destination:\n\n- jaːnticcirsu → for the neighbours\n- maːgtirsu → for the young man\n- eldeːnsu → for me\n- magaski → to the thief\n- bijaːndi → to the dogs?\n\nWait — in 3: “biticcirra” → chicken, “tirsa” → to the dogs\n\nIn 14: tirti argi kamgi deːccirsa → “the owner gave the camels to the dogs”?\n\n\"tirti\" = the owner? = tirt + i? → earlier tirt = owner → so tirti = the owner (possessive or form with i?)\n\n\"argi\" = give? → verb?\n\n\"camgi\" = the camels? → kamgi = the camels?\n\n\"kamgi\" = camels → yes.\n\n\"deːccirsa\" = to the dogs?\n\nIn 3: “tirsa” → to the dogs → so deːccirsa?\n\nCompare to 3: “tirsa” = to the dogs.\n\nIn 8: “magaski” = to the thief.\n\nSo likely deːccirsa = to the dogs.\n\nSimilarly, in 14: tirti argi kamgi deːccirsa → the owner gives the camels to the dogs.\n\nNow, subject markers:\n\n- ar → we\n- tirt → owner\n- jahali → young men\n- man → he\n- ay → I\n- wal → the dog\n- iːdi → the men\n- magas → the thief\n\nNow, for each item:\n\n11. magasi argi ajomirra.\n\n“magasi” → thief? (like “magas”)\n“argi” → give?\n“ajomirra” → to the necklaces? Or what?\n\nWait — in 5: “ay beyyeːcciːg ajaːnirri” → I am buying the necklaces → “ajaːnirri” = necklaces.\n\nSo “ajomirra” → necklaces?\n\n“aj” + “omirra” → possibly same root?\n\nIn 5: “ajaːnirri” = necklaces.\n\nSo “ajomirra” → likely “necklaces”?\n\nBut is it \"to the necklaces\" or \"the necklaces\"?\n\nIn 5: “beyyeːcciːg ajaːnirri” → buying the necklaces → object.\n\nIn 11: “magasi argi ajomirra” → thief gives to the necklaces?\n\n“argi” = give? But in 3: \"darbadki\" = give.\n\nIn 7: “ticcirsu” = give.\n\nSo “argi” — is it a form of give?\n\n“argi” → likely “give”.\n\nBut is it “to the necklaces”?\n\nYes — in 5: “beyyeːcciːg ajaːnirri” = buying the necklaces → object.\n\nSo “ajomirra” = the necklaces → “aj” base, “omirra” = necklaces?\n\nSo “magasi” = the thief, “argi” = gives, “ajomirra” = the necklaces.\n\nSo: The thief gives the necklaces.\n\nBut is that the correct translation?\n\nIn 11: magasi argi ajomirra → “The thief gives the necklaces.”\n\nBut what about tense? No tense marker — likely present or active.\n\nSimilarly, 12. ay kanarriːg baːbki alletirsi.\n\n“ay” = I \n“kanarriːg” = bought (from 1) — base form “kanarriː” → buy → “kanarriːg” = bought \n“baːbki” = for the doors? → “baːbiːg” = the doors → “baːbki” = for the doors? — in 6: “eldeːnsu” = for me, so “baːbki” → for the doors?\n\nYes — in 6: “baːbiːg” = the doors, “eldeːnsu” = for me → so “baːbki” = for the doors.\n\nSo: I bought the doors for the doors? That doesn’t make sense.\n\nWait — “ay kanarriːg baːbki alletirsi”\n\n“alletirsi” → what is this?\n\nIn 1: “kamiːg jaːnticcirsu” → for neighbours.\n\nIn 2: “allesi” → dress.\n\nIn 4: “maːgtirsu” → for young man.\n\nIn 10: “sarkaːyi aygi beyyeːcciːg adeːnda” → cowards are giving me the necklaces → “adeːnda” = to me?\n\n“adeːnda” = to me?\n\nIn 6: “eldeːnsu” = for me → so “adeːnda” = to me?\n\nBut 10: “giving me the necklaces” → “adeːnda” = to me?\n\nYes.\n\nSo “adeːnda” = to me.\n\nBut here, “alletirsi” — does that mean “to me”?\n\nCompare to “eldeːnsu” → for me → not same.\n\n“alletirsi” → does it mean to me?\n\nLook at possible pattern.\n\nIn 5: “ay beyyeːcciːg ajaːnirri” → I am buying the necklaces → object.\n\nNo recipient.\n\nIn 10: sarkaːyi aygi beyyeːcciːg adeːnda → cowards are giving me the necklaces → “adeːnda” = to me.\n\nSo “adeːnda” = to me.\n\nWhat about “alleg” → “alleg” + “tirsi”?\n\nIn 6: “eldeːnsu” = for me.\n\n“eldeːnsu” = for me.\n\n“adeːnda” = to me.\n\nSo different prepositions: “for” vs “to”.\n\nIn 8: “magaski” = to the thief.\n\nIn 3: “tirsa” = to the dogs.\n\nSo “tirsa” = to\n\n“eldeːnsu” = for\n\n“adeːnda” = to me\n\nSo “alletirsi” — possibly a form of “to me”?\n\n“alletirsi” → could be “to me”?\n\nYes — likely.\n\nSo “ay kanarriːg baːbki alletirsi” → I bought the doors for me?\n\nBut “baːbki” = for the doors? Or “for me”?\n\nNo — “baːbki” → what is base?\n\n“baːbiːg” = the doors → so “baːbki” = for the doors? (like “for” + doors)\n\nIn 6: “baːbiːg eldeːnsu” → doors for me → so “baːbki” = for the doors?\n\nBut that would make “I bought the doors for the doors” → cyclic.\n\nUnlikely.\n\nAlternative: “baːbki” = for me?\n\nBut in 6: “baːbiːg” = the doors — object.\n\nSo “eldeːnsu” = for me → recipient.\n\nSo “baːbki” must be for the doors.\n\nSo “I bought the doors for the doors” → impossible.\n\nPossibility: “kanarriːg” is not \"bought\", but \"buy\" (base), and has tense?\n\nIn 1: “ar kanarriːcciːg kamiːg jaːnticcirsu” → we bought the camels for neighbours → so “kanarriːcciːg” = bought (past)\n\nSo “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10928.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 3, + "output": "Step 1: Identify reusable morphemes and structures across the examples.\n\nLook for common verbs and affixes:\n\n- \"kanarriːcciːg\" → \"buy\" (ex. 1 and 12)\n- \"tirt\" → \"repair\" (ex. 2 and 13)\n- \"kadeːg\" → \"dress\" (ex. 2, 4, 10)\n- \"waliːg\" → \"young man\" (ex. 3, 4, 7)\n- \"jahali\" → \"young men\" (ex. 3, 12)\n- \"magas\" → \"thief\" (ex. 7, 8)\n- \"ay\" → first person singular (I, ex. 5, 9, 15)\n- \"hanu\" → strike (ex. 9, 13)\n- \"bijaːndi\" → strike (ex. 15)\n- \"baːbki\" → \"the doors\" (ex. 6)\n- \"eldeːnsu\" → \"the doors\" (ex. 6)\n- \"argi\" → \"to give\" (ex. 11, 14)\n- \"deːccirsa\" → \"to give\" (ex. 14)\n- \"kamgi\" → \"camels\" (ex. 1, 8, 14)\n- \"darbadki\" → \"give\" (ex. 3, 15)\n- \"kadeːcciːg\" → \"stole\" (ex. 4)\n- \"waliːg\" → young men, plural (ex. 3, 4, 7)\n\nStep 2: Analyze verb structure and case markers.\n\nNotice that verbs often take a direct object and a recipient (or beneficiary). For example:\n\n- \"ay kanarriːg baːbki alletirsi\" → \"I am buying the doors for the owners\" (similar to \"We bought the camels for the neighbours\")\n\n\"kanarriːg\" = buy; \"baːbki\" = doors; \"alletirsi\" → \"for the owners\"\n\n\"alletirsi\" likely means \"for the owners\" → \"for someone\"\n\nSimilarly, \"tirt\" = repair, \"elirsu\" = \"the doors\"\n\n\"hanu tirtiːg elirsu\" → \"He strikes the doors\" → \"hanu\" = strike; \"tirtiːg\" = repair (same as tirt, suffixed to mean repair the?) → \"tirtiːg\" may be \"repairing\" or \"fixing\"\n\nBut \"hanu\" = strike, so \"hanu tirtiːg\" = \"I strike the repair\"? No.\n\nAlternative: \"hanu\" = strike, so \"hanu tirtiːg elirsu\" → \"I strike the doors\" → \"hanu\" verb, \"tirtiːg\" = something else?\n\nWait — look at example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\n\"hanuːg\" = will strike → yes, \"hanu\" is \"strike\", \"hanuːg\" is future\n\nSo \"hanu\" = strike; \"hanuːg\" = future strike\n\n\"hanu tirtiːg elirsu\" — \"hanu\" → strike, \"tirtiːg\" → ? \"tirt\" = repair → is tirtiːg a substantive?\n\nWait — example 13: \"hanu tirtiːg elirsu\"\n\nCompare to example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\"\n\n\"adeːnda\" = to me\n\n\"aygi\" = give → \"aygi\" is \"give\"\n\nSo \"argi\" = give → \"argi\" likely a verb\n\nExamples 11 and 14: \"magasi argi ajomirra\" → \"the thief gives the dog to the men\"? Or to whom?\n\n\"argi\" = give; \"ajomirra\" → \"to the men\"?\n\n\"ajomirra\" → possibly \"to the men\"\n\n\"magasi\" = thief\n\nSo \"the thief gives the dogs to the men\"?\n\nBut \"ajomirra\" — not in any direct translation.\n\nNow check example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\"\n\n\"ikki\" = you (pl.) → \"ikki\" → \"you\"\n\n\"ticcirsu\" = gave\n\n\"ticcirsu\" → verb form for \"gave\"\n\nSimilarly, \"argi\" might be \"give\", but in different form.\n\nIs \"argi\" in example 11: \"magasi argi ajomirra\" → \"the thief gives [to] the men\"?\n\nYes — likely \"gives the dogs to the men\"\n\nDo we have \"dogs\" anywhere?\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"young men will give the chicken to the dogs\"\n\n\"darbadki\" = give → same root\n\n\"biticcirra\" = chicken\n\n\"to the dogs\"\n\nSo \"darbadki\" = give, \"to the dogs\"\n\nThus, \"argi\" = give, same root as \"darbadki\"?\n\nBut \"argi\" and \"darbadki\" — different forms.\n\nBut \"argi\" likely is \"give\", so in 11: \"magasi argi ajomirra\" → \"the thief gives the dogs to the men\"\n\nBut \"ajomirra\" = ? → to the men?\n\nSimilarly, example 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" → possibly \"the owner\" or \"the one who repairs\"\n\nWait — example 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\"\n\nSo \"tirt\" = repaired (by the owner)\n\n\"tirt\" is used as a transitive verb with object (dress)\n\n\"tirt\" alone = repair\n\n\"tirti\" might be \"the one who repairs\"\n\n\"tirti argi kamgi deːccirsa\" → \"the owner gives the camels to the thief\"?\n\n\"deːccirsa\" → likely \"to the thief\"\n\n\"argi\" = give\n\n\"kamgi\" = camels\n\n\"deːccirsa\" = to the thief?\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\"\n\n\"magaski\" = gave (to the thief)\n\n\"tirsa\" = to the thief?\n\nSo \"tirsa\" = to the thief?\n\nThus, \"deːccirsa\" = to the thief?\n\nSimilarly, \"alletirsi\" = to the owners?\n\nFrom example 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\"\n\n\"aygi\" = give\n\n\"baːbiːg\" = doors\n\n\"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me\n\n\"adeːnda\" = to me (example 10)\n\nThus, \"adeːnda\" = to me\n\n\"allegi\" → relates to \"for the owners\"?\n\n\"alletirsi\" → \"for the owners\"\n\nIn example 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\"\n\n\"allesu\" = the dress\n\nSo \"allesu\" = dress\n\n\"eldeːnsu\" = doors\n\n\"elirsu\" = doors\n\nSo \"elirsu\" = doors\n\n\"eldeːnsu\" = doors\n\nThus, \"elirsu\" = doors\n\n\"tirtiːg elirsu\" → \"the one who repairs the doors\"?\n\n\"tirtiːg\" = repair verb + possessive or thematic?\n\nWait — example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike\n\n\"tirtiːg\" → not \"repair\" — conflict\n\nBut \"tirt\" = repair\n\n\"tirtiːg\" → could be \"repair\" + object?\n\nBut \"hanu\" = strike\n\nSo \"hanu tirtiːg\" = \"I strike the repair\"? Unlikely.\n\nAlternative: \"tirtiːg\" = the person who repairs?\n\nLike \"tirt\" = repair, \"tirti\" = one who repairs?\n\nLike \"tirti\" = repairer\n\nSo \"hanu tirtiːg elirsu\" → \"I strike the repairer of the doors\"?\n\nThat seems odd.\n\nBut example 13: \"hanu tirtiːg elirsu\"\n\nCompare to example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\nSo \"hanu\" = strike, \"hanuːg\" = future\n\n\"hanu tirtiːg\" = strike the repairer?\n\nBut \"elirsu\" = doors\n\nSo \"I strike the one who repairs the doors\"\n\nThat seems plausible.\n\nThus, \"tirtiːg\" = \"the one who repairs\"\n\n\"elirsu\" = doors\n\nSo \"hanu tirtiːg elirsu\" = \"I strike the repairer of the doors\"\n\nNow example 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" → the repairer / owner?\n\n\"argi\" = give\n\n\"kamgi\" → camels\n\n\"deːccirsa\" → to the thief\n\nSo \"the repairer gives the camels to the thief\"\n\nExample 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\"\n\nSo \"tirt\" = repair, subject appears as \"tirt\" → \"the owner\"\n\nSimilarly, \"tirti\" → the owner (possessive form)\n\nSo \"tirti\" = the one who repairs\n\nTherefore, \"tirti argi kamgi deːccirsa\" = \"the repairer gives the camels to the thief\"\n\nNow example 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief\n\n\"argi\" = give\n\n\"ajomirra\" → to whom?\n\n\"ajomirra\" → similar to \"tirsa\" or \"deːccirsa\"\n\n\"deːccirsa\" = to thief → \"deːccirsa\"\n\n\"tirsa\" = to thief\n\n\"eldeːnsu\" = for me\n\n\"adeːnda\" = to me\n\nSo \"deːccirsa\" = to thief?\n\n\"ajomirra\" → likely \"to the men\"?\n\n\"magasi\" = thief → gives to the men?\n\nBut \"ajomirra\" → where is it used?\n\nNo direct match.\n\nLook at example 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs\n\n\"ikki\" = you (pl.)\n\n\"ticcirsu\" = gave\n\nSo \"ikki\" = you (pl.)\n\n\"ajomirra\" → could be \"to the men\"?\n\n\"men\" = waliːg\n\n\"ajomirra\" = to the men?\n\nPossibly.\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → young men will give the chicken to the dogs\n\n\"darbadki\" = give\n\n\"waliːg\" = young men\n\n\"biticcirra\" = chicken\n\n\"to the dogs\"\n\nSo \"to the dogs\" → object?\n\nBut \"ajomirra\" → not present.\n\nBut \"argi\" → give\n\n\"ajomirra\" = to the men?\n\nYes — likely.\n\nSo \"magasi argi ajomirra\" → \"the thief gives the dogs to the men\"?\n\nIs there a \"dogs\" part?\n\nExample 7: \"magas ikki waliːg ticcirsu\" → gives dogs to young men\n\nSo \"the thief gave the dogs to the young men\"\n\nSo \"gives the dogs to the men\"\n\nThus, \"magasi argi ajomirra\" → \"the thief gives the dogs to the men\"\n\nNow 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I\n\n\"kanarriːg\" = buy\n\n\"baːbki\" = the doors\n\n\"alletirsi\" = for the owners?\n\n\"alletirsi\" → from \"allesu\" = dress → \"for the owners\"\n\n\"eldeːnsu\" = doors\n\nSo \"allegi\" → for owners?\n\nYes — used in example 6: \"found the doors for me\"\n\nSo \"alletirsi\" = for the owners\n\nThus, \"I buy the doors for the owners\"\n\n13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike\n\n\"tirtiːg\" = the one who repairs\n\n\"elirsu\" = doors\n\n→ \"I strike the repairer of the doors\"\n\n14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" = the one who repairs\n\n\"argi\" = give\n\n\"kamgi\" = camels\n\n\"deːccirsa\" = to the thief\n\n→ \"the repairer gives the camels to the thief\"\n\n15: \"ay darbadki bijaːndi\"\n\n\"ay\" = I\n\n\"darbadki\" = give\n\n\"bijaːndi\" = strike (from \"hanuːg bijomri\" → \"I will strike the donkey\")\n\nSo \"bijaːndi\" = strike\n\n\"darbadki bijaːndi\" = give strike?\n\nGives the strike? Unlikely.\n\n\"darbadki\" = give\n\n\"bijaːndi\" = strike\n\nSo \"I give a strike\" → \"I give a beating to the dog\"?\n\nPossibly.\n\nLike in example 9: \"I will strike the donkey\"\n\nSo \"give\" → \"darbadki\", \"strike\" → \"bijaːndi\"\n\nSo \"I give the strike to someone\"?\n\nBut who?\n\nNo object.\n\n\"bijaːndi\" = strike (as action)\n\nSo \"I give a strike\" → \"I am giving a strike\"\n\nBut to whom? Not specified.\n\nBut in example 3: \"give the chicken to the dogs\" — object is explicit.\n\nHere no object.\n\nThus, \"I give a strike\" → \"I am giving a strike to someone\"?\n\nBut since no object, perhaps \"I give (a strike)\" → \"I give the strike\"\n\nBut \"the strike\" is not present.\n\nAlternatively, could be \"I will strike\" — but \"darbadki\" not future.\n\n\"hanuːg\" = future\n\n\"ay\" = present\n\n\"darbadki\" = present\n\nSo likely \"I give the strike\"\n\nBut what to whom?\n\nNo object — so perhaps it's about giving the action of striking.\n\nBut it's awkward.\n\nAlternatively, \"bijaːndi\" could be \"to the donkey\" — but no.\n\nCompare to example 9: \"I will strike the donkey\"\n\n\"hanuːg bijomri\" → future direct\n\nHere: \"ay darbadki bijaːndi\" → present — \"I give the strike\"\n\nBut the only noun for strike is \"bijaːndi\"\n\nSo likely \"I give the strike\"\n\nBut to whom? Not specified.\n\nPossibly it's a direct translation — \"I give a strike\" (to someone implied)\n\nBut target is translation.\n\nWe must assign meaning.\n\nGiven that \"hanu\" = strike, \"bijaːndi\" = strike, so \"give a strike\" is possible.\n\nBut maybe \"bijaːndi\" is not the object, but the verb?\n\nNo — structure: \"darbadki\" = give, \"bijaːndi\" = object?\n\nIn example 3: \"darbadki biticcirra\" → \"give chicken\"\n\n\"biticcirra\" = chicken\n\nSo \"bijaːndi\" = strike — a noun?\n\nSo \"I give the strike\"\n\n→ \"I give a beating\"\n\nThus, final translations:\n\n11. magasi argi ajomirra → the thief gives the dogs to the men \n12. ay kanarriːg baːbki alletirsi → I buy the doors for the owners \n13. hanu tirtiːg elirsu → I strike the repairer of the doors \n14. tirti argi kamgi deːccirsa → the repairer gives the camels to the thief \n15. ay darbadki bijaːndi → I give the strike\n\nBut \"give the strike\" is odd — perhaps better as \"I give a strike\"\n\nBut \"strike\" as noun?\n\nYes — in \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey\n\n\"bijaːndi\" = strike → noun\n\nSo \"I give the strike\"\n\nIn context, may imply \"I give (to someone) a strike\"\n\nBut no object — so the verb is \"give the strike\"\n\nWe go with that.\n\nFinal answers:\n\na.1: the thief gives the dogs to the men \na.2: I buy the doors for the owners \na.3: I strike the repairer of the doors \na.4: the repairer gives the camels to the thief \na.5: I give the strike\n\n\\boxed{a.1: the thief gives the dogs to the men; a.2: I buy the doors for the owners; a.3: I strike the repairer of the doors; a.4: the repairer gives the camels to the thief; a.5: I give the strike}", + "generated_tokens": 3935, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: the thief gives the dogs to the men; a.2: I buy the doors for the owners; a.3: I strike the repairer of the doors; a.4: the repairer gives the camels to the thief; a.5: I give the strike", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 10764.0, + "ioling_final_answer_chars": 191.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "First, build alignment from source sentences to identify patterns.\n\nExample 1: \nar kanarriːcciːg kamiːg jaːnticcirsu. \nWe bought the camels for the neighbours. \n→ \"ar\" = we (subject) \n→ \"kanarriːcciːg\" = bought (verb stem) \n→ \"kamiːg\" = the camels (object) \n→ \"jaːnticcirsu\" = for the neighbours (prepositional phrase with \"jaːnti-\" = neighbour)\n\nExample 2: \ntirt kadeːg allesu. \nThe owner repaired the dress. \n→ \"tirt\" = the owner (subject) \n→ \"kadeːg\" = repaired (verb) \n→ \"allesu\" = the dress (object)\n\nExample 3: \njahali waliːg darbadki biticcirra. \nThe young men will give the chicken to the dogs. \n→ \"jahali\" = young men (subject) \n→ \"waliːg\" = will (future) \n→ \"darbadki\" = give (verb) \n→ \"biticcirra\" = the chicken (object) \n→ \"to the dogs\" = implied prepositional object, structured as [to the X] with X = dogs\n\nExample 4: \nman jahalgi kadeːcciːg maːgtirsu. \nHe stole the dresses for the young man. \n→ \"man\" = he (subject) \n→ \"jahalgi\" = stole (past tense, third person) \n→ \"kadeːcciːg\" = the dresses (object) \n→ \"maːgtirsu\" = for the young man (for-phrase)\n\nExample 5: \nay beyyeːcciːg ajaːnirri. \nI am buying the necklaces. \n→ \"ay\" = I (subject) \n→ \"beyyeːcciːg\" = buying (present) \n→ \"ajaːnirri\" = the necklaces (object)\n\nExample 6: \nwal aygi baːbiːg eldeːnsu. \nThe dog found the doors for me. \n→ \"wal\" = the dog (subject) \n→ \"aygi\" = found (verb) \n→ \"baːbiːg\" = the doors (object) \n→ \"eldeːnsu\" = for me (for-phrase)\n\nExample 7: \nmagas ikki waliːg ticcirsu. \nThe thief gave you (pl.) the dogs. \n→ \"magas\" = the thief (subject) \n→ \"ikki\" = gave (verb) \n→ \"waliːg\" = you (pl.) \n→ \"ticcirsu\" = the dogs (object)\n\nExample 8: \niːdi magaski kamiːg tirsa. \nThe men gave the camels to the thief. \n→ \"iːdi\" = the men (subject) \n→ \"magaski\" = to the thief (prepositional object) \n→ \"kamiːg\" = the camels (object) \n→ \"tirsa\" = gave (verb)\n\nNote: verb often has marking for direction or recipient (to X). \nWhen there's a \"to X\" structure, it appears as a prepositional phrase after the verb.\n\nPattern for \"A gives B to C\": \n[A] [verb] [B] [to C] \nWith object (B), then [to C] where C is marked by prepositional phrase.\n\nIn example 8: \"iːdi\" (men) + \"magaski\" (to the thief) + \"kamiːg\" (camels) + \"tirsa\" (gave) \nBut \"tirsa\" is verb, and \"magaski\" = to the thief → so object comes after prepositional phrase.\n\nBut in example 3: \"jahali\" gives \"biticcirra\" to \"dogs\" → \"darbadki biticcirra\" → \"to dogs\" comes after object? No: \n\"jahali waliːg darbadki biticcirra\" → \"waliːg\" = will, \"darbadki\" = give, \"biticcirra\" = chicken → so object before recipient? \nWait: \"waliːg darbadki biticcirra\" – object is \"biticcirra\", then \"to dogs\" missing.\n\nBut in 3: it says “to the dogs” → must be missing a prepositional phrase. \nUnless “darbadki” is the verb and takes an object, and a recipient is attached.\n\nActually in 3: final phrase is “to the dogs” → so we need a structure where a prepositional phrase with \"to\" + noun appears.\n\nCheck example 8: “iːdi magaski kamiːg tirsa” → “to the thief” is “magaski”, then object “kamiːg”, then verb “tirsa” → so verb comes after object.\n\nBut in 3: “jahali waliːg darbadki biticcirra” → “waliːg darbadki” (will give), then object “biticcirra”, no \"to dogs\". \nBut translation says: \"the young men will give the chicken to the dogs\" → so must be \"to dogs\" exists.\n\nPossibility: prepositional phrase is morphed in verb or attached.\n\nExample 6: “wal aygi baːbiːg eldeːnsu” → “the dog found the doors for me” → “eldeːnsu” = for me → so “for” is a preposition with \"me\".\n\nSimilarly, ex 4: “maːgtirsu” = for the young man.\n\nIn all cases, “for X” or “to X” uses a prepositional phrase with a noun.\n\nNow verify which prepositions are used.\n\n- \"for\" appears in: \n ex1: “jaːnticcirsu” → “for the neighbours” → “jaːnti” = neighbour → so \"jaːnti-\" + -ccirsu (possibly) \n ex4: “maːgtirsu” → for young man → “maːgti” = young man? \n ex6: “eldeːnsu” → for me → “elde” may mean for?\n\nLook at endings:\n\n- \"ccirsu\" → appears in: \n ex1: jaːnticcirsu → for neighbours \n ex3: biticcirra → the chicken \n ex5: beyyeːcciːg → buying necklaces \n ex7: waliːg ticcirsu → the dogs \n → \"ccir\" appears in object noun: \"kamiːg\", \"tirsa\", \"ticcirsu\"\n\nPrepositional phrases:\n\n- \"kamiːg\" = the camels \n- \"allesu\" = the dress \n- \"biticcirra\" = the chicken \n- \"maːgtirsu\" = for the young man \n- \"eldeːnsu\" = for me \n- \"tirsa\" = gave \n- \"waliːg\" = will give \n- \"jaːnticcirsu\" = for the neighbours \n- \"magaski\" = to the thief\n\nSo object nouns end in -ciriː/ -cirsu? \n\"biticcirra\" → chicken → ends in -cira? \n\"ticcirsu\" → dogs → -cirsu \n\"kamiːg\" → camels → -amiːg \n\"baːbiːg\" → doors → -biːg \n\"beyyeːcciːg\" → necklaces → -cciːg \n\"maːgtirsu\" → young man → -tirsu? \n\"eldeːnsu\" → me → -nsu?\n\nNotice: \"for X\" is marked with a suffix like -tirsu, -nsu, -ccirsu.\n\nIn ex1: \"jaːnticcirsu\" → \"jaːnti\" = neighbour → \"-ccirsu\" \nIn ex4: \"maːgtirsu\" → \"maːgti\" = young man → \"-tirsu\"? \nBut \"tirsu\" vs \"ccirsu\" — different suffixes?\n\nPossibility: suffix -ccirsu = for/for the \n- jaːnticcirsu = for the neighbours \n- maːgtirsu = for the young man → but \"maːgti\" + \"tirsu\"? \n\"tirsu\" is not clearly a variant.\n\nAlternatively, \"for\" is a prefix or suffix?\n\nLook across:\n\n1. \"jaːnticcirsu\" → for neighbours → uses -ccirsu \n2. \"maːgtirsu\" → for young man → uses -tirsu? \n3. \"eldeːnsu\" → for me → -nsu \n\nSo prepositions appear as a suffix on a noun:\n\n- neighbours → -ccirsu \n- young man → -tirsu \n- me → -nsu\n\nSo: \n- \"jaːnti\" + \"ccirsu\" = for the neighbours \n- \"maːgti\" + \"tirsu\" = for the young man \n- \"elde\" + \"nsu\" = for me \n\nNow, \"tirsa\" = give \n\"darbadki\" = give \n\"kadeːg\" = repair \n\"aygi\" = found \n\"jahalgi\" = stole \n\"beyyeːcciːg\" = buying \n\nSo verbs:\n\n- \"tirsa\" → gave \n- \"darbadki\" → give \n- \"kadeːg\" → repaired \n- \"beyyeːcciːg\" → buying (present) \n- \"aygi\" → found \n\nNotice: present tense uses \"-eːcciːg\" in \"beyyeːcciːg\" \nPast tense: \"jahalgi\", \"tirsa\" (gave), \"kadeːg\" (repaired), \"aygi\" (found)\n\nSo \"gave\" → \"tirsa\" (past), \"darbadki\" (future)\n\nFuture: \"waliːg\" = will → appears in \"jahali waliːg darbadki\" = the young men will give\n\nSo: \n- Present: verb stem + -eːcciːg \n- Past: verb stem + -gi \n- Future: verb stem + -waliːg (or -g?)\n\n\"aygi\" = found → past \n\"jahalgi\" = stole → past \n\"tirsa\" = gave → past \n\"darbadki\" = give → future? (waliːg attached) \nSo \"darbadki\" is base form, future is \"waliːg darbadki\"\n\nLikely: \n- Present: + -eːcciːg \n- Past: base + -gi \n- Future: base + waliːg?\n\nNow check: \nex5: “ay beyyeːcciːg ajaːnirri” → I am buying → “beyyeːcciːg” = buying → present form\n\nex3: “waliːg darbadki” → will give → future\n\nex7: “ikki waliːg ticcirsu” → gave → “ikki” = gave → past? \n“ikki” = gave, no “waliːg” \nWait: “magas ikki waliːg ticcirsu” → “ikki” = gave, “waliːg” = you (pl.)\n\nSo “ikki” = gave (past tense)\n\nThus, verb forms:\n- Present: + eːcciːg \n- Past: + gi \n- Future: + waliːg (attached to verb)\n\nSo \"give\" = basic stem → future: \"waliːg + give\", past: \"give + gi\", present: \"give + eːcciːg\"\n\nSimilarly, \"buy\" → \"beyyeːcciːg\"\n\nNow, how about \"to\" vs \"for\"?\n\n\"to the X\" appears with different prepositions:\n\n- \"to the thief\" → magaski → \"maːg\" + \"aski\"? \n \"magas\" = the thief → \"magaski\" = to the thief \n- \"for the young man\" → maːgtirsu → \"maːgti\" + \"tirsu\" → \"tirsu\" = for?\n\nBut \"maːgtirsu\" is \"for the young man\"\n\nSo \"for\" = suffix on noun?\n\nSimilarly, \"jaːnticcirsu\" = for the neighbours → \"jaːnti\" + \"ccirsu\"\n\n\"eldeːnsu\" = for me → \"elde\" + \"nsu\"\n\nSo \"for\" is marked by a suffix on the noun: \n- ccirsu = for the neighbours \n- tirsu = for the young man \n- nsu = for me\n\n\"to\" is marked by different suffix: \n- \"magaski\" → to the thief → \"magas\" + \"ski\"\n\nThus, \"to\" = suffix -ski? \n\"magaski\" → \"ski\"\n\nPattern:\n\n- For [X] → [noun] + [suffix] \n e.g., for neighbours → jaːnti + ccirsu \n for young man → maːgti + tirsu \n for me → elde + nsu \n\n- To [X] → [noun] + ski \n e.g., to thief → magas + ski \n\nNow, object: noun base with specific suffix\n\nList object nouns:\n\n- camels → kamiːg \n- dress → allesu \n- chicken → biticcirra \n- dresses → kadeːcciːg → kade + eːcciːg → object with eːcciːg \n- necklaces → ajaːnirri \n- doors → baːbiːg \n- dogs → ticcirsu \n- thief → magas \n\nSo object nouns are marked with:\n\n- kamiːg → camels \n- allesu → dress \n- biticcirra → chicken \n- kadeːcciːg → dresses (plural?) \n- ajaːnirri → necklaces \n- baːbiːg → doors \n- ticcirsu → dogs \n- magas → thief \n\nNow, plausibly, the object is the noun (base), and the possessive or agent is marked separately.\n\nNow translate:\n\n16. The neighbours are giving the necklace to the owner.\n\nSubject: \"the neighbours\" → \"jaːnti\" \nVerb: \"are giving\" → present tense → present form of \"give\" → \"darbadki\" + eːcciːg? \n\"give\" = darbadki → present = darbadki eːcciːg? \nBut \"beyyeːcciːg\" = buying → so \"give\" = darbadki, present = darbadki eːcciːg?\n\nIn ex5: \"beyyeːcciːg\" = buying → so verb base + eːcciːg = present\n\nSo give → darbadki → present = darbadki eːcciːg\n\nObject: \"the necklace\" → \"ajaːnirri\" → necklaces\n\n\"to the owner\" → owner → ? \nWhat is owner?\n\nIn ex2: \"tirt\" = the owner → so \"tirt\" = owner → then \"to the owner\" = \"tirt\" + what?\n\nIn ex2: \"tirt kadeːg allesu\" → owner repaired dress → so \"tirt\" = owner\n\n\"to the owner\" → which form?\n\nIn ex8: \"iːdi magaski kamiːg tirsa\" → men gave camels to thief → \"magaski\" = to thief → \"magas\" + \"ski\"\n\nSo \"to thief\" = magas + ski\n\nSimilarly, \"to owner\" → owner → \"tirt\" → then \"tirt\" + ski?\n\nBut \"ski\" used in \"magaski\"\n\nSimilarly, \"to neighbour\" → \"jaːnti\" + ski?\n\nSo all prepositional phrases follow pattern: [noun] + [ski] for \"to\"\n\nBut earlier: \"for\" = suffix on noun\n\nSo \"to the X\" = X + ski\n\nThus: \"to the owner\" = tirt + ski → tirtski?\n\nCheck pattern.\n\n\"magas\" + \"ski\" = to the thief \nSo \"tirt\" + \"ski\" = to the owner\n\nThus, 16: \nSubject: jaːnti (the neighbours) \nVerb: darbadki eːcciːg (are giving) \nObject: ajaːnirri (the necklace) \nPrepositional phrase: tirtski (to the owner)\n\nSo: jaːnti darbadki eːcciːg ajaːnirri tirtski\n\nBut subject is \"the neighbours\" → jaːnti, which is agent\n\nIn ex1: \"ar\" = we, subject, then \"kanarriːcciːg\" (bought), object \"kamiːg\", then \"jaːnticcirsu\" → for neighbours\n\nSo in that case, \"for\" is with \"neighbours\" → jaːnti + ccirsu.\n\nIn 16, \"to owner\" → so tirt + ski\n\nStructure: subject + verb (present) + object + to-recipient\n\nSo: jaːnti darbadki eːcciːg ajaːnirri tirtski\n\nBut is \"ajaːnirri\" the necklace? Yes → from ex5: \"beyyeːcciːg ajaːnirri\" → buying necklaces\n\nSo object is ajaːnirri\n\nNow 17. The young man bought the dog for us.\n\nSubject: young man → \"jahali\" \nVerb: bought → past tense → borrowed? → \"kade\" → from \"kadeːg\" (repaired), so \"kade\" = verb root \n\"bought\" → likely past form → base verb + gi\n\nBut what is the verb? \"bought\" = bought → similar to \"stole\" = jahalgi\n\n\"Stole\" in ex4: man jahalgi kadeːcciːg → \"jahalgi\" = stole → past\n\n\"Repaired\" = kadeːg → past \nSo \"bought\" = likely \"kade\" → \"kadegi\"? \n\nBut in \"kadeːg\" → repaired → not \"bought\"\n\nIs \"buy\" used?\n\nIn ex5: \"beyyeːcciːg\" → buying", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11030.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "We are given translations of sentences in Kunuz Nubian and their English equivalents. We need to translate five new sentences into Kunuz Nubian, based on patterns observed in the examples.\n\nStep 1: Identify common structures in the given examples.\n\nStructure of verb phrases:\nMost verbs are in the form:\n[Subject] [verb form] [object] [for/for whom] [recipient]\n\nExamples:\n1. ar kanarriːcciːg kamiːg jaːnticcirsu. \n→ \"We bought the camels for the neighbours.\" \n\"bought\" = kanarriːcciːg → subject \"we\" = ar; object \"camels\" = kamiːg; for \"neighbours\" = jaːnticcirsu\n\n2. tirt kadeːg allesu. \n→ \"The owner repaired the dress.\" \nSubject = tirt (owner), verb = kadeːg (repaired), object = allesu (dress)\n\n3. jahali waliːg darbadki biticcirra. \n→ \"The young men will give the chicken to the dogs.\" \nSubject = jahali (young men), verb = darbadki (will give), object = biticcirra (chicken), recipient = dogs (implied as object)\n\n4. man jahalgi kadeːcciːg maːgtirsu. \n→ \"He stole the dresses for the young man.\" \nSubject = man, verb = jahalgi (stole), object = kadeːcciːg (dresses), for = maːgtirsu (young man)\n\n5. ay beyyeːcciːg ajaːnirri. \n→ \"I am buying the necklaces.\" \nSubject = ay (I), verb = beyyeːcciːg (buying), object = ajaːnirri (necklaces)\n\n6. wal aygi baːbiːg eldeːnsu. \n→ \"The dog found the doors for me.\" \nSubject = wal (dog), verb = aygi (found), object = baːbiːg (doors), for = eldeːnsu (me)\n\n7. magas ikki waliːg ticcirsu. \n→ \"The thief gave you (pl.) the dogs.\" \nSubject = magas (thief), verb = ikki (gave), object = waliːg (you pl.), recipient = ticcirsu (dogs)\n\n8. iːdi magaski kamiːg tirsa. \n→ \"The men gave the camels to the thief.\" \nSubject = iːdi (men), verb = magaski (gave), object = kamiːg (camels), to = tirsa (thief)\n\n9. ay hanuːg bijomri. \n→ \"I will strike the donkey.\" \nSubject = ay (I), verb = hanuːg (will strike), object = bijomri (donkey)\n\n10. sarkaːyi aygi beyyeːcciːg adeːnda. \n→ \"The cowards are giving me the necklaces.\" \nSubject = sarkaːyi (cowards), verb = aygi (are giving), object = beyyeːcciːg (necklaces), to = adeːnda (me)\n\nPatterns observed:\n\n- Verb forms show a basic stem + particle for aspect:\n - Present/future: beyyeːcciːg (buying), aygi (are giving), hanuːg (will strike)\n - Past: kanarriːcciːg (bought), kadeːg (repaired), jahalgi (stole)\n - Future: darbadki (will give)\n\n- For/recipient structures:\n - \"for X\" is often expressed by a clausal or prepositional suffix or particle:\n - \"for the neighbours\" = jaːnticcirsu → used in (1)\n - \"for me\" = eldeːnsu → (6)\n - \"for the young man\" = maːgtirsu → (4)\n - \"for us\" = ? → likely adeːnda or eldeːnsu variant?\n\n- Plurality markers:\n - \"young men\" = jahali → plural of jahal (young man)\n - \"men\" = iːdi → plural of i (man)\n - \"owners\" = ? — not directly given, but could be tirt (owner) pluralized?\n - \"thieves\" = magas → singular; possibly magas plural = magas (repeated or compound)\n\n- Object marking:\n - Object is marked by a noun, often with a genitive or dative suffix:\n - \"camels\" = kamiːg\n - \"dresses\" = kadeːcciːg\n - \"chicken\" = biticcirra\n - \"doors\" = baːbiːg\n\n- \"to X\" = recipient marked as final noun:\n - In (8): gave camels to thief → \"tirsa\"\n - In (6): found doors for me → \"eldeːnsu\"\n - In (4): stole dresses for young man → \"maːgtirsu\"\n - In (3): gave chicken to dogs → \"biticcirra\" is object, \"dogs\" is recipient — not clearly marked, but object and recipient appear separate\n\n→ In many cases, the recipient is a noun at the end.\n\nNow analyze each translation:\n\n16. The neighbours are giving the necklace to the owner.\n\n- \"neighbours\" → from (1): jaːnticcirsu (neighbours) → appears as recipient or object?\n- \"giving\" → verb form: \"are giving\" → used in (10): aygi (are giving)\n- \"necklace\" → singular → from (5): beyyeːcciːg (necklaces) → so \"necklace\" = beyyeːcciːg (singular)\n- \"to the owner\" → \"owner\" = tirt (from (2): tirt repaired the dress)\n- The structure in (10): the cowards are giving me the necklaces → subject, verb, object, recipient\n\nSo: [subject] + [verb] + [object] + [to recipient]\n\n→ \"jaːnticcirsu\" (neighbours) = subject \n→ \"aygi\" = \"are giving\" \n→ \"beyyeːcciːg\" = the necklace (singular) \n→ \"tirsa\" = the owner (from (8): gave to thief → \"tirsa\")\n\n→ Therefore: jaːnticcirsu aygi beyyeːcciːg tirsa\n\nCheck: in (8): iːdi magaski kamiːg tirsa → \"men gave camels to thief\" → phrase structure: subject verb object to recipient\n\nYes — matches.\n\nSo 16: jaːnticcirsu aygi beyyeːcciːg tirsa\n\n17. The young man bought the dog for us.\n\n- \"young man\" → jahali (from (3): young men, jahali) → singular = jahal?\n- But (3) says \"young men\" = jahali (plural), and no singular form given.\n- Check (4): \"he stole the dresses for the young man\" → \"maːgtirsu\" = young man → so \"young man\" = maːgtirsu\n\n→ Therefore \"young man\" = maːgtirsu\n\n- \"bought\" → verb: kanarriːcciːg (from (1))\n- \"the dog\" → dog = wal (from (6): dog found doors)\n- \"for us\" → \"us\" → in (10): \"for me\" = eldeːnsu; \"for us\" → likely same or plural form?\n\nNo direct plural form. (10): sarkaːyi aygi beyyeːcciːg adeːnda → \"the cowards are giving me the necklaces\" → \"adeːnda\" = me → \"us\"? possibly \"eldeːnsu\" is for me, and \"adeːnda\" may be a form for us?\n\nWait — in (6): \"the dog found the doors for me\" → eldeːnsu → \"me\"\n\nIs there a form \"us\" in examples?\n\n(10): \"giving me\" → adeːnda → only me\n\nNo \"us\" directly.\n\nBut in (4): \"for the young man\" → maːgtirsu → person.\n\nSimilarly, (6): \"for me\" → eldeːnsu\n\nSo likely \"for us\" = eldeːnsu or a plural variant?\n\nBut no form given.\n\nHowever, in (17): \"for us\" — likely equivalent to \"for me\" but plural → maybe \"eldeːnsu\" is used with pluralization?\n\nBut in (10), \"adeːnda\" = me (first person singular), not \"us\"\n\nIs there a noun for \"us\"?\n\nNo. So perhaps \"for us\" is expressed by plural form of \"me\"?\n\nBut no such form given.\n\nWait — in (10), \"sarkaːyi\" (cowards) are giving \"me\" → adeːnda\n\nIn (6): \"for me\" → eldeːnsu\n\nSo \"me\" = eldeːnsu\n\n\"us\" = ? → not directly present.\n\nBut in meaning, \"for us\" may be formed with \"eldeːnsu\" if we assume it's a pronoun used in plural context.\n\nAlternatively, could \"we\" be used? But no.\n\nBut look at (1): \"bought the camels for the neighbours\" → recipient = jaːnticcirsu\n\nIn (4): \"stole the dresses for the young man\" → recipient = maːgtirsu\n\nTherefore, \"for us\" = ? — not in examples.\n\nBut in (3): \"will give the chicken to the dogs\" → recipient = dogs\n\n→ So in all cases, recipient is final noun — not marked by separate word.\n\nSo likely, \"for us\" → same as \"for me\" but plural → use a plural form of \"me\"?\n\nBut no such form.\n\nAlternatively, is there a word for \"us\" in objects?\n\nNo.\n\nBut in (5): \"I am buying the necklaces\" → no recipient.\n\nSo perhaps the pattern is: [subject] [verb] [object] [for recipient]\n\nFor recipient: use noun form of person.\n\n\"us\" may be represented by \"eldeːnsu\" with plural context.\n\nBut no plural form given.\n\nWait — in (10), \"giving me\" = adeːnda — me\n\n\"the cowards are giving me\" — so \"me\" is object?\n\nBut in (6): \"found the doors for me\" → for me = eldeːnsu\n\nSo in (17): \"for us\" — perhaps \"eldeːnsu\" is used, but with plural interpretation?\n\nBut no.\n\nIs there a possibility \"we\" appears as subject?\n\nNo — only \"we\" in (1): \"we bought\" → ar\n\n(1): \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → ar = we\n\nSo \"we\" = ar\n\nSo for \"for us\" → not directly preserved.\n\nBut in (10): \"the cowards are giving me\" → mine\n\nSo \"for us\" must be inferred.\n\nAssume that \"us\" = eldeːnsu (me) in plural context, or possibly a separate form.\n\nBut no such form exists.\n\nAlternative: in (17), \"bought the dog for us\" → likely use the same structure as \"for the neighbours\" or \"for the young man\"\n\nBut no word for \"us\".\n\nWait — in (6): \"found the doors for me\" → for me = eldeːnsu\n\nIn (2): owner → tirt\n\nSo recipient people are: tirt (owner), maːgtirsu (young man), tirsa (thief)\n\n\"us\" — not in list.\n\nCould \"for us\" be expressed by \"eldeːnsu\" with plural implied?\n\nPerhaps.\n\nAlternatively, might \"us\" be expressed as \"waliːg\" (young men)? No — young men are different.\n\nBut (18): \"We will steal him\" → \"we\" = ar; \"him\" = some person\n\nSimilarly, (19): \"The owners struck the thieves\" → owners = tirt (plural), thieves = magas\n\n(20): \"The dogs found the chickens for the coward\" → \"for the coward\" → wow — \"coward\" = sarkaːyi (from example 10)\n\nSo in (10): sarkaːyi = cowards → plural\n\nSo \"coward\" = sarkaːyi?\n\nBut sarkaːyi = plural — so singular = sarkaːy?\n\nNot given.\n\nSo no direct form for \"coward\".\n\nBut we can infer patterns.\n\nBack to 17: \"The young man bought the dog for us.\"\n\nSo: subject = young man = maːgtirsu \nverb = bought = kanarriːcciːg \nobject = dog = wal \nfor us → ?\n\nIn all examples with \"for\", the recipient is a noun or pronoun.\n\nNo \"us\" form.\n\nBut in (10): \"giving me\" — adeːnda = me\n\n\"for me\" = eldeːnsu\n\nSimilarly, \"for us\" = ? → not present.\n\nBut perhaps \"us\" is expressed as \"eldeːnsu\" with plural tag? No.\n\nWait — could \"us\" be expressed as \"waliːg\" — young men? But that’s a group.\n\nBut \"young man\" is maːgtirsu — person.\n\nNo match.\n\nMaybe \"for us\" is equivalent to \"for me\" without ownership — but no.\n\nConclusion: likely, the pronoun \"us\" is missing. But in (10): sarkaːyi aygi beyyeːcciːg adeːnda → gives to me → so \"us\" might be \"adeːnda\" in plural?\n\nNot clear.\n\nBut if we assume that \"for us\" is the same as \"for me\", and in context, it's acceptable, then use eldeːnsu.\n\nBut better: look at (17): \"for us\" — so the recipient should be a pronoun.\n\nIn (6): \"for me\" = eldeːnsu\n\nSo for \"us\", possibly a separate form? Not given.\n\nBut in example (6): \"the dog found the doors for me\" — eldeːnsu\n\nIn (4): \"he stole for the young man\" — maːgtirsu\n\nSo for a group, it's an object.\n\nSo perhaps \"for us\" = eldeːnsu → assumed to mean \"for us\" in context.\n\nAlternatively, is there a word \"we\"?\n\nNo.\n\nSo go with eldeːnsu.\n\nThus: maːgtirsu kanarriːcciːg wal eldeːnsu\n\nCheck: subject = young man, verb = bought, object = dog, for us = eldeːnsu\n\nYes — matches pattern.\n\n18. We will steal him.\n\n- \"we\" = ar (from (1))\n- \"will\" = in (9): ay hanuːg bijomri → \"I will strike\" → hanuːg\n- So \"will\" = hanuːg → but in future tense\n- \"steal\" → from (4): jahalgi (stole) — past\n- So future of \"steal\" = ? → not directly given\n\n\"steal\" in past: jahalgi\n\n\"buy\" in future: beyyeːcciːg? No — beyyeːcciːg = buying (present)\n\n\"will buy\" = not directly present.\n\nBut (9): \"I will strike\" → ay hanuːg bijomri → \"hanuːg\" = will\n\nSo future verb form = hanuːg (as with strike)\n\nSo \"will steal\" = hanuːg + stem of steal\n\nWhat is stem of steal?\n\n(4): man jahalgi kadeːcciːg maːgtirsu → \"he stole the dresses for the young man\" → verb = jahalgi\n\nSo \"steal\" = jahalgi\n\nSo future of steal = jahalgi with future marker?\n\nBut (9): hanuːg = future of strike → strike = hanuːg → not jahalgi\n\nSo likely, future is marked by hanuːg for future intransitive verbs?\n\nBut \"steal\" is transitive.\n\nIs there a future form for jahalgi?\n\nNot given.\n\nBut (3): jahali waliːg darbadki biticcirra → young men will give → darbadki = future \"will give\"\n\nSo \"will give\" = darbadki\n\nSimilarly, (9): \"I will strike\" = hanuːg\n\nSo different verbs have different future markers.\n\nSo for \"give\" → darbadki; for \"strike\" → hanuːg\n\nSo for \"steal\", what future form?\n\nNo example.\n\nBut (4): \"he stole\" → past → jahalgi\n\nSo future = ? → not available.\n\nBut in (18): \"we will steal him\"\n\nSo: \"we\" = ar \n\"will\" = need future particle\n\nBut no consistent form.\n\nBut in (3): young men will give → darbadki\n\nIn (9): I will strike → hanuːg\n\nSo maybe verbs have different future forms.\n\nIs there a verb for \"steal\" with future?\n\nNot in examples.\n\nBut perhaps the stem is jahalgi, and future is marked by hanuːg?\n\nBut in (9), hanuːg is with \"strike\" — not with \"steal\".\n\nSo likely, the future of steal is not directly given.\n\nBut perhaps \"steal\" is not a main verb — or perhaps in context, use jahalgi with future marker.\n\nAnother idea: in (4), \"stole\" = jahalgi — past\n\nIn (18), \"will steal\" — future — so must be marked.\n\nSince no example of future steal, but with similar verbs — give, strike — different markers, perhaps \"steal\" uses darbadki?\n\nBut \"give\" uses darbadki.\n\n\"steal\" might use same?\n\nBut only \"give\" and \"strike\" have future forms.\n\nPossibility: future of steal = jahalgi with future suffix? Not clear.\n\nBut in absence of other evidence, assume that \"will steal\" = jahalgi with future particle.\n\nBut which?\n\nLook at (10): \"are giving\" = aygi\n\n\"will give\" = darbadki\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12365.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "Step 1: Identify recurring patterns in the given examples.\n\nLook at sentences involving \"give\", \"buy\", \"steal\", \"strike\", \"found\".\n\nPattern 1: \"give\" constructions \nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu → We bought the camels for the neighbours. \n→ \"ar\" = we; \"kanarriːcciːg\" = bought; \"kamiːg\" = the camels; \"jaːnticcirsu\" = for the neighbours.\n\nExample 8: iːdi magaski kamiːg tirsa → The men gave the camels to the thief. \n→ \"iːdi\" = the men; \"magaski\" = gave; \"kamiːg\" = the camels; \"tirsa\" = to the thief.\n\nExample 3: jahali waliːg darbadki biticcirra → The young men will give the chicken to the dogs. \n→ \"jahali\" = young men; \"waliːg\" = will; \"darbadki\" = give; \"biticcirra\" = the chicken; \"tirsa\" = to the dogs.\n\nPattern: [Subject] + [verb] + [object] + [prepositional phrase to recipient].\n\nNote: The prepositional phrase uses \"to\" = \"tirsa\".\n\n\"tirsa\" appears in: 8, 3, and possibly others.\n\nPattern 2: \"buy\" \nExample 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces. \n→ \"ay\" = I; \"beyyeːcciːg\" = buying; \"ajaːnirri\" = the necklaces.\n\nExample 4: man jahalgi kadeːcciːg maːgtirsu → He stole the dresses for the young man. \n\"man\" = he; \"jahalgi\" = stole; \"kadeːcciːg\" = the dresses; \"maːgtirsu\" = for the young man.\n\n\"for\" = \"maːgtirsu\" → appears in 4.\n\n\"for\" is used in: 4 (maːgtirsu), 1 (jaːnticcirsu), 10 (adeːnda)\n\nSo: \"for\" = maːgtirsu (and possibly other forms)\n\nPattern: [Subject] + [verb] + [object] + [for recipient] → \"maːgtirsu\" \nBut \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" may be \"for + group\"\n\n\"jaːnticcirsu\" = for the neighbours → in 1.\n\n\"maːgtirsu\" = for the young man → in 4.\n\nSo: \n- \"for\" + noun → \"maːgtirsu\" for young man → \"maːgtirsu\" \n- \"for\" + group → \"jaːnticcirsu\"\n\n\"tirsa\" = to, \"maːgtirsu\" = for\n\nPattern 3: \"steal\" \nExample 4: man jahalgi kadeːcciːg maːgtirsu → He stole the dresses for the young man.\n\n\"jahalgi\" = stole\n\nPattern 4: \"strike\" \nExample 9: ay hanuːg bijomri → I will strike the donkey. \n\"hanuːg\" = strike; \"bijomri\" = the donkey.\n\n\"hanuːg\" = strike, possibly used as verb for striking.\n\nExample 19: The owners struck the thieves. → should use \"hanuːg\" for strike.\n\nPattern 5: \"found\" \nExample 6: wal aygi baːbiːg eldeːnsu → The dog found the doors for me. \n\"wal\" = the dog; \"aygi\" = found; \"eldeːnsu\" = the doors; \"maːgtirsu\" = for me.\n\n\"aygi\" = found.\n\nSo: \n- \"found\" = aygi \n- \"strike\" = hanuːg \n- \"buy\" = beyyeːcciːg \n- \"steal\" = jahalgi \n- \"give\" = darbadki (in 3) / magaski (in 8)\n\nWait: 3 says \"darbadki\" = give; 8 says \"magaski\" = gave → possibly different verb forms.\n\nBut 3: jahali waliːg darbadki biticcirra → young men will give the chicken to the dogs → \"darbadki\" = give\n\n8: iːdi magaski kamiːg tirsa → men gave camels to thief → \"magaski\" = gave\n\nSo verb of giving: \"darbadki\" (present/future?) and \"magaski\" (past tense)\n\nSimilarly, \"beyyeːcciːg\" = buying (present), \"jahalgi\" = stole (past), \"hanuːg\" = strike (present/future)\n\nSo tenses: \n- Present: ay beyyeːcciːg → I am buying \n- Future: jahali waliːg darbadki → will give \n- Past: man jahalgi kadeːcciːg → he stole \n- Future: ay hanuːg bijomri → I will strike\n\nSo focus on getting tense and verb alignment.\n\nNow parse each requested sentence.\n\n16. The neighbours are giving the necklace to the owner.\n\n- Subject: the neighbours → from 1: \"jaːnticcirsu\" for neighbours → \"jaːnticcirsu\" = for the neighbours?\n\nIn 1: ar kanarriːcciːg kamiːg jaːnticcirsu → we bought camels for the neighbours → \"jaːnticcirsu\" = for the neighbours.\n\nThus: \"jaːnticcirsu\" = for the neighbours → so \"to the owner\" = \"tirsa\" + owner?\n\nBut in 8: iːdi magaski kamiːg tirsa → men gave camels to the thief → \"tirsa\" = to the thief.\n\nSo \"to\" = tirsa → must have \"tirsa\" + noun.\n\n\"the owner\" = from 2: tirt kadeːg allesu → owner repaired dress → so \"tirt\" = repaired, \"kadeːg\" = dress → \"kadeːg\" = dress → so \"owner\" is an entity.\n\nBut no direct word for \"owner\". In 2: \"tirt kadeːg allesu\" → owner repaired the dress → \"kadeːg\" = dress.\n\nBut in 1: \"jaːnticcirsu\" = for the neighbours → group.\n\nIn 4: \"maːgtirsu\" = for the young man → person.\n\nSo \"to the owner\" → likely \"tirsa + owner\".\n\nBut do we have \"owner\"?\n\nIn 2: \"tirt kadeːg allesu\" → owner = subject? \"tirt\" = verb (repaired), so \"tirt\" = repaired.\n\nNo clear noun for \"owner\".\n\nBut in 16: \"to the owner\" → the owner is recipient.\n\nSo likely same structure as 1: \"for the neighbours\" → jaːnticcirsu\n\nBut \"to\" and \"for\" are different.\n\nIn 8: \"tirsa\" = to the thief → so \"to\" is used.\n\nIn 4: \"maːgtirsu\" = for the young man → so \"for\" is used.\n\nSo for given object → \"for\" and \"to\" are separate.\n\nIn 16: \"to the owner\" → \"tirsa\" + owner.\n\nSo: subject = the neighbours → in 1: \"jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\" appears in 1 with \"neighbours\".\n\nBut subject in 1 is \"we\" → \"ar\".\n\nSo \"the neighbours\" must be a noun phrase.\n\nFrom 1: \"jaːnticcirsu\" → for the neighbours → so \"jaːnticcirsu\" = for the neighbours.\n\nSo \"neighbour\" → likely formed as \"jaːnti\" + \"ccirsu\"? Not clear.\n\nBut in 16, subject is \"the neighbours\", which is a group.\n\nWe see in 3: \"jahali waliːg\" = the young men → \"jahali\" = young men.\n\nSo \"the neighbours\" → likely a noun phrase — different from \"young men\".\n\nIn 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnti\" may be base → \"jaːnti\" + \"ccirsu\" → \"neighbours\"?\n\nLikely the noun \"neighbour\" = \"jaːnti\"?\n\nBut in 1: \"jaːnticcirsu\" = for the neighbours → so perhaps \"jaːnti\" = neighbour.\n\nThus: \"the neighbours\" → \"jaːnti\" with definite article?\n\nNo definite article in examples.\n\nBut \"the\" is not marked.\n\nIn 8: \"iːdi\" = the men → \"iːdi\" → men.\n\nSo \"the men\" = \"iːdi\" → so \"iːdi\" = the men.\n\nSimilarly, \"jahali\" = young men → so \"jahali\" = young men.\n\n\"wal\" = dog → \"wal\" = the dog.\n\n\"ay\" = I.\n\nSo noun phrases:\n\n- young men = jahali \n- men = iːdi \n- dog = wal \n- donkey = bijomri \n- dress = kadeːg \n- camels = kamiːg \n- necklaces = ajaːnirri \n- chickens = biticcirra \n- owners = ? \n- thieves = ? \n- owner = ? → in 2: \"owner\" is implied, but no word.\n\nIn 2: \"tirt kadeːg allesu\" → owner repaired the dress → \"tirt\" = repaired, so \"owner\" is subject.\n\nBut no noun form.\n\nIn 19: \"The owners struck the thieves.\" → so \"owners\" and \"thieves\" are noun phrases.\n\nNo direct word in examples.\n\nBut in 7: \"magas ikki waliːg ticcirsu\" → the thief gave you the dogs → \"magas\" = thief, \"ikki waliːg\" = you (pl.), \"ticcirsu\" → gave?\n\n\"ticcirsu\" = gave?\n\nBut 8: iːdi magaski kamiːg tirsa → men gave camels to thief → \"magaski\" = gave.\n\nSo \"gave\" → magaski (past), darbadki (future)\n\nSo for 16: \"are giving\" → present tense → future tense in 3 has \"waliːg\" = will.\n\nSo future = waliːg (in 3)\n\nPresent = ? in 1 or 5.\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying → \"beyyeːcciːg\" = buying → present.\n\nSimilarly, \"are giving\" → likely uses a present marker.\n\nIn 3: \"jahali waliːg darbadki\" → future.\n\nIn 8: no tense marker → past?\n\nIn 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → past.\n\nIn 5: \"ay beyyeːcciːg\" → present.\n\nSo present: no explicit future marker.\n\nBut 16: \"are giving\" → present → use verb form with no tense marker?\n\nNo clear tense indicator.\n\nBut in 5: \"beyyeːcciːg\" = buying → present.\n\nSo \"giving\" → darbadki?\n\nIn 3: \"darbadki\" = give → with \"waliːg\" = will.\n\nSo basic verb \"give\" = darbadki.\n\nSo \"are giving\" → possibly just darbadki without tense marker?\n\nBut in 5, present is \"beyyeːcciːg\" → not \"dabrdaki\".\n\nSo different verbs?\n\nWait — buying and giving are different verbs?\n\n\"buy\" = beyyeːcciːg \n\"give\" = darbadki or magaski?\n\nIn 3: \"darbadki\" = give → present/future? \nIn 8: \"magaski\" = gave → past.\n\nSo \"gave\" = magaski (past), \"give\" = darbadki (present/future).\n\nThus, \"are giving\" → darbadki.\n\nSo verb: darbadki.\n\nSubject: the neighbours → no word for \"neighbours\" in examples.\n\nIn 1: \"jaːnticcirsu\" = for the neighbours → so \"neighbours\" is implied in \"jaːnticcirsu\".\n\nSo noun \"neighbour\" = \"jaːnti\"?\n\nPossibly.\n\nSo \"the neighbours\" → how to express?\n\nIn 8: \"iːdi\" = the men → so noun class?\n\nPossibly, in 1, \"jaːnticcirsu\" implies \"neighbours\" as recipient.\n\nBut \"the neighbours\" as subject → likely uses \"jaːnti\" or similar.\n\nBut in 3: \"jahali\" = young men → so person group.\n\nSo perhaps \"neighbours\" = \"jaːnti\" with definite?\n\nBut not marked.\n\nLikely: \"jaːnti\" = neighbour, \"jaːntiː\" = the neighbours?\n\nBut no such form.\n\nAlternative: in 1, \"ar\" = we, so not group.\n\nBut we have no instance of \"the neighbours\" as subject.\n\nOnly as recipient in 1.\n\nBut 16: subject is \"the neighbours\".\n\nSo need to form subject noun phrase.\n\nUse pattern from 3: jahali = young men → so \"neighbours\" could be a similar group.\n\nBut no word.\n\nPerhaps the word \"neighbours\" is not directly given, but inferred from \"jaːnticcirsu\" → so \"jaːnti\" = neighbour.\n\nSo \"the neighbours\" → \"jaːnti\" (as in \"neighbours\")?\n\nBut no definite article.\n\nPossibly formed as \"jaːnti\" with context.\n\nBut in translation, must form full sentence.\n\nSo likely: [subject] + [verb] + [object] + [to recipient]\n\nSubject: the neighbours → use \"jaːnti\" (as a noun phrase meaning \"the neighbours\")\n\nVerb: present \"give\" = darbadki\n\nObject: the necklace → in 5: \"ajaːnirri\" = necklaces → so \"ajaːnirri\"\n\nRecipient: to the owner → \"tirsa\" + owner\n\nBut no word for \"owner\"\n\nIn 2: \"tirt kadeːg allesu\" → \"tirt\" = repaired, \"kadeːg\" = dress → so \"owner\" is subject → but no noun.\n\nIn 4: \"maːgtirsu\" = for the young man → so \"for\" = maːgtirsu\n\n\"in 1: jaːnticcirsu = for neighbours\"\n\nSo \"to\" = \"tirsa\"\n\nSo \"to the owner\" → \"tirsa\" + owner\n\nBut no word for owner.\n\nIn 7: \"magas\" = thief\n\nSo \"thieves\" = plural of \"magas\"?\n\nIn 19: \"owners\" and \"thieves\"\n\nIn 7: \"magas\" = thief → so plural = \"magas\" (same)?\n\n\"ikkig\" = you (pl.)? In 7: \"ikkig waliːg\" → \"ikkig\" = you (pl.), \"waliːg\" = gave?\n\nNo.\n\nIn 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs → \"ticcirsu\" = gave?\n\nBut in 8: \"tirsa\" = to the thief.\n\nSo \"gave\" = ticcirsu or magaski?\n\nInconsistency.\n\n3: darbadki = give \n8: magaski = gave \n7: ticcirsu = gave?\n\nSo multiple verbs for \"give\"?\n\nPossibly different forms.\n\nBut in 3: \"jahali waliːg darbadki\" → give → \"darbadki\" \nIn 8: \"iːdi magaski kamiːg tirsa\" → gave → \"magaski\" \nIn 7: \"magas ikki waliːg ticcirsu\" → thief gave you dogs → \"ticcirsu\"\n\n\"ticcirsu\" → possibly future or present?\n\nNo clear tense marker.\n\n\"ikki waliːg\" = you (pl.) → \"ikki\" = you (pl.)\n\nSo \"ticcirsu\" = gave.\n\nThus, \"give\" has multiple forms: darbadki, magaski, ticcirsu → possible different persons or tenses.\n\nBut ticcirsu may be a different form.\n\nLikely \"give\" is expressed via a base, with tense context.\n\nBut in 3, \"waliːg\" = will → future \nIn 5, \"ay beyyeːcciːg\" = present → buying\n\nSo perhaps for present \"give\" → darbadki \nFor past → magaski \nFor future → darbadki with waliːg\n\nIn 16: \"are giving\" → present → darbadki\n\nSo verb = darbadki\n\nSubject: \"the neighbours\" → from 1: \"jaːnticcirsu\" → for neighbours → so \"jaːnti\" = neighbour → so \"jaːnti\" = the neighbours?\n\nBut \"jaːnti\" alone may be used.\n\nIn 3: \"jahali\" = young men → so \"neighbours\" may be \"jaːnti\" in a similar sense.\n\nSo subject = jaːnti\n\nBut \"jaːnti\" = neighbour, so \"the neighbours\" → probably \"jaːnti\"\n\nObject: \"the necklace\" → in 5: \"ajaːnirri\" = necklaces → plural.\n\n\"necklace\" = ajaːnirri\n\nSo \"the necklace\" → ajaːnirri (assuming singular)\n\nIn 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → plural.\n\nSo \"necklace\" may be in plural.\n\nBut in 16: \"the necklace\" → singular?\n\nPossibly.\n\nIn 1: \"kamiːg\" = camels → plural.\n\nIn 2: \"kadeːg\" = dress → singular.\n\nIn 4: \"kadeːcci", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11449.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "First, build a word alignment table from the given examples to extract consistent morphological patterns.\n\nExamples:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu. \n We bought the camels for the neighbours. \n → \"ar\" = we (subject) \n → \"kanarriːcciːg\" = bought (verb, past) \n → \"kamiːg\" = the camels (object) \n → \"jaːnticcirsu\" = for the neighbours (prepositional phrase, recipient)\n\n2. tirt kadeːg allesu. \n The owner repaired the dress. \n → \"tirt\" = the owner (subject) \n → \"kadeːg\" = repaired (verb, past) \n → \"allessu\" = the dress (object)\n\n3. jahali waliːg darbadki biticcirra. \n The young men will give the chicken to the dogs. \n → \"jahali\" = the young men (subject, plural) \n → \"waliːg\" = will (future tense) \n → \"darbadki\" = give (verb) \n → \"biticcirra\" = the chicken (object) \n → \"to the dogs\" = \"biticcirra\" is object; \"to the dogs\" must be marked by a preposition + recipient noun\n\n4. man jahalgi kadeːcciːg maːgtirsu. \n He stole the dresses for the young man. \n → \"man\" = he (subject) \n → \"jahalgi\" = stole (past tense) \n → \"kadeːcciːg\" = the dresses (object) \n → \"maːgtirsu\" = for the young man (recipient)\n\n5. ay beyyeːcciːg ajaːnirri. \n I am buying the necklaces. \n → \"ay\" = I (subject) \n → \"beyyeːcciːg\" = buying (present) \n → \"ajaːnirri\" = the necklaces (object)\n\n6. wal aygi baːbiːg eldeːnsu. \n The dog found the doors for me. \n → \"wal\" = the dog (subject) \n → \"aygi\" = found (past) \n → \"baːbiːg\" = the doors (object) \n → \"eldeːnsu\" = for me (recipient)\n\n7. magas ikki waliːg ticcirsu. \n The thief gave you (pl.) the dogs. \n → \"magas\" = the thief (subject) \n → \"ikki\" = gave (verb) \n → \"waliːg\" = you (pl.) (recipient) \n → \"ticcirsu\" = the dogs (object)\n\n8. iːdi magaski kamiːg tirsa. \n The men gave the camels to the thief. \n → \"iːdi\" = the men (subject) \n → \"magaski\" = to the thief (prepositional phrase, recipient) \n → \"kamiːg\" = the camels (object) \n → \"tirsa\" = gave (verb)\n\n9. ay hanuːg bijomri. \n I will strike the donkey. \n → \"ay\" = I \n → \"hanuːg\" = will (future) \n → \"bijomri\" = strike (verb) \n → \"donkey\" = object\n\n10. sarkaːyi aygi beyyeːcciːg adeːnda. \n The cowards are giving me the necklaces. \n → \"sarkaːyi\" = the cowards (subject) \n → \"aygi\" = are giving (present) \n → \"beyyeːcciːg\" = the necklaces (object) \n → \"adeːnda\" = me (recipient)\n\nNow, identify core patterns:\n\n- Subject: marked by demonstrative (tirt, jahali, man, wal, iːdi, sarkaːyi, ay) or personal pronoun (ay, man)\n- Object: noun in nominative, e.g., kanarriːcciːg, kadeːg, biticcirra, etc.\n- Verb: root with aspect affixes:\n - Past: kadeːg, jahalgi, aygi, tirsa\n - Present: beyyeːcciːg, aygi (in \"are giving\")\n - Future: waliːg, hanuːg\n- Recipient: appears as prepositional phrase, often with \"for\" = \"kamiːg\" or \"maːgtirsu\" or \"eldeːnsu\", or structural \"to X\" using \"magaski\" or similar.\n- \"For\" is expressed by:\n - \"maːgtirsu\" = for the young man\n - \"eldeːnsu\" = for me\n - \"adeːnda\" = for me\n - \"jaːnticcirsu\" = for the neighbours\n - \"magaski\" = to the thief (in 8)\n\n→ Pattern: \n[Subject] [verb] [object] [for recipient]\n\nIn Example 8: \"iːdi magaski kamiːg tirsa\" → subject + to + object + verb \n→ so the prepositional phrase \"to X\" appears with [magaski] + noun\n\nAlso, in 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → subject + verb + object + for me\n\nThus, \"for\" is established as a complement in the form of:\n- [the recipient noun] after \"for\" (e.g., \"the neighbours\", \"the owner\", \"me\")\n- Preposition used: \"magaski\" for \"to the X\", or \"jaːnticcirsu\" for \"for the neighbours\"\n\nNow, apply to each request.\n\n16. The neighbours are giving the necklace to the owner. \n→ Subject: the neighbours → \"jaːnticcirsu\" (from 1) \n→ Verb: are giving → \"aygi\" (present tense, from 10) \n→ Object: the necklace → \"beyyeːcciːg\" (from 5) \n→ Recipient: to the owner → \"magaski kamiːg\" (the thief in 8 is \"magaski kamiːg\"; \"kamiːg\" = the owner?) \nWait: in 8, \"magaski kamiːg\" = to the thief → \"kamiːg\" = the thief \n→ So \"kamiːg\" = the one being given to, i.e., recipient noun \n→ Thus, \"to the owner\" = \"magaski iːnăg\" or \"magaski kadig\"? \nBut \"kamiːg\" appears in \"kamiːg\" in examples as \"the camels\", not \"the owner\"\n\nWait: in 1: \"for the neighbours\" = \"jaːnticcirsu\" \nSo: \"for X\" = \"jaːnticcirsu\" (for neighbours), \"maːgtirsu\" (for young man), \"eldeːnsu\" (for me), \"adeːnda\" (for me)\n\nThus, for \"the owner\", we need \"for the owner\" → likely \"kamiːg\" is for camels, not owner.\n\nCheck example 8: \"iːdi magaski kamiːg tirsa\" → gave the camels to the thief \nSo \"magaski kamiːg\" = to the thief → \"kamiːg\" = the thief \nThus, \"kamiːg\" = the recipient (the thief)\n\nBut in 1: \"jaːnticcirsu\" = for the neighbours \nSo no \"kamiːg\" for owner?\n\nTry to find \"the owner\" in the list. \nExample 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner \nSo \"tirt\" = the owner \nBut where does \"the owner\" appear as a recipient?\n\nIn 8: \"to the thief\" → \"magaski kamiːg\" → \"kamiːg\" is thief\n\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → dog found doors for me → \"eldeːnsu\" = for me\n\nIn 4: \"man jahalgi kadeːcciːg maːgtirsu\" → stole dresses for young man → \"maːgtirsu\" = for young man\n\nIn 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → bought camels for the neighbours → \"jaːnticcirsu\" = for neighbours\n\nSo: \n\"for X\" = \n- for neighbours → jaːnticcirsu \n- for young man → maːgtirsu \n- for me → eldeːnsu / adeːnda \n- for thief → magaski kamiːg (but \"kamiːg\" = thief)\n\nBut \"the owner\" is not used as recipient yet.\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → no recipient\n\nBut in 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → giving to me → \"adeːnda\"\n\nSo only two fixed recipient markers:\n- jaːnticcirsu → for neighbours \n- maːgtirsu → for young man \n- eldeːnsu / adeːnda → for me \n- magaski X → to X (only used with thief)\n\nBut no clear \"for owner\" in examples.\n\nBut we need: \"to the owner\" → so we must construct a form.\n\nPossibility: \"kamiːg\" is used for \"the X\" as a noun. \nIn 1: \"kamiːg\" = the camels \nIn 8: \"kamiːg\" = the camels \nIn 4: \"kadeːcciːg\" = the dresses → \"kadeːg\" + \"cciːg\" \nSo likely, \"kamiːg\" = the [noun] → so \"to the owner\" = \"magaski kamiːg\" → but only if \"kamiːg\" = owner.\n\nBut \"kamiːg\" = camels in examples.\n\nHypothesis: \"kamiːg\" is not a noun for owner.\n\nBut perhaps \"tirt\" is the owner.\n\nIs there a structure where \"to the owner\" is expressed as a prepositional phrase?\n\nIn example 2: \"tirt kadeːg allesu\" → owner repaired dress → no recipient\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → gave camels to thief → \"kamiːg\" = thief\n\nSo if we assume that \"kamiːg\" = the thief, then perhaps \"the owner\" is expressed with a different form.\n\nTry to see if \"tirt\" can be used in recipient.\n\nIs there a sentence with \"to the owner\"?\n\nNo.\n\nBut we can infer that the recipient prepositional phrase uses:\n- for [noun X] → with a prepositional form like jaːnticcirsu (for neighbours), maːgtirsu (for young man), etc.\n- to [noun X] → magaski [X]\n\nSo, for \"the owner\", we need a noun form.\n\nWhat is the noun form for \"owner\"?\n\nIn example 2: \"tirt\" = the owner → so \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nTherefore, \"to the owner\" = magaski tirt?\n\nBut in 8: \"magaski kamiːg\" = to the thief → \"kamiːg\" = thief\n\nSo \"to the owner\" = magaski tirt?\n\nYes, this seems plausible.\n\nSimilarly, \"for the neighbours\" = jaːnticcirsu → \"jaːnticcirsu\" = for neighbours\n\n\"for young man\" = maːgtirsu → maːgtirsu (for young man)\n\n\"for me\" = eldeːnsu or adeːnda\n\nSo: \n\"to the owner\" = magaski tirt\n\nNow, verb: \"are giving\" → present tense (from 10: sarkaːyi aygi beyyeːcciːg adeːnda)\n\n\"aygi\" = are giving\n\nSubject: \"the neighbours\" = jaːnticcirsu (from 1)\n\nObject: \"the necklace\" = beyyeːcciːg (from 5)\n\nSo 16: jaːnticcirsu aygi beyyeːcciːg magaski tirt\n\nWait, but in 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"for the neighbours\" at end.\n\nSo word order seems to be: subject, verb, object, recipient\n\nSo yes: [subject] [verb] [object] [recipient]\n\nThus 16: jaːnticcirsu aygi beyyeːcciːg magaski tirt\n\n→ The neighbours are giving the necklace to the owner.\n\nCheck: \n- Subject: jaːnticcirsu = the neighbours ✔ \n- Verb: aygi = are giving (present) ✔ \n- Object: beyyeːcciːg = the necklace ✔ \n- Recipient: magaski tirt = to the owner ✔\n\nNow 17. The young man bought the dog for us.\n\nSubject: the young man → in 3: \"jahali\" = the young men → plural \nBut \"young man\" = singular → use \"jahalgi\"? \nIn 4: \"man jahalgi kadeːcciːg\" → \"man\" = he → \"jahalgi\" = stole → verb form \nIn 3: \"jahali\" = the young men (subject) \n\"Jahali\" = plural\n\nIs there a singular form?\n\nIn 4: \"man\" = he (subject) → not young man \nNo example of singular \"young man\"\n\nBut \"young man\" → in 3: \"jahali\" = young men → plural\n\nPossibility: \"jahal\" = young man (singular)? Not attested.\n\nBut example 3: \"jahali waliːg\" = the young men will give → so \"jahali\" = young men\n\nBut in translation, \"the young man\" (singular) → need singular form.\n\n\"man\" is \"he\" → no match.\n\nPerhaps use \"jahl\" or infer from pattern.\n\nAlternative: in 4: \"man jahalgi kadeːcciːg\" → \"man\" = subject, \"jahalgi\" = verb (stole) \nSo \"jahalgi\" is a verb root.\n\n\"jahal\" = young man?\n\nNo such form.\n\nBut in 3: \"jahali\" = young men → likely \"jahal\" = young man.\n\nSince only \"young men\" appears, and the verb \"give\" is used with \"jahali\", we must assume that \"young man\" is a subset, and possibly the language has a form \"jahal\" or \"jahl\".\n\nBut no such form given.\n\nPerhaps the sentence uses \"jahal\" as subject.\n\nBut available forms: jahali = young men, jahal? Not present.\n\nWait — example 4: \"man jahalgi kadeːcciːg\" → \"jahalgi\" = stole → verb \nSo verb form with \"jahal\" as root?\n\nBut subject is \"man\", not \"young man\".\n\nSo no direct evidence.\n\nBut in translation: \"the young man bought\" → so subject = young man (singular)\n\nWe must use a form for \"young man\".\n\nCould it be \"jahal\" (singular)?\n\nOr is there a noun?\n\nIn example 3: \"jahali waliːg darbadki biticcirra\" → young men will give the chicken to the dogs\n\nSo \"jahali\" = young men\n\nNo singular form.\n\nBut in Kunuz Nubian, \"young man\" may be a reduplicated form or a different root.\n\nBut we are to use patterns.\n\nPossibility: the word \"jahal\" appears as verb root.\n\nPerhaps the subject is \"jahal\" (young man)?\n\nBut not in any noun form.\n\nAlternatively, perhaps in the future, \"the young man\" is just \"jahal\" as subject.\n\nAssume \"jahal\" is the form for \"young man\", as inferred from \"jahali\" (plural) → \"jahal\" (singular)\n\nThis is standard in linguistic reconstruction: from plural, singular is root.\n\nSo subject: jahal\n\nVerb: bought → \"kanarriːcciːg\" from 1: \"we bought\"\n\n\"kanarriːcciːg\" = bought (past)\n\nSo verb = kanarriːcciːg\n\nObject: the dog → in 3: \"biticcirra\" = the chicken → so \"dog\" is unknown.\n\nIn 7: \"magas ikki waliːg ticcirsu\" → \"ticcirsu\" = the dogs (plural)\n\n\"ticcirsu\" = the dogs\n\nSo dog = \"ticcir\" (singular)? Or \"ticcir\"?\n\nIn 3: \"biticcirra\" = the chicken → \"biticcirra\" → likely \"biticcir\" = chicken?\n\nSo \"ticcir\" = dog? Or \"tikcirsu\"?\n\nBut no \"dog\" entry.\n\nBut object is \"the dog\" → in 7: \"the dogs\" = ticcirsu → so singular \"ticcir\"?\n\nPossibly.\n\nBut in 7: \"ticcirsu\" = dogs (plural) → so \"ticcir\" = dog (singular)\n\nSo object = ticcir\n\nRecipient: \"for us\" = who? \"us\" = plural, in examples, \"me\" = eldeːnsu or adeːnda\n\n\"us\" = plural → not directly given.\n\nIn 10: \"adeːnda\" = for me\n\nIs there \"for us\"?\n\nNo.\n\nBut in example 6: \"wal aygi baːbiːg eldeːnsu\" → for me\n\nIn 4: \"man jahalgi kadeːcciːg maːgtirsu\" → for young man\n\nNo \"for us\"\n\nBut \"us\" → might be used with \"eldeːnsu\" in plural?\n\nUnlikely.\n\nPossibility", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11571.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 0, + "output": "Start by building an alignment table from the given examples to detect morphological and syntactic patterns in Kilivila.\n\nExample 1: \n“One man will catch these four fish.” → “Bibani navasi yena minasina tetala tau.” \n- \"Bibani\" = one \n- \"navasi\" = man \n- \"yena\" = these \n- \"minasina\" = four fish \n- \"tetala\" = will catch \n→ \"tetala\" is future; \"minasina\" = plural fish, with numeral structure.\n\nExample 2: \n“This white man arrived.” → “Lekota dimdim mtona.” \n- \"Lekota\" = this \n- \"dimdim\" = white \n- \"mtona\" = man \n- \"arrived\" → implied by word order and context.\n\nExample 3: \n“That child will arrive.” → “Bikota gwadi magudiwena.” \n- \"Bikota\" = that \n- \"gwadi\" = child \n- \"magudiwena\" = will arrive\n\nExample 4: \n“This old woman saw those canoes.” → “Legisi waga makesiwena namwaya minana.” \n- \"Legisi\" = this \n- \"waga\" = old \n- \"makesiwena\" = saw \n- \"namwaya\" = those \n- \"minana\" = canoes\n\nExample 5: \n“Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?” \n- \"Amtona\" = which \n- \"tau\" = man \n- \"lekalimati\" = killed \n- \"nayu\" = two \n- \"bunukwa\" = pigs\n\nExample 6: \n“The old women looked after two men.” → “Leyamatasi teyu tauwau nunumwaya.” \n- \"Leyamatasi\" = old \n- \"teyu\" = women \n- \"tauwau\" = looked after \n- \"nunumwaya\" = two men\n\nExample 7: \n“That clever woman will see something.” → “Bigisi kwetala vivila minawena nakabitam.” \n- \"Bigisi\" = that \n- \"kwetala\" = clever \n- \"vivila\" = woman \n- \"minawena\" = will see \n- \"nakabitam\" = something\n\nExample 8: \n“How many dogs arrived?” → “Navila ka’ukwa lekotasi?” \n- \"Navila\" = how many \n- \"ka’ukwa\" = dogs \n- \"lekotasi\" = arrived\n\nExample 9: \n“Which canoe did the chiefs see?” → “Amakena waga legisesi gweguyau?” \n- \"Amakena\" = which \n- \"waga\" = canoe \n- \"legisesi\" = the \n- \"gweguyau\" = saw\n\nExample 10: \n“That beautiful child saw this stone.” → “Legisi dakuna makwena gwadi magudiwena gudimanabweta.” \n- \"Legisi\" = that \n- \"dakuna\" = beautiful \n- \"makwena\" = child \n- \"gwadi\" = this \n- \"magudiwena\" = saw \n- \"gudimanabweta\" = stone\n\nExample 11: \n“How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?” \n- \"Kwevila\" = how many \n- \"lekamkwamsi\" = things \n- \"dimdim\" = white \n- \"mtosiwena\" = ate\n\nExample 12: \n“The clever chief killed one wild pig.” → “Lekalimati natala bunukwa nagasisi guyau tokabitam.” \n- \"Lekalimati\" = killed \n- \"natala\" = one \n- \"bunukwa\" = wild pig \n- \"nagasisi\" = chief \n- \"guyau\" = clever\n\nExample 13: \n“How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n- \"Navila\" = how many \n- \"vivila\" = women \n- \"biyamatasi\" = will look after \n- \"tau\" = this \n- \"mtona\" = man\n\nNow identify patterns:\n\n1. Numerals:\n- \"bibani\" = one \n- \"tetala\" = will catch \n- \"nayu\" = two \n- \"natala\" = one \n- \"tetala\" = future verb \n- \"vivila\" = woman \n- \"tau\" = man \n- \"minasina\" = four fish → \"minasina\" = four + fish \n- \"nayu\" = two + pigs \n- \"nunumwaya\" = two men \n- \"tauwau\" = looked after \n→ Numerals seem to be suffixes or root + number, number often appears before noun.\n\n2. Demonstratives:\n- \"le\" = this \n- \"bi\" = that \n- \"lekota\" = this \n- \"bikota\" = that \n- \"legisi\" = that \n- \"le\" + noun → \"lekotasi\" = arrived (for \"this\" + arrival) \n→ All demonstratives attach before noun or verb? \nActually: \n- \"Bibani\" = one man \n- \"Lekota\" = this white man \n→ \"lekota\" = this + man \n→ So demonstrative comes before noun.\n\n3. Verbs:\n- \"tetala\" = will catch \n- \"makesiwena\" = saw \n- \"kwevila\" = how many \n→ \"kwevila\" = how many → interrogative \n→ \"navila\" = how many → also used in questions → \"navila\" = how many\n\n4. Adjectives:\n- \"dimdim\" = white \n- \"dakuna\" = beautiful \n- \"kwetala\" = clever \n- \"waga\" = old \n→ Adjectives precede nouns: \n\"dimdim mtona\" = white man \n\"kwetala vivila\" = clever woman \n→ Ordering: adjective + noun\n\n5. Possession, reference, and question words:\n- \"Amtona\" = which \n- \"Amakena\" = which \n- \"Kwevila\" = how many \n- \"Navila\" = how many \n→ \"Navila\" and \"Kwevila\" both = how many → likely stem \n→ \"am\" + noun = which noun?\n\n6. Noun phrases:\n- Noun base: \"navasi\" (man), \"mtona\" (man), \"gwadi\" (child), \"vivila\" (woman), \"waga\" (old), \"minana\" (canoes), \"bunukwa\" (pig), \"tauwau\" (look after) → some are adjectives, some nouns\n\nKey pattern:\n- Numerals appear before nouns or attached to the noun (e.g., \"minasina\" = four fish, \"nayu bunukwa\" = two pigs)\n- Demonstratives appear before noun: \"lekota\" = this man\n- Adjectives before noun: \"dimdim mtona\" = white man\n- Verbs: “tau” = will, “mtona” = arrived → future and past? \n→ “tetala” = will catch → future \n→ “makesiwena” = saw → past \n→ “mtosiwena” = ate → past \n→ “gudimanabweta” = stone → noun\n\nNow parse the target sentences:\n\n14. Navila vivila biyamata tomwaya mtona? \n“Navila” = how many \n“vivila” = women \n“biyamata” = will look after \n“tomwaya” = this \n“mtona” = man \n→ Structure: how many women will look after this man? \n→ Matches Example 13: “Navila vivila biyamatasi tau mtona?” → only difference is \"biyamata\" vs \"biyamatasi\" \n→ \"biyamatasi\" = will look after \n→ \"biyamata\" → could be a different verb form? \nPossibility: \"biyamata\" could be \"will look after\", but is it different from \"biyamatasi\"? \nIn example 13: \"biyamatasi\" \nIn 14: \"biyamata\" \nSmall suffix difference: -si vs -ta → may indicate different tense or mood. \n\nBut in example 13: \"will look after\" is \"biyamatasi\" \nIn 14: \"biyamata\" — possibly a defective or variant form? \n\nWait: Example 13 is: “Navila vivila biyamatasi tau mtona?” = how many women will look after this man? \nSentence 14: “Navila vivila biyamata tomwaya mtona?” \n“tomwaya” = this man → whereas in 13 it was “tau” → same meaning? \n\"tau\" vs \"tomwaya\" → \"tau\" = this man, \"tomwaya\" = this man → likely equivalent \nBut \"biyamatasi\" vs \"biyamata\" — could this be tense variation?\n\nCompare:\n- Example 7: \"vivila minawena nakabitam\" → will see \n- Example 13: \"biyamatasi\" → will look after \n→ \"biyamata\" might be the same as \"biyamatasi\" but with different affix — not clear.\n\nBut \"biyamatasi\" has -asi → \"look after\" \n\"biyamata\" has -ata — could be simpler form? \nNo parallel for \"biyamata\".\n\nHowever, note that in example 11: \"lekamkwamsi\" = things → \"le\" + \"kamkwamsi\" \nIn example 12: \"nagasisi guyau\" → chief + clever → \"guyau\" = clever\n\nSo adjectives come after nouns? No — in \"dimdim mtona\" = white man → adjectives before noun.\n\nSo in 14: “vivila biyamata tomwaya mtona” \n→ “vivila” = woman → noun \n→ “biyamata” = will look after → verb? \nBut “biyamata” is not a verb of “look after” — “biyamatasi” is.\n\nIs it possible that “biyamata” is not a verb? Could it be “belong to” or something else?\n\nNo. “Look after” is the only relevant verb.\n\nAlternatively, could “biyamata” be “see” or “watch”? But “minawena” = see.\n\nTry to reconstruct based on earlier examples.\n\nExample 6: “Leyamatasi teyu tauwau nunumwaya.” \n→ “teyu” = women \n→ “tauwau” = looked after \n→ verb: “tauwau” = looked after\n\nExample 13: “Navila vivila biyamatasi tau mtona” → how many women will look after this man?\n\nThus “biyamatasi” = will look after.\n\nIn sentence 14: “biyamata” — differs in suffix. Is it a past, present, or different verb?\n\nNo parallel. May be an error or variant.\n\nBut sentence 14 has “tomwaya” instead of “tau” — “tomwaya” = this man? \n“tau” = this man, “tomwaya” = this man → likely identical.\n\nConclusion: “Navila vivila biyamata tomwaya mtona” \n→ Possibly intended to mean “How many women will look after this man?” \n→ But verb is “biyamata” instead of “biyamatasi”. \nIs “biyamata” a valid form?\n\nNo parallel. But in example 7: “vivila minawena” = will see \n→ “minawena” = will see \n→ “biyamatasi” = will look after → so “biyamata” may be a mismatch.\n\nWait — other sentence might be ambiguous.\n\nNow look at sentence 15: \n15. Bikamkwamsi kweyu vivila minasina. \n“Bikamkwamsi” = that thing? \n“kweyu” = two \n“vivila” = woman \n“minasina” = fish? → but fish is “minasina” — in example 1, “minasina” = four fish → so “minasina” = fish (pl) \nBut “kweyu” = two? → “nayu” = two, “kweyu” = same or variant?\n\nIn example 5: “nayu bunukwa” = two pigs \nIn example 15: “kweyu vivila minasina” \n→ \"kweyu\" = two → likely “kweyu” = two \n→ \"vivila\" = woman \n→ \"minasina\" = four fish? But “minasina” is four fish → can't be fish in context of woman?\n\n“minasina” is “four fish” — so would not go with “woman”\n\nPossibility: word order → “kweyu vivila minasina” = “two women fish” → nonsense \nAlternatively: “kweyu” = two → “vivila” = women → “minasina” = something? But not matching.\n\n“minasina” = fish — so likely this is “two women saw these fish”?\n\nBut sentence is not in past or future.\n\nWords: “Bikamkwamsi” = that → “that” \nThen “kweyu” = two \n“vivila” = women \n“minasina” = fish\n\nSo likely: “That two women saw fish?” — no, “two women saw fish”?\n\nBut no verb.\n\nNo verb? No verb specified. But all sentences have verbs.\n\nIn example 12: \"killed\" → \"lekalimati\"\n\nHere, no verb present.\n\nWait — “minasina” → could be a verb? No.\n\n“kweyu” → could be a verb? Unlikely.\n\nPossibility: “Bikamkwamsi” = “which” or “that” → “which two women”? \n“kweyu vivila minasina” = two women fish → no\n\nAlternatively, “minasina” = something else?\n\nIn example 1: “minasina” = four fish \nIn example 4: “namwaya minana” = those canoes \nNo other use.\n\nSo “minasina” = fish.\n\nThus “kweyu vivila minasina” — two women fish → nonsense.\n\nThus likely: “that two women saw fish” → need verb.\n\nBut no verb → missing.\n\nUnless “minasina” has a verb function — no.\n\nWait — sentence 15: “Bikamkwamsi kweyu vivila minasina.” \nCompare to sentence 10: “Legisi dakuna makwena gwadi magudiwena gudimanabweta.” → “saw this stone”\n\nSentence 15 might be missing a verb.\n\nBut in sentence 10, “magudiwena” = saw → verb.\n\nIn sentence 12, “lekalimati” = killed.\n\nBut in 15: no verb.\n\nUnless “kweyu” is a verb? Unlikely.\n\nAlternative: Could “kweyu” be “will” or “past”?\n\nNo — “kweyu” = two.\n\nAnother possibility: word order — “Bikamkwamsi” = “that” → “that two women” → “kweyu vivila” = “two women” → “minasina” = fish → “that two women fish”?\n\nNo.\n\nPerhaps the verb is “make” or “see”?\n\nNot present.\n\nWait — look at sentence 16: \n16. Amagudina gwadi lekota? \n“Amagudina” = which? \n“gwadi” = this \n“lekota” = this man? → “this man” \n→ “which this man” → nonsense \n“Amagudina” = which → “which” \n“gwadi” = this → “this” \n“lekota” = this man → redundant?\n\nBut in example 2: “Lekota dimdim mtona” → this white man \nSo “lekota” = this man \n“gwadi” = this → could be “this” + something.\n\n“gwadi lekota” = this this man? → redundant \nLikely it’s “which this [man]” → could mean “which of these men”?\n\nBut “gwadi” = this — could be a demonstrative.\n\nCompare to example 9: “Amakena waga legisesi gweguyau?” → which canoe did the chiefs see?\n\n“Amakena” = which \n“waga” = canoe \n→ “which canoe”\n\nHere: “Amagudina gwadi lekota” = which this man?\n\nBut “gwadi” and “lekota” both mean “this” — possible double emphasis.\n\nBetter: “gwadi lekota” = this man? → “gwadi” = this, “lekota” = this man → redundant.\n\nAlternatively: “gwadi” = this, “lekota” = (demonstrative) → “which this man” → could mean “which of the men?” → ambiguous if “gwadi” is the thing.\n\nPossibility: “Amagudina gwadi lekota” = which of these men is it? → “which man?”\n\nBut “gwadi lekota” = this man → could be mistyped or misaligned?\n\nAlternatively, could it be “which man”?\n\n“amagudina” = which → “which man”?\n\nThen “gwadi” = this → “this man” → so “which this man” — still awkward.\n\nCompare to sentence 8: “Navila ka’ukwa lekotasi?” → how many dogs arrived → “lekotasi” = arrived\n\nSo verbs are often in the clause.\n\nNo verb in 16.\n\nSo sentence 16 has no verb — but all others do.\n\nSo likely, sentence 16 is: “Which of these men?” → “amagudina gwadi lekota” = which this man?\n\nBut “gwadi lekota", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11805.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 1, + "output": "Start by building an alignment table from the given examples to extract patterns.\n\nTrack core elements across sentences:\n\n| English | Kilivila | Notes |\n|--------|---------|-------|\n| One man will catch these four fish. | Bibani navasi yena minasina tetala tau. | \"one\" = bibani; \"man\" = navasi; \"will catch\" = yena minasina; \"four fish\" = tetala tau |\n| This white man arrived. | Lekota dimdim mtona. | \"this\" = lekota; \"white\" = dimdim; \"man\" = mtona (verb root possibly) |\n| That child will arrive. | Bikota gwadi magudiwena. | \"that\" = bikota; \"child\" = gwadi; \"will arrive\" = magudiwena |\n| This old woman saw those canoes. | Legisi waga makesiwena namwaya minana. | \"this\" = legisi; \"old\" = waga; \"woman\" = makesiwena; \"saw\" = makesiwena; \"those canoes\" = namwaya minana |\n| Which man killed two pigs? | Amtona tau lekalimati nayu bunukwa? | \"which man\" = amtona tau; \"killed\" = lekalimati; \"two pigs\" = nayu bunukwa |\n| The old women looked after two men. | Leyamatasi teyu tauwau nunumwaya. | \"old women\" = leyamatasi; \"looked after\" = teyu tauwau; \"two men\" = nunumwaya |\n| That clever woman will see something. | Bigisi kwetala vivila minawena nakabitam. | \"that\" = bigisi; \"clever\" = kwetala; \"woman\" = vivila; \"will see\" = minawena; \"something\" = nakabitam |\n| How many dogs arrived? | Navila ka’ukwa lekotasi? | \"how many\" = navila; \"dogs\" = ka’ukwa; \"arrived\" = lekotasi |\n| Which canoe did the chiefs see? | Amakena waga legisesi gweguyau? | \"which canoe\" = amakena waga; \"chiefs\" = legisesi; \"saw\" = gweguyau |\n| That beautiful child saw this stone. | Legisi dakuna makwena gwadi magudiwena gudimanabweta. | \"that\" = legisi; \"beautiful\" = dakuna; \"child\" = gwadi; \"saw\" = makwena; \"this stone\" = gudimanabweta |\n| How many things did those white men eat? | Kwevila lekamkwamsi dimdim mtosiwena? | \"how many\" = kwevila; \"things\" = lekamkwamsi; \"those white men\" = dimdim mtosiwena |\n| The clever chief killed one wild pig. | Lekalimati natala bunukwa nagasisi guyau tokabitam. | \"clever\" = natala; \"chief\" = guyau; \"killed\" = lekalimati; \"one wild pig\" = tokabitam |\n| How many women will look after this man? | Navila vivila biyamatasi tau mtona? | \"how many women\" = navila vivila biyamatasi; \"will look after\" = tau mtona |\n\nNow extract patterns:\n\n- \"how many\" = navila (in 8, 13, 14)\n- \"which\" = amtona, amakena, ambona?\n- \"this\" = lekota, legisi\n- \"that\" = bikota, bigisi\n- \"white\" = dimdim\n- \"old\" = waga\n- \"clever\" = kwetala, natala\n- \"woman\" = makesiwena, vivila, biyamatasi\n- \"man\" = navasi, mtona, tau\n- \"fish\" = tetala, minasina\n- \"pigs\" = bunukwa\n- \"canoes\" = namwaya\n- \"saw\" = makesiwena, makwena, gweguyau\n- \"killed\" = lekalimati\n- \"looked after\" = teyu tauwau\n- \"arrived\" = magudiwena, lekotasi\n\nNow look at case patterns:\n\n- Demonstratives: lekota (this), bikota (that), legisi (this), bigisi (that)\n- Adjective morphology: waga (old), dakuna (beautiful), dimdim (white), kwetala (clever), natala (clever)\n- Subject markers: navasi (man), mtona (man), gwadi (child), vivila (woman), biyamatasi (women)\n- Verbs:\n - saw = makesiwena / makwena / gweguyau\n - arrived = magudiwena / lekotasi\n - killed = lekalimati\n - looked after = teyu tauwau\n\nNumber system:\n\n- \"one\" = bibani, tokabitam\n- \"two\" = nayu (in 4 and 5), nunumwaya (two men)\n- \"four\" = tetala (in 1), tetala can be “four”\n- \"how many\" = navila (used in questions)\n\nNow examine the requested translations:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"how many\" = navila \n\"women\" = biyamatasi → biyamata? likely same as biyamatasi but with change in plural or typo? \n\"tomwaya\" → similar to \"towayna\"? \"that\" or \"which\"? \n\"mtona\" = man\n\n\"how many women will look after this man?\"\n\nBut \"tomwaya\" = \"that\" (like tomwaya = bigisi, but there's a known \"bigisi\" for that)\n\nPossible reading: \"how many women will look after that man?\"\n\nBut \"tomwaya\" may be a variant of \"that\" (like \"gugwadi\" is \"that\", but \"tomwaya\" may be same?)\n\nAnother clue: sentence 13: \"How many women will look after this man?\" → navila vivila biyamatasi tau mtona\n\nHere: \"navila vivila biyamatasi tau mtona\" → how many women will look after this man?\n\nNow 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n\"biyamata\" → likely plural of \"biyamata\" vs \"biyamatasi\"\n\n\"tomwaya\" → could be \"that\" → similar to \"legisi\", \"bigisi\"\n\nSo “how many women will look after that man?”\n\n→ So one translation: \"How many women will look after that man?\"\n\nBut is \"tomwaya\" only \"that\"? Possibly.\n\nBUT: in 13 we have \"this man\" → mtona (this), in 14 → \"tomwaya\" → that?\n\nYes. So likely a shift from \"this\" to \"that\".\n\nThus: translation: \"How many women will look after that man?\"\n\nIs this the only one?\n\nNo — could \"tomwaya\" be interpreted as \"which\"?\n\n\"Which woman will look after this man?\" — but \"which\" is amtona / amakena, not \"tomwaya\"\n\n\"tomwaya\" is not a known \"which\" marker. \"which\" appears in 5: amtona tau, 9: amakena\n\nSo \"tomwaya\" likely refers to \"that\" → so \"that man\"\n\nHence one translation.\n\nBut the problem says: one of these has **two possible translations**\n\nCheck others.\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n\"bikamkwamsi\" → \"which\" (bika) + \"amkwamsi\"? \n\"amkwamsi\"? in 11: \"kwevila lekamkwamsi\" → \"how many things\"\n\n\"lekamkwamsi\" = \"things\"\n\n\"bikamkwamsi\" = which things?\n\n\"vivila\" = woman\n\n\"minasina\" = man?\n\n\"vivila minasina\" = woman man? Grammatical?\n\n\"vivila\" = woman; \"minasina\" = man (in 1: \"men\" = minasina)\n\nSo \"which woman-man\"? Ungrammatical.\n\nWait — perhaps \"bikamkwamsi\" = which (bika) + \"amkwamsi\" → where \"amkwamsi\" = \"things\"?\n\nBut in 11: \"lekamkwamsi\" = things\n\nSo \"bikamkwamsi\" = which things?\n\nThen \"kweyu\" → what?\n\n\"kweyu\" = \"how many\"?\n\n\"bikamkwamsi kweyu\" = which how many?\n\nUnnatural.\n\nWait: \"kweyu\" → in 5: \"amtona tau\" → no; in 11: \"kwevila\" → how many\n\nIn 11: \"kwevila\" = how many\n\nIn 15: \"kweyu\" → possibly a mistake? Or \"kweyu\" = \"how many\"?\n\nBut only \"navila\" and \"kwevila\" for how many.\n\n\"navila\" = how many (used in 8,13)\n\n\"kwevila\" = how many (in 11)\n\n\"kweyu\"? Not found.\n\n\"bikamkwamsi\" → may be \"which things\"?\n\n\"vivila minasina\" → woman man?\n\nBut \"vivila\" is woman, \"minasina\" is man.\n\nCould it be \"which woman\" and \"which man\"?\n\nNo — \"vivila minasina\" = woman-man?\n\nAlternatively, \"bikamkwamsi\" = which (bika) + \"amkwamsi\" = which thing?\n\nBut \"amkwamsi\" not standalone.\n\nIn 11: \"lekamkwamsi\" = things → so \"amkwamsi\" = things?\n\nSo \"bikamkwamsi\" = which things?\n\n\"kweyu\" — possible error or variant?\n\nBut parimorphic: \"kweyu\" could be \"how many\" → like \"kwevila\"\n\nBut \"kwevila\" appears in 11: \"kwevila lekamkwamsi dimdim mtosiwena\" → how many things did those white men eat?\n\nSo \"kwevila\" = how many\n\n\"navila\" = how many\n\nSo both \"navila\" and \"kwevila\" = how many?\n\nBut never used together.\n\nNow: \"bikamkwamsi kweyu vivila minasina\"\n\n→ if \"kweyu\" = how many → then \"how many which women men\"?\n\nUnnatural.\n\nPossible: \"which woman will [do] something with man\"?\n\nNo.\n\nAlternative: \"which woman did [something] to the man\"?\n\nBut no verb.\n\nWait — \"kweyu\" may be a typo? Or \"kweyu\" = how many?\n\nBut in context: sentences using \"kwevila\" are about quantity.\n\nIn 15: \"Bikamkwamsi kweyu vivila minasina\"\n\nMay be: \"Which woman will catch the man?\" → but no verb.\n\nNo verb.\n\nAnother possibility: \"which woman is there among the men?\"\n\nBut not supported.\n\nBetter: \"kweyu\" likely meant to be \"how many\" — so \"how many women\" → \"navila\", not \"bikamkwamsi\"\n\n\"bikamkwamsi\" = which things?\n\n\"vivila minasina\" = woman and man?\n\nPossibly: \"which woman-man\"?\n\nUnlikely.\n\nPerhaps a question about which woman caught the man?\n\nBut no verb.\n\nWait — in 1: \"one man will catch these four fish\" — \"yena minasina\" = will catch\n\n\"catch\" is \"yena\"\n\nSo in 15, is \"kweyu vivila minasina\" = \"how many women will catch the man\"?\n\nBut \"kweyu\" = how many?\n\nNo verb.\n\nUnless \"kweyu\" is a verb? Unlikely.\n\nAnother idea: in 13: \"how many women will look after this man\" → navila vivila biyamatasi tau mtona\n\nSo \"navila\" = how many\n\n\"bikamkwamsi\" = which?\n\nSo sentence 15 may be: \"Which woman will catch the man?\"\n\nBut no verb.\n\n\"vivila minasina\" — woman man?\n\nCould be \"a woman and a man\"? But not clear.\n\nBut in the context, \"minasina\" might be \"man\", so \"which woman and which man\"?\n\nStill not.\n\nBut we have sentence 10: \"that beautiful child saw this stone\" → \"legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"makwena\" = saw\n\n\"gwadi\" = child\n\n\"magudiwena\" = this stone\n\nSo verb \"saw\" = makwena\n\nSo verbs: *saw*, *arrived*, *looked after*, *killed*, *will catch*\n\nIn 15: no verb.\n\nSo the sentence is malformed?\n\nBut it must be decipherable.\n\nPerhaps \"kweyu\" is a misreading of \"kwevila\" — \"kwevila\" = how many\n\nThen \"kwevila vivila minasina\" = how many women men?\n\nStill broken.\n\nAlternative: \"bikamkwamsi\" = which (bika) and \"amkwamsi\" = things?\n\nSo \"which things\"?\n\nThen \"kweyu\" = how many?\n\nThen \"how many which things\"?\n\nStill broken.\n\nAnother idea: in 13, \"navila vivila biyamatasi tau mtona\" = how many women will look after this man?\n\nIn 14, \"navila vivila biyamata tomwaya mtona\" → how many women will look after that man?\n\nNow 15: \"bikamkwamsi kweyu vivila minasina\"\n\n\"bikamkwamsi\" = which?\n\n\"kweyu\" = how many? → only two how many: navila, kwevila\n\n\"vivila minasina\" = woman and man?\n\nCould be \"which woman and man\"?\n\nBut not a grammatical noun phrase.\n\nWait — in 12: \"The clever chief killed one wild pig\" — \"lekalimati natala bunukwa nagasisi guyau tokabitam\"\n\n\"nagasisi\" = chief\n\n\"tokabitam\" = one wild pig\n\n\"bunukwa\" = pig\n\nSo \"pig\" = bunukwa\n\n\"minasina\" = fish? In 1: \"fish\" = tetala\n\n\"minasina\" = man\n\nSo likely not fish.\n\nPossibility: \"bikamkwamsi kweyu vivila minasina\" = \"which woman will go after the man\"?\n\nNo.\n\nWait — could \"vivila minasina\" be \"a woman-man\"?\n\nUnlikely.\n\nBut perhaps \"kweyu\" is not \"how many\", but \"who\" or \"which\"?\n\nThen \"bikamkwamsi kweyu vivila minasina\" = \"which woman and man will do what?\"\n\nStill no.\n\nAnother: in 14, we have a possible ambiguity: \"tomwaya\" can be \"that\" or \"which\"?\n\nIn 13: \"this man\" → mtona\n\nIn 14: \"tomwaya mtona\" → \"that man\"\n\nBut in 14, no verb — the verb is \"will look after\", so subject is women, action to man.\n\nSo translation: \"How many women will look after that man?\"\n\nIs that one translation?\n\nCould \"tomwaya\" mean \"which\" — as in \"which woman\"?\n\nBut \"which\" is \"amtona\" or \"amakena\"\n\n\"Tomwaya\" is not a known which.\n\nSo unlikely.\n\nNow 16. Amagudina gwadi lekota?\n\n\"amagudina\" = which? (am) + \"gudina\"?\n\n\"gudina\"? in 10: \"gudimanabweta\" = stone\n\n\"gudina\" → possible? not found.\n\n\"gwadi\" → child\n\n\"lekota\" → this\n\n\"amagudina\" — like \"am\" + \"gudina\"? But no \"gudina\" in data.\n\nIn 10: \"gudimanabweta\" → stone\n\n\"agudin\" not found.\n\n\"amagudina\" — possibly \"which child\"?\n\nBecause \"gwadi\" = child\n\n\"lekota\" = this\n\nSo \"which child this\"?\n\nUnnatural.\n\n\"amagudina\" = which (am) + \"gudina\" → gudina = something?\n\nBut \"gudimanabweta\" = stone — could gudina = stone?\n\nThen \"which stone this\"?\n\n\"gwadi\" = child — so not.\n\nNo.\n\nPerhaps typo: \"amagudina\" should be \"amakwena\" or \"amajad\"?\n\nNo.\n\nAnother possibility: \"amagudina\" = \"what\" or \"which\"?\n\nIn 11: \"kwevila lekamkwamsi\" = how many things\n\nNo.\n\nSo \"amagudina gwadi lekota\" → \"which child this\"?\n\nUnlikely.\n\nBut \"lekota\" = this, \"gwadi\" = child\n\nSo \"which child this\"?\n\nCould be: \"which child is this?\"\n\nBut no \"is\" in sentence.\n\nPossibility: \"this child is which one?\"\n\nStill awkward.\n\nBut in 10: \"that beautiful child saw this stone\" — \"legisi dakuna gwadi magudiwena gudimanabweta\"\n\nSo \"gwadi magudiwena\" = this child\n\nSo \"gwadi\" = child, \"magudiwena\" = this\n\nSo \"gwadi\" alone = child\n\nTherefore, \"amagudina gwadi lekota\" = \"which child is this?\"\n\nLikely meaning: \"Which child is this?\"\n\nYes — so translation: \"Which child is this?\"\n\nNow 17. Tev", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11637.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build an alignment table from the given examples to identify consistent linguistic patterns.\n\nExample 1: \nOne man will catch these four fish. \nBibani navasi yena minasina tetala tau.\n\n- \"one man\" → Bibani navasi \n- \"will catch\" → tetala \n- \"these four fish\" → yena minasina tetala tau \n→ \"minasina\" = fish, \"tau\" = four\n\n\"tetala\" = catch → verb, \"tau\" = four → numeral\n\nExample 2: \nThis white man arrived. \nLekota dimdim mtona. \n\"this\" → lekota, \"white\" → dimdim, \"man\" → mtona\n\nExample 3: \nThat child will arrive. \nBikota gwadi magudiwena. \n\"that\" → bikota, \"child\" → gwadi, \"will arrive\" → magudiwena\n\n\"magudiwena\" = will arrive\n\nExample 4: \nThis old woman saw those canoes. \nLegisi waga makesiwena namwaya minana. \n\"this\" → legisi, \"old\" → waga, \"woman\" → makesi, \"saw\" → makesiwena, \"those\" → namwaya, \"canoes\" → minana\n\n\"makesiwena\" = saw → verb, \"waga\" = old\n\nExample 5: \nWhich man killed two pigs? \nAmtona tau lekalimati nayu bunukwa? \n\"which\" → amtona, \"man\" → lekalimati, \"killed\" → nayu, \"two\" → tau, \"pigs\" → bunukwa\n\n\"nayu\" = killed, \"tau\" = two\n\nExample 6: \nThe old women looked after two men. \nLeyamatasi teyu tauwau nunumwaya. \n\"old women\" → leymatasi, \"looked after\" → teyu tauwau, \"two men\" → nunumwaya\n\n\"teyu tauwau\" = looked after, \"nunumwaya\" = two men\n\nExample 7: \nThat clever woman will see something. \nBigisi kwetala vivila minawena nakabitam. \n\"that\" → bigisi, \"clever\" → kwetala, \"woman\" → vivila, \"will see\" → minawena, \"something\" → nakabitam\n\n\"minawena\" = will see\n\nExample 8: \nHow many dogs arrived? \nNavila ka’ukwa lekotasi? \n\"how many\" → navila, \"dogs\" → ka’ukwa, \"arrived\" → lekotasi\n\n\"lekotasi\" = arrived\n\nExample 9: \nWhich canoe did the chiefs see? \nAmakena waga legisesi gweguyau? \n\"which\" → amakena, \"canoe\" → waga, \"did the chiefs see\" → legisesi gweguyau\n\n\"legisesi\" = saw, \"gweguyau\" = the chiefs\n\nExample 10: \nThat beautiful child saw this stone. \nLegisi dakuna makwena gwadi magudiwena gudimanabweta. \n\"that\" → legisi, \"beautiful\" → dakuna, \"child\" → gwadi, \"saw\" → magudiwena, \"this\" → gudimanabweta, \"stone\" → gudimanabweta\n\n\"magudiwena\" = saw\n\nExample 11: \nHow many things did those white men eat? \nKwevila lekamkwamsi dimdim mtosiwena? \n\"how many\" → kwevila, \"things\" → lekamkwamsi, \"did those white men eat\" → dimdim mtosiwena\n\n\"dimdim\" = white, \"mtosiwena\" = ate\n\nExample 12: \nThe clever chief killed one wild pig. \nLekalimati natala bunukwa nagasisi guyau tokabitam. \n\"clever\" → natala, \"chief\" → lekalimati, \"killed\" → nagasisi, \"one\" → guyau, \"wild pig\" → tokabitam\n\n\"nagasisi\" = killed, \"guyau\" = one\n\nExample 13: \nHow many women will look after this man? \nNavila vivila biyamatasi tau mtona? \n\"how many\" → navila, \"women\" → vivila, \"will look after\" → biyamatasi, \"this man\" → tau mtona\n\n\"biyamatasi\" = will look after\n\nNow, analyze the key patterns:\n\n1. Numerals:\n- \"tau\" = four\n- \"two\" → \"tau\" (again, in 5,6), \"one\" → \"guyau\"\n- \"two\" → \"tau\", \"one\" → \"guyau\", \"many\" → \"navila\" (in question forms)\n\n2. Determiners:\n- \"this\" → lekota, \"that\" → bikota, \"this\" → legisi, \"that\" → bigisi\n- \"those\" → namwaya, \"these\" → yena\n\n3. Verbs:\n- \"arrive\" → magudiwena, lekotasi → arrived\n- \"see\" → makesiwena, minawena\n- \"killed\" → nayu, nagasisi\n- \"look after\" → teyu tauwau, biyamatasi\n\n4. Articles/adjectives:\n- \"white\" → dimdim\n- \"old\" → waga\n- \"clever\" → kwetala, natala\n\n5. Question forms:\n- \"how many\" → navila, kwevila\n- \"which\" → amtona, amakena\n\n6. Subject markers:\n- \"man\" → mtona, navasi\n- \"woman\" → makesi, vivila\n- \"chief\" → lekalimati\n\nNow, analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"how many\" → navila \n\"women\" → vivila \n\"will look after\" → biyamatasi → biyamata? Possibly a variant \n\"tomwaya\" → likely \"this\" → tomwaya \n\"mtona\" → man\n\nSo: How many women will look after this man?\n\n→ This matches example 13: \"Navila vivila biyamatasi tau mtona?\" \n\"biyamata\" may be a variant of \"biyamatasi\", possibly a morphological variant.\n\nCorrect translation: How many women will look after this man?\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n\"bikamkwamsi\" → \"bikamkwamsi\" → \"bikamkwamsi\" appears in example 11: \"lekamkwamsi\" + \"dimdim\" → \"white men\"\n\n\"bikamkwamsi\" = plural of \"kamkwamsi\" → possibly \"things\"\n\n\"kweyu\" → \"kweyu\" → \"kweyu\" appears in example 11: \"kwevila\" → how many\n\n\"vivila\" = woman, \"minasina\" = fish\n\n\"kweyu\" = how many? Likely \"how many\"\n\n\"bikamkwamsi\" → \"how many things\"? But \"kamkwamsi\" → \"things\"\n\n\"vivila\" = woman → possibly misaligned?\n\n\"minasina\" = fish\n\nBut \"bikamkwamsi\" might be \"which things\"?\n\nBut syntax: \"kweyu\" = how many?\n\nIn example 11: \"kwevila lekamkwamsi dimdim mtosiwena\" → how many things did those white men eat?\n\nSo \"kwevila\" = how many, \"lekamkwamsi\" = things\n\n\"bikamkwamsi\" → same as \"lekamkwamsi\"? → things\n\nBut \"kweyu\" → possibly a variant of \"kwevila\", \"how many\"\n\n\"vivila\" = woman → but here \"vivila minasina\" = woman fish?\n\n\"minasina\" = fish\n\nBut woman fish? Unlikely.\n\nWait: in example 15: \"Bikamkwamsi kweyu vivila minasina\"\n\nPerhaps \"which\" = \"bikamkwamsi\"? But \"bikamkwamsi\" appears in clue 3: \"Bikota gwadi\" = that child\n\nNo.\n\n\"bikamkwamsi\" — if \"bikamkwamsi\" = which things?\n\nBut \"kweyu\" = how many?\n\nNo.\n\nAlternative: \"bikamkwamsi\" = what? → but \"bikamkwamsi\" not in known forms.\n\nWait — example 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" — stone\n\n\"makwena\" = child\n\n\"makwena\" — in example 4: \"makesiwena\" = saw\n\n\"makwena\" → child?\n\nBut \"kamkwamsi\" → things\n\nSo \"bikamkwamsi\" = which things?\n\n\"vivila minasina\" = woman fish?\n\nNo.\n\nBut \"vivila\" → woman, \"minasina\" → fish → woman and fish?\n\nNo.\n\nWait — look at 5: \"Amtona tau lekalimati nayu bunukwa?\" → which man killed two pigs?\n\n\"Amtona\" = which\n\n\"bikamkwamsi\" — is \"bik\" = \"which\"?\n\n\"bik\" → in example 3: \"bikota\" = that\n\n\"bik\" → possibly \"which\"?\n\nBut \"bikamkwamsi\" → \"which things\"?\n\nThen \"kweyu\" = how many?\n\n\"vivila minasina\" = woman fish?\n\nNot likely.\n\nAlternative: misalignment.\n\nPerhaps \"kweyu\" = \"which\", \"vivila\" = woman, \"minasina\" = fish → which woman fish?\n\nBut no such phrase.\n\nNo examples with \"kweyu\" or \"bikamkwamsi\" directly.\n\nBut look at 15: Bikamkwamsi kweyu vivila minasina.\n\nCompare to example 13: Navila vivila biyamatasi tau mtona → how many women will look after this man?\n\nHere: Bikamkwamsi kweyu vivila minasina → possibly which woman fish?\n\nBut that seems odd.\n\nAnother idea: \"kweyu\" = how many? But \"how many\" is \"navila\", not \"kweyu\".\n\nExample 8: \"Navila ka’ukwa lekotasi?\" = how many dogs arrived?\n\nSo \"navila\" = how many\n\n\"kweyu\" → not present.\n\nBut in example 11: \"kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"kwevila\" = how many\n\nSo \"kwevila\" = how many\n\n\"kweyu\" = possibly a variant? Possible typo or morphological variant.\n\n\"bikamkwamsi\" — may be \"which things\"\n\n\"vivila\" = woman, \"minasina\" = fish\n\nSo which woman fish? Unlikely.\n\nAlternative: \"minasina\" = fish, but \"vivila\" = woman → perhaps \"a woman who has fish\"?\n\nNo.\n\nPerhaps it's \"which of the women saw those fish\"?\n\nBut no \"saw\" in it.\n\nAlternatively, is \"kweyu\" a question word for which?\n\nIn example 9: \"Amakena waga legisesi gweguyau?\" → which canoe did the chiefs see?\n\n\"amakena\" = which\n\nSo \"kweyu\" → likely not \"which\"\n\nBut example: \"amtona\" = which man\n\n\"amakena\" = which canoe\n\nSo \"which\" → amtona / amakena\n\n\"bikamkwamsi\" — not a known \"which\" form.\n\n\"bik\" = in \"bikota\" = that\n\nSo \"bikamkwamsi\" = not clearly \"which\"\n\nPossibility: \"bikamkwamsi\" = which things?\n\nThen \"kweyu\" = how many?\n\nBut \"how many things\" is \"navila lekamkwamsi\"\n\nSo this seems inconsistent.\n\nWait — is it possible that the two possible translations exist because of ambiguity in \"vivila\" meaning?\n\n\"vivila\" appears in:\n- 7: \"Bigisi kwetala vivila minawena\" → clever woman\n- 13: \"vivila biyamatasi\" → women\n- 15: \"vivila minasina\"\n\nSo \"vivila\" → woman\n\n\"minasina\" → fish\n\nSo \"woman fish\" — no.\n\nBut \"minasina\" = fish → could be \"the fish\" (object)\n\nSo \"which woman has fish\"?\n\nBut no verb.\n\nAnother possibility: \"kweyu\" = \"what\" → which one?\n\n\"bikamkwamsi\" = which things?\n\nSo \"which things did the women see?\" — no \"see\" in this.\n\nBut compare to sentence 18.\n\n16. Amagudina gwadi lekota?\n\n\"amagudina\" → likely \"which\" → amato? amakena?\n\n\"amagudina\" — not in list.\n\n\"amagudina\" — could be \"which\" → like \"amtona\" or \"amakena\"\n\n\"gwadi\" = child\n\n\"lekota\" = this\n\nSo \"which child? this?\"\n\n\"which child is this?\"\n\nPossibly → \"Which child is this?\"\n\nOr → \"What child is this?\"\n\n\"amagudina\" → possibly \"which\" or \"what\"\n\nIn example 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → that beautiful child saw this stone\n\nSo \"gwadi\" = child\n\n\"amagudina\" — not used\n\nBut in example 3: \"Bikota gwadi magudiwena\" → that child will arrive\n\n\"bikota\" = that\n\nSo \"amagudina\" → likely \"which\"\n\nSo \"which child is this?\"\n\n\"this\" → lekota\n\nSo → \"Which child is this?\"\n\nBut could \"amagudina\" mean \"what\" or \"which\"?\n\nYes — ambiguous.\n\nLikely two translations:\n\n- Which child is this?\n- What child is this?\n\nNow 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n\n\"tevila\" → how many? (from example 8: \"navila\", example 13: \"navila\")\n\n\"tauwau\" → looked after (from example 6: \"teyu tauwau\")\n\n\"bigisesi\" → see (example 4: \"legisesi\", example 9: \"legisesi gweguyau\")\n\n\"gugwadi\" → \"gugwadi\" = ? Possibly \"gugwadi\" = \"gugwadi\" → not clear\n\n\"gudigasisi\" → ? \"gudigasisi\" — example 12: \"tokabitam\", \"guyau\" = one\n\n\"gudigasisi\" → not found\n\nBut \"gugwadi\" → looks like \"gugwadi\" — \"gugwadi\" might be \"the woman\"?\n\nFrom example 4: \"legisi waga makesiwena namwaya minana\" — \"namwaya\" = those, \"minana\" = canoes\n\n\"legisi\" = this\n\n\"makesiwena\" = saw\n\n\"bigisesi\" = saw → same as \"legisesi\"\n\n\"bigisesi\" = saw\n\n\"gugwadi\" → unclear\n\n\"gudigasisi\" → possibly \"gugwadi\" = woman?\n\n\"gudigasisi\" → might be \"gugwadi gudigasisi\" = the woman?\n\n\"bigisesi\" = saw\n\nSo \"tevila tauwau bigisesi gugwadi gudigasisi\" → how many people looked after the woman who saw the woman?\n\nNo.\n\nPossibility: \"gugwadi\" = woman, \"gudigasisi\" = the person?\n\nBut \"gudigasisi\" → not in examples.\n\nNotice \"gudigasisi\" → \"gudigasisi\" — example 10: \"gudimanabweta\" = stone\n\n\"gudigasisi\" → perhaps \"gugwadi\" = woman, \"gudigasisi\" = who?\n\nPossibly \"who\" → need to see.\n\nBut \"tevila\" = how many?\n\n\"tauwau\" = looked after\n\n\"bigisesi\" = saw\n\n\"so: how many people looked after the woman who saw the woman?\"\n\nUnlikely.\n\nAlternative: mis-aligned elements.\n\n\"gugwadi gudigasisi\" → possibly \"the woman\"?\n\n\"gugwadi\" = woman, \"gudigasisi\" = from \"gudigasisi\" — no\n\nExample 4: legisi waga makesiwena namwaya minana — this old woman saw those canoes\n\n\"legisi\" = this, \"waga\" = old, \"makesiwena\" = saw\n\n\"gugwadi\" → appears only in this sentence.\n\nAnother idea: \"gugwadi\" = stone? \"gudimanabweta\" = stone\n\n\"gugwadi\" ≠ gudimanabweta\n\nNo.\n\nPossibility: \"gugwadi\" = \"that\", \"gudigasisi\" = woman?\n\nNo.\n\nHold: perhaps the only ambiguous sentence is 16.\n\nNow 18. Legisesi ketala waga vivila minasiwena.\n\n\"legisesi\" = saw (as in \"makesiwena\", \"legisesi\")\n\n\"ketala\" = will see (example 7: \"minawena\" = will see)\n\n\"vivila\" = woman\n\n\"minasiwena\" = ? \"minasina\" = fish, \"minasiwena\" → may be \"will see fish\"?\n\n\"minasiwena\" — does it mean \"will see\"?\n\nIn example 7: \"minawena\" = will see\n\n\"minasiwena\" — \"min", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11145.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "solver_checklist", + "sample_index": 3, + "output": "First, build an alignment table from the given examples to identify patterns in construction, affixes, and word order.\n\n---\n\n**Step 1: Categorize examples by structure**\n\nLook for recurring morphemes and syntactic patterns.\n\nExample 1: \nOne man will catch these four fish. \nBibani navasi yena minasina tetala tau. \n→ \"One man\" = Bibani navasi \n→ \"will catch\" = tetala tau \n→ \"these four fish\" = yena minasina tetala tau (yena = these; minasina = fish; tetala = four)\n\nNote: \"tetala\" appears with \"minasina\" = \"four fish\"\n\nExample 2: \nThis white man arrived. \nLekota dimdim mtona. \n→ \"this white man\" = Lekota dimdim \n→ \"arrived\" = mtona \n→ \"lekota\" = this; \"dimdim\" = white\n\nExample 3: \nThat child will arrive. \nBikota gwadi magudiwena. \n→ \"that\" = Bikota; \"child\" = gwadi; \"will arrive\" = magudiwena\n\nExample 4: \nThis old woman saw those canoes. \nLegisi waga makesiwena namwaya minana. \n→ \"this old woman\" = Legisi waga (legisi = this; waga = old); \"saw\" = makesiwena; \"those canoes\" = namwaya minana (namwaya = those; minana = canoes)\n\nExample 5: \nWhich man killed two pigs? \nAmtona tau lekalimati nayu bunukwa? \n→ \"which man\" = Amtona tau; \"killed\" = lekalimati; \"two pigs\" = nayu bunukwa (nayu = two; bunukwa = pigs)\n\nExample 6: \nThe old women looked after two men. \nLeyamatasi teyu tauwau nunumwaya. \n→ \"old women\" = Leyamatasi (Leyama = old; tasi = women); \"looked after\" = teyu tauwau; \"two men\" = nunumwaya (nu = two; numwaya = men)\n\nExample 7: \nThat clever woman will see something. \nBigisi kwetala vivila minawena nakubitam. \n→ \"that clever woman\" = Bigisi kwetala; \"will see\" = vivila minawena; \"something\" = nakubitam\n\nExample 8: \nHow many dogs arrived? \nNavila ka’ukwa lekotasi? \n→ \"how many\" = Navila; \"dogs\" = ka’ukwa; \"arrived\" = lekotasi\n\nExample 9: \nWhich canoe did the chiefs see? \nAmakena waga legisesi gweguyau? \n→ \"which canoe\" = Amakena waga; \"did the chiefs see\" = legisesi gweguyau (legisesi = chiefs; gweguyau = saw)\n\nExample 10: \nThat beautiful child saw this stone. \nLegisi dakuna makwena gwadi magudiwena gudimanabweta. \n→ \"that beautiful child\" = Legisi dakuna gwadi; \"saw\" = makwena; \"this stone\" = magudiwena gudimanabweta (magudiwena = this; gudimanabweta = stone)\n\nExample 11: \nHow many things did those white men eat? \nKwevila lekamkwamsi dimdim mtosiwena? \n→ \"how many\" = Kwevila; \"things\" = lekamkwamsi; \"did those white men eat\" = dimdim mtosiwena (dimdim = white; mtosiwena = eat)\n\nExample 12: \nThe clever chief killed one wild pig. \nLekalimati natala bunukwa nagasisi guyau tokabitam. \n→ \"clever chief\" = nagasisi guyau (guyau = chief; nagasi = clever); \"killed\" = natala; \"one wild pig\" = bunukwa tokabitam (tokabitam = wild pig; bunukwa = one)\n\nExample 13: \nHow many women will look after this man? \nNavila vivila biyamatasi tau mtona? \n→ \"how many women\" = Navila vivila biyamatasi; \"will look after\" = tau mtona (tau = will; mtona = look after)\n\nNow begin to extract patterns:\n\n---\n\n**Morphemes and affixes:**\n\n- Demonstratives: \n - lekota = this (subject) \n - bikota = that (subject) \n - legisi = this (subject, often in agent) \n - lekota → \"this\" (definite, proximal) \n - bikota → \"that\" (distal) \n - lekotasi → \"arrived\" (but \"lekota\" + \"si\"?) \n - \"is\" or \"has\" is rare. Instead, tense is marked by verbs or affixes.\n\n- Quantity markers: \n - tetala = four \n - nayu = two \n - nu = two (in \"nunumwaya\") \n - bunukwa = one (appears with \"wild pig\" or \"pig\") \n - vivila = something \n - tau = will (in \"will look after\", \"will catch\") \n - teyu = looked after\n\n- Object markers: \n - minasina = fish \n - minana = canoes \n - numwaya = men \n - makwena = stone \n - mtosiwena = eat \n - waga = old \n - dimdim = white \n - kwetala = clever \n - gudimanabweta = stone \n - guyau = chief \n - tokabitam = wild pig\n\n- Verb patterns: \n - \"will X\" = vivila + noun? \n - \"arrive\" = mtona, lekotasi \n - \"see\" = makesiwena, makwena, ketala (in 18) \n - \"look after\" = teyu tauwau \n - \"killed\" = lekalimati, natala \n - \"eat\" = mtosiwena\n\n- Question forms: \n - \"how many\" = Navila, Kwevila \n - \"which\" = Amtona, Amakena \n - \"what\" → not directly present \n - questions use: Amtona (which man), Amakena (which canoe), Navila (how many)\n\n- Noun phrases: \n - \"the old women\" = Leyamatasi \n - \"the clever chief\" = nagasisi guyau \n - \"this white man\" = lekota dimdim\n\n- Plurality: \n - -sia = plural? \n - -tasi = women (tasi = women) \n - -wena = marked for object? \n - \"women\" → tasi; \"men\" → numwaya; \"fish\" → minasina\n\n- Affix patterns for numerals: \n - tetala = four \n - nayu = two \n - nu = two \n - bunukwa = one \n - \"two pigs\" = nayu bunukwa \n - \"two men\" = nunumwaya → nu = two, numwaya = men \n - \"one wild pig\" = bunukwa tokabitam → bunukwa = one\n\n→ So numerals are separate, with numeral + noun (e.g., nayu bunukwa)\n\n→ Use of \"tau\" = future tense? In “will catch”, “will look after”\n\n→ \"vivila\" appears in “vivila minawena” → “will see something”\n\n→ In (13): “Navila vivila biyamatasi tau mtona” → “how many women will look after this man?”\n\n→ \"vivila\" = will; \"biyamatasi\" = women; \"tau\" = will? Or \"vivila\" = something; \"tau\" = will?\n\nBut in (13) “vivila biyamatasi” = women? “vivila” is not clearly a subject marker.\n\nBut in (7): \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\"\n\nSo \"vivila minawena\" = will see something → vivila = will, minawena = something\n\nBut in (13): \"Navila vivila biyamatasi tau mtona\" → how many women will look after?\n\n\"vivila\" appears as if a future verb (will), and \"tau mtona\" = will look after.\n\nPattern: \"vivila\" = will → appears in future tense (e.g., \"will catch\", \"will see\", \"will look after\")\n\n\"tau\" = look after\n\nSo \"tau\" = verb meaning \"look after\"\n\nExample 13: “Navila vivila biyamatasi tau mtona” → \"how many women will look after this man?\"\n\n\"Navila\" = how many \n\"vivila\" = will \n\"biyamatasi\" = women \n\"tau mtona\" = look after\n\nBut \"vivila\" also appears as \"will see\" in (7): \"vivila minawena\"\n\nSo \"vivila\" = form of \"will\", used as modal verb, attached to object?\n\n→ Again, in (1): \"Bibani navasi yena minasina tetala tau\" → \"one man will catch these four fish\"\n\n\"navasi\" = man; \"yena\" = these; \"minasina\" = fish; \"tetala\" = four; \"tau\" = catch\n\nSo \"tau\" is not \"will\", it's \"catch\"\n\nThus: \n- \"tau\" is a verb (catch, see, look after) \n- \"vivila\" is a modal (will) \n- \"vivila\" is used before a verb stem to indicate future\n\nSo: “vivila + verb stem” = will + verb\n\nE.g., \n- vivila minawena → will see something \n- vivila biyamatasi → will women (problem) \n→ Must be: vivila + verb, not subject\n\nIn (13): Navila vivila biyamatasi tau mtona \n→ how many women will look after this man? \n\nBut “vivila biyamatasi” = will women? No.\n\nLikely: \"biyamatasi\" = women; \"tau mtona\" = look after → future of \"look after\" \nBut \"vivila\" is not part of that.\n\nPattern: in (7): \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" \n→ \"vivila minawena\" = will see something\n\nSo \"vivila minawena\" = will see (something)\n\nThus, \"vivila\" + object = will + verb \"see\"\n\nBut in (13), \"vivila biyamatasi tau mtona\" → still odd.\n\nBut look at (5): \"Amtona tau lekalimati nayu bunukwa?\" \n\"which man will kill two pigs?\" → Amtona = which man; tau = will; lekalimati = kill; nayu bunukwa = two pigs\n\nSo \"tau\" = will\n\nIn (2): Lekota dimdim mtona → \"this white man arrived\" → mtona = arrived\n\n\"mtona\" is past tense → arrival\n\nIn (3): Bikota gwadi magudiwena → \"that child will arrive\" → magudiwena = will arrive\n\nSo \"magudiwena\" = will arrive\n\nIn (4): Legisi waga makesiwena namwaya minana → saw (makesiwena) + object\n\nSo \"makesiwena\" = saw\n\nThus: \n- \"vivila\" = will → appears as modal in future \n- \"tau\" = will → appears in other verbs \n→ But in (13), \"Navila vivila biyamatasi tau mtona\" → how many women will look after this man?\n\nPossibility: the structure is \"how many + subject + will + verb\"\n\nBut \"vivila\" is used as modal in the verb phrase.\n\nBest guess: \"vivila\" is a future tense marker attached to a verb stem.\n\nSo: \"minawena\" = see → vivila minawena = will see \n\"mtona\" = look after → but without \"vivila\" → only \"tau mtona\" = will look after?\n\nWait: in (7): vivila minawena → will see \nIn (13): vivila biyamatasi tau mtona?\n\n→ Perhaps \"vivila\" is just the future marker and attaches to the verb part.\n\nBut \"vivila biyamatasi\" doesn’t make sense.\n\nAlternative: in (13): \"Navila vivila biyamatasi tau mtona\"\n\nBreak down: \n- Navila = how many \n- vivila biyamatasi = women who will do something? \n→ No.\n\nCompare with example (1): \"Bibani navasi yena minasina tetala tau\" → \"one man will catch these four fish\"\n\n\"navasi\" = man; \"tau\" = catch\n\nSo tau is verb: catch\n\nSimilarly, \"mtona\" = look after (in example 13)\n\n(13) has \"tau mtona\" → look after\n\nSo “vivila” must be the modal. Where is it used?\n\nIn (1): “Bibani navasi... tetala tau” → “will catch” → no “vivila”\n\nIn (3): “Bikota gwadi magudiwena” → “will arrive” → “magudiwena”\n\nIn (7): “Bigisi kwetala vivila minawena” → “will see”\n\nIn (5): “Amtona tau lekalimati nayu bunukwa” → “will kill” → “tau” as modal?\n\nBut “tau” appears with “lekalimati” → so “tau” is modal.\n\nSo consistently, “tau” = will (future tense)\n\nSimilarly, “mtona” = arrived, “look after”\n\nSo \"tau\" = future tense marker (like \"will\")\n\nIn (13): \"Navila vivila biyamatasi tau mtona\" → how many women will look after this man?\n\nBut \"vivila\" is superfluous or misplaced?\n\nWait — in (13): \"Navila vivila biyamatasi tau mtona\"\n\nBut in (6): \"Leyamatasi teyu tauwau nunumwaya\" → \"old women looked after two men\"\n\n\"teyu\" = looked; \"tauwau\" = look after\n\n\"tauwau\" = look after → \"tau\" + \"wau\"\n\n\"tauwau\" = past tense of \"look after\"\n\nIn (13), \"tau mtona\" → future of \"look after\"\n\nSo likely \"tau\" is future tense marker.\n\nBut in (7): vivila minawena → \"will see\"\n\n\"vivila\" and \"tau\" are both used?\n\nSo possible: \n- \"vivila\" = will \n- \"tau\" = future tense verb stem\n\nBut in sentence 1: tetala tau → “four fish caught” → “tau” = catch (verb)\n\nNo “vivila” → so “vivila” is not used with “catch”\n\nIn (2): mtona → arrived\n\nNo future modal.\n\nIn (3): magudiwena → will arrive → “magudiwena” = future form?\n\nIn (4): makesiwena → saw\n\nSo only in examples 3, 7, 5, 13 is there future.\n\nPatterns:\n\n- Demonstratives: \n - lekota = this \n - bikota = that \n - legisi = this (in subject) \n - amtona = which man \n - amakena = which canoe \n - navila = how many\n\n- Numerals: \n - tetala = four \n - nayu = two \n - nu = two \n - bunukwa = one \n - vivila = something (object) \n - object nouns are: minasina, minana, numwaya, makwena, mtosiwena, waga, guyau\n\n- Verbs with tense: \n - mtona = arrived, arrived (past) \n - magudiwena = will arrive \n - makesiwena = saw \n - lekalimati = killed \n - natala = killed \n - mtosiwena = ate \n - teyu = looked \n - tau = look after (past or future?) \n - vivila + object = will see / will do \n\nBut in (13), \"Navila vivila biyamatasi tau mtona\" → how many women will look after this man?\n\nIf \"vivila\" is future modal, it should be attached to a verb stem, like \"vivila mtona\" = will look after \n\n\"vivila\" + \"mtona\" = will look after \n\nBut in (13) it is \"vivila biyamatasi tau mtona\" — so “vivila biyamatasi” = women (subject)? Then “tau mtona” = look after?\n\nBut that would be “women will look after” — possible if biyamatasi is subject.\n\nBut biyamatasi = women — so “vivila biyamatasi” = “women will do something”\n\nBut “tau mtona” is the verb.\n\nSo likely structure: \n[how many] + [subject] + [will] + [verb] \n\nThus: \n- Navila = how many \n- biyamatasi = women \n- vivila = will \n- tau mtona = look after \n\nBut “tau mtona” = look after — so it's a verb phrase.\n\nIs “vivila” only attached to the verb?\n\nIn (7): “Bigisi kwetala vivila minawena” → \"clever woman will see something\"\n\nSo “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11826.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 0, + "output": "Step 1: Identify recurring patterns in the examples.\n\nLook at question forms:\n- \"How many X did Y see?\" → \"Navila [X] [Y]\" or \"Navila [X] [Y]\" structure.\n- \"Which X did Y see?\" → \"Amakena [X] [Y]\" or \"Amakena [X] [Y]\"\n- \"Will look after\" → \"tauwau\" or \"vivila\" with \"tua\" (will/future) in examples like (6): \"teyu tauwau nunumwaya\"\n- \"Killed\" → \"bunukwa\" (example 5, 12)\n- \"Saw\" → \"makesiwena\" (example 4, 10)\n- \"White\" → \"dimdim\" (example 2, 11)\n- \"Old\" → \"legisi\", \"lelisi\", \"bikota\" (used with women, women, children)\n- \"Clever\" → \"kwetala\", \"vivila\" (example 7, 20)\n- \"Fish\" → \"minasina\", \"minawena\"\n- \"Canoe\" → \"namwaya\", \"waga\"\n- \"Child\" → \"gwadi\", \"magudiwena\"\n- \"Man\" → \"mtona\", \"navasi\", \"tona\"\n- \"Women\" → \"leyamatasi\", \"legisi\"\n- \"Pig\" → \"bunukwa\", \"nunumwaya\"\n- \"Dogs\" → \"ka'ukwa\"\n- \"One\" → \"navasi\", \"waga\"\n- \"Two\" → implied in \"four\", \"two\"\n- Numbers: \"four\" is \"tetala\" (1, 2, 3, 4), \"two\" is \"nayu\"\n- Question forms use \"navila\" (how many), \"amakena\" (which), \"tau\" (will/future)\n\nStep 2: Build alignment.\n\nExample (4): \"That old woman saw those canoes\" \n→ \"Legisi waga makesiwena namwaya minana\" \n\"Legisi\" = old woman \n\"waga\" = those (demonstrative) \n\"makesiwena\" = saw \n\"namwaya\" = canoes \n\"minana\" = those (demonstrative, agrees with canoes)\n\nStructure: [Demonstrative] + [verb] + [object] \nBut \"minana\" = \"those canoes\", so object is \"namwaya minana\"\n\nSo: \"How many canoes did those old women see?\" \n→ \"Navila namwaya leyamatasi makesiwena?\"\n\n\"Navila\" = how many \n\"namwaya\" = canoes \n\"leyamatasi\" = those old women \n\"makesiwena\" = saw\n\nThus: **19. Navila namwaya leyamatasi makesiwena**\n\nCheck for agreement: \n- \"leyamatasi\" is plural (women), \"makesiwena\" agrees with plural subject → correct \n- \"namwaya\" = canoes → object → correct \n- \"navila\" = how many → question form → correct \n\n→ b.1: Navila namwaya leyamatasi makesiwena\n\n---\n\nExample (20): \"These four white men will look after this clever child.\"\n\nStructure: \"These\" → \"mtona\" (white men), \"four\" = \"tetala\", \"will\" = \"tau\", \"look after\" = \"tauwau\" (example 6), \"this\" → \"gwadi\", \"clever\" → \"kwetala\", \"child\" → \"magudiwena\"\n\nSo:\n- \"These four white men\" → \"tetala dimdim mtona\" (example 2) → here, \"mtona\" = white men\n- \"will look after\" → \"tauwau\" (example 6: \"teyu tauwau nunumwaya\")\n- \"this clever child\" → \"gwadi kwetala magudiwena\"\n\nStructure: [subject] + [will] + [look after] + [object]\n\nSo: \"tetala dimdim mtona tauwau gwadi kwetala magudiwena\"\n\nNote: \"tauwau\" means \"will look after\", so it's the verb of the future action.\n\n→ b.2: tetala dimdim mtona tauwau gwadi kwetala magudiwena\n\n---\n\nExample (21): \"How many children will eat these pigs?\"\n\n\"how many\" → \"navila\" \n\"children\" → \"gwadi\" \n\"will eat\" → \"taiwa\" or \"mtona\" → look for \"eat\"\n\nExample (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"mtosiwena\" = eat? → \"mtosiwena\" is likely \"eat\"\n\nIn example (11): \"lekamkwamsi\" = things, \"mtosiwena\" = eat\n\nSo \"eat\" = \"mtosiwena\"\n\n\"these pigs\" → \"nayu bunukwa\"? \"two pigs\" → \"nayu bunukwa\", \"pig\" = \"bunukwa\"\n\n\"these\" → \"waga\" in (4), (10)\n\n\"how many\" → \"navila\"\n\nSo: \"Navila gwadi mtona mtsiwena waga bunukwa\"?\n\nBut \"mtosiwena\" is the verb \"eat\", so use that.\n\n→ \"Navila gwadi mtsiwena waga bunukwa\"\n\n\"mtsiwena\" appears in (11) as \"mtosiwena\" — likely \"eat\"\n\nThus: **21. Navila gwadi mtsiwena waga bunukwa**\n\nNote: No subject given → passive or general → \"how many children will eat these pigs\" → agentless, so verb applies to children.\n\n→ b.3: Navila gwadi mtsiwena waga bunukwa\n\n---\n\nExample (22): \"Which woman caught those beautiful fish?\"\n\n\"which\" → \"amakena\" (examples 9, 22 style)\n\n\"woman\" → \"legisi\" (old woman), or \"bikota\" (that woman) — in (3): \"bikota gwadi magudiwena\" → \"that child\"\n\n\"caught\" → \"navasi\" / \"navasi\" = one man \"caught\" → example (1): \"bansi navasi yena minasina tetala tau\"\n\n\"navasi\" = catch\n\n\"those beautiful fish\" → \"waga\" (demonstrative) + \"dakuna\" (beautiful) + \"minasina\" (fish)\n\nExample (10): \"That beautiful child saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"makwena\" = child, \"dakuna\" = beautiful\n\nSo \"beautiful fish\" = \"dakuna minasina\"\n\n\"those\" = \"waga\"\n\nSo: \"amakena legisi navasi waga dakuna minasina\"\n\n\"amakena\" = which \n\"legisi\" = woman (general, like old woman) \n\"navasi\" = caught \n\"waga dakuna minasina\" = those beautiful fish\n\nYes → matches pattern.\n\n→ b.4: amakena legisi navasi waga dakuna minasina\n\n---\n\nExample (23): \"Two wild dogs saw that old man.\"\n\n\"two\" = \"nayu\" (example 5: \"two pigs\" = \"nayu bunukwa\")\n\n\"wild dogs\" → \"ka'ukwa\" (example 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\")\n\n\"wild\" → not explicitly in word list, but \"wild dog\" likely = \"ka'ukwa\"\n\n\"man\" → \"mtona\", \"old\" → \"legisi\"\n\n\"that old man\" → \"bikota legisi mtona\" (example 3: \"That child\" = \"bikota gwadi magudiwena\")\n\nSo: \"nayu ka'ukwa makesiwena bikota legisi mtona\"\n\n\"makesiwena\" = saw → matches (4,10)\n\n→ b.5: nayu ka'ukwa makesiwena bikota legisi mtona\n\n---\n\nFinal answer:\n\n\\boxed{b.1: Navila namwaya leyamatasi makesiwena; b.2: tetala dimdim mtona tauwau gwadi kwetala magudiwena; b.3: Navila gwadi mtsiwena waga bunukwa; b.4: amakena legisi navasi waga dakuna minasina; b.5: nayu ka'ukwa makesiwena bikota legisi mtona}", + "generated_tokens": 1963, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: Navila namwaya leyamatasi makesiwena; b.2: tetala dimdim mtona tauwau gwadi kwetala magudiwena; b.3: Navila gwadi mtsiwena waga bunukwa; b.4: amakena legisi navasi waga dakuna minasina; b.5: nayu ka'ukwa makesiwena bikota legisi mtona", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 5245.0, + "ioling_final_answer_chars": 239.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 1, + "output": "First, build an alignment table from the given examples to identify patterns in subject, object, demonstratives, adjectives, tense, number, and question forms.\n\nKey observations:\n\n1. **Q-words and question types**:\n- \"How many?\" → usually “Navila” (18, 11, 13), in questions with count.\n- \"Which?\" → “Amtona” (5, 9, 22), used with determiner + noun.\n- \"Will\" → future tense marker: “will” → “tau” (1, 3, 6, 7, 13)\n\n2. **Demonstratives**:\n- \"This\" → “Lekota”, “Bikota”, “Legisi”, “Navila” (in Qs)\n- \"That\" → “Bikota”, “Bikota” in 3, 7\n- \"These\" → “Lekota”, “Navila” (in 20, “these four white men”)\n- \"Those\" → “Lekota” (in 4, 9, 11)\n\n3. **Adjectives**:\n- \"White\" → “dimdim” (2, 11)\n- \"Old\" → “legisi” (4, 12, 13)\n- \"Beautiful\" → “dakuna” (10)\n- \"Clever\" → “kwetala” (7, 20)\n- \"Wild\" → “bunukwa” (5, 12, 23)\n\n4. **Noun classes and order**:\n- Subject → noun (demonstrative + adjective + noun)\n- Verb → often follows structure with object\n- Object → after verb, often postpositioned or embedded\n- The word order is: [demonstrative] + [adjective] + [noun] for noun phrases\n\n5. **Plurality**:\n- Highlighted by suffixes or doubling: “minasina” (four fish), “nunumwaya” (two men), “namwaya” (canoes), “minana” (four?)\n- Numerals: “four” → “minasina”, which appears in 1, 4, 10 — appears in compound objects\n\n6. **Question word mappings**:\n- “How many?” → “Navila” + noun phrase (e.g., 8, 11, 13)\n- “Which?” → “Amtona” + noun phrase (e.g., 5, 9, 22)\n\n7. **Verb forms**:\n- “will” → “tau” in future\n- “saw” → “makesiwena” (4, 10)\n- “arrived” → “mtona” (2, 3, 9)\n- “looked after” → “teyu” (6, 20)\n- “killed” → “nagasisi” (12)\n\n8. **Adjective placement**:\n- Adjectives precede the noun: “white man” = “dimdim mtona”, “old woman” = “legisi waga”\n\nNow, translate:\n\n**19. How many canoes did those old women see?**\n\n- “How many?” → “Navila”\n- “canoes” → “namwaya”\n- “did” → past tense → “makesiwena” (see)\n- “those old women” → “legisi waga” (old) + “waga” (women)\n- So: “Navila namwaya legisi waga makesiwena?”\n\nBut structure in examples: “How many X did Y?” → “Navila X lekotasi?” (example 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?”)\n\nWait — in 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” → “Navila” + noun + “lekotasi?” (did)\n\n“lekotasi” = “did”?\n\nIn 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\nWait — relative structure.\n\nBut 8: “Navila ka’ukwa lekotasi?” — “ka’ukwa” = dogs, “lekotasi” = past tense of “arrive”?\n\nNo — in 8, “arrived” = “mtona”, not “lekotasi”.\n\nWait — in 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?”\n\nBut “arrived” is “mtona”, so inconsistency?\n\nNo — check:\n\n8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?”\n\nBut “mtona” = arrived in (2,3)\n\nThus, “lekotasi” is not “arrived”\n\nPerhaps “lekotasi” is a mishearing?\n\nWait — 8: “Navila ka’ukwa lekotasi?”\n\nPerhaps “lekotasi” = \"did\" (auxiliary), not the verb.\n\nCompare to 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” — likely “how many” — so “Navila” vs “Kwevila”?\n\nNo — 8 is “Navila ka’ukwa lekotasi?” → but 11 is “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” → possibly “how many”?\n\nBut 8: “Navila”\n\nWait — 8: “Navila ka’ukwa lekotasi?”\n\n“Navila” = how many, “ka’ukwa” = dogs, “lekotasi” = arrived?\n\nBut “arrived” is “mtona” — not “lekotasi”\n\nThus, “lekotasi” cannot be “arrived”\n\nUnlikely.\n\nAlternative: “lekotasi” is auxiliary “did” — used in questions with past tense.\n\nIn 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” → possibly “how many”?\n\nBut 8 uses “Navila”\n\nSo “Navila” = how many\n\nIn 11, why “Kwevila”?\n\nPerhaps a typo or misalignment.\n\nLook at 13: “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?”\n\n“Navila” = how many\n\nSo, “how many” → “Navila”\n\nThus, 19: “Navila namwaya legisi waga makesiwena?”\n\nBut in 4: “That old woman saw those canoes” → “Legisi waga makesiwena namwaya minana”\n\nSo verb “makesiwena” + object “namwaya minana”\n\nThus, “makesiwena” is “saw”\n\nSo “those old women saw canoes” → “legisi waga makesiwena namwaya”\n\nThus, “how many canoes did those old women see?” → “Navila namwaya legisi waga makesiwena?”\n\nBut the object comes before verb? No — in 4: “makesiwena namwaya minana” — object after verb.\n\nSo object after verb.\n\nSo pattern: [how many] + [object] + [subject] + [verb]\n\nBut in 4: “Legisi waga makesiwena namwaya minana” — “makesiwena” (saw), then “namwaya minana” (canoes)\n\nSo verb first, then object.\n\nThus: “Navila namwaya legisi waga makesiwena?”\n\nBut in 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” → how many?\n\nBut 13 uses “Navila”\n\nInconsistency.\n\nWait — 13: “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?”\n\nSo “Navila” = how many\n\nIn 11: “Kwevila” — perhaps it's a different form?\n\nWait — in 11: “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” → is “how many”?\n\n“lekamkwamsi” → things? “dimdim” → white?\n\nBut “dimdim” is white, and “mtosiwena” = “ate”?\n\nCompare to 2: “This white man arrived” → “Lekota dimdim mtona”\n\nSo “mtona” = arrived\n\nSo “mtosiwena” = ate?\n\nYes — example 11: “eat” = “mtosiwena”\n\nThus, “lekamkwamsi” → things\n\nSo “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\nBut “how many” should be “Navila”?\n\nUnless “Kwevila” is “how many”?\n\nBut in 13, “Navila” is used.\n\nThis suggests that “Navila” is used in all count questions.\n\nBut 11 has “Kwevila” — may be a typo in the problem or misrecord.\n\nWait — in 11: “How many things did those white men eat?” → given in original as:\n\n“Kwevila lekamkwamsi dimdim mtosiwena?”\n\nSo it uses “Kwevila”\n\nBut in 13: “Navila vivila biyamatasi tau mtona?”\n\nSo “Navila” used.\n\nThus, alignment error?\n\nNo — in 13: “How many women will look after this man?” — “Navila”\n\nIn 11: “How many things did those white men eat?” — “Kwevila”\n\nBut both are count questions.\n\nAlternative: “Kwevila” = “how many” only in certain contexts?\n\nBut in 19, “how many canoes” — similar.\n\nAlternatively, look at the verb:\n\nIn 11: “mtosiwena” = eat\n\nIn 8: “lekotasi” = arrived?\n\nBut “arrived” = “mtona”\n\nUnless “lekotasi” is “did”?\n\nIn 11: verb is “mtosiwena” — not “lekotasi”\n\nIn 8: “Navila ka’ukwa lekotasi?” — but “arrived” is not “lekotasi”\n\nThis is inconsistent.\n\nWait — maybe a typo in the problem.\n\nCheck original:\n\n8. How many dogs arrived? → Navila ka’ukwa lekotasi?\n\nBut 2: “This white man arrived” → Lekota dimdim mtona\n\nSo “mtona” = arrived\n\nThus, “lekotasi” cannot be “arrived”\n\nConclusion: likely typo; “lekotasi” is not the verb.\n\nPerhaps “lekotasi” = past tense \"did\"\n\nThen “Navila ka’ukwa lekotasi” = how many dogs did?\n\nIn place of “did [verb]”?\n\nBut in 11: “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“mtosiwena” = ate\n\nSo “did eat” = “mtosiwena”\n\nSo “did” is not a separate auxiliary.\n\nIn 8, “lekotasi” → is not “did”\n\nTherefore, “Navila” + noun + verb?\n\nBut in 8: “Navila ka’ukwa lekotasi” — if “lekotasi” is not “arrived”, then error.\n\nAlternative: “ka’ukwa” = dogs, “lekotasi” = arrived?\n\nBut “arrived” is “mtona”\n\nSo unless “lekotasi” is a variant, no.\n\nThus, likely the sentence is “Navila namwaya legisi waga makesiwena?”\n\nParse:\n\n- “how many” = Navila\n- canoes = namwaya\n- “those old women” = legisi waga\n- “saw” = makesiwena\n\nStructure: Navila namwaya legisi waga makesiwena?\n\nBut object “namwaya” after verb “makesiwena” — same as 4.\n\nSo yes — in 4: “makesiwena namwaya minana” → verb + object\n\nThus, 19: “Navila namwaya legisi waga makesiwena?”\n\nBut “those old women” = legisi waga — from 4: “legisi waga makesiwena”\n\nSo yes.\n\nThus, b.1: Navila namwaya legisi waga makesiwena\n\n---\n\n**20. These four white men will look after this clever child.**\n\n- “These” → “Lekota”\n- “four” → “minasina”\n- “white” → “dimdim”\n- “men” → “mtona”\n- “will” → “tau”\n- “look after” → “teyu” (from 6: “The old women looked after two men” → “leyamatasi teyu tauwau nunumwaya”)\n\nSo: “Lekota minasina dimdim mtona tau teyu lekota kwetala gwadi”\n\n“this clever child”:\n- “this” → “lekota”\n- “clever” → “kwetala”\n- “child” → “gwadi”\n\nSo: “lekota kwetala gwadi”\n\nThus: “Lekota minasina dimdim mtona tau teyu lekota kwetala gwadi”\n\nOrder: subject → “lekota minasina dimdim mtona” → these four white men\n- “will” → “tau”\n- “look after” → “teyu”\n- “this clever child” → “lekota kwetala gwadi”\n\nYes — matches 6: subject + verb + object\n\nThus, b.2: Lekota minasina dimdim mtona tau teyu lekota kwetala gwadi\n\n---\n\n**21. How many children will eat these pigs?**\n\n- “How many” → “Navila”\n- “children” → “gwadi”\n- “will” → “tau”\n- “eat” → “mtosiwena” (from 11)\n- “these pigs” → “these” → “lekota”, “pigs” → “bunukwa” (since 5: “killed two pigs” → “bunukwa”)\n\nSo: “Navila gwadi tau mtsiwiwena lekota bunukwa”\n\nWait — “eat” = “mtosiwena” — from 11: “mtosiwena”\n\nBut no “mtsiwiwena”? In 11: “mtosiwena”\n\nSo “eat” = “mtosiwena”\n\nThus: “Navila gwadi tau mtsosiwena lekota bunukwa”\n\nBut “mtosiwena” is not “mtsiwiwena” — spelling?\n\nIn example 11: “mtosiwena” — likely “mtosiwena”\n\nSo: “Navila gwadi tau mtsosiwena lekota bunukwa”\n\nBut in 5: “killed two pigs” → “bunukwa”\n\nSo “pig” = “bunukwa”\n\n“these pigs” = “lekota bunukwa”\n\n“will eat” = “tau mtsosiwena”\n\n“how many children” = “Navila gwadi”\n\nOrder: how many + object + will + eat + these pigs\n\nBut in examples, how many comes first.\n\nLike 19: Navila object subject verb\n\nSo: Navila gwadi tau mtsosiwena lekota bunukwa\n\nYes.\n\nb.3: Navila gwadi tau mtsosiwena lekota bunukwa\n\n---\n\n**22. Which woman caught those beautiful fish?**\n\n- “Which” → “Amtona”\n- “woman” → “waga”\n- “caught” → “navasi” (1: “one man will catch these four fish” → “navasi”)\n- “those” → “lekota”\n- “beautiful” → “dakuna” (10: “beautiful child” → “dakuna gwadi”)\n- “fish” → “minasina” (1: “four fish” → “minasina”)\n\nSo: Amtona waga navasi lekota dakuna minasina\n\n“which woman” → “amtona waga”\n\n“caught” → “navasi” (from 1)\n\n“those beautiful fish” → “lekota dakuna minasina”\n\nOrder: Amtona waga navasi lekota dakuna minasina\n\nMatches pattern in 5: “Amtona tau lekalimati nayu bunukwa?” — “Amtona” + noun (with num, adj, noun)\n\nSo “Amtona waga navasi lekota dakuna minasina”\n\nb.4: Amtona waga navasi lekota dakuna minasina\n\n---\n\n**23. Two wild dogs saw that old man.**\n\n- “Two” → “nunumwaya” (from 6: “two men” → “nunumwaya”)\n- “wild” → “bunukwa” (from 5, 12)\n- “dogs” → “ka’ukwa” (from 8: “dogs” = “ka’ukwa”)\n- “saw” → “makesiwena” (from 4, 10)\n- “that” → “bikota” (from 3: “that child” → “bikota gwadi”)\n\nSo: Nunumwaya bunukwa ka’ukwa makesiwena bikota legisi\n\n“two wild dogs” → “nunumwaya bunukwa ka’ukwa”\n\n“saw” → “makesiwena”\n\n“that old man” → “bikota legisi”\n\nStructure: subject + verb + object\n\nMatches 4: “legisi waga makesiwena namwaya minana”\n\nSo yes.\n\nb.5: Nunumwaya bunukwa ka’ukwa makesiwena bikota legisi\n\n---\n\nFinal answer:\n\n\\boxed{b.1: Navila namwaya legisi waga makesiwena; b.2: Lekota minasina dimdim mtona tau teyu lek", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10934.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 2, + "output": "First, build an alignment table from the given English–Kilivila pairs to extract patterns.\n\n---\n\n**1. One man will catch these four fish.** \nEnglish: One man → \"navasi\" (one) + \"yena\" (man) → \"navasi yena\" \nWill catch → \"minasina\" (will catch) \nThese four fish → \"tetala\" (four) + \"tau\" (fish) → \"tetala tau\" \n→ \"navasi yena minasina tetala tau\"\n\n**2. This white man arrived.** \nThis → \"lekota\" \nWhite → \"dimdim\" \nMan → \"mtona\" \nArrived → \"mtona\" (also used as verb?) \nWait: \"lekota dimdim mtona\" → \"This white man arrived\" → \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man, and verb? \nBut \"mtona\" is also used as a noun in (1). \nActually, in (1), \"yena\" = man. In (2), \"mtona\" = man. \nSo \"mtona\" = man, \"dimdim\" = white → \"lekota dimdim mtona\" → \"this white man\"\n\nBut no verb? → \"mtona\" used as verb? But in (1), \"minasina\" is the verb. \nSo (2): \"lekota dimdim mtona\" → probably \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man and verb (verb = “arrived”) — suggests \"mtona\" is a bare form meaning “to arrive”.\n\nWait: (3) \"That child will arrive\" → \"bikota gwadi magudiwena\" \n\"bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive → so “will arrive” = “magudiwena”\n\nIn (2): \"lekota dimdim mtona\" → “this white man arrived” — so “mtona” = verb \"arrive\"? But in (3) the verb is “magudiwena”. \nIn (2), “mtona” is used as both noun and verb? Unlikely. \n\nPossibility: verb form is independent.\n\n(3) That child will arrive → \"bikota gwadi magudiwena\" → “magudiwena” = will arrive \n(4) That old woman saw those canoes → \"legisi waga makesiwena namwaya minana\" \n\"legisi\" = that, \"waga\" = old, \"makesiwena\" = saw, \"namwaya\" = canoes, \"minana\" = those\n\nSo “saw” = “makesiwena” — verb \nSimilarly, “arrived” = “magudiwena” — verb \n“In (2), 'mtona' used as verb? But no. In (2), 'lekota dimdim mtona' — ‘mtona’ is man? Same as (1) 'yena'. In (1), ‘navasi yena’ = one man. In (2), ‘lekota dimdim mtona’ — this white man. So \"mtona\" = man noun.\n\nThe verb \"arrived\" is not in (2). Wait: sentence 2 says \"this white man arrived\" — so verb must exist.\n\nBut in (3), “that child will arrive” → “bikota gwadi magudiwena” → verb = magudiwena (will arrive)\n\nIn (4), “saw” = makesiwena\n\nIn (1), “will catch” = minasina\n\nSo are there separate verbs?\n\n\"minasina\" = catch \n\"magudiwena\" = arrive \n\"makesiwena\" = see\n\nThus, verbs appear to be clearly marked.\n\nIn (2): \"this white man arrived\" → must have arrived, so \"magudiwena\"? But no direct match.\n\nWait: sentence 2: \"lekota dimdim mtona\" — but no verb? That can't be.\n\nUnless \"mtona\" is both man and verb? But in (3), man = “gwadi”, not “mtona”.\n\n(3): \"bikota gwadi magudiwena\" — \"gwadi\" = child\n\n(4): \"legisi waga makesiwena namwaya minana\" — \"waga\" = old, \"makesiwena\" = saw\n\nSo verbs: \n- catch: minasina \n- arrive: magudiwena \n- see: makesiwena\n\nTherefore, (2): “This white man arrived” → \"lekota dimdim mtona magudiwena\"? But the translation is given as \"lekota dimdim mtona\"\n\nNo verb! Contradiction.\n\nWait: perhaps the translation is missing verb?\n\nNo — the translation is given: “Lekota dimdim mtona” — only 5 words.\n\nBut clearly, ‘arrived’ must be a verb.\n\nPossibility: “mtona” is the verb “to arrive” in a verb-root form.\n\nBut in (3), “gwadi magudiwena” — “magudiwena” = will arrive → so existing form.\n\nThus, “mtona” cannot be “arrive” — only in (1) and (2) is it used as noun.\n\nIn (1): “navasi yena” = one man \nIn (2): “lekota dimdim mtona” = this white man — suggests “mtona” is man\n\nIn (3): “bikota gwadi magudiwena” — “gwadi” = child\n\nIn (4): “legisi waga makesiwena” — “makesiwena” = saw\n\nSo “mtona” is used as man noun.\n\nThen what is the verb in (2)? Missing?\n\nBut the sentence is “this white man arrived” — so must have a verb.\n\nPossibility: typo or misalignment.\n\nWait — perhaps in Kilivila, “mtona” is the verb “to arrive” in a bare form? But in (3), “magudiwena” is used, which has “-wena” — might be suffix.\n\nIn (3): “arrive” → “magudiwena” — so “magudi” + “wena” = arrive\n\nIn (1): “minasina” → “minas” + “ina” = catch\n\nIn (4): “makesiwena” → “makesi” + “wena” = saw\n\nSo the verb endings: “-wena” = past? or marked aspect?\n\n(3): \"will arrive\" → “magudiwena” — future?\n\n(1): “will catch” → “minasina” — not with “-wena”? “minasina” → “ina” → present?\n\nPattern: \n- catch (present/future): minasina \n- arrive (future): magudiwena \n- see: makesiwena \n\nIn (2): “this white man arrived” — so should be “lekota dimdim mtona magudiwena”? But translation says “lekota dimdim mtona”\n\nThis is inconsistent.\n\nUnless the translation is incomplete?\n\nBut the problem says: \"Here are some sentences in English and their Kilivila translations\" — so translations are given.\n\nSo all translations are correct.\n\nPossibility: “mtona” is used both as noun and verb, and in (2), “mtona” = arrived — but in (1), “navasi yena” = one man, “minasina” = catch, so “mtona” used as noun.\n\nAlternative: perhaps the word “mtona” means both man and to arrive.\n\nBut in (3): “bikota gwadi magudiwena” — “magudiwena” = arrive — so more likely “magudi” + “wena”\n\nSo likely, “mtona” is man.\n\nThus, (2) must have lost a verb? But translation is given.\n\nWait — recheck sentence 2: \"This white man arrived.\" → translation: \"lekota dimdim mtona\"\n\nNo verb. That's problematic.\n\nUnless “mtona” is a verb meaning “arrived”?\n\nBut in (1), “minasina” is used for “will catch”\n\nIn (3), “magudiwena” for “will arrive” — so different verb.\n\nSo (2) has no verb — contradiction.\n\nPerhaps a typo in problem.\n\nBut look at (13): “How many women will look after this man?” → translation: “Navila vivila biyamatasi tau mtona” \n“vivila” = will look after? “biyamatasi” = women? “tau” = this man → “look after” = “vivila”?\n\nIn (12): “The clever chief killed one wild pig” → “lekalimati natala bunukwa nagasisi guyau tokabitam” \n“lekalimati” = chief, “natala” = killed, “bunukwa” = one, “guyau” = wild pig, “tokabitam” = clever?\n\n“tokabitam” = clever — so “nagasisi guyau” = killed wild pig? “guyau” = wild pig?\n\nBut “tokabitam” = clever — which goes with “chief”?\n\nSo “lekalimati” = chief, “tokabitam” = clever → “clever chief”\n\nSo “lekalimati” = chief, with “tokabitam” as adjective.\n\nSimilarly, in (10): “That beautiful child saw this stone” → “legisi dakuna makwena gwadi magudiwena gudimanabweta” \n“dakuna” = beautiful, “gwadi” = child, “makwena” = saw, “gudimanabweta” = stone\n\nSo “dakuna” = beautiful → adjective\n\n“makwena” = saw\n\nThus, adjective directly precedes noun — “dakuna gwadi” = beautiful child\n\nSimilarly, (4): “legisi waga makesiwena namwaya minana” → “waga” = old, “namwaya” = canoes → “old canoes”\n\nSo adjectives precede nouns.\n\nVerbs: “minasina” (catch), “magudiwena” (arrive), “makesiwena” (see)\n\nIn (2): “this white man arrived” → should be “lekota dimdim mtona magudiwena” — but given as “lekota dimdim mtona”\n\nOnly explanation: typo or misprint. Likely, the translation is “lekota dimdim mtona” meaning “this white man” — and “arrived” is omitted? Unlikely.\n\nAlternative: “mtona” is the verb “to arrive” — and “dimdim” = white, “lekota” = this → “lekota dimdim mtona” = this white man arrived\n\nSo “mtona” = verb “arrive”\n\nBut in (3), “bikota gwadi magudiwena” → “magudiwena” = will arrive → different verb.\n\nSo uses different verb roots.\n\nSo in (2): “mtona” = arrive (intransitive)\n\nIn (3): “magudiwena” = arrive (future)\n\nIn (1): “minasina” = catch (present)\n\nSo verb roots: \n- catch: minasina \n- arrive: mtona or magudiwena? \n- see: makesiwena\n\nBut in (3), “will arrive” uses “magudiwena” — imperative? future?\n\nIn (4), “saw” uses “makesiwena” — past?\n\nSo “makesiwena” = past saw\n\n“minasina” = catch — may be present/future\n\n“magudiwena” = future arrive\n\nThus, (2): “this white man arrived” → must use “mtona” or “magudiwena”? Only “mtona” appears.\n\nUnless “mtona” is a bare form of arrive — and used without suffix.\n\nBut in (3), arrive is “magudiwena” — with “-wena”\n\nSo likely, “mtona” = arrived (past), and “magudiwena” = will arrive.\n\nBut in (2), \"arrived\" — past — so “mtona” verb.\n\nBut in (3), arrive is future.\n\nSo “mtona” = arrived (past), “magudiwena” = will arrive (future)\n\nBut in (1): “will catch” → “minasina” — no “wena”\n\nSo “minasina” is present/future catch.\n\nSo verb forms:\n\n- present/future catch: minasina \n- past arrive: mtona \n- past see: makesiwena \n- future arrive: magudiwena\n\nThis is messy.\n\nBut perhaps the verb is not marked by “wena” — only aspect is marked.\n\nIn (1): “will catch” → “minasina” — non-past \nIn (3): “will arrive” → “magudiwena” — future \nIn (4): “saw” → “makesiwena” — past\n\nSo “wena” marks past/future?\n\nBut (3) has “wena” and “will” → future? \n(4) has “wena” and “saw” → past\n\nBut (1) no “wena” — “minasina” — “will catch” → future? So perhaps “wena” = past, \"ina\" = present?\n\nNo: “minasina” has “-ina”, not “-wena”\n\nSo active vs passive?\n\nNot clear.\n\nAlternative approach: focus on patterns in question pairs.\n\nLook at questions with numerals.\n\nSentence 1: “one man will catch these four fish” → “navasi yena minasina tetala tau”\n\n“navasi” = one \n“tetala” = four \n“yena” = man \n“minasina” = catch \n“tau” = fish\n\nSo numerals are separate: “navasi” = one, “tetala” = four\n\nSentence 5: “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?”\n\n“Amtona” = which man? \n“tau” = man? \n“lekalimati” = chief? \n“nayu” = two? \n“bunukwa” = one pig? \n“bunukwa” = one?\n\n“nayu” = two — so numeral “nayu” used for two\n\n“bunukwa” = one — so “bunukwa” = one pig?\n\nBut “two pigs” → “nayu bunukwa” — “nayu” = two, “bunukwa” = one? Not “two pigs”\n\nIn (12): “The clever chief killed one wild pig” → “lekalimati natala bunukwa nagasisi guyau tokabitam”\n\n“bunukwa” = one, “guyau” = wild pig\n\nSo “bunukwa” = one\n\nIn (5): “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?”\n\n“Amtona” = which \n“tau” = man \n“lekalimati” = chief \n“nayu” = two \n“bunukwa” = one — but one pig?\n\nInconsistent.\n\nUnless “bunukwa” = one pig, and “nayu” = two — so “two pigs” not expressed as “nayu bunukwa” — but as “two pigs”?\n\nBut in (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona”\n\n“Navila” = how many \n“biyamatasi” = women \n“tau” = this man\n\nSo “navila” = how many\n\nSentence 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?”\n\n“Navila” = how many \n“ka’ukwa” = dogs \n“lekotasi” = arrived? “lekotasi” → “lekota” = this, “asi” = arrived? Or “lekotasi” = arrived?\n\n“lekotasi” = arrived (doubt)\n\nIn (8): “Navila ka’ukwa lekotasi?” → how many dogs arrived?\n\nSo “lekotasi” = arrived\n\nIn (11): “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” = how many \n“lekamkwamsi” = those white men \n“mtosiwena” = ate? “mtosiwena” = eat?\n\nIn (10): “saw” → “makesiwena” → so “eat” = “mtosiwena”?\n\n(13): “Navila vivila biyamatasi tau mtona” → how many women will look after this man → “vivila” = will look after\n\nSo verbs:\n\n- catch: minasina \n- arrive: magudiwena or mtona \n- see: makesiwena \n- eat: mtosiwena \n- look after: vivila\n\nIn (11): “how many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?”\n\n“Kwevila” = how many \n“lekamkwamsi” = those white men \n“dimdim” = white \n“mtosiwena” = ate\n\nSo past tense: “did eat” → “mtosiwena”\n\nIn (13): “will look after” → “vivila” — present/future?\n\nSo “vivila” = will look after\n\nNow, for demonstratives:\n\n- this: lekota \n- that: bikota, legisi \n- these: lekotasi? (in (8) “lekotasi”) \n- those: lekamkwamsi (in (11))\n\nIn (4): “that old woman saw those canoes” → “legisi waga makesiwena namwaya minana” \n“legisi” = that \n“minana” = those canoes\n\n“minana” = those\n\nIn (6): “The old women looked after two men” → “leyamatasi teyu tauwau nunumwaya” \n“leyamatasi” = old women \n“teyu” = two \n“", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11650.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "solver_checklist", + "sample_index": 3, + "output": "First, build alignment table from given examples to extract patterns.\n\n---\n\n**Step 1: Identify core components and patterns**\n\nLook at questions involving:\n- Quantity (how many, four, two)\n- Agents (man, woman, child, chief)\n- Actions (see, catch, eat, arrive, look after)\n- Objects (fish, pigs, canoes, stone)\n- Demonstratives (this, that, these, those)\n- Adjectives (white, old, clever, beautiful, wild)\n- Tense/aspect: future (\"will\"), present (\"saw\", \"arrived\")\n- Question forms: interrogative structure (how many, which)\n\n---\n\n**Step 2: Extract structure from examples**\n\nExample 1: \nEng: One man will catch these four fish. \nKilivila: Bibani navasi yena minasina tetala tau. \n→ \"One man\" = Bibani navasi \n→ \"will catch\" = yena minasina \n→ \"these four fish\" = tetala tau → \"four fish\" (tetala = fish; tau = four)\n\nNote: “four” is numerically translated as “tau”, used as a number.\n\nExample 2: \nEng: This white man arrived. \nKilivila: Lekota dimdim mtona. \n→ \"this white man\" = lekota dimdim (lekota = this, dimdim = white) \n→ \"arrived\" = mtona\n\nExample 3: \nEng: That child will arrive. \nKilivila: Bikota gwadi magudiwena. \n→ \"that child\" = bikota gwadi \n→ \"will arrive\" = magudiwena\n\nNote: \"will\" = magudiwena (in future), \"that\" = bikota\n\nExample 4: \nEng: This old woman saw those canoes. \nKilivila: Legisi waga makesiwena namwaya minana. \n→ \"this old woman\" = legisi waga (legisi = this, waga = old) \n→ \"saw\" = makesiwena \n→ \"those canoes\" = namwaya minana → \"those canoes\" (namwaya = canoes; minana = those)\n\nExample 5: \nEng: Which man killed two pigs? \nKilivila: Amtona tau lekalimati nayu bunukwa? \n→ \"which man\" = amtona (question for which) \n→ \"killed\" = lekalimati \n→ \"two pigs\" = nayu bunukwa → \"two pigs\" (nayu = two, bunukwa = pig)\n\nSo: numerals are directly coded (tau = four, nayu = two), and adjectives precede nouns.\n\nExample 6: \nEng: The old women looked after two men. \nKilivila: Leyamatasi teyu tauwau nunumwaya. \n→ \"the old women\" = leyamatasi teyu → may be \"the\" = le, \"old\" = teyu, \"women\" = matasi \n→ \"looked after\" = tauwau \n→ \"two men\" = nunumwaya → \"two men\" (nunum = two? no → perhaps \"tauwau\" = look after, \"nunumwaya\" = two men)\n\nWait: \"tauwau\" is not a verb, seems like “look after” = tauwau, and \"two men\" = nunumwaya → so \"nunum\" likely means two.\n\n\"nayu\" = two, \"nunum\" = two? — possibly nayu and nunum are both \"two\", but in different contexts.\n\nExample 7: \nEng: That clever woman will see something. \nKilivila: Bigisi kwetala vivila minawena nakabitam. \n→ \"that clever woman\" = bigisi kwetala → bigisi = that, kwetala = clever \n→ \"will see\" = vivila minawena → vivila = see, minawena = something \n→ \"nakabitam\" = ? Seems like a demonstration or marker? Might be “something” or “viv” class.\n\nExample 8: \nEng: How many dogs arrived? \nKilivila: Navila ka’ukwa lekotasi? \n→ \"how many\" = navila \n→ \"dogs\" = ka’ukwa \n→ \"arrived\" = lekotasi\n\nSo: \"how many\" → navila (in questions)\n\nExample 9: \nEng: Which canoe did the chiefs see? \nKilivila: Amakena waga legisesi gweguyau? \n→ \"which canoe\" = amakena → question for which \n→ \"the chiefs\" = waga legisesi → waga = old? or maybe \"chiefs\" = legisesi → not clear \n→ \"saw\" = gweguyau\n\nSo “which” = amakena, “saw” = gweguyau\n\nExample 10: \nEng: That beautiful child saw this stone. \nKilivila: Legisi dakuna makwena gwadi magudiwena gudimanabweta. \n→ \"that beautiful child\" = legisi dakuna gwadi → legisi = that, dakuna = beautiful, gwadi = child \n→ \"saw\" = magudiwena \n→ \"this stone\" = gudimanabweta → \"this\" + \"stone\"\n\n\"this\" appears as gudima? → gudimanabweta → perhaps gudima = this, nabadweta = stone\n\nExample 11: \nEng: How many things did those white men eat? \nKilivila: Kwevila lekamkwamsi dimdim mtosiwena? \n→ \"how many things\" = kwevila \n→ \"those white men\" = lekamkwamsi dimdim → leka = those, amkwamsi = men, dimdim = white \n→ \"ate\" = mtosiwena\n\nExample 12: \nEng: The clever chief killed one wild pig. \nKilivila: Lekalimati natala bunukwa nagasisi guyau tokabitam. \n→ \"clever chief\" = natala bunukwa → natala = clever, bunukwa = pig? no — bunukwa = pig, but 'guyau' = wild? \n→ \"killed\" = lekalimati \n→ \"one wild pig\" = nagasisi guyau tokabitam → nagasi = one? guyau = wild, tokabitam = pig?\n\nWait: \"nagasisi\" → “one”? \"nagasi\" may be one; \"guyau\" = wild; \"tokabitam\" = pig\n\nThus: \"one wild pig\" = nagasisi guyau tokabitam → suggests \"nagasi\" = one (numeral), \"guyau\" = wild, \"tokabitam\" = pig\n\nExample 13: \nEng: How many women will look after this man? \nKilivila: Navila vivila biyamatasi tau mtona? \n→ \"how many women\" = navila vivila → how many + women = biyamatasi \n→ \"will look after\" = vivila — wait, vivila also = \"see\"? \nConflict: earlier vivila = see, now vivila = look after?\n\nWait — in example 7: \"will see\" = vivila minawena \nIn example 13: \"will look after\" = vivila biyamatasi?\n\nSo: “look after” is vivila?\n\nBut in ex 6: “looked after” = tauwau \nEx 13: “will look after” = vivila → suggests different verbs\n\nPossibly “see” and “look after” are distinct.\n\nClarify:\n\n- “see” → magudiwena (ex 3, 4, 10) \n- “look after” → tauwau (ex 6), vivila (ex 13)? But vivila is also in “will see”\n\nEx 7: \"will see something\" → vivila minawena \nEx 13: \"will look after this man\" → vivila biyamatasi → so “vivila” is used for “see” or “look after”?\n\nPossibility: vivila = “see” in general, and “look after” is a different verb.\n\nBut ex 6: “looked after two men” = leyamatasi teyu tauwau nunumwaya → tauwau = look after\n\nThus: \n- “look after” = tauwau \n- “see” = magudiwena or vivila?\n\nEx 7: “that clever woman will see something” → bigisi kwetala vivila minawena nakabitam → so vivila = see\n\nThus “see” = vivila \n“look after” = tauwau\n\nSo now:\n\n| Action | Kilivila verb |\n|--------|---------------|\n| see | vivila / magudiwena? — conflict in example 10 and 7 |\nIn ex 10: “saw this stone” = magudiwena \nIn ex 7: “will see something” = vivila minawena \nSo “see” = vivila (future), “saw” = magudiwena (past)? \nBut ex 4: “saw” = makesiwena (not seen)\n\nContradiction.\n\nEx 4: \"This old woman saw\" → makesiwena \nEx 7: \"will see\" → vivila \nEx 10: \"saw\" → magudiwena\n\nSo \"saw\" and \"see\" are different verbs.\n\nBut ex 4: \"saw\" = makesiwena \nEx 10: \"saw\" = magudiwena \nEx 3: \"will arrive\" = magudiwena\n\nSo magudiwena = \"will arrive\" or \"will see\"? \nIn ex 3: \"that child will arrive\" = bikota gwadi magudiwena → so magudiwena = will arrive \nIn ex 10: \"saw this stone\" = legisi dakuna makwena gwadi magudiwena → so magudiwena = saw? \nBut that contradicts.\n\nConclusion: “magudiwena” appears in both past and future.\n\nPossibility: the verb \"magudiwena\" = \"to arrive\", and \"to see\" is a different verb.\n\nEx 4: \"saw\" = makesiwena \nEx 10: \"saw\" = magudiwena → not consistent.\n\nWait: ex 10: \"that beautiful child saw this stone\" → legisi dakuna makwena gwadi magudiwena gudimanabweta \nBreak: \"saw\" = magudiwena → so magudiwena = saw\n\nBut ex 3: \"will arrive\" = magudiwena → so magudiwena = will arrive?\n\nThis is a contradiction.\n\nPossibility: typo or misreading.\n\nEx 3: \"That child will arrive\" → Bikota gwadi magudiwena \nEx 10: \"saw this stone\" → ... gwadi magudiwena → \"saw\" = magudiwena?\n\nSo both \"will arrive\" and \"saw\" use magudiwena?\n\nThat cannot be.\n\nAlternative: spelling or translation error.\n\nCheck original:\n\n3. That child will arrive. \n→ Bikota gwadi magudiwena\n\n10. That beautiful child saw this stone. \n→ Legisi dakuna makwena gwadi magudiwena gudimanabweta\n\nSo: \"saw\" = magudiwena\n\nBut \"will arrive\" = magudiwena → same verb?\n\nUnlikely. Likely a language-specific verb that means \"to arrive\" or \"to come\", and \"to see\" uses a different form.\n\nBut ex 4: \"saw\" = makesiwena\n\nSo:\n\n- \"saw\" (past) → varies: makesiwena (ex 4), magudiwena (ex 10) \n- \"will arrive\" → magudiwena (ex 3)\n\nThus “magudiwena” likely means “to arrive” or “to come” in future, and “to see” is elsewhere.\n\nBut in ex 10: “saw” → magudiwena → so likely “saw” and “arrive” share verb.\n\nPerhaps in Kilivila, “arrive” and “see” are synonyms?\n\nUnlikely.\n\nBest to assume:\n\n- \"see\" = makesiwena (ex 4) or vivila (ex 7)\n- \"arrive\" = magudiwena (ex 3)\n- In ex 10: “saw” → magudiwena → possibly error in transcription.\n\nAlternatively, \"saw\" = makesiwena, and in ex 10 the verb is misassigned.\n\nEx 4: \"This old woman saw\" → makesiwena \nEx 7: \"will see\" → vivila \nEx 10: \"saw\" → magudiwena — contradiction.\n\nGiven that in ex 7: “will see” = vivila minawena → suggests “see” = vivila \nIn ex 4: “saw” = makesiwena \nSo perhaps “saw” = makesiwena (past), “will see” = vivila (future)\n\nIn ex 10: “saw” → magudiwena? But that would be past.\n\nPerhaps \"magudiwena\" is future tense of \"arrive\", and in ex 10, the structure is wrong.\n\nBut ex 10: \"that child saw this stone\" = legisi dakuna makwena gwadi magudiwena gudimanabweta \nIf “saw” is magudiwena, then it must be future, but “saw” is past.\n\nSo likely, magudiwena is not “saw”.\n\nPossibility: “gwadi” = child, “magudiwena” = something else.\n\nLook at ex 7: bigisi kwetala vivila minawena nakabitam \n“vivila” = see, “minawena” = something\n\nEx 10: legisi dakuna makwena gwadi magudiwena gudimanabweta \nBreak: \"gudimanabweta\" = this stone \n\"magudiwena\" — what is it?\n\n“makwena” = this? “gwadi” = child \nSo “makwena gwadi” = “this child”? \nThen “magudiwena” = saw?\n\nBut only if “saw” is magudiwena.\n\nBut in ex 3: “will arrive” = magudiwena → so both events use same verb.\n\nConclusion: the verb \"magudiwena\" is used for both “arrive” and “see”, indicating that in Kilivila, “to arrive” and “to see” may be semantically linked or have overlapping forms.\n\nBut to avoid complexity, work on consistent patterns:\n\n---\n\n**Key patterns derived:**\n\n1. **Demonstratives**:\n - This: lekota, legisi, lekamkwamsi, waga → varies per noun\n - That: bikota, bigisi\n - These/Those: lekota, lekamkwamsi, lekotasi\n\n2. **Numerals**:\n - One: bibani (ex 1) → possibly one\n - Four: tetala → tau? → ex 1: \"these four fish\" = tetala tau → so tetala = fish, tau = four\n - Two: nayu (ex 5), nunum? (ex 6) — likely nayu = two\n - One: nagasi (ex 12) → one wild pig → nagasi = one\n - So numerals: \n - one → bibani, nagasi \n - two → nayu, nunum (possibly same) \n - four → tau \n So: \"two\" = nayu \n \"four\" = tau\n\n3. **Adjectives**:\n - white = dimdim \n - old = waga, teyu \n - clever = kwetala, natala \n - beautiful = dakuna \n - wild = guyau\n\n4. **Verbs**:\n - see → makesiwena (ex 4), vivila (ex 7) — likely makesiwena = see (past), vivila = see (future) \n - catch → yena minasina (ex 1) \n - arrive → magudiwena (ex 3,10) — possibly also see \n - look after → tauwau (ex 6) \n - kill → lekalimati (ex 5,12)\n\n5. **Question words**:\n - how many → navila (ex 8,13) \n - which → amtona (ex 5), amakena (ex 9) \n - who → not explicitly, but \"which woman\" = amakena waga?\n\n6. **Subject-Object Order**:\n - Usually subject + verb + object \n - Adjectives before nouns \n - Demonstratives vary per noun class\n\n---\n\n**Now translate each of (b):**\n\n19. How many canoes did those old women see?\n\n- How many → navila \n- canoes → namwaya \n- those → lekotasi (used in ex 4: \"those canoes\" = namwaya minana; ex 8: \"how many dogs arrived\" = navila ka’ukwa lekotasi → lekotasi = those) \n- old women → lekotasi teyu matasi → \"those old women\" = lekotasi teyu matasi (like \"those old women\" in ex 6: \"the old women\" = leyamatasi teyu) \n→ \"lekotasi\" = those \n→ \"tyu\" = old (from teyu) \n→ \"matasi\" = women \n→ \"see\" = makesiwena (past) — but in ex 4: \"saw\" = makesiwena\n\nSo: navila namwaya lekotasi teyu matasi makesiwena?\n\nOrder: how many + object (canoes) + subject (old women) + verb?\n\nBut ex 8: \"how many dogs arrived\" = navila ka’ukwa lekotasi?", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11645.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "unit_audit", + "sample_index": 0, + "output": "We are asked to find the theoretically possible translations of the words **‘word’** and **‘to exhaust’** into Rotuman, given only the provided vocabulary.\n\nWe cannot directly translate these two words from the given list, so we must analyze the linguistic patterns to deduce plausible forms based on morphology, phonology, and semantic derivation.\n\n---\n\n### Step 1: Look for semantic candidates\n\nWe are to infer **theoretically possible** forms — not exact translations — based on the given words. This means we look for *possible derivational patterns*, such as:\n\n- Root + suffix\n- Compound forms\n- Repeated or mirrored elements\n- Words with similar meanings (e.g., ‘to cut’, ‘to pierce’, ‘to turn’)\n\n---\n\n### Step 2: Analyze root and suffix patterns\n\nList of words with forms:\n\n- ‘ele’ — to be near \n- ‘olo’ — to cut \n- ‘fau’ — year \n- ‘ha.fha.fu’ — rocky \n- ‘huag’ + ‘el‘ele’ — impatient \n- ‘huag’ + ‘to‘a’ — courageous \n- ‘hül’ + ‘ha.fu’ — to blow (hurricane) \n- ‘hün’ + ‘kia’ — base of neck \n- ‘huli’ — to turn over \n- ‘huni’ — lower end \n- ‘is’ + ‘susu’ — nipple \n- ‘lala’ — deep \n- ‘maf’ + ‘tiro’ — spectacles \n- ‘mamasa’ — solid \n- ‘ma.titi’ — coldness \n- ‘ma.tit’ + ‘mamasa’ — ice \n- ‘moafmofa’ — littered with rubbish \n- ‘niu’ — copra \n- ‘nu‘suar’ + ‘tiro’ — window \n- ‘nu‘sura’ — door \n- ‘pala’ — pierce \n- ‘piri’ — to curl \n- ‘poagpoga’ = ‘palapala’ — covered with holes \n- ‘pogi’ — night \n- ‘puhra.ki’ — to boil, to bubble up \n- ‘pulu’ — glue \n- ‘ka.lu’ — bracelet; to encircle \n- ‘riamrima’ — shiny \n- ‘rū huga’ — stomach-ache \n- ‘to‘a’ — hero\n\nWe need to find how to form:\n\n1. **‘word’** \n2. **‘to exhaust’**\n\n---\n\n### Step 3: Search for compounds involving ‘to’ or root meaning of ‘exhaust’\n\n- ‘to‘a’’ means hero → may not relate \n- ‘to’ appears in ‘to‘a’, ‘to‘a’ in ‘huag to‘a’ (courageous) \n- ‘to’ might be a particle or prefix — but in ‘to‘a’ it's used as a noun\n\nNo clear word for “to exhaust”\n\nBut note: \n- ‘puhra.ki’ — to boil, to bubble up → might imply “to fill up” or “to overfill” \n- ‘huli’ — to turn over → might imply “to turn over and over” \n- ‘lala’ — deep → deep something? \n- ‘ma.tit mamasa’ — ice → cold, hard \n- ‘moafmofa’ — littered with rubbish → messy \n\nNow, think: “to exhaust” might mean: \n→ to use up \n→ to deplete \n→ to wear out\n\nLook for verbs meaning \"to consume\", \"to use up\".\n\nIn the list:\n\n- ‘ele’ — to be near → not relevant \n- ‘olo’ — to cut → cut a resource? \n- ‘pala’ — to pierce → not clearly related \n- ‘huli’ — to turn over → if repeatedly turned over, might imply \"to use repeatedly\"? \n- ‘huni’ — lower end → location \n- ‘ka.lu’ — to encircle → to go around → could imply \"to go around repeatedly\"? \n- ‘poagpoga’ — covered with holes → something that has been perforated → could be “broken” or “worn out”? \n\nCould \"to exhaust\" be a compound involving **repetition** or **a verb with a negative consequence**?\n\nLook at **'pala'** — pierce. \nIf something is pierced repeatedly, it might be “exhausted” — wear out.\n\nBut “pala” is noun and verb. Could “pala” be used as “to pierce”, and repeated usage leads to exhaustion?\n\nAlternatively: \n‘huli’ = to turn over → repeated turning over → can suggest “used up”, “worn out”?\n\nIs there a verb meaning “to remove”? \n‘olo’ = to cut → could be used to remove something? \n‘pala’ = to pierce → might imply cutting through, thus using up?\n\nBut nothing directly says “to use up”.\n\nCould “to exhaust” be formed from “to use”?\n\nWe have: \n‘fäeag ‘u‘u’ — to use sign language → so “to use” is possible in a compound.\n\n‘fäeag’ means “to use” → used in “fäeag ‘u‘u’”, i.e., to use sign language.\n\nSo **‘fäeag’** = **to use**\n\nThus, “to use” exists.\n\nNow, “to exhaust” may mean “to use completely” or “to use up”.\n\nSo perhaps “to exhaust” = **to use completely**?\n\nBut how to express “completely”?\n\nWe have:\n\n- ‘lala’ = deep \n- ‘ma.titi’ = coldness \n- ‘mamasa’ = solid \n- ‘huni’ = lower end \n\nCould a compound like ‘fäeag’ + something mean “to use up”?\n\nPossible: ‘fäeag’ + ‘lala’ → to use deeply? → “to use thoroughly” → close to “to exhaust”?\n\nAlternatively, consider: \n- ‘pala’ — pierce → could “pierce through” to the end? → to exhaust?\n\nBut no clear link.\n\nAlternatively: look at **‘poagpoga’ = palapala** — covered with holes → could be metaphorical for something worn out?\n\nAlso: **‘mama’** may be a root → ‘mamasa’ = solid → might imply “to fill” or “to make full”?\n\nNow, “to exhaust” might be close to **to use up**, and since ‘fäeag’ means ‘to use’, perhaps a compound with a suffix indicating fullness or end?\n\nBut in Rotuman, compound formation: \n- ‘fäeag’ + ‘u‘u’ → to use sign language \n- ‘huag’ + ‘el‘ele’ → impatient \n- ‘huag’ + ‘to‘a’ → courageous \n\nSo the pattern is: [adjective/noun] + [noun/verb]\n\nSo for \"to exhaust\", could it be a compound? \nLike ‘fäeag’ + something → meaning “to use completely”?\n\nBut we don’t have an explicit “completely” or “to fullness”.\n\nAlternatively, could “exhaust” be derived from “to fill up” or “to leave empty”?\n\nWe have: ‘puhra.ki’ = to boil, to bubble up → to become full?\n\nSo boiling up → fills up → to build up → opposite of exhaust?\n\nBut “to exhaust” might be the opposite of “to fill up”.\n\nThus, “to exhaust” = to use up → to deplete.\n\nBut in the list, no direct verb for “to use up”.\n\nCould there be a word like “to use all”?\n\nNo.\n\nBut “to exhaust” may be a possible derivative of the root **‘fäeag’** (to use) + a suffix indicating end or finish?\n\nBut no word for “end” directly present.\n\nWe see: \n- ‘fau’ = year → year’s end = ‘a‘öf fau’ \n→ so “year’s end” is formed as ‘a‘öf fau’ — meaning “the end of the year”\n\nSo compound form: [a‘öf] + [fau] → end of year\n\nThus, **‘a‘öf’** = “end” → in “a‘öf fau” meaning “end of year”\n\nThis is a key pattern.\n\nSo: **a‘öf** means “end” → so the suffix “a‘öf” can mean “end”\n\nSimilarly, to “exhaust” might be **to use to the end** → “to use to the end”\n\nThus, **‘fäeag a‘öf’** = to use to the end → to exhaust?\n\nThat makes sense.\n\nSo **to exhaust** = **fäeag a‘öf** — meaning “to use to the end”\n\nThis is a plausible theoretical translation based on known compounds and derivational patterns.\n\nNow for **‘word’**?\n\nAre there words in the list that might suggest “word”?\n\nWe have:\n- ‘pala’ — pierce \n- ‘poagpoga’ — covered with holes \n- ‘nu‘suar’ — window \n- ‘nu‘sura’ — door \n- ‘mamasa’ — solid \n- ‘riamrima’ — shiny \n- ‘to‘a’ — hero \n- ‘pogi’ — night \n- ‘lala’ — deep \n- ‘is’ — sharp-pointed \n- ‘is susu’ — nipple \n\nNo clear word for “word”.\n\nBut consider: \n- ‘fäeag’ = to use \n- ‘pala’ = to pierce \n- ‘piri’ = to curl \n\nIs there a noun meaning “speech”? Not directly.\n\nBut sometimes in Austronesian languages, word-related terms come from body parts or actions.\n\nFor example, “word” might be derived from the action of “cutting” or “piercing” — since “word” can be seen as a “cut” or “notch”?\n\nWe have: \n- ‘olo’ — to cut \n- ‘pala’ — to pierce \n- ‘huli’ — to turn over \n- ‘huni’ — lower end \n\n“Word” might be linked to “cut” → a word is a cut?\n\nNot strong.\n\nAlternatively: \n“word” might be formed as a compound of “to say” or “to speak” — no such word.\n\nBut in the list: \n- ‘rū huga’ — stomach-ache → body part \n- ‘hün kia’ — base of neck → body part \n- ‘nu‘sura’ — door → opening \n- ‘nu‘suar’ — window \n\nDo any of these suggest a concept of “speech”?\n\nAlternatively, could “word” be a root with a suffix?\n\nCould it be a calque from “to speak”?\n\nBut no verb for “to say”.\n\nWe don’t have a direct term.\n\nBut we notice:\n- ‘fäeag’ = to use \n- ‘pala’ = to pierce \n- ‘ka.lu’ = to encircle \n\nBut “to encircle” might suggest a boundary — so a “word” might be something that boundaries a thought?\n\nUnlikely.\n\nAlternatively, in some languages, ‘word’ is derived from the spoken form.\n\nBut no evidence here.\n\nHowever, in the pattern: \nWe have a compound: ‘a‘öf fau’ = year’s end → uses the root ‘a‘öf’ (end) + ‘fau’ (year)\n\nSimilarly, we have a compound: ‘huag el‘ele’ = impatient \n→ ‘huag’ + ‘el‘ele’\n\nSo root + root.\n\nNow, could a word like ‘pala’ be used as “word”?\n\nNot in any translation given.\n\nAlternatively, is there a possibility that “word” is expressed as a noun derived from a verb?\n\nLook at: \n- ‘mamasa’ — solid \n- ‘ma.tit’ — coldness \n- ‘lala’ — deep \n- ‘pulu’ — glue \n\nNo.\n\nBut consider: ‘ka.lu’ — bracelet → a ring that encircles something → could be a “word” in a metaphorical sense?\n\nUnlikely.\n\nAlternatively, in some languages, “word” is linked to “speech” or “to say” — and since we have no such word, perhaps the only possible form is based on sound or scything?\n\nAlternatively, could “word” be derived from “to cut”?\n\nWe have: ‘olo’ — to cut\n\nIn some languages, “word” = “cut” → e.g., in Proto-Austronesian, *kawa* or *kolo* might mean “to cut”, and could be extended to “cut” as in “a piece” → a “word” = a “piece” of speech?\n\nSo “word” = a piece — could be a piece of a language → derived from a cutting verb?\n\nSo “word” might be **olo** → \"to cut\", and thus a noun meaning “piece”?\n\nBut olo is used as verb.\n\nCould “a piece” be derived from “cut”?\n\nPossibly.\n\nBut we have no noun for “piece”.\n\nAnother idea: \nWe have ‘fau’ = year \n‘a‘öf fau’ = end of year → so end of time?\n\nCould “word” be a noun meaning “a name” or “a thing”?\n\nStill not clear.\n\nBut in the absence of a direct word, we must deduce *theoretically possible* forms.\n\nCould “word” be formed as a compound?\n\nLook at: \n- ‘pala’ — pierce → to pierce a thing, like a word \n- ‘pala’ could mean “to pierce a message” → a word is a piercing?\n\nNot convincing.\n\nAlternatively, consider: \nIn many Austronesian languages, verbs of cutting or piercing are used for linguistic items.\n\nBut literature suggests that words may be formed from **'pala'** or **'olo'**.\n\nBut we have no evidence.\n\nGiven that, and since we cannot translate “word” with certainty, the *theoretically possible* form must be a word that could arise in the language based on known structures.\n\nNow, the only possible known root that could relate is **'pala'** or **'olo'** — both are verbs related to cutting/piercing — and in concept, “a word” could be conceived as a **cut** or a **notch** in language.\n\nThus, “word” might be a noun derived from “to cut” or “to pierce”.\n\nSo a plausible candidate: \n→ **olo** (to cut) → used as noun meaning “a cut” → could be “a word”?\n\nBut “a cut” is not clearly “a word”.\n\nAlternatively, could it be **'pala'**?\n\n‘pala’ = pierce → could “piercing” be the act of creating a word?\n\nUnlikely.\n\nAlternatively, what about **'kia’** — base of neck? No.\n\nAnother angle: are there any words that could be interpreted as “name” or “label”?\n\nWe have ‘fäeag’ — to use — used with language.\n\nIs “to use” associated with a named thing?\n\n‘fäeag ‘u‘u’’ — to use sign language → so using a form of language → so “word” might be part of that?\n\nBut no noun.\n\nGiven that, and since we cannot know for sure, the *theoretically possible* translation of “word” must be a compound or derived form from existing roots.\n\nThe most plausible root that could produce a word in a linguistic context is **pala** or **olo**.\n\nBut both are verbs.\n\nCould a noun like **'pala'** stand for “word”?\n\nPossibly.\n\nCould **'olo'**?\n\nIn some languages, “word” is a “cut” — e.g., in Malagasy, “fahana” means “to have”, and “fahima” = to know, etc.\n\nBut without direct evidence, the only possible theoretical derivation is from known verbs.\n\nFurther, in compound words:\n\n- ‘a‘öf fau’ = end of year → uses “a‘öf” (end) + “fau”\n\nSo “end” is a prefix/suffix.\n\nSimilarly, “word” might be derived from a root meaning “to speak” or “to produce sound”.\n\nWe have no such root.\n\nBut could “word” be formed from **'fäeag'** + **'lala'** = “to use deeply” → possibly a word of deep meaning?\n\nBut “to use deeply” is not “word”.\n\nAlternatively, consider: \n- ‘mamasa’ = solid → a solid thing → could be a “word”?\n\nBut it's a noun meaning “solid” — not “word”.\n\nAfter careful analysis: \nThere is no direct or indirect evidence of a word meaning “word” in the provided list.\n\nSo the only theoretically possible translation is based on a root that could be extended — such as **olo** or **pala**, due to their action-based semantics (cutting, piercing) which may be metaphorically extended to linguistic units.\n\nIn many languages, a \"word\" is a \"cut\" or \"piece\" — derived from cutting.\n\nThus, a plausible theoretical translation is **olo**.\n\nBut wait — is “olo” used as a noun?\n\nIn the list, it is only used as “to cut” — verb.\n\nBut could it be used as a countable noun for “a cut”?\n\nPossible.\n\nSimilarly, “pala” is used as “to pierce” — could it be used as “a pierce” → a word?\n\nStill weak.\n\nAlternatively, is there a compound like “a‘öf olo” = end of cut? — nonsense.\n\nNo.\n\nGiven the lack of direct evidence, and the fact that “to exhaust” can be reasonably formed as **fäeag a‘öf** (to use to the end), which mirrors the structure of “a‘öf fau” (end of year), we can reasonably derive that “to exhaust” is **fäeag a‘öf**.\n\nAs for “word”, the only plausible theoretical candidate is a root from a cutting or piercing verb — possibly **olo** or **pala**.\n\nBut the most basic, and inductive, choice is **olo** — since “to cut” is a fundamental action, and a “word” might be seen as a “cut” in a language.\n\nHence:\n\n- d.1 / word: olo \n- d.2 / to exhaust: fäeag a‘öf\n\nBut is “olo” likely to mean “word”?\n\nDouble-check: could “word” be derived from “to encircle”? — ‘ka.lu’ → to encircle → a circular thing → could be a “word” in a ring?\n\nUnlikely.\n\n“door” = nu‘sura → could “word” be like a door? Not clear.\n\n“window” = nu‘s", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13532.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "unit_audit", + "sample_index": 1, + "output": "unit id: d.1 / word \nrequested meaning/value: word \nderived candidate: pala \nevidence: \"pala\" means \"to pierce\" – in many languages, \"to pierce\" may be metaphorically extended to \"to create a hole\" or \"to make a mark\", which might be associated with \"word\" (as words are \"pierced\" into language or inscribed). Also, \"poagpoga = palpala\" means \"covered with holes\" – \"palpala\" is related to \"pala\" (to pierce). \"Word\" may be conceptualized as something pierced or inscribed. No direct word for \"word\" appears in the list, but \"pala\" is the only root that relates to creation or formation through perforation. Though not direct, \"pala\" is the most plausible candidate via analogy.\n\nunit id: d.2 / to exhaust \nrequested meaning/value: to exhaust \nderived candidate: puhra.ki \nevidence: \"puhra.ki\" means \"to boil, to bubble up\" – boiling may symbolize exhaustion, as something is being \"boiled dry\" or \"pumped out\". In metaphorical use, \"to boil\" can mean \"to empty\", \"to deplete\", or \"to exhaust\". No direct word means \"to exhaust\", but \"puhra.ki\" is the only verb involving depletion or overflow. \"To exhaust\" is conceptually similar to \"to boil away\" or \"to consume completely\". This is the only verb with a degenerative or consuming semantic outcome in the data.\n\n\\boxed{d.1: pala; d.2: puhra.ki}", + "generated_tokens": 353, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: pala; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 1302.0, + "ioling_final_answer_chars": 24.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "unit_audit", + "sample_index": 2, + "output": "We are asked to determine the theoretically possible translations of “word” and “to exhaust” into Rotuman, given the provided vocabulary.\n\nStep 1: Look for clues related to “word” \nThe given list includes: \n- “nu‘suar tiro” → window \n- “nu‘sura” → door \n- “mamasa” → solid \n- “ma.titi” → coldness \n- “ma.tit mamasa” → ice \n- “pala” → pierce \n- “piri” → to curl \n- “poagpoga = palpala” → covered with holes \n- “huli” → to turn over \n- “huni” → lower end \n- “pogi” → night \n- “puhra.ki” → to boil, to bubble up \n- “pulu” → glue \n- “ka.lu” → bracelet; to encircle \n- “riamrima” → shiny \n- “rū huga” → stomach-ache \n- “to‘a” → hero \n\nNo direct mention of “word” or “language” or “speech”. However, observe that: \n- “fäeag ‘u‘u” → to use sign language \n- “‘u‘u” appears as a component of a phrase. \n- “‘u‘u” is used in “fäeag ‘u‘u” meaning \"to use sign language\". \n- “sign language” is a form of communication, and may be associated with “word”, especially in the sense of a form of expression. \n- The word “word” may be linked to “sign” or “symbol”, which is already in the data via “sign language”. \n\nBut “word” is a more abstract concept — a unit of language. \nIn the absence of a direct word for “word”, we must consider possible morphological or semantic patterns. \n\nThe phrase “fäeag ‘u‘u” uses the verb “fäeag” (to use) + “‘u‘u” (sign language). \nCould “‘u‘u” be used to form a root meaning “word” or “to speak”? Possibly. \nBut “‘u‘u” is specifically “sign language”. \n\nAlternatively, look at the word “pali” or lexical items associated with “speech”. \nNo clear candidate exists directly. \n\nBut recall: “pala” → pierce; “pala” may be a verb. \nIs there any root that can be expanded to form \"word\"? \n\nAlso note: “poagpoga = palpala” → covered with holes. \nThis may suggest a morphological pattern with compound or formed roots. \n\nBut still, nothing directly yields “word”. \n\nThus, given the absence of a direct lexical item for “word”, and the presence of “sign language” (‘u‘u), one might consider that “word” in a non-literal or conceptual sense (as in “a sign of communication”) could be derived from “‘u‘u” or formed using similar roots. \n\nBut the question asks for a *theoretically possible* translation — not a guaranteed one. \n\nWe must now consider what forms are plausible in Rotuman based on phonology and morphology. \n\nIn Austronesian languages, many abstract concepts are formed via compounding or with prefixed verbs. \n\nGiven “sign language” involves signs, and “words” are a form of signs, it is plausible that “word” could be expressed using a root like “‘u‘u” or a derivative thereof. \n\nBut “‘u‘u” means “sign language”, not a “word”. \n\nAnother possibility: the root “fau” (year) or “fau” appears again in “a‘öf fau” → year’s end. \n\nBut no word meaning “word” appears. \n\nNow, consider if “word” could be derived via a compound using a root meaning “to speak” or “to express”. \n\nWe do have: \n- “pala” → pierce \n- “lala” → deep \n- “ka.lu” → to encircle \n\nBut nothing clearly means “to speak” or “word”. \n\nIn absence of data, the only way to derive a plausible translation is through analogy to known roots. \n\nOne root that might be relevant is “to‘a” → hero. \nBut that is unrelated. \n\nAlternatively, could “word” be expressed via a compound with “mamasa” (solid), “lala” (deep), etc.? Unlikely. \n\nSo, what is the theoretically possible form? \n\nWe may consider that in Rotuman, meaning “word” could be derived from a root related to “speech” or “expression”. \n\nBut the only related item is “sign language” → “fäeag ‘u‘u” \nThus, “‘u‘u” is a root for a sign-based communication. \n\nCould “word” be expressed as a derived form from “‘u‘u”? \n\nPossibly: “‘u‘u” = sign language → each “sign” is a “word”. So a “word” could be “a sign”. \n\nBut that is a stretch. \n\nAlternatively, the root “hün” appears in “hün kia” → base of the neck. \nBut no relevant pattern. \n\nWe must conclude that without explicit vocabulary, the *only* possible derived root related to language is “‘u‘u” or similar. \n\nThus, a theoretically possible translation for “word” could be **‘u‘u** (as in sign, a unit of expression). \n\nBut “‘u‘u” means \"sign language\", not a single word. \n\nAlternatively, maybe “word” could be expressed via “pala” (to pierce), as “piercing” a symbol? Unlikely. \n\nAnother idea: “huli” → to turn over. Does that relate? Not obviously. \n\nAlternatively, consider that “word” might be void of a direct translation, and in absence of data, the only possible derived root that relates to communication is “‘u‘u”. \n\nTherefore, a theoretically possible translation of “word” is **‘u‘u**, as a root for \"sign\", and a sign may be considered a \"word\" in a sign language context. \n\nNow for “to exhaust”: \n\nWhat verbs exist that might mean “to exhaust”? \n\nWe have: \n- “hül ha.fu” → to blow (of a hurricane) \n- “puhra.ki” → to boil, to bubble up \n- “huli” → to turn over \n- “huni” → lower end \n- “pala” → pierce \n- “piri” → to curl \n- “pulu” → glue \n\n“to boil” is a strong candidate for “to exhaust” — boiling can imply depleting or using up. \n\nFor example, \"to boil away\" means to exhaust. \n\n\"Boiling\" implies a process of consuming or expending. \n\nThus, “puhra.ki” → to boil, to bubble up → could be used to represent “to exhaust” in a metaphorical sense. \n\nAdditionally, “to blow” (hül ha.fu) — “to blow out” could also imply to exhaust (e.g., blow out a flame). \n\nSo both “puhra.ki” and “hül ha.fu” might be used metaphorically. \n\nBut which is more likely? \n\n“puhra.ki” is directly a process that can deplete or bubble up in a physically consuming way — more directly related to exhaustion. \n\n“to blow out” could imply exhaustion, e.g., “the fire blew out” → no longer burning → exhausted. \n\nBut “puhra.ki” is broader: to boil up, which can mean to rise violently, to consume. \n\nHowever, in absence of a clear verb for “to exhaust”, the only plausible candidate from given data is “puhra.ki” — as an action that consumes or bubbles up. \n\nCould “to exhaust” be formed from “to blow”? Possibly. \n\nBut “blow” is specifically of a hurricane — which is a storm. \n\nThus, “to blow” (hül ha.fu) is not semantically clear. \n\n“to boil” (puhra.ki) is more general. \n\nTherefore, the most plausible theoretically possible translation of “to exhaust” is “puhra.ki”. \n\nFinal candidates: \n- “word” → ‘u‘u (as a root related to communication/sign) \n- “to exhaust” → puhra.ki (as a verb of consumption/bubbling up) \n\nNote: We cannot be certain due to lack of direct data, but these are the only plausible options based on word formation and meaning. \n\nScratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|--------|--------------------------|-------------------|---------|\n| d.1 / word | word | ‘u‘u | ‘u‘u is in “fäeag ‘u‘u” = to use sign language; sign is a unit of language → a “word” may be a “sign” |\n| d.2 / to exhaust | to exhaust | puhra.ki | puhra.ki = to boil, to bubble up → can metaphorically mean to exhaust (to boil away) |\n\nAll units present, no swaps.\n\n\\boxed{d.1: ‘u‘u; d.2: puhra.ki}", + "generated_tokens": 2009, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: ‘u‘u; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7110.0, + "ioling_final_answer_chars": 24.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "unit_audit", + "sample_index": 3, + "output": "Unit id: d.1 / word \nRequested meaning: \"word\" \nAnalysis: \nThe given list contains no direct word for \"word\". However, some compound words involve the element \"tiro\", which means \"spectacles\", and \"nu‘suar tiro\" means \"window\", suggesting \"tiro\" as a component in other nouns. There is no clear lexical element that directly corresponds to “word” in the list. \n\nBut consider \"pogi\" meaning \"night\", and \"pala\" meaning \"to pierce\". No known \"word\" compounds. \n\nWe look for possible word-formation patterns. In Austronesian languages, borrowing or minimal roots can indicate possibility. The word \"word\" may be derived from verb roots or abstract nouns. \n\nHowever, no root in the list has a semantic field that directly matches \"word\". \n\nBut “to exhaust” is also absent. \n\nLook at “puhra.ki” — “to boil, to bubble up”. This implies processes involving saturation or fullness. \n\n“huli” — “to turn over” \n“ma.tit” — “coldness” \n“ma.tit mamasa” — “ice” \n“mamasa” — “solid” \n“lala” — “deep” \n“pala” — “to pierce” \n“piri” — “to curl” \n\nNo word meaning “to exhaust” is present. \n\nBut “kia” appears in “hün kia” — “base of the neck”. “kia” alone not meaningful. \n\n“huli” could be interpreted as turning over, possibly implying depletion? Unclear. \n\n“moafmofa” — “littered with rubbish” — implies fullness of trash, perhaps overabundance. \n\n“to exhaust” might mean to deplete something, to make empty. \n\nRoots like \"pala\" (to pierce), \"piri\" (to curl), \"huli\" (to turn over) — none show exhaustion. \n\nBut consider: “to exhaust” could be linked to “to fill” or “to fill to capacity”, then “to empty”. \n\nNo known verb means “to exhaust”. \n\n“puhra.ki” — to boil, bubble → implies reaching a limit, potentially the end. \n\n“fau” — year \n“a‘öf fau” — year’s end → “end” is implied. \n\nCould “end” or “limit” be associated with “exhaust”? Possibly. \n\n“kia” might suggest a boundary. \n\nNo direct match. \n\nThus, both “word” and “to exhaust” are not directly attested. \n\nIn Austronesian languages, compounds may be formed by roots. Common semantic fields: things made of material, movement, body parts. \n\n“word” is likely not a primary root, so it may be formed from a compound: e.g., “tiro” (spectacles) — not relevant. “nu‘sura” — door. “pala” — pierce. \n\nBut in absence of any direct link, the only possible forms are hypothetical, based on known roots or common patterns. \n\nStill, we must give theoretically possible translations. \n\nPossible root for “word” — “fa‘a” (common Austronesian root for action), but not in list. \n\nNo root given for “word”. \n\nSimilarly, “to exhaust” may be linked to “to empty”, “to deplete”, “to empty out”. \n\n“huli” — turn over — could imply turning something over until empty? Possible. \n\n“hün kia” — base of neck — no. \n\n“moafmofa” — littered — overfilled, but not emptied. \n\nNo verb means “exhaust”. \n\nHowever, the only verb with a process that can extend to fullness or end is “puhra.ki” — to boil up to the top — which may imply reaching a limit. \n\nThus, a possible candidate for “to exhaust” is “puhra.ki” — if interpreted as reaching the peak of a state. \n\nBut that’s weak. \n\nAlternatively, consider that “to exhaust” could be derived from a verb of fullness or overflow. \n\nIn Rotuman, lack of evidence for direct root means the theoretical possible translation must be based on plausible compounds or known structure. \n\nGiven no evidence, and lack of lexical data, the only theoretical possible translations are hypothetical root compounds. \n\nBut the question asks: “what would the theoretically possible translations be?” \n\nThus, we infer from pattern: \n\n- \"word\" may be related to \"pala\" (to pierce) — strange. \n- \"word\" may be related to \"tiro\" — spectacles — unclear. \n\nAlternatively, in many Austronesian languages, \"word\" is derived from a root like “mā” or “lau” — not present. \n\nNo evidence. \n\nStill, possible: word might be formed from “pala” and “niu” (copra) — not directly. \n\nNo meaningful compound. \n\nBut perhaps “hua” or “huga” — stomach-ache — not related. \n\nNo reliable compound. \n\nBut observe: “riamrima” — shiny, “pala” — pierce, “piri” — curl. \n\nNo root for “word”. \n\nThus, the only theoretically possible translation of “word” is a constructed root like “pala” or “tiro”, but neither fits. \n\nAlternatively, possibly “ta‘a” — not present. \n\nTherefore, with no evidence, the only possible theoretical translation is to use a root that implies a unit of discourse — perhaps “fau” — year — “fau” could be a unit, but not a word. \n\nNo. \n\nBut consider: “ha.fha.fu” — rocky — not relevant. \n\nAfter extensive analysis, no root in the list supports \"word\" or \"to exhaust\". \n\nThus, the theoretically possible translation is inferred via pattern-based construction using known elements: \n\nFor “word” — no candidate in list. But “word” may be related to “to express” — not in list. \n\n“pala” — to pierce — could imply a “mark” or “sign” — fitting for “word” as a word is a sign? \n\n“fäeag ‘u‘u” — to use sign language — so “sign” is possible. \n\n“fäeag ‘u‘u” implies the use of signs — and “sign” can be a synonym for “word” in some contexts. \n\nThus, “sign” could be a possible root. \n\nIs there a root for “sign”? “fäeag” — to use — “u‘u” — sign language. \n\n“u‘u” might be the root for “sign”. \n\nSo “u‘u” could be a candidate for \"word\", as “sign” is a common synonym. \n\nThus, “u‘u” — could theoretically serve as a translation for “word” in Rotuman. \n\nSimilarly, “to exhaust” — could be linked to “to boil”, “to bubble” — “puhra.ki” — which implies reaching end or limit. \n\nThus, “puhra.ki” might be used for “to exhaust” (to reach end, to deplete). \n\nThis is speculative but pattern-supported. \n\nEvidence: \n- “a‘öf fau” — year’s end → \"end\" is a known concept. \n- “puhra.ki” — to boil, to bubble up → implies fullness, reaching end. \n- “u‘u” — in “fäeag ‘u‘u” — sign language → \"sign\" is a synonym for \"word\". \n\nTherefore: \n- d.1 / word: u‘u \n- d.2 / to exhaust: puhra.ki \n\nThese are the only theoretically plausible translations based on known expressions and semantic fields.\n\n\\boxed{d.1: u‘u; d.2: puhra.ki}", + "generated_tokens": 1707, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: u‘u; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 6123.0, + "ioling_final_answer_chars": 23.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 0, + "output": "We are given a list of Jaqaru words and their English translations. The goal is to translate three specific Jaqaru phrases into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe will use the provided examples to infer the morphological and syntactic patterns.\n\n---\n\n### Step 1: Identify known forms and their meanings\n\nFrom the given:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- chushuntxi = is it in the corner? \n- marka = the town \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- utamt”a = from your house \n- utnha = my house \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n\n---\n\n### Step 2: Identify patterns in adjective/noun + verbal or locative structure\n\nLook at the structure of words with \"is\" or \"is it\" questions:\n\n- chushuntxi = is it in the corner? → \"chushp”a\" (corner) + \"untxi\" → \"is it in the [corner]?\" \n- markstxi = is it our1+2 town? → \"marka\" (town) + \"stxi\" → \"is it [our] town?\" \n- yaputxi = is it the field? → \"yap\" + \"utxi\" → \"is it the field?\" \n- yapsanpsa = in our1+2 field too → \"yap\" + \"sanpsa\" → \"in our1+2 field too\"\n\nSo — it appears that **\"untxi\"** and **\"stxi\"** and **\"utxi\"** are markers of questions like \"is it in X?\" \nLikewise, **\"sanpsa\"** and **\"npsa\"** look like locative/descriptive additions.\n\nBut more importantly, we notice the pattern:\n\n- \"in the cave\" = aq”na \n- \"in our1+2 lake too\" = qucxst”psa \n- \"in our1+2 field too\" = yapsanpsa \n- \"my house\" = utnha \n- \"my pot too\" = p”ak”unhpsa \n- \"from his town\" = markp”t”a \n- \"from your house\" = utamt”a \n- \"from our1+2 lake too\" = qucxst”psa \n- \"from our1+2 town\" = markstxi? Wait — markstxi is \"is it our1+2 town?\" — not \"from our1+2 town\"\n\nWait: \"markp”t”a\" = from his town → \"marka\" (town) + \"p”t”a\" → \"from his town\" \n\"utamt”a\" = from your house → \"utnha\" (my house) → but with pragmatic shift? \nBut \"utnha\" = my house → so \"utamt”a\" = from your house → so \"utnha\" becomes \"utam\" (from) + \"t”a\" → from your house?\n\n\"p”ak”u\" = the pot \n\"p”ak”unhpsa\" = my pot too → \"p”ak”u\" + \"unhpsa\" → \"my pot too\"\n\nSimilarly: \n\"aq”ipsa\" = the cave too → \"aq”ipsa\" \n\"aq”na\" = in the cave\n\nAh! \"unhpsa\" = \"my + too\" → like \"my pot too\"\n\nAlso: \n\"yapsanpsa\" = in our1+2 field too → \"yap\" (field) + \"sanpsa\" → \"in our1+2 field too\"\n\nLikewise: \n\"qucxst”psa\" = from our1+2 lake too → \"qucxap”a\" (through the lake?) → possibly \"qucx\" (lake) + \"st”psa\" → from our1+2 lake too?\n\nBut \"qucxap”a\" = through the lake — perhaps a locative verb? \n\"qucxst”psa\" = from our1+2 lake too → so \"st”psa\" = from our1+2 lake too?\n\nCompare: \n\"markstxi\" = is it our1+2 town? \n\"chushuntxi\" = is it in the corner?\n\nSo when a noun has \"untxi\", it is \"is it in X?\" \nWhen a noun has \"stxi\", it is \"is it our1+2 X?\" → like \"is it our town?\" \nWhen a noun has \"npsa\", it is \"in our1+2 X too\"\n\n\"yapsanpsa\" = in our1+2 field too \n\"qucxst”psa\" = from our1+2 lake too\n\nSo: \n- \"npsa\" = in our1+2 X too \n- \"st”psa\" = from our1+2 X too \n- \"untxi\" = is it in X?\n\nAlso, possessive markers:\n\n- \"my\" → appears in: utnha, p”ak”unhpsa \n- \"your\" → utamt”a \n- \"his\" → markp”t”a \n- \"our1+2\" → appears in questions and locatives\n\nNow look at question (a):\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa\n\n---\n\n### Unit 1: utnhantxi\n\n\"utnha\" = my house → so \"utnhantxi\" → likely \"is it in my house?\" \nBecause: chushuntxi = is it in the corner? → corner is a noun, \"untxi\" = is it in X?\n\nSo: \n\"utnhantxi\" = is it in my house?\n\nSimilarly: \n\"ishinhna\" = in my bed → so \"untxi\" would be \"is it in my bed?\" → not directly given, but possible.\n\nSo by analogy: \nutnhantxi → is it in my house?\n\n✅ Evidence: chushuntxi = is it in the corner? → so \"untxi\" = is it in X?\n\n\"utnha\" = my house → so \"utnhantxi\" = is it in my house?\n\n---\n\n### Unit 2: yapp”psa\n\n\"yap\" = field? Because \"yaputxi\" = is it the field? \nSo \"yap\" = field → \"yapp”psa\" = ? \nWe have: \"yapsanpsa\" = in our1+2 field too → so \"sanpsa\" = in our1+2 too\n\nWhat about \"p”psa\"? \n\nCompare: \n\"p”ak”unhpsa\" = my pot too → \"unhpsa\" = my + too \n\"yap\" + \"p”psa\" = ?\n\nDo we have any word with \"p”psa\"?\n\nNote: \n\"utnha\" = my house \n\"utamt”a\" = from your house \n\"marka\" = the town \n\"markp”t”a\" = from his town\n\nSo has \"p”t”a\" = from his town → \"p”t”a\" is a locative form?\n\n\"p”psa\" might be similar.\n\n\"yapsanpsa\" = in our1+2 field too → \"sanpsa\" = in our1+2 too\n\nWhat about \"yapp”psa\"? Could it be \"in our1+2 field\" or \"the field\"?\n\nBut \"yap\" = field → so \"yap\" + \"p”psa\"?\n\nCompare \"p”ak”unhpsa\" = my pot too → \"unhpsa\" = my + too\n\n\"markstxi\" = is it our1+2 town?\n\nIs there a word like \"in our1+2 field\"?\n\nYes — \"yapsanpsa\" = in our1+2 field too.\n\n\"yapp”psa\" → perhaps \"the field\" with \"p”psa\" as a possessive or locative?\n\nWait — is there a pattern where a noun + a marker means \"in our1+2 X\"?\n\nYes: \n- yapsanpsa = in our1+2 field too \n- qucxst”psa = from our1+2 lake too \n- markstxi = is it our1+2 town?\n\nSo \"sanpsa\" = in our1+2 X too \n\"st”psa\" = from our1+2 X too \n\"untxi\" = is it in X?\n\nSo \"p”psa\" is not one of these.\n\nCould \"p”psa\" mean \"my field\"? Like \"yap\" + \"p”psa\"?\n\nWe have: \n\"p”ak”u\" = the pot \n\"p”ak”unhpsa\" = my pot too \n\nSo \"unhpsa\" = my + too → so \"p”psa\" might be \"my\"?\n\nBut \"p”psa\" is not \"unhpsa\" → different suffix.\n\n\"yap\" + \"p”psa\" → perhaps \"my field\"?\n\nBut we don’t have that.\n\nAlternatively, could it be \"in the field\"?\n\nBut \"yaputxi\" = is it the field?\n\nNo equivalent for \"in the field\".\n\nBut we have: \n\"yapsanpsa\" = in our1+2 field too\n\nSo if \"sanpsa\" = in our1+2 too → then \"p”psa\" might be something else.\n\nBut look: \"yap\" + \"p”psa\" — what about the connection to \"yapsanpsa\"?\n\n\"yapsanpsa\" → field + sanpsa \n\"yapp”psa\" → field + p”psa\n\nOnly difference is \"p”psa\" vs \"sanpsa\"\n\nBut \"p”psa\" is not clearly a locative.\n\nWait — check if \"p”psa\" is derived from \"unhpsa\"\n\n\"unhpsa\" = my pot too → could be \"my + too\" → where \"unh\" = my, \"psa\" = too?\n\nBut \"p”psa\" is not \"unhpsa\" — \"unh\" vs \"p”\"\n\nAlternative: perhaps \"p”psa\" means \"in the field\"?\n\nBut \"yaputxi\" = is it the field?\n\nNo.\n\nAnother idea: look at \"qucxap”a\" = through the lake \n\"qucxst”psa\" = from our1+2 lake too → so \"st”psa\" = from our1+2 \n\nSimilarly, \"markstxi\" = is it our1+2 town? → so \"stxi\" = is it our1+2?\n\n\"markp”t”a\" = from his town → so \"p”t”a\" = from his\n\nSo \"p”psa\" → could be from his field? Or \"in the field\"?\n\nBut no such word given.\n\nWait — let's look at the third word.\n\n---\n\n### Unit 3: yapup”psa\n\n\"yap\" = field → \"yapup”psa\" → \"yap\" + \"up”psa\"\n\nCompare: \n\"yaputxi\" = is it the field? \n\"yapsanpsa\" = in our1+2 field too \n\"yapp”psa\" = ?\n\n\"yapup”psa\" — what is \"up”psa\"?\n\nCompare: \"p”ak”unhpsa\" = my pot too → \"unhpsa\" = my + too\n\n\"utnhantxi\" = is it in my house?\n\nSo \"up”psa\" — could it be \"in our1+2\"?\n\nBut we already have \"sanpsa\" as \"in our1+2 X too\"\n\nSo why is \"sanpsa\" used in \"yapsanpsa\", but not here?\n\nAnother pattern: the suffix \"-npsa\" is used for \"in our1+2 X too\" \n\"st”psa\" = from our1+2 X too \n\"untxi\" = is it in X?\n\nSo the suffix \"npsa\", \"st”psa\", \"untxi\" are only attached to nouns.\n\nNow \"yapp”psa\" and \"yapup”psa\" — both contain \"p”psa\" and \"up”psa\"\n\n\"up”psa\" — could it be \"my\"?\n\n\"utnha\" = my house \n\"utamt”a\" = from your house \n\"markp”t”a\" = from his town\n\nIn \"p”ak”unhpsa\" = my pot too → \"unh\" = my\n\nSo \"up”psa\" might be \"in my field\"? Like \"in my field\" = \"up”psa\"?\n\nBut no direct evidence.\n\nWait — what if the pattern is:\n\n- \"untxi\" → is it in X? \n- \"npsa\" → in our1+2 X too \n- \"st”psa\" → from our1+2 X too \n- \"unh\" → my \n- \"p”t”a\" → from his \n- \"utam\" → from your?\n\nBut in the target words:\n\n1. utnhantxi → utnha (my house) + antxi → probably \"is it in my house?\" \n→ supports \"untxi\" = is it in X?\n\n2. yapp”psa → yap (field) + p”psa → could it be \"my field\"? → \"p”psa\" = my? \nBut \"unh\" = my — not \"p”\" → so unlikely.\n\n3. yapup”psa → yap (field) + up”psa → could it be \"in my field\"? → \"up”psa\" = in my?\n\nNo clear parallel.\n\nAlternative: could \"p”psa\" and \"up”psa\" be errors or different forms?\n\nBut let's look back: is there a word like \"in my field\"?\n\nWe have: \"ishinhna\" = in my bed \n\"ishma\" = your bed \n\"p”ak”unhpsa\" = my pot too \n\"utnha\" = my house\n\nSo \"in my bed\" exists — \"ishinhna\" → in my bed\n\nSo perhaps \"in my field\" would be similar?\n\nSo if we have a word structure: [noun] + [possessive] + [locative marker]?\n\nBut the pattern seems to be:\n\n- Nouns can be modified with:\n - possessive markers: my, your, his, our\n - locative: in, from, is it in\n - or multiple elements like \"too\"\n\nSpecifically:\n\n- \"p”ak”unhpsa\" = my pot too → \"unh\" = my, \"psa\" = too\n- \"yapsanpsa\" = in our1+2 field too → \"npsa\" = in our1+2 too\n- \"qucxst”psa\" = from our1+2 lake too → \"st”psa\" = from our1+2 too\n- \"markstxi\" = is it our1+2 town? → \"stxi\" = is it our1+2?\n\nSo the suffix \"psa\" appears in:\n\n- \"unhpsa\" → my + too\n- \"npsa\" → in our1+2 too\n- \"st”psa\" → from our1+2 too\n- \"psa\" alone? → maybe in \"yapp”psa\"\n\nSo \"p”psa\" might be a possessive form.\n\nBut what possessive?\n\n\"yap\" = field\n\n\"yapp”psa\" — could be \"in the field\" or \"my field\"?\n\nBut \"yaputxi\" = is it the field?\n\nNo equivalent for \"in the field\".\n\nUnless \"yapp”psa\" = in the field?\n\nBut we have \"yapsanpsa\" = in our1+2 field too — which is more specific.\n\nAnother idea: perhaps \"p”psa\" = in the field \n\"up”psa\" = in the field too?\n\nBut \"yapsanpsa\" = in our1+2 field too — so \"too\" is added.\n\n\"p”psa\" might be \"the field\" (without possessor, no \"too\")\n\nBut \"yaputxi\" = is it the field?\n\nSo \"yap\" = field\n\nSo \"yapp”psa\" = the field? \n\"yapup”psa\" = the field too?\n\nBut no such word in the list.\n\nWait — in \"aq”ipsa\" = the cave too → \"ipsa\" = the cave too\n\n\"p”ak”unhpsa\" = my pot too\n\nSo \"too\" is marked by suffix \"psa\"?\n\nIn \"aq”ipsa\" = the cave too → \"ipsa\" \nIn \"p”ak”unhpsa\" = my pot too → \"unhpsa\"\n\nSo \"psa\" appears when \"too\" is indicated.\n\nSimilarly: \n\"qucxst”psa\" = from our1+2 lake too → \"st”psa\"\n\n\"yapsanpsa\" = in our1+2 field too → \"sanpsa\"\n\nSo \"psa\" = \"too\"\n\nTherefore, in:\n\n1. utnhantxi → utnha (my house) + antxi → \"is it in my house?\" → \"antxi\" = in? \n2. yapp”psa → yap (field) + p”psa → \"field too\"? \n3. yapup”psa\" → yap + up”psa → \"field too\"?\n\nBut \"p”psa\" and \"up”psa\" — both end in \"psa\", so both mean \"too\"?\n\nBut with different nuclei.\n\nCould \"p”psa\" and \"up”psa\" be equivalent to \"in our1+2\" or \"my\"?\n\nBut earlier, \"in our1+2\" is marked by \"npsa\".\n\n\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10435.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 1, + "output": "We are given Jaqaru words and their English translations. Our task is to translate three new words into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe must infer the linguistic pattern from the provided examples.\n\n---\n\nFirst, observe the structure of the given examples:\n\n- aq”ipsa → \"the cave too\" \n- aq”na → \"in the cave\" \n- qucxap”a → \"through the lake\" \n- qucxst”psa → \"from our1+2 lake too\" \n- chushp”a → \"his corner\" \n- chushuntxi → \"is it in the corner?\" \n- marka → \"the town\" \n- markp”t”a → \"from his town\" \n- markstxi → \"is it our1+2 town?\" \n- ishinhna → \"in my bed\" \n- ishma → \"your bed\" \n- utamt”a → \"from your house\" \n- utnha → \"my house\" \n- p”ak”u → \"the pot\" \n- p”ak”unhpsa → \"my pot too\" \n- yaputxi → \"is it the field?\" \n- qaqat”a → \"from the cliff\" \n- yapsanpsa → \"in our1+2 field too\"\n\nNow, observe how compounds are formed — especially the use of suffixes and how questions are formed.\n\n### Step 1: Identify affix patterns\n\nLook at the syntactic structure:\n\n- \"in the cave\" = aq”na \n → \"in\" is likely a preposition, and \"cave\" is root aq”ipsa \n → aq”ipsa + na → \"in the cave\"\n\n- \"from the lake\" = qucxap”a → \"through the lake\"? That seems inconsistent.\n\nWait: qucxap”a = \"through the lake\" \nBut qucxst”psa = \"from our1+2 lake too\"\n\nSo \"from\" appears in qucxst”psa — which has suffix -st”psa, possibly derived from a root with \"our1+2\" and \"-too\"\n\nSimilarly:\n- markp”t”a = \"from his town\" → marka = \"town\", p”t”a = \"his\" \n- markstxi = \"is it our1+2 town?\" → marka + stxi → \"is it our1+2 town?\" \n- utamt”a = \"from your house\" → utnha = \"my house\", t”a = \"your\" \n- p”ak”unhpsa = \"my pot too\" → p”ak”u = \"the pot\", unhpsa = \"my too\"? \n- yaputxi = \"is it the field?\" → yapu = field, txi = question marker? \n- yapsanpsa = \"in our1+2 field too\" → yapsa = field, nanpsa = \"in our1+2 too\"?\n\nAlso, notice:\n- ishinhna = \"in my bed\" → ishi = my bed? ishinhna → infix + na = in? \n- ishma = \"your bed\" \n- utnha = \"my house\" \n- p”ak”unhpsa = \"my pot too\" → pot + unhpsa → \"my too\" \n\nSo pattern: \n- Possessive markers: \n - -na → \"in\" (as in aq”na) \n - -t”a → \"his\", \"your\", \"my\"? \n - chushp”a → \"his corner\" \n - markp”t”a → \"from his town\" \n - utamt”a → \"from your house\" \n - utnha → \"my house\" \n → So -t”a seems to mark possessive with the first-person (my), second (your), third (his) \n - But \"his\" is -p”t”a? chushp”a → chush + p”a → \"his corner\" \n So \"p”a\" = his? \"p”t”a\" = your? \n - markp”t”a → from his town → \"mark\" + \"p”t”a\" \n - So \"p”t”a\" = your, \"p”a\" = his? Not consistent.\n\nWait — look at possessive markers:\n\n- chushp”a → his corner → p”a \n- markp”t”a → from his town → p”t”a \n→ This suggests a morpheme that changes depending on person.\n\nBut also: \n- ishinhna → in my bed → ishi + in? \n- ishma → your bed \n- utnha → my house \n- p”ak”unhpsa → my pot too\n\nSo: \n- my → utnha (house), utnha → \"my house\" \n- \"my\" appears in utnha, so likely \"my\" is marked by a root with -nha \n- double marker: p”ak”unhpsa → \"my pot too\" → p”ak”u + unhpsa \n → \"unhpsa\" = \"my too\"? \n → similar to aq”ipsa + \"too\" → aq”ipsa + psa → \"the cave too\" \n → aq”ipsa + psa → \"the cave too\" \n → aq”na → in the cave \n → aq”ipsa + psa → \"the cave too\" \n So -psa = \"too\"\n\nSimilarly: \n- qucxst”psa = \"from our1+2 lake too\" → qucxap”a = through lake? \n But qucxst”psa = from our1+2 lake too → -st”psa? \n qaqat”a = from the cliff \n yapsanpsa = in our1+2 field too → \"in\" + \"our1+2 field too\" \n → so \"in\" is a preposition \n → -npsa → \"in too\"? or \"in our1+2 too\"? \n\nHold on: \n- \"in our1+2 field too\" = yapsanpsa \n- \"is it the field?\" = yaputxi \n- \"in our1+2 field too\" → yapu + anpsa → seems like \"anpsa\" = \"in our1+2 too\" \n\nAlso: \n- markstxi = \"is it our1+2 town?\" → marka + stxi → \"is it our1+2 town?\" \n- yaputxi = \"is it the field?\" → yapu + txi \n→ so \"txi\" = question marker → \"is it...?\"\n\nThus, we infer:\n- txi → question marker → \"is it X?\"\n- psa → \"too\"\n- anpsa → \"in our1+2 too\" or \"in the field too\"\n- na → in\n- t”a → possessive (your, his, my)\n\nNow examine:\n\n1. utnhantxi \n→ utnha = my house → so utnha + txi → \"is it my house?\"\n\n2. yapp”psa \n→ yapu + p”psa \n→ yapu = field? → in \"is it the field?\" = yaputxi → so yapu = field \n→ p”psa → ? \n→ look for patterns: \n- aq”ipsa → the cave → aq”ipsa \n- aq”ipsa + psa → the cave too \n→ psa = too \n- qucxst”psa = from our1+2 lake too → from + our1+2 lake + too \n→ so psa = too \n\nSo p”psa → possibly \"too\" \nBut with what? \nyapp”psa → field + too? → \"the field too\"?\n\nSimilarly: \n3. yapup”psa → yapu + up”psa → \"the field too\"?\n\nBut why p”psa vs up”psa?\n\nWait — compare: \n- yapsanpsa = in our1+2 field too → yapu + sanpsa \n→ sanpsa = in our1+2 too? \n→ so \"sanpsa\" = \"in our1+2 too\"\n\nBut is there a marker for \"too\" in different forms?\n\nCheck: \n- p”ak”unhpsa = my pot too → p”ak”u + unhpsa → \"my pot too\" \n→ unhpsa → my too? \n→ doesn't match aq”ipsa + psa \n\nBut aq”ipsa + psa = \"the cave too\" → so psa = too \n\nSo probably: \n- addition of -psa = \"too\"\n\nNow, yapp”psa → yapu + p”psa → \"the field too\"? \nyapup”psa → yapu + up”psa → \"the field too\"? \nIs there a difference?\n\nLook at the other \"too\" examples:\n\n- aq”ipsa + psa → \"the cave too\" \n- qucxst”psa → \"from our1+2 lake too\" → qucxst”psa = from our1+2 lake too → so -st”psa → includes \"too\" \n- yapsanpsa → \"in our1+2 field too\" — again, includes \"too\"\n\nSo -psa appears to be the \"too\" suffix.\n\nBut in yapp”psa, is it \"the field too\"? \nSimilarly, yapup”psa?\n\nBut why two variations?\n\nWait: \nIs there a distinct form of \"too\"?\n\nAnother idea: maybe the suffix is attached at different positions.\n\nCompare: \n- p”ak”unhpsa → \"my pot too\" → likely \"unhpsa\" = \"my too\" \n- aq”ipsa + psa → \"the cave too\" → so psa = too \n→ perhaps the suffix -psa is used across cases \n→ but in p”ak”unhpsa, \"unhpsa\" may be a possessive + too\n\nAlternatively, look at the structure of other compounds:\n\n- chushuntxi → \"is it in the corner?\" → chushp”a → his corner → chushuntxi → \"is it in the corner?\" \n→ so \"untxi\" = \"in the corner?\" \n→ txi = question \n→ \"in\" is marked as \"un\"? \"untxi\" → perhaps \"un\" = \"in\"? \n→ aq”na → \"in the cave\" → na = in \n→ so \"un\" may not be in, unless it's a variant\n\nBut ishinhna = \"in my bed\" → ishi + in? \n- probably ishi = my bed → no, ishma = your bed \n- ishinhna = in my bed → so ishi + in? \n- so \"in\" appears as \"na\" or \"nh\"?\n\nWait — aq”na = in the cave \n- ishinhna = in my bed → contains \"inh\" — could \"in\" be \"inh\"? \n- na → \"in\", inha → \"in\" with possession?\n\nBut ishinhna: i- + shin + hna? Doesn't match.\n\nAlternatively, perhaps \"in\" is a suffix: \n- aq”na = \"in the cave\" \n- ishinhna = \"in my bed\" → \"shi\" + \"inhna\"? \n→ ishinhna → ish + inha → could be \"my bed in\" — doesn't make sense\n\nBetter: perhaps \"in\" is part of a prefix.\n\nAlternatively, observe that:\n\n- markstxi = \"is it our1+2 town?\" \n- yaputxi = \"is it the field?\" \n- chushuntxi = \"is it in the corner?\" \n→ so txi = \"is it X?\" → question about existence \n\nThus: \n- txi → question form → \"is it X?\"\n\nThus:\n\n1. utnhantxi → utnha + txi → \"is it my house?\"\n\n2. yapp”psa → yapu + p”psa → yapu = field, p”psa = too → \"the field too\"\n\n3. yapup”psa → yapu + up”psa → \"the field too\"?\n\nBut why different suffix?\n\nWait — p”psa vs up”psa → only difference is the position of the p” and \"up\"\n\nBut there is no other example with \"up\" or \"p”psa\".\n\nBut in the root: \n- aq”ipsa → \"the cave\" \n- aq”ipsa + psa → \"the cave too\" → psa only \n\nIn p”ak”unhpsa → \"my pot too\" → this seems like \"unhpsa\" = \"my too\" \n→ but \"unhpsa\" may be \"un\" + \"hpsa\" — could \"hpsa\" be something else?\n\nBut we have no example of \"up”psa\"\n\nLook at yapsanpsa = \"in our1+2 field too\" → \"yapu\" + \"sanpsa\" \n→ sanpsa → \"in our1+2 too\" \n→ so \"sanpsa\" = in + our1+2 + too? \n→ so \"anpsa\" = in + too? \n→ but \"psa\" = too\n\nSo the suffix -psa = \"too\"\n\nThus, yapp”psa = \"field too\" \nyapup”psa = \"field too\" — same?\n\nBut is there a difference?\n\nNote: in \"yaputxi\" → \"is it the field?\" → so yapu + txi \n- txi = question \n- p”psa → if p” is a possessive, but no evidence \n\nWait: could \"p”\" be a possessive?\n\nchushp”a → \"his corner\" → p”a = his \nmarkp”t”a → \"from his town\" → p”t”a → his? \nBut in \"markp”t”a\", it's p”t”a → not p”a \n\nBut chushp”a = chush + p”a → his \nmarkp”t”a = mark + p”t”a → his? \n→ so p”t”a = his? \n→ so the possessive marker depends on the noun? \n\nBut p”a and p”t”a — t”a might be distinct.\n\nBut in our target:\n\nyapp”psa → no possessive, just field + too \nyapup”psa → same?\n\nBut both seem to be field too.\n\nIs there a named pattern?\n\nLook at the root:\n\n- yapu = field (from yaputxi = \"is it the field?\")\n\nThus:\n\n1. utnhantxi = utnha + txi → \"is it my house?\" \n2. yapp”psa = yapu + p”psa → \"the field too\" \n3. yapup”psa = yapu + up”psa → \"the field too\"?\n\nBut why two forms?\n\nWait — could it be a typo or variation of the same suffix?\n\nAlternatively, could \"p”psa\" and \"up”psa\" be different?\n\nBut the only other \"too\" is in:\n\n- aq”ipsa + psa → the cave too → psa = too \n- qucxst”psa → from our1+2 lake too → st”psa → perhaps st”psa = too? \n- yapsanpsa → in our1+2 field too → sanpsa → includes too\n\nSo the suffix -psa appears multiple times.\n\nThus, likely all forms with -psa mean \"too\".\n\nTherefore:\n- yapp”psa = field + too → \"the field too\"\n- yapup”psa = field + too → \"the field too\"\n\nBut that's the same meaning.\n\nBut perhaps one is possessive?\n\nex: \"your field too\"?\n\nBut no evidence.\n\nStill, in yapp”psa — is p” a possessive?\n\np” appears in:\n- p”ak”u → the pot \n- p”ak”unhpsa → \"my pot too\"\n\nSo p”ak”u → p”ak”u → the pot \np”ak”unhpsa → p”ak”u + unhpsa → \"my pot too\" — so \"unhpsa\" may be \"my too\"\n\nSo no \"p”psa\" instance — it's a new form.\n\nSo yapp”psa → yapu + p”psa → likely \"the field too\"\n\nSimilarly, yapup”psa → field + up”psa → possibly same?\n\nBut let's go back to the question: \nIs there any clue about possessive in 'p”'?\n\nNo — in the given, p” appears as part of root (p”ak”u), and in possession only in \"unhpsa\"\n\nSo likely yapp”psa and yapup”psa both mean \"the field too\"\n\nBut perhaps one is different.\n\nWait — could \"p”psa\" be \"too\" and \"up”psa\" be something else?\n\nBut no pattern.\n\nAnother idea: the suffix is attached to the root. \nIn aq”ipsa + psa → \"the cave too\" \nSo root + psa = \"too\"\n\nSimilarly, yapu + psa = \"field too\"\n\nThus, both yapp”psa and yapup”psa have the suffix psa.\n\nBut they differ in the position of the p” — one has p” before psa, one after?\n\nyapp”psa → yap + p” + psa → root yap + p” + psa \nyapup”psa → yapu + up”psa → yapu + up” + psa\n\nBut \"yapu\" is the root — from \"yaputxi\" = is it the field? → yapu = field\n\nSo yapu = field\n\nThus:\n\n- yapp”psa = field + p” + psa → \"field + p” + too\" → if p” = possessive, \"your field too\"? \n- yapup”psa = field + up” + psa → \"field + up” + too\" → could be a different possessive?\n\nBut no evidence.\n\nStill, in the examples, the only possessive markers are:\n- na → in \n- -t”a → his, your, my? \n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10888.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by analyzing the provided Jaqaru-English word pairs to infer the grammatical pattern.\n\nKey observations:\n\n1. The structure often involves:\n - A noun (e.g., \"cave\", \"lake\", \"corner\", \"town\", \"house\", \"field\")\n - A possessive or locational marker (e.g., \"our1+2\", \"his\", \"my\", \"your\")\n - A verb of inquiry such as \"is it?\" (e.g., \"is it in the corner?\", \"is it our town?\")\n\n2. Look for patterns in the presence of \"psa\" or \"txi\":\n - \"qucxap”a\" = \"through the lake\"\n - \"qucxst”psa\" = \"from our1+2 lake too\"\n - \"markstxi\" = \"is it our1+2 town?\"\n - \"yaputxi\" = \"is it the field?\"\n - \"yapsanpsa\" = \"in our1+2 field too\"\n\n→ \"txi\" appears in questions: \"is it X?\" \n→ \"psa\" appears in locative or adverbial clauses, often with \"too\"\n\n3. Possession:\n - \"our1+2\" appears as a group (likely plural inclusive)\n - \"his\" → chushp”a, chushuntxi\n - \"my\" → ishinhna, p”ak”unhpsa, p”ak”u, utnhpsa, utnha\n - \"your\" → ishma, utamt”a\n\n4. Look at compound forms:\n - \"p”ak”u\" = the pot\n - \"p”ak”unhpsa\" = my pot too → \"unh\" likely = \"my\", \"psa\" = \"too\"\n - \"utnha\" = my house\n - \"utamt”a\" = from your house\n - \"utnhantxi\" = ? → possibly \"is it my house?\"\n\nCompare:\n- \"markstxi\" = \"is it our1+2 town?\"\n- \"yaputxi\" = \"is it the field?\"\n- \"utnhantxi\" → likely \"is it my house?\"\n\nCheck \"yapp”psa\":\n- \"p”ak”u\" = the pot\n- \"p”ak”unhpsa\" = my pot too\n- \"yapp”psa\" → similar to \"yaputxi\" = \"is it the field?\"\n→ \"yapp”\" may be \"is it the pot?\" OR \"is it my pot?\"\n\nBut \"yapp”\" does not have \"unh\" → so more likely \"is it the pot?\"\n\nSimilarly, \"yapup”psa\" = \"is it the pot too?\"\n\nNow, note:\n- \"p”ak”unhpsa\" = my pot too → \"unh\" = my, \"psa\" = too\n- \"yaputxi\" = is it the field?\n- \"yapsanpsa\" = in our1+2 field too → \"in\", \"our\", \"too\"\n\nThus:\n- \"psa\" = \"too\" in a locative or additive sense\n- \"txi\" = \"is it?\"\n\nSo:\n- \"utnhantxi\" = is it my house?\n- \"yapp”psa\" = is it the pot?\n- \"yapup”psa\" = is it the pot too?\n\nBut \"yapup”psa\" → \"up”\" instead of \"p”\"? Is this a typo?\n\nWait — original pair: \"yapup”psa\" → likely a typo or mis-rendering?\n\nBut in the original: \n\"yaputxi\" = is it the field? \n\"yapsanpsa\" = in our1+2 field too \n\nSo \"yapup”psa\" → perhaps is it the pot too?\n\nBut \"yapp”psa\" has \"p”\" while \"yapup”psa\" has \"up”\"\n\nPossibility: only one \"p”\" → consonant alternation?\n\nCompare:\n- p”ak”u → pot\n- p”ak”unhpsa → my pot too → \"unh\" + \"psa\"\n- yapp”psa → could be \"is it the pot?\" → \"yap\" + \"p”\" + \"psa\"?\n- yapup”psa → \"is it the pot too?\"\n\nAssume:\n- all forms with \"txi\" = \"is it X?\"\n- all forms with \"psa\" = \"too\" in some sense, like additive or locative\n\nSo:\n1. utnhantxi → \"is it my house?\"\n2. yapp”psa → \"is it the pot?\"\n3. yapup”psa → \"is it the pot too?\"\n\nBut is there a marker for \"my\" in \"yapp”psa\"? No.\n\n\"utnha\" = my house \n\"utnhantxi\" = is it my house?\n\nYes — consistent.\n\n\"p”ak”u\" = the pot \n\"yapp”psa\" → \"is it the pot?\" → \"yap\" = is it, \"p”\" = pot?\n\nBut \"yaputxi\" = is it the field?\n\nSo yes — \"yap\" + noun = \"is it [noun]?\"\n\nAnd \"psa\" adds \"too\"\n\nSo \"yapup”psa\" → is it the pot too?\n\nBut is there a difference between \"yapp”psa\" and \"yapup”psa\"?\n\n\"p”\" vs \"up”\" → can \"up”\" be a variant?\n\nAlternatively, could \"p”\" be part of the root?\n\nIn \"yaputxi\", it's \"yap\" + \"utxi\" → no, it's \"yaputxi\" = \"is it the field?\"\n\nThus, \"yap\" + X = \"is it X?\"\n\nThus:\n- yapp”psa = is it the pot?\n- yapup”psa = is it the pot too?\n\nBut \"p”\" and \"up”\" — is \"up”\" a different form?\n\nPossibly a typo. Let’s check original list:\n\nGiven:\n- yaputxi: is it the field?\n- yapsanpsa: in our1+2 field too\n\nSo \"yap\" + [noun] → \"is it [noun]?\"\n\nThen:\n- yapp”psa → is it the pot?\n- yapup”psa → is it the pot too?\n\nBut \"yapup”psa\" has \"up”\" — maybe it's a rendering error?\n\nBut no — in the original problem, it's \"yapup”psa\", not \"yapp”psa\".\n\nUnless \"p”\" and \"up”\" are different.\n\nWait — in \"p”ak”u\" → \"p”\" is marked.\n\nIn \"yaputxi\" → \"utxi\", not \"p”\"\n\nBut \"p”\" appears at the end of \"yapp”psa\".\n\nPossibility: \"yap\" + \"p”\" = is it the pot?\n\nAnd \"yap\" + \"up”\" = is it the pot too?\n\nCould \"up”\" be a variant of \"p”\" with possession?\n\nNo clear mark.\n\nBut \"p”ak”unhpsa\" = my pot too → \"unh\" = my, \"psa\" = too\n\nSo \"psa\" = \"too\"\n\nSimilarly, \"yapsanpsa\" = in our1+2 field too → \"in\", \"our\", \"too\"\n\nSo when \"psa\" appears, it adds \"too\"\n\nHence:\n- yapp”psa → is it the pot?\n- yapup”psa → is it the pot too?\n\nBut why \"up”\" instead of \"p”\"?\n\nPossibly a typo in rendering. But let's assume the forms are intentional.\n\nAlternatively, is \"up”\" a different root?\n\nNo — the only forms with \"p”\" are:\n- p”ak”u = pot\n- p”ak”unhpsa = my pot too\n- yapp”psa?\n- yapup”psa?\n\nIf there is no possessive prefix, then \"yapp”psa\" and \"yapup”psa\" both refer to the pot.\n\nSo likely:\n- yapp”psa = is it the pot?\n- yapup”psa = is it the pot too?\n\nThus:\n\n1. utnhantxi → is it my house?\n2. yapp”psa → is it the pot?\n3. yapup”psa → is it the pot too?\n\nThis fits the pattern of:\n- \"txi\" = \"is it?\"\n- \"psa\" = \"too\"\n\nAnd the nouns are known from the lexicon.\n\nFinal table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|--------------------------|----------------------------------|--------|\n| 1 | utnhantxi | is it my house? | utnha = my house; markstxi = is it our town; similar structure |\n| 2 | yapp”psa | is it the pot? | yaputxi = is it the field; p”ak”u = pot; pattern of \"yap + noun\" |\n| 3 | yapup”psa | is it the pot too? | yapup”psa has \"psa\" → \"too\"; yaputxi has \"txi\" → \"is it\" |\n\nAll units derived consistently.\n\n\\boxed{a.1: is it my house?; a.2: is it the pot?; a.3: is it the pot too?}", + "generated_tokens": 2125, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: is it my house?; a.2: is it the pot?; a.3: is it the pot too?", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 5606.0, + "ioling_final_answer_chars": 66.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 3, + "output": "Start by analyzing the given Jaqaru-English word pairs to identify grammatical patterns, especially those involving possession, location, and negation or repetition.\n\nGiven data:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- qaqat”a = from the cliff \n- yapsanpsa = in our1+2 field too \n\nKey observations:\n\n1. Possession markers: \n - \"our1+2\" appears in qucxst”psa, markstxi, yapsanpsa — suggests a plural possessive prefix \"our1+2\". \n - \"my\" appears in ishinhna, p”ak”unhpsa, utnhpsa (implied from utnha = my house). \n - \"his\" in chushp”a, markp”t”a \n - \"your\" in ishma → \"your bed\", and \"your house\" → utamt”a\n\n2. Structural pattern: \n - Many words end in -txi: chushuntxi, markstxi, ishinhna, utamt”a, yapsanpsa → likely questions or \"is it...\" \n - Words ending in -psa meaning \"too\" or \"also\" — e.g., aq”ipsa = the cave too; p”ak”unhpsa = my pot too; yapsanpsa = in our1+2 field too\n\n3. \"my\" + noun → utnha = my house \n - ishinhna = in my bed \n - p”ak”unhpsa = my pot too \n → So \"my\" is a possessive particle; \"nha\" = house, \"basic noun\", and \"unh\" = my in some cases?\n\n4. \"in + noun\" constructions: \n - aq”na = in the cave \n - ishinhna = in my bed \n - yapsanpsa = in our1+2 field too → so \"in\" is likely a locative prefix\n\n5. \"from + location\" → \n - qucxat”a = from the cliff \n - markp”t”a = from his town \n - qaqat”a = from the cliff \n → so \"from\" is likely a prefixed locative or direction marker\n\n6. \"is it in X?\" → labeled with -txi → e.g., chushuntxi, markstxi, ishinhna is not this (ishinhna = in my bed, not a question) \n But chushuntxi = is it in the corner? → so -txi = interrogative or \"is it in X?\"\n\n7. The -psa suffix appears with \"too\": \n - aq”ipsa = the cave too → aq”i + psa → \"cave\" + too \n - p”ak”unhpsa = my pot too → p”ak”u + unh + psa → my pot too \n - qucxst”psa = from our1+2 lake too → qucx + st + psa → from our1+2 lake too \n → So -psa means \"too\" or \"also\"\n\n8. \"our1+2\" appears in: \n - qucxst”psa → from our1+2 lake too \n - markstxi → is it our1+2 town? \n - yapsanpsa → in our1+2 field too \n → So \"our1+2\" = a possessive prefix, likely following the noun or preposition\n\n9. \"yaputxi\" = is it the field? → so yap + utxi = is it the field? \n - yap + ? → is it \n - so \"yap\" + noun → is it [noun]? \n → Thus, \"yap\" = is it?\n\nSo: \n- \"yap\" + noun → is it [noun]? \n- \"in + noun\" → in that place \n- \"from + noun\" → from that place \n- \"X + psa\" → X too \n- \"X + txi\" → is it in X? (interrogative)\n\nNow apply to translation targets:\n\n1. utnhantxi \n- utnha = my house \n- so utnhantxi = is it in my house? \n→ supports pattern: \"yap\" + noun → is it [noun]? → \"yap\" + \"utnha\" = is it in my house? \nBut here: \"utnhantxi\" → if \"antxi\" = \"in\", then \"in my house?\", but that would be \"in my house\" — not \"is it in my house\". \nWait — the form \"xantxi\" doesn't appear. Instead: \nwe have \"ishinhna\" = in my bed → using \"in\" \n\"markstxi\" = is it our1+2 town? → \"xstxi\"\n\nSo can we generalize the structure?\n\nLook at the question forms:\n\n- chushuntxi → is it in the corner? → covers \"in the corner\" \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nThus: \n- \"x + txi\" = is it X? \nBut structure varies: \n- chushuntxi = in the corner → so \"chushu\" = corner, \"ntxi\" = is it in the corner? \n→ \"ntxi\" might mean \"in the corner?\" or \"is it in X?\"\n\nBut qucxst”psa = from our1+2 lake too → no \"txi\"\n\nSo where is \"txi\" used?\n\nOnly in: chushuntxi → is it in corner? \nmarkstxi → is it our1+2 town? \nyaputxi → is it the field?\n\nSo \"txi\" = question form for \"is it X?\" → but only when X is a place?\n\nNow: \nutnhantxi — \n\"utna\" → likely a form of house? \n\"utnha\" = my house → so \"utna\" might be house? \n\"utnhantxi\" → if txi = is it in X, then \"in my house?\" \n\nBut ishinhna = in my bed → simpler. \nSo \"utnhantxi\" → \"is it in my house?\"\n\nBut \"utnhantxi\" has \"ntxi\", not \"txi\"\n\nWait — ishinhna = in my bed → no txi \nchushuntxi = is it in corner → has \"untxi\"\n\nSo perhaps \"untxi\" = in X? \nBut \"untxi\" appears only once.\n\nNo consistent root.\n\nAlternative: \n\"yap\" + noun → is it [noun]? \n- yaputxi → is it the field? → yes \n- markstxi → is it our1+2 town? → but \"markstxi\" has \"stxi\", not \"yap\" → so not matching\n\nBut markstxi → is it our1+2 town? → matches \"is it X?\" \nSo perhaps the form is: \n- \"n\" + txi = is it [X]? \nAnd \"X\" is the noun base.\n\nSo:\n- chushuntxi → is it in the corner? → corner is \"chushu\", with \"untxi\" → but \"untxi\" not in the others \n- markstxi → is it our1+2 town? → \"mark\" = town, \"stxi\" → so \"stxi\" = is it [X]? \n- yaputxi → is it the field? → \"yap\" + \"utxi\" → \"utxi\" = field → \"is it the field?\"\n\nThus: \n- When a stem ends with “txi” → it means “is it [X]?” \n- The stem is the noun — so “chushu” in corner → is it in the corner? \n- “mark” in town → is it our1+2 town? \n- “yap” in field → is it the field?\n\nBut “yaputxi” = is it the field? → so \"yap\" is not the field — the field is \"utxi\"? \n\"yap\" + \"utxi\" → \"is it the field?\" → so \"utxi\" = field?\n\nBut in yapsanpsa = in our1+2 field too → field is \"utxi\"\n\nYes.\n\nSo \"utxi\" = field\n\nSimilarly, \"chushu\" = corner \n\"mark\" = town \n\"aq”i\" = cave \n\"p”ak”u\" = pot \n\nSo when we have X + txi → is it X? \n\nNow, back to the questions:\n\n1. utnhantxi \n- \"utnh\" → likely \"my house\" → \"utnha\" = my house \n- so \"utnhantxi\" → if \"antxi\" = txi, then \"in my house?\" → but that doesn’t fit \n- but “ntxi” pattern? No — we have “untxi” or “stxi” or “utxi”\n\nWait: \"utnha\" = my house → so \"utnha\" is a noun \n\"utnhantxi\" → if \"antxi\" is the interrogative form, is it in my house?\n\nBut no such form exists.\n\nAlternatively: \n\"ishinhna\" = in my bed → clearly \"in + my bed\" \n\"utnha\" = my house → so \"in my house\" = \"utnhantai\"? no such form.\n\nBut we have \"utnha\" → my house \n\"ishinhna\" → in my bed → \"in\" is a prefix? \nIn aq”na = in the cave → \"aq”na\" → so \"in\" is not a prefix — might be derived from the noun?\n\nWait — \"aq”na\" = in the cave \nAlso, \"aq”ipsa\" = the cave too → so \"cave\" + too\n\nSo \"na\" = in the cave → so \"na\" = in the cave? \nBut \"ishinhna\" = in my bed → so \"inhna\" = in my bed → so in + noun?\n\nSo \"na\" and \"inhna\" → both \"in + noun\", but different noun?\n\n- aq”na → in the cave \n- ishinhna → in my bed \n- yapsanpsa → in our1+2 field too\n\nSo prefix may be \"in\" — but appears in different forms.\n\nIn aq”na → \"na\" → in the cave \nIn ishinhna → \"inhna\" → in my bed \n→ perhaps “in” is encoded in the suffix?\n\nSo perhaps the \"in\" is built into the suffix.\n\nSimilarly, \"from\" = prefix in \"qucxat”a\", \"markp”t”a\", \"qaqat”a\"\n\nNow, look at utnhantxi:\n\n\"utnha\" = my house \n\"utnhantxi\" → if it means \"is it in my house?\" — consistent with \"is it in X?\"\n\nBut X is \"my house\", so need to see if \"utnha\" can be used in this form.\n\nWe have: \n- chushuntxi → is it in the corner? → corner = chushu \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nAll have the form: [base noun] + txi → is it [that noun]?\n\nBut \"utnha\" is the base — so utnhantxi = is it in my house?\n\nBut \"in\" is not present. In chushuntxi, \"untxi\" — the word may be “corner” with “untxi” meaning “is it in the corner?”\n\nIn ishinhna, “inhna” = in my bed — not a question.\n\nSo the question form seems to be when the word ends in -txi → is it [X]?\n\nSo:\n\n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo the pattern is: \nX + txi → is it X?\n\nBut \"X\" is the noun stem.\n\nSo for utnhantxi: \n- \"utnha\" → my house → so utnhantxi → is it my house?\n\nBut we have \"in my bed\", which is a location — is \"my house\" a place?\n\nLikely yes.\n\nAlso, \"markstxi\" = is it our1+2 town? → not \"in the town?\"\n\nSo sometimes it's \"is it the town?\" and not \"is it in the town?\"\n\nSo it seems the -txi form is for \"is it X?\" including possession.\n\nTherefore, utnhantxi = is it my house?\n\nBut stem is \"utnha\" → my house\n\nSo utnhantxi → is it my house?\n\nBut no \"in\" prefix — only \"txi\"\n\nSimilarly, yapp”psa:\n\n- yapp”psa → yap + p”psa \n- \"yap\" = is it \n- \"p”psa\" → what is that?\n\nWe have: \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → so \"unh\" = my \n- \"p”psa\" — not directly seen.\n\nWe have \"aq”ipsa\" = the cave too → \"ipsa\" = too \n\"qucxst”psa\" = from our1+2 lake too → \"st”psa\" = from our1+2 lake too\n\nSo the -psa suffix = \"too\"\n\nTherefore: \n- any word ending in -psa → means \"X too\"\n\nSo yapp”psa → yap + p”psa → is it [something] too?\n\nAnd \"p”psa\" → what is the base?\n\nThe base must be a noun.\n\nWe have \"p”ak”u\" = the pot → so pot is \"p”ak”u\"\n\nSo \"p”p\" could be a variant? But no.\n\n\"yapp”psa\" → if \"p”psa\" = pot too → but \"p”ak”u\" = the pot\n\nBut \"p”psa\" is not a direct match.\n\nPossibly a mistake? Or a reduced form?\n\nBut in aq”ipsa → cave too → \"ipsa\" = too \nIn p”ak”unhpsa → my pot too → \"unhpsa\" = my pot too\n\nSo the pattern is: \n- noun + -psa = X too \n- possessive + -psa = X too\n\nSo yapp”psa = \"yap\" + p”psa → is it [pot] too?\n\nSo \"pot\" → pot base is \"p”ak”u\", so \"p”psa\" might be a variant or error?\n\nBut perhaps \"p”psa\" = pot → in a different form?\n\nUnlikely. Perhaps p”psa is not a noun.\n\nAlternative: yapp”psa = is it in the pot too? → but \"in the pot\" is not seen.\n\nWe have no word like \"in the pot\"\n\nSo only -psa = \"too\"\n\nThus, \"yap\" = is it \n\"p”psa\" = pot → but \"p”ak”u\" is pot, not \"p”psa\"\n\nSo perhaps the base is \"p”psa\" = pot?\n\nNo evidence.\n\nAnother thought: all -psa = \"too\", so the entire phrase \"is it the pot too?\" → but \"yap\" is \"is it\", so yapp”psa = is it the pot too?\n\nBut \"the pot\" is \"p”ak”u\", so why \"p”psa\"?\n\nPossibly a grammatical reduction or error — but in the data, \"p”ak”u\" = the pot, and no form of \"pot\" with -psa.\n\nBut in aq”ipsa → the cave too → \"aq”i\" = cave\n\nSo only certain nouns get -psa.\n\nBut in \"p”ak”unhpsa\" → my pot too → so \"unhpsa\" = my pot too → so the -psa is attached to the possessor part.\n\nSo in yapp”psa, no possessive — so maybe it's \"is it the pot too\"?\n\nBut no direct support.\n\nWait — \"yapsanpsa\" = in our1+2 field too → \"yapsanpsa\" = in our1+2 field too → includes \"too\" — so -psa = too\n\nSimilarly, \"qucxst”psa\" = from our1+2 lake too → -psa = too\n\nSo -psa = too\n\nTherefore, \"yapp”psa\" = yap + p”psa = is it [X] too → where X = p”psa\n\nBut what is p”psa?\n\nIt may be \"pot\" — possibly a misalignment in spelling? Or the stem is missing a letter.\n\n\"p”ak”u\" = the pot → so \"ak”u\" = pot\n\n\"p”psa\" — if it's a variant, perhaps it's \"pot\" shortened?\n\nUnlikely.\n\nPerhaps it's a typo — but in the original, it's written as \"yapp”psa\", not \"yapak”u\" or something.\n\nAlternative: p”psa = pot? Not found.\n\nUnless the base is \"p”ak”u\" and \"p”psa\" is a different form.\n\nBut no.\n\nAnother idea: \"p”psa\" might be a construction like \"the pot\" or \"pot\" with no article, and \"ap\" or something.\n\nBut no.\n\nPerhaps the word is \"is it in the pot too?\" but no \"in\".\n\nWe have \"ishinhna\" = in my bed → so \"in\" is a prefix.\n\nSo maybe yapp”psa = is it in the pot too? → but no such word.\n\nAlternatively, the pattern is:\n\n- yap + noun → is it [noun]? \n-", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11208.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "First, analyze the given examples to find patterns in Dyirbal structure.\n\nEach sentence follows a similar pattern:\n- A noun (subject) + a nominal modifier (descriptive phrase) + \"baNgul\" (meaning \"is making\" or \"is causing\") + a noun + a resulting state or condition.\n\nFrom the examples:\n- \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → Booze is making the man that is always being blamed tired.\n- \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" → The strong man is blaming the mother that is always following death adders.\n\nKey patterns:\n1. \"baNgul\" links a subject and a result.\n2. The subject often has a descriptive nominal phrase (e.g., \"the man that is always being blamed\").\n3. The result is encoded in a descriptive phrase (e.g., \"tired\", \"fat\", \"following\").\n4. The result modifies the noun after \"baNgul\".\n\nNow break down the structure:\n\n- \"baNgul\" = \"is making\" or \"is causing\" (intransitive effect on a noun)\n- The subject is modified by a nominal phrase with a property or action (e.g., \"the big grasshopper\", \"the tired wallaby\")\n- The object (result) is a noun with a descriptive suffix or phrase (e.g., \"tired doctor\", \"fat mother\")\n\nNow, examine each sentence:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n- \"balan\" = the quiet one (from sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at...\") \n→ \"ñalNga\" = quiet (from 15) \n→ So \"balan ñalNga\" = the quiet one (a man, as \"balan\" is the masculine subject) \n→ \"baNgul\" = is making \n→ \"NumaNgu\" = the strong one (from 16: \"man that is always being followed\") \n→ \"guniymuNagu\" = the one that is always following (from 16: \"guli baNgul yaóaNgu banéalmuNagu munduman\" → \"man that is always being followed\") \n→ \"bambunman\" = fat (from 3: \"sugar is making the healthy mother-in-law fat\") → \"bambun\" = fat \nThus: The quiet man is making the strong one who is always following (someone) fat.\n\nBut carefully: structure is: [Subject] + [descriptive phrase] + baNgul + [object] + [resulting state]\n\nSee sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard\" \n→ \"biñéiriñ\" = quiet \n→ \"baNgul\" = \"is looking at\" \n→ \"ñalNgaNgu\" = tired lizard → so \"baNgul\" links subject to object via a \"looking at\" or \"making\" relation \n\nWait — \"baNgul\" is not consistently \"making\" in all. Review:\n\nIn (1): \"booz is making\" → \"baNgu gurugugu\" → baNgu is the main verb, not baNgul. \nIn (2): \"the strong man is blaming\" → \"yabu bimabanéalNaymuNa baNgul yaóaNgu\" → \"baNgul\" = blaming? \n(2) structure: [subject] [modifier] baNgul [object] [modifier]\n\n(2): \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"balan\" = strong man \n→ \"yabu\" = blaming (from context) \n→ \"baNgul\" = verb: blaming \n→ \"yaóaNgu\" = mother \n→ \"guliNgu\" = following death adders \n\nSo \"baNgul\" = verb of action (blaming, searching, carrying, etc.) \n\nBut in (1): \"bayi yaóa NunéaymuNa baNgu gurugugu\" — \"baNgu\" = is making? Yes. \nIn (15): \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"is looking at\" \nSo \"baNgul\" = \"is looking at\" or \"is causing to be\" \n\nThus, \"baNgul\" seems to be a verb meaning \"is causing\" or \"is making\", and the object gets a resulting state. But in (2), it is \"blaming\" — not the same.\n\nWait — look at 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"The dragonfly is searching for the stinging tree\" \n→ \"duNan\" = big → \"duNan baNgul\" = searching? → \"baNgul\" = searching \n→ \"yiriñéilagu\" = stinging tree \n→ \"guniñu\" = is being searched for? Or \"the one that is searching for\"? \n\nNot matching. \n\nBetter pattern: \n\nSentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard\" \nHere, \"biNgun\" = tired \n→ So \"baNgul\" = is looking at \n→ object: \"ñalNgaNgu\" = tired lizard → cannot be both subject and object \n\nWait. Subject: bayi → boy \nbiñéiriñ → quiet \nbiNgun → tired → modifying \"lizard\"? \nbaNgul → is looking at \nñalNgaNgu → tired lizard \n→ so \"quiet boy is looking at the tired lizard\" \n\nThus, \"baNgul\" = \"is looking at\" \nSimilarly, 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" \n→ \"tired wallaby is searching for the little feather\" \n→ \"yila wura\" = tired \n→ \"baNgul\" = searching for \n→ \"bargandu\" = little feather \n→ \"biNgundu\" = the one that is being searched for? Or for \"feather\"? \"guniñu\" → \"little\" → \"little feather\" \n\nNo: \"guniñu\" = little → describes \"bargandu\"? \nSo \"bargandu guniñu\" = little feather \n\nThus, \"baNgul\" = searching for, and the object is \"bargandu guniñu\" (little feather)\n\nTherefore, structure is:\n\n[Subject] [modifier] baNgul [object] [object modifier]\n\nSo in 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman\n\n- \"balan\" = the strong or man? From 2: \"balan\" = strong man \n→ But \"balan\" is both subject and in other sentences → clearly masculine \n→ \"ñalNga\" = quiet (from 15) \n→ So \"balan ñalNga\" = the quiet man \n→ \"baNgul\" = is making / is causing → not \"is looking at\" \nWait — 15: \"looking at\" → different verb? \n\nBut in 1: \"bayi yaóa\" → \"booze is making\" → \"baNgu\" → verb? \n\"baNgu\" and \"baNgul\" are similar but not identical. \n\nAre \"baNgu\" and \"baNgul\" the same? \n\n1: \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"baNgu\" connects \"booze\" to \"man\" → \"booze is making the man tired\" \n\n2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"balan\" = strong man \n→ \"yabu\" = blaming \n→ \"baNgul\" = verb of blaming \n→ \"yaóaNgu\" = mother \n→ \"guliNgu\" = following death adders \n\nSo \"baNgul\" is not \"making\" — it's \"blaming\"\n\nTherefore, \"baNgul\" is the verb of a relationship (e.g., blaming, searching, following, pushing, making)\n\nFrom 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"dragonfly is searching for stinging tree\" \n→ \"duNan\" = big \n→ \"baNgul\" = searching for \n→ \"yiriñéilagu\" = stinging tree \n→ \"guniñu\" = little → so \"little\" describes tree? → \"guniñu\" modifies \"yiriñéilagu\" \n\nSo structure: [subject] [modifier] baNgul [object] [modifier]\n\nHence, in 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n- \"balan\" = man \n- \"ñalNga\" = quiet \n- \"baNgul\" = is making / causing (in context of causing a state) \n- \"NumaNgu\" = strong one \n- \"guniymuNagu\" = one that is always following \n- \"bambunman\" = fat \n\nThus: The quiet man is making the strong one who is always following fat.\n\nFrom 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is offending the strong father\" \n→ \"Numa\" = strong → \"Numa guli\" = man that is always being followed \n→ \"baNgul\" = offending \n→ \"yaóaNgu\" = strong father → so \"offending the strong father\"\n\nSo \"baNgul\" = offending, blaming, making, searching — context-dependent form.\n\nNow for 18: bala diban bilmbalmuNa baNgun biñéiriñéu guniñu \n- \"bala\" = the one (feminine?) — in 9: \"bala garan baNgun biñéiriñéu banéan\" → \"lizard is following the smoke\" \n→ \"baNgun\" = following \n→ So \"baNgun\" = \"is following\" \n→ \"bala\" = subject \n→ \"diban\" = fat \n→ \"bilmbalmuNa\" = the one that is always pushing stones (from 13: \"mother-in-law that is always pushing stones\") \n→ \"baNgun\" = is following \n→ \"biñéiriñéu\" = tired (from 15: \"biñéiriñ\" = quiet, \"biñéiriñéu\" = tired?) \n\"biñéiriñéu\" likely = tired \n→ \"guniñu\" = little? \n\nSo: The fat one (mother) is following the tired one (lizard) who is little?\n\nBut \"guniñu\" = little → modifies \"biñéiriñéu\"? → \"tired little one\"? \n\n13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law that is always pushing stones is looking at the smoke\" \n→ \"garan\" = looking at \n→ \"baNgun\" = looking at \n→ \"waymindu\" = little → \"little one\" \n→ So \"guniñu\" = little \n\nThus: \"biñéiriñéu guniñu\" = tired little one \n\nSo: The fat one is following the tired little one.\n\nBut subject is \"bala diban\" = fat one \n\"bilmbalmuNa\" = the one that is always pushing stones → likely the object being followed? \n\nWait: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\" \n→ \"bala diban\" = fat one \n→ \"bilmbalmuNa\" = the one that is always pushing stones → descriptive phrase \n→ \"baNgun\" = is following \n→ \"biñéiriñéu guniñu\" = tired little one \n\nSo: The fat one (who always pushes stones) is following the tired little one.\n\nBut 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"bala\" = mother-in-law \n→ \"garan\" = looking at \n→ \"baNgun\" = looking at \n→ \"waymindu\" = little \n→ \"dibanbilmbalNaymuNagu\" = the mother-in-law that always pushes stones → so \"dibanbilmbalNaymuNagu\" = the one who always pushes stones \nSo \"bilmbalmuNa\" = same as \"bilmbalNaymuNagu\" — one that always pushes stones\n\nThus: The fat one who always pushes stones is following the tired little one.\n\nNow 19: bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan \n- \"bayi\" = the one (exciting/being) → in 1: \"booz is making\" \n- \"bargan\" = the one that is always being blamed? From 1: \"NunéaymuNa\" → \"being blamed\" \n- \"baNgul\" = is making \n- \"yaóaNgu\" = mother \n- \"gubimbuluNunéanaymuNagu\" = the one that is always being blamed / being followed? \n\"bubimbulu\" → from 16: \"gubi\" = being blamed? \n16: \"Numa guli\" = man that is always being followed \n\"bubimbulu\" → likely from \"gubimbulu\" = being blamed \n\nIn 1: \"bayi yaóa ...\" → \"booz is making the man that is always being blamed tired\" → \"NunéaymuNa\" = being blamed \nSo \"gubimbuluNunéanaymuNagu\" = the one that is always being blamed? \n\"gubimbulu\" = being blamed → \"NunéanaymuNagu\" = the one being blamed? \n\"banéan\" = the possum? (from 7: \"following the possum\") \n\n\"banéan\" = possum (from 7: \"following the possum\") \n\nSo: The one that is always being blamed is making the mother that is always being blamed (or being followed) fall asleep? No.\n\n\"bargan\" → the one that is always being blamed? \nBut \"gubimbuluNunéanaymuNagu\" = the one that is always being blamed? \nAnd \"banéan\" = possum \n\nSo: The one that is always being blamed is making the mother that is always being blamed fall asleep?\n\nBut \"banéan\" = possum → and 7: \"the death adder that is always searching for scorpions is following the possum\" → so \"banéan\" = possum \n\nIn 1: \"bayi yaóa ... biNgunman\" → \"tired\" → so result is state \n\nIn 19: \"baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\" \n→ \"baNgul\" = is making \n→ \"yaóaNgu\" = mother \n→ \"gubimbuluNunéanaymuNagu\" = the one (possibility: that is always being blamed or followed?) \n→ \"banéan\" = possum \n\nBut \"gubimbuluNunéanaymuNagu\" = the one that is always being blamed (from \"gubimbulu\") \nSo: The one that is always being blamed is making the mother (who is always being blamed) fall asleep? \n\nBut \"banéan\" = possum — not mother. \n\nWait: \"yaóaNgu\" = mother → so \"gubimbuluNunéanaymuNagu\" might be describing the mother? \n\nPossibly: \"yaóaNgu gubimbuluNunéanaymuNagu\" = mother that is always being blamed \n\nThen: \"baNgul\" → \"is making\" \n→ \"banéan\" → possum → \"is making the mother (always being blamed) fall asleep\"? \n\nBut no state after → \"banéan\" might be the resulting object with state?\n\nBack to 1: \"bayi yaóa ... biNgunman\" → \"tired\" → so state is attached to object after \"baNgul\"\n\nIn 19: \"baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\" → \n→ Object: \"yaóaNgu gubimbuluNunéanaymuNagu\" = mother that is always being blamed \n→ Result: \"banéan\" = possum? — but no state → missing?\n\nWait — in 1: \"biNgunman\" → \"tired\" → state \nIn 10: \"guniñu\" → small → descriptive \nIn 15: \"biNgun\" → tired → state \n\nSo in 19, after \"baNgul\", we have \"yaóaNgu gubimbuluNunéanaymuNagu banéan\" — no state? \n\nPossibly \"banéan\" is modified by state?\n\nBut no — in 7: \"bayi ... is following the possum\" → \"banéan\" = possum → no state \n\nIn 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\" \n→ \"bargan\" = the one that is always being blamed \n→ \"baNgul\" = making \n→ \"yaóaNgu\" = mother \n→ \"gubimbuluNunéanaymuNagu\" =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11807.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "Start by analyzing the structure of the given Dyirbal sentences and their English translations to detect patterns in how attributes (such as state, action, and subject) are encoded.\n\nKey observations from examples:\n\n- The verb often appears at the end of the sentence and takes a subject + modification pattern.\n- Noun phrases are built with modifiers (e.g., “that is always X”) which are marked by prepositional or genitive phrases.\n- The structure typically follows: [Agent or state] + [modifier X] + [verb] + [object or state]\n- The morphemes like *yabu*, *yaóa*, *gurugugu*, *biNgunman*, etc., seem to denote specific nouns or actions.\n\nPattern analysis:\n\n1. Example 1: bayi yaóa NunéaymuNa baNgu gurugugu biNgunman → \"Booze is making the man that is always being blamed tired.\"\n - bayi = booze\n - yaóa NunéaymuNa = man that is always being blamed\n - baNgu = causing\n - gurugugu → tired\n - biNgunman = (makes) tired → verb form\n\n2. Example 3: balan waymin bambun baNgu éugaNgu éamiman → \"Sugar is making the healthy mother-in-law fat.\"\n - balan = sugar\n - waymin = healthy\n - bambun = mother-in-law\n - baNgu = causing\n - éugaNgu = fat → this is likely the adjective for fat\n\n3. Example 5: balan malayigara baNgu garandu biNgunman → \"The smoke is making the scorpion tired.\"\n - malayigara = smoke\n - garandu = scorpion\n - baNgu = making\n - biNgunman = tired\n\n4. Example 9: bala garan baNgul biñéiriñéu banéan → \"The lizard is following the smoke.\"\n - bala = lizard\n - garan = following\n - baNgul = the smoke\n - biñéiriñéu banéan = the smoke (named or described?)\n\nWait: Example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"The lizard is following the smoke.\"\n\nSo \"garan\" = following; \"baNgul\" = the smoke (object); \"biñéiriñéu banéan\" seems to be the object, but here it's the verb phrase.\n\nRe-express structure:\n- [Subject] + [verb] + [object] + [modifier of object or subject]\n\nBut more clearly, in 9: \"bala garan baNgul biñéiriñéu banéan\"\n- \"bala\" = lizard\n- \"garan\" = following\n- \"baNgul\" = smoke\n- \"biñéiriñéu banéan\" = the smoke (redundant or defining? seems to be the object with a state)\n\nBut sentence 15: bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\n→ \"The quiet boy is looking at the tired lizard.\"\n- bayi = quiet boy\n- biñéiriñ = looking at\n- biNgun = the tired (adjective)\n- baNgul = lizard\n- ñalNgaNgu = the tired (again?) → wait, biNgun is 'tired'? From 1 and 8.\n\nIn example 8: bayi gubimbulu biNgun baNgu gurugugu éagunman → \"Booze is making the tired doctor fall asleep.\"\n- gubimbulu = tired\n- biNgun = the tired doctor\n- baNgu = making\n- gurugugu = fall asleep\n\nSo \"biNgun\" = (the) tired one → adjective meaning \"tired\"\n\nSimilarly:\n- \"biNgunman\" = makes tired → verb\n- \"gurugugu\" = fall asleep / tired\n- \"éaga\" or \"éagunman\" = fall asleep\n- \"malayigara\" = smoke\n- \"garandu\" = scorpion\n\nNow look at Example 14: balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\n→ \"The big grasshopper is searching for the bent spear.\"\n- balan = ? → actually, balan is used for \"strong man\" in example 2, but here it's \"big grasshopper\"? But in the verb structure, is \"baNgay\" a noun?\n\n→ par1. In 14: \"balan baNgay\" = big grasshopper? Or does \"balan\" mean \"big\" here?\n\nNo — in example 2: \"balan yabu\" → the strong man.\n\nSo \"balan\" = strong man (in that context)\n\nBut here “balan” used independently with “baNgay” → possibly “baNgay” = grasshopper?\n\nBut later: \"baNgay waóu\" → possibly \"big grasshopper\"\n\nSo “baNgay” = grasshopper; “waóu” = big?\n\nSo in 14: \"balan baNgay waóu\" = the big grasshopper\n\nAnd \"baNgun bundiñéu éagiñéu guniñu\" → searching for the bent spear\n\nSo \"baNgun\" = searching for\n\nTherefore: “baNgun” = searching for (a prepositional verb)\n\nSimilarly:\n- Example 10: \"balan duNan baNgul yiriñéilagu guniñu\" → dragonfly searching for stinging tree\n → \"duNan\" = stinging? or \"dragonfly\"?\n → \"baNgul\" = the stinging tree?\n → so \"baNgul\" marks the object\n\nRecurring pattern:\n- [Noun] + [adjective modifier] → describes a subject or object\n- [Verb] + [object] → action\n- [baNgun], [garan], [yabu], etc. are verbs (to make, to follow, to search)\n\nThus:\n- \"baNgu\" = to make (cause to become)\n- \"baNgul\" = to follow\n- \"baNgun\" = to search for\n- \"garan\" = to follow\n- \"gurugugu\" = to become tired (causative result)\n\nNow, sentence 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak down:\n- \"balan\" = strong man / agent\n- \"ñalNga\" = quiet (as in example 15: \"biñéiriñ biNgun\" = the quiet boy)\n- \"baNgul\" = following\n- \"NumaNgu\" = the strong man (can be reflexive or generic)\n- \"guniymuNagu\" = something with \"always following\" or \"always being followed\"? \n - Compare to example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\"\n → \"man that is always being followed is offending the strong father\"\n → \"Numa\" = always being followed → recurring pattern: \"Numa\" = always being followed\n - So \"Numa\" = always being followed\n - \"NumaNgu\" = the one that is always being followed → subject\n- \"bambunman\" = fat\n → \"bambun\" = mother-in-law\n → \"man\" → possibly same as \"biNgunman\" → makes fat\n\nBut in 3: \"waymin bambun baNgu éugaNgu éamiman\" → \"healthy mother-in-law is making fat\"\n\n\"baNgu\" = causes to become → so \"baNgu\" = causes to become [a state]\n\nThus: \"bambunman\" = makes (someone) fat\n\nIn 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n→ \"the quiet man\" is following \"the one that is always being followed\" (NumaNgu) → \"guniymuNagu\" = always followed?\n\n\"guniymuNagu\" → likely \"always being followed\" (like \"Numa\" in example 16)\n\nSo:\n- \"balan\" = the strong man\n- \"ñalNga\" = quiet\n- \"baNgul\" = following\n- \"NumaNgu\" = the one that is always being followed\n- \"guniymuNagu\" = “always being followed”? But already in Numa?\n\nPossibly a redundancy or misphrasing.\n\nWait — \"guniymuNagu\" may be a specific state meaning \"always being searched for\" or \"always being followed\"?\n\nAlternatively, compare with:\nExample 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\"\n→ \"the quiet boy is looking at the tired lizard\"\n\nSo \"biñéiriñ\" = looking at\n\"biNgun\" = tired\n\"baNgul\" = at (prepositional)\n\"ñalNgaNgu\" = the tired lizard\n\nSo \"baNgul\" = at → \"is looking at\" → so \"baNgul\" = at (preposition)\n\nBut earlier we thought \"baNgul\" = following\n\nContradiction?\n\nWait: in example 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n→ \"garan\" = following\n→ \"baNgul\" = smoke → object\n\nSo \"baNgul\" marks the object → not a preposition.\n\nIn example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\"\n→ \"the quiet boy is looking at the tired lizard\"\n\n\"biñéiriñ\" = looking at\n\"biNgun\" = tired (modifies lizard)\n\"baNgul\" = at\n\"ñalNgaNgu\" = lizard\n\nSo here \"baNgul\" = at → prepositional object marker?\n\nBut in example 9: “garan baNgul X” → “follows X” → here “baNgul” is object of “follow”\n\nSo in both cases, \"baNgul\" is a noun, and associated with a verb?\n\nNo — clearly, in 9: \"garan baNgul\" = follows the (smoke)\n\nIn 15: \"biñéiriñ baNgul\" = is looking at → the verb is biñéiriñ, and baNgul is object\n\nSo \"biñéiriñ\" = to look at\n\nSimilarly, \"baNgun\" = to search for\n\nThus, verbs are:\n- gurugugu → becomes tired\n- biNgunman → makes tired\n- biNgun → tired (adjective)\n- éuga → fat (adjective)\n- éami → healthy?\n- malayigara → smoke\n- garandu → scorpion\n- yabu → strong man\n- wura → feather\n- diban → fat\n- garan → follow\n- yaóaNgu → mother, or mother that is always being blamed\n- Numa → always being followed\n\nSo now, sentence 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman\n\nBreak it:\n- balan = strong man\n- ñalNga = quiet\n- baNgul = follows\n- NumaNgu = the one that is always being followed\n- guniymuNagu = always being searched for? or always being followed?\n- bambunman = makes fat\n\nWait — \"gunning\" (guni) is not in earlier examples.\n\nCompare example 16: bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed\n\"Numa guli\" → the man that is always being followed\n\"baNgul yaóaNgu\" → is offending the mother\n→ so \"baNgul\" is modifying a verb? No — \"guli\" = offending? \"baNgul\" = the mother?\n\nWait — \"baNgul yaóaNgu\" → the mother that is always being blamed\n\nSo in example 16: \"Numa\" = always being followed\n\"Numa guli\" → the man that is always being followed is offending\n\"baNgul yaóaNgu\" = the mother that is always being blamed\n\nSo \"baNgul\" = modifies an entity (the mother)\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n→ \"the quiet strong man is following the strong man that is always being followed (guniymuNagu) and is making him fat\"\n\nBut “guniymuNagu” — prefix “guni” → “to search for” or “to always follow”?\n\nCompare to example 13: bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\n→ “the mother-in-law that is always pushing stones is looking at the smoke.”\n\n“waymindu” = pushing\n“dibanbilmbalNaymuNagu” = stones\n“buóan” = smoke\n\nSo “diban” = fat → again\n\nNow, “guniymuNagu” — possibly “always being followed” or “always being searched for”\n\nSince in 16, “Numa” = always being followed, and “guni” = search, perhaps “guni” is search\n\nExample 14: balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\n→ “the big grasshopper is searching for the bent spear”\n\nSo “baNgun” = searching for\n“bundiñéu éagiñéu” = bent spear\n“guniñu” = the spear\n\nSo “guni” = search\n\nTherefore, “guni” = to search for / always searching?\n\nSo “guniymuNagu” = the one that is always being searched for?\n\nThus, “NumaNgu” = the one that is always being followed\n“guniymuNagu” = the one that is always being searched for?\n\nBut they are both about a person.\n\nSo sentence 17: \"The quiet strong man is following the one who is always being followed and is making him fat.\"\n\nBut “making him fat” — “bambunman” → causes to become fat\n\nAnd “bambun” = mother-in-law? But in sentence 13, \"bambun\" = mother-in-law\n\nBut in example 17: “bambunman” → not a noun\n\nWait — in sentence 3: \"waymin bambun baNgu éugaNgu\" → \"healthy mother-in-law is making fat\"\n\nSo \"bambun\" is a noun (mother-in-law), and \"baNgu\" = causing to become\n\nSo \"bambunman\" = causes to become fat → same pattern\n\nBut is \"bambunman\" a verb?\n\nYes — likely a verbal form meaning \"making fat\"\n\nSimilarly, \"biNgunman\" = causing to be tired\n\nSo in 17: \"balan ñalNga\" = the quiet strong man\n\"baNgul\" = following\n\"NumaNgu\" = the one that is always being followed\n\"guniymuNagu\" = the one that is always being searched for?\n\"bambunman\" = making fat\n\nBut only one object? So perhaps “guniymuNagu” is a modifier of “NumaNgu”?\n\nSo: “the one that is always being followed and searched for”?\n\nBut in 16, we have “Numa” = always being followed\n\nSo possibly, \"guniymuNagu\" = always being searched for\n\nThus: \"The quiet strong man is following the person who is always being followed and searched for, and is making him fat.\"\n\nBut in example 16, “Numa” = always being followed, and it’s the subject of a passive.\n\nNow sentence 18: bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n\n- \"bala\" = the lizard\n- \"diban\" = fat\n- \"bilmbalmuNa\" = big stone\n- \"baNgun\" = searching for\n- \"biñéiriñéu\" = the smoke\n- \"guniñu\" = the smoke (object)\n\nBut \"baNgun biñéiriñéu guniñu\" = searching for the smoke\n\nSo: \"The fat lizard is searching for the smoke.\"\n\nBut \"bilmbalmuNa\" = big stone — so why \"big stone\"?\n\nWait — in example 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\"\n→ \"The fat doctor is pushing the big stone.\"\n\nSo \"bilmban\" = big stone\n\nSo \"bilmbalmuNa\" = big stone\n\nThus: \"bala diban bilmbalmuNa\" = the fat lizard is pushing the big stone?\n\nBut \"baNgun\" = searching for\n\nContradiction?\n\nSo: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ \"The fat lizard is searching for the smoke\"\n\nBut then \"bilmbalmuNa\" is not the object — it's a modifier?\n\nWait — in 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\"\n→ \"fat doctor is pushing the big stone\"\n\nSo \"éagiñ\" = pushing (verb)\n\"baNgul\" = the (pushing of) big stone?\n\nNo — \"baNgul\" = the (object)\n\nActually: structure is:\n[Subject] + [adjective] + [verb] + [object] + [modifier of object]\n\nSo 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\"\n→ \"fat doctor is pushing the big stone\"\n\n\"baNgul\" = the big stone\n\"baNgul gubimbulugu\" → \"the big stone\" with \"gubimbulugu\" = big stone?\n\n\"baNgul\" +", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12218.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by analyzing the patterns in the given Dyirbal sentences and their English translations to determine how the grammatical structure works, particularly focusing on the role of particles, possessors, and descriptors.\n\nKey observations from examples:\n\n- In sentence 1: \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → \"Booze is making the man that is always being blamed tired.\"\n - \"bayi\" = booze\n - \"yaóa\" + \"NunéaymuNa\" = \"the man that is always being blamed\"\n - \"baNgu\" = making\n - \"gurugugu\" = tired\n - So: [A] is making [B] [C], where [C] is a state (tired, fat, etc.)\n\n- In sentence 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\"\n - \"balan\" = strong man\n - \"bimabanéalNaymuNa\" = the man that is always following death adders\n - \"baNgul\" = blaming\n - \"yaóaNgu\" = mother\n - \"guliNgu\" = following\n - \"Nunéañu\" = death adders\n - So: [A] is blaming [B] that is always following [C]\n\nPattern emerges:\n- The structure is often: [Subject] [verb] [object] [modifier] → e.g., \"A is making B [that is always X] tired\"\n- The verb stem (e.g., yaóaNgu, biNgunman) is tied to a noun (e.g., mother, man) and a modifier (e.g., always being blamed)\n- Modifiers are often of the form [adjective] + [Noun] + [aspect marker], e.g., \"always being blamed\" = yaóa NunéaymuNa → \"yaóa\" (being blamed), \"NunéaymuNa\" (the man)\n- The form \"NunéaymuNa\" appears in 1, 2, 5, 7, 8: all involve \"is always being blamed\", \"following\", or \"searching\"\n\nLook at the verb-stem patterns:\n- \"gurugugu\" → tired\n- \"éugunman\" → tired (in 8: \"gurugugu éagunman\")\n- \"bimabanéalNaymuNa\" → following\n- \"yabu\" → blaming\n- \"bimaban\" → (something about following)\n- \"waymin\" → (something about sugar or fat)\n- \"diban\" = fat\n- \"biban\" = (pushing, carrying)\n- \"garan\" = following\n- \"bala\" = [subject like lizard, fat doctor] → more peripheral\n- \"bayi\" = booze, death adder\n\nNow identify structural components:\n\n1. The form [X] [Y] [Noun] [modifier] consistently maps to:\n - [X] = noun (e.g., balan = strong man)\n - [Y] = verb (e.g., yabu = blaming)\n - [Z] = of the form [Modifier] + [Noun] (e.g., yaóaNgu guliNgu → mother that is following death adders)\n\nNow examine each target sentence.\n\nSentence 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman\n\n- \"balan\" = strong man (subject)\n- \"baNgul\" = blaming\n- \"NumaNgu\" = the strong father? (from 16: \"man that is always being followed\" is \"Numa guli baNgul\")\n- \"guniymuNagu\" = likely \"that is always being followed\"\n- \"bambunman\" = fat\n\nSo: \"The strong man is blaming the strong father that is always being followed fat?\"\n\nBut \"fat\" is an adjective. \"bambunman\" = fat.\n\nBut \"fat\" in previous contexts:\n- 3: \"gurugugu biNgunman\" → \"tired\"\n- 5: \"malayigaraguninaymuNagu\" → \"searching\"\n- 11: \"NaéilmuNagu dimbañu\" → \"mother that is always being ignored\"\n- 12: \"diban\" → fat doctor\n\nSo \"diban\" = fat → \"fat doctor\"\n\n\"bambunman\" → fat\n\nSo \"guniymuNagu\" → \"that is always being followed\" → pattern: 'guni' + 'ymuN' → related to 'guli' in 2: \"guliNgu\" = following\n\n→ guni = following?\n\nSo \"guniymuNagu\" = \"that is always being followed\"\n\nIn 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is offending the strong father\"\n\n→ \"Numa guli\" = man that is always being followed\n\nSo \"guli\" → being followed\n\nThus: \"guniymuNagu\" → the one that is always being followed\n\nThus: \"NumaNgu\" = strong father → from 16: \"Numa\" + \"guli\" → man that is always being followed → so \"Numa\" likely = strong father\n\nThus: \"balan\" (strong man) is blaming the strong father that is always being followed, who is fat.\n\nBut \"bambunman\" = fat → so this man is fat.\n\nBut “fat” is not a verb; it's an adjective. We have to place it.\n\nStructure: [Subject] [verb] [object] [object modifier] → [object is X that is always Y, Z]\n\nSo: \"The strong man is blaming the strong father that is always being followed and fat.\"\n\nBut no compound adjectives.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\"\n→ \"The mother-in-law that is always pushing stones is looking at the smoke\"\n\nSo: [subject] [verb] [object] [modifier] → object has [modifier] = \"always pushing stones\"\n\nSo modifiers are of form [modifier stem] + [noun or phrase]\n\nSimilarly, in 17:\n- \"guniymuNagu\" = that is always being followed → \"guli\" as in \"guli\" = following → \"guni\" = following? → yes, \"guli\" = following, \"guni\" = follows\nSo \"guniymuNagu\" = following → always being followed?\n\nIn 2: \"guliNgu Nunéañu\" → \"following death adders\"\n\nSo: \"guli\" = following\n\nHence \"guni\" → following → likely same root\n\nThus \"guniymuNagu\" = the one that is always being followed\n\nSimilarly, \"bambunman\" = fat\n\nSo object is: \"the strong father that is always being followed\" → and is fat\n\nSo full sentence: \"The strong man is blaming the strong father that is always being followed and fat.\"\n\nBut “and fat” — is this acceptable?\n\nLook at 13: \"mother-in-law that is always pushing stones\" → \"dibanbilmbalNaymuNagu\" → \"pushing stones\"\n\nSo \"diban\" = fat → fits\n\n\"bilmbal\" = pushing stones?\n\nIn 12: \"diban éagiñ baNgul gubimbulugu éamiNgu bilmban\"\n→ \"fat doctor is pushing the big stone\"\n\n→ \"bilmban\" = big stone\n\nSo \"bilmban\" = big stone\n\nSimilarly, \"dibanbilmbal\" = fat doctor pushing stones?\n\nBut in 13: \"dibanbilmbalNaymuNagu\" = mother-in-law that is always pushing stones\n\n→ So \"dibanbilmbal\" = one that is pushing stones\n\nThus, the structure is:\n[subject] [verb] [object] [modifier phrase]\n\nWhere modifier phrase is [adjective] + [verb stem] + [noun]\n\nIn 13: \"dibanbilmbalNaymuNagu\" = one that is always pushing stones → \"diban\" = fat, \"bilmbal\" = pushing stones (with \"NaymuNa\" = \"that is always\")\n\nSo \"NaymuNa\" = that is always\n\nSo all such constructions: [X] + [modifier] + [NaymuNagu] = the one that is always [verb-ing] with noun\n\nSo in 17: \"NumaNgu guniymuNagu bambunman\"\n\nBreak it:\n- \"NumaNgu\" = strong father (same as in 16)\n- \"ganiymuNagu\" = that is always being followed (guni = follow, ymuN = that is always? → in 16: Numa guli → man that is always followed)\n- \"bambunman\" = fat\n\nBut \"bambunman\" = fat → so likely \"fat\" as attribute\n\nSo this entire phrase: \"the strong father that is always being followed and fat\"\n\nBut no \"and\" — could be compound modifier.\n\nIn 16: \"Numa guli baNgul yaóaNgu banéalmuNagu munduman\"\n→ \"The man that is always being followed is offending the strong father\"\n\nSo: \"Numa guli\" = man that is always being followed\n\nSo \"Numa\" = strong father\n\nSimilarly, \"guli\" = following → \"guni\" = same?\n\n\"guniymuNagu\" → \"that is always being followed\"\n\nYes.\n\nSo 17: \"The strong man is blaming the strong father that is always being followed and fat.\"\n\nBut is “fat” a separate attribute? Yes — same as in 11: \"mother that is always being ignored\" → \"NaéilmuNagu dimbañu\"\n\nSo attributes are added with patterns.\n\nTherefore, 17: \"The strong man is blaming the strong father that is always being followed and is fat.\"\n\nBut let’s shorten to: \"The strong man is blaming the strong father who is always being followed and fat.\"\n\nBut still — is there a better structure?\n\nNow sentence 18: bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\n\n\"bala\" = lizard or subject\n\"diban\" = fat\n\"bilmbalmuNa\" = one that is always pushing stones? But stem \"bilmba\" → from 12: \"bilmban\" = big stone → \"bilmba\" = pushing?\n\nIn 12: \"diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → fat doctor pushing big stone\n\n→ \"gubimbulugu\" = big stone? → no: gubimbulu → \"offended father\" → not stone\n\n\"bilmban\" = big stone\n\n\"bilmba\" = pushing? → not directly\n\nBut 13: \"dibanbilmbalNaymuNagu\" = mother-in-law that is always pushing stones → so \"bilmbalNaymuNagu\" = always pushing stones → \"bilmbal\" = pushing stones\n\nSo \"bilmba\" = pushing → \"bilmbal\" = pushing stones\n\nThus \"bilmbalmuNa\" = the one that is always pushing stones? (with \"muNa\" replacing \"NaymuNagu\"?)\n\nBut in 13: \"dibanbilmbalNaymuNagu\" → full phrase\n\nIn 18: \"bila diban bilmbalmuNa\" → \"fat\" + \"one that is always pushing stones\"\n\nThen \"baNgun\" = looking at\n\n\"biñéiriñéu\" = the smoke? → in 9: \"bala garan baNgun biñéiriñéu banéan\" → \"the lizard is following the smoke\"\n\n→ \"biñéiriñéu\" = smoke\n\n\"guniñu\" = little feather? → in 4: \"wura baNgul bargandu biNgundu guniñu\" → searching for little feather\n\n→ \"guniñu\" = little feather\n\nSo: \"bala diban bilmbalmuNa\" = the fat one that is always pushing stones\n\n\"baNgun\" = looking at\n\n\"biñéiriñéu\" = smoke\n\nSo: \"The fat one that is always pushing stones is looking at the smoke.\"\n\nBut \"one\" is not specified — but the structure implies \"the fat one that is always pushing stones\"\n\nYes.\n\nNow sentence 19: bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\n\n\"bayi\" = death adder\n\"bargan\" = ? (in 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → death adder that is always searching for scorpions is following the possum)\n\n\"bargan\" → not directly seen\n\n\"bargan\" → likely \"searching\"? In 7: \"midin\" = searching\n\nIn 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → death adder searching for scorpions\n\nSo \"midin\" = searching\n\n\"bargan\" → similar?\n\nPossibly a variant.\n\nBut \"bargan\" — could be related to \"midin\"?\n\n\"yaóaNgu\" = mother\n\n\"gubimbuluNunéanaymuNagu\" → that is always being followed by the offended father? (from 6: \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" → offended father is carrying booze)\n\n\"gubimbulu\" = offended father?\n\nIn 6: \"gubimbulu\" → offended father\n\nSo \"gubimbuluNunéanaymuNagu\" = the one that is always being followed by the offended father?\n\n\"nunéanaymuNagu\" = always being followed?\n\nYes — in 16: \"Numa guli\" → being followed\n\nSo \"gubimbuluNunéanaymuNagu\" = the one that is always being followed by the offended father\n\n\"banéan\" = possum\n\nSo: \"The death adder is following the mother that is always being followed by the offended father and possum?\"\n\nBut \"gubimbuluNunéanaymuNagu banéan\" → the one that is always being followed by the offended father → is the mother?\n\nNo: it's \"yaóaNgu\" + \"gubimbuluNunéanaymuNagu banéan\" = mother that is always being followed by the offended father and [is] the possum?\n\nBut “banéan” = possum → so likely: the mother that is always followed by the offended father → is the possum?\n\nNo — grammar suggests: [subject] [verb] [object] [object modifier]\n\nSo: death adder [bargan] → searching for ?\n\n\"bargan\" → likely \"searching\" — like \"midin\"\n\nSo \"bargan\" = searching\n\nThen: \"is searching for the mother that is always being followed by the offended father and is the possum?\"\n\nNo — \"gubimbuluNunéanaymuNagu banéan\" → the one that is always being followed by the offended father → is the possum?\n\n\"banéan\" = possum → so the object is the possum?\n\nBut the structure is: [X] is searching for [Y] where Y has a modifier.\n\nIn 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\"\n→ \"The quiet boy is looking at the tired lizard\"\n\n\"biñéiriñ\" = quiet\n\"biNgun\" = tired\n\"ñalNgaNgu\" = lizard → so \"quiet boy is looking at the tired lizard\"\n\nSo \"biñéiriñ biNgun\" → quiet and tired → compound attributes\n\nSo modifiers can be multiple.\n\nIn 19: \"yaóaNgu gubimbuluNunéanaymuNagu banéan\" = mother that is always being followed by the offended father and is the possum?\n\nBut \"banéan\" = possum → so if the mother is the possum, then it's a name?\n\nUnlikely.\n\nPerhaps the phrase is: the mother that is always being followed by the offended father → and the possum?\n\nBut no.\n\nMore likely: \"yaóaNgu\" = mother\n\"gubimbuluNunéanaymuNagu\" = that is always being followed by the offended father\n\"banéan\" = possum → so the mother is the possum?\n\nBut in 7: \"death adder that is always searching for scorpions is following the possum\"\n\nSo \"following the possum\" → → \"is following\" + \"possum\"\n\nIn 19: \"bargan baNgul yaóaNgu...\" → \"searching for\" mother?\n\nBut \"yaóaNgu\" is the object.\n\nSo: \"bayi bargan\" → death adder is searching for [object]\n\nObject: \"yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nThus: \"the mother that is always being followed by the offended father and is the possum\"?\n\nBut that makes no sense.\n\nAlternative: \"gubimbuluNunéanaymuNagu\" = the one that is always being followed by the offended father → and is the possum?\n\nBut \"banéan\" = possum → so object = the possum?\n\nBut \"yaóaNgu\" = mother → so \"mother\" is the subject?\n\nSo: \"the mother that is always being followed by the offended father\" — and the possum is a separate noun?\n\nNo — structure is one noun phrase.\n\nPossibility: \"gubimbuluNunéanaymuNagu banéan\" = the one that is always being followed by the offended father — and is the possum?\n\nSo the mother is the possum?\n\nBut \"banéan\" = possum → and \"yaóaNgu\" = mother — could be identity?\n\nBut that would be strange.\n\nIn sentence 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\"\n→ \"The death", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12607.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "First, analyze the structure of the Dyirbal sentences and their English translations to identify consistent patterns.\n\nWe note that many sentences have a basic structure: \n[Actor] [verb] [noun-noun phrase] [modifier phrase] \nThe verb often indicates a relationship (e.g., \"is making\", \"is blaming\", \"is carrying\", \"is searching\", etc.). The modifiers are typically descriptive (e.g., \"that is always being blamed\", \"that is always following\", etc.), and appear in a consistent pattern involving postposed possessive or relative clauses.\n\nLook at the verb templates:\n\n- \"bayi X\" = \"booze is making\" → in 1,8 → becomes [booze is making] + [subject] + [tired/fat/etc.]\n- \"balan X\" = \"the strong man is blaming\" / \"the smoke is making\" → \"balan\" = \"the [something] is [making/blaming/carrying/etc.]\"\n- \"bala X\" = \"the [something] is [searching/carrying/pushing/etc.]\"\n\nThe nominal phrase structure often follows: \n[Agent] + [transitive verb] + [patient/changed object] + (optional adjective phrase)\n\nModifiers like \"that is always being blamed\" appear as phrases like \"biNgunman\", \"guliNgu Nunéañu\", \"éamiman\", etc.\n\nNow analyze each target sentence:\n\n---\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak down: \n\"balan\" → \"the [X] is making\" \n\"ñalNga\" → corresponds to \"quiet boy\" in sentence 15 (\"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\") → \"ñalNga\" = \"quiet boy\" (from \"biñéiriñ\" = quiet) \n\"baNgul\" = \"is carrying / is making\" verb (in 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" — \"is blaming\") \nIn sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\" → \"biñéiriñ\" = quiet → \"biNgun\" = looking at → \"baNgul\" = looking at\n\nSo in sentence 17: \n\"balan ñalNga baNgul\" → \"the [X] is making the [quiet boy]\" \nBut \"ñalNga\" is the subject of \"baNgul\", which is likely \"is looking at\" or \"is carrying\"\n\nWait: \"balan\" is the subject, then \"ñalNga\" is the object? But in sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" — \"the quiet boy is looking at (the) tired lizard\"\n\nSo \"baNgul\" is the verb, attached to the object.\n\nThus, in 17: \"balan ñalNga baNgul\" — \"the [something] is making the quiet boy\"\n\n\"NumaNgu\" → from sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"the man that is always being followed\" → \"Numa\" = \"that is always being followed\", \"guli\" = \"is following\" → \"Numa\" is a modifier (always being followed)\n\n\"NumaNgu\" → same as \"Numa\" + \"guli\" = \"man that is always being followed\" → \"Numa\" = being followed → \"guli\" = following → \"NumaNgu\" = the man that is following?\n\nBut in sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is offending the strong father\"\n\nSo \"Numa guli\" = \"the man that is always being followed\"\n\nThus \"NumaNgu\" likely means \"man that is always being followed\"\n\n\"guniymuNagu\" → compare with sentence 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"dragonfly is searching for stinging tree\" → \"guniñu\" = stinging tree → \"guniymuNagu\" likely = \"stinging tree\" (same stem, with suffix?) \nIn 15: \"mugurugu buóan\" → \"tired lizard\"\n\n\"guniymuNagu\" → likely = \"stinging tree\"\n\n\"bambunman\" → in 3: \"balan waymin bambun baNgu éugaNgu éamiman\" → \"sugar is making the healthy mother-in-law fat\" → \"bambun\" = fat → \"bambunman\" = fat\n\nSo \"bambunman\" = fat\n\nThus, 17: \n\"balan ñalNga baNgul\" = \"the [X] is making the quiet boy\" → but subject is \"balan\", so \"the [something] is making the quiet boy\"\n\nBut what is the \"something\"? \n\"NumaNgu\" = man that is always being followed \n\"guniymuNagu\" = stinging tree \nSo \"NumaNgu guniymuNagu\" = \"the man that is always being followed is following the stinging tree\"?\n\nBut structure: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n→ \"the [X] is making (the quiet boy) [with] NumaNgu guniymuNagu bambunman\"\n\nBut \"baNgul\" is the verb \"is making\", and \"baNgul\" is attached to the object \"ñalNga\"\n\nThus: \"balan\" = subject \n\"ñalNga\" = object \n\"baNgul\" = verb \"is carrying or making\" \n\"NumaNgu guniymuNagu bambunman\" = describes the modification of the object?\n\nBut in sentence 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n\nSo \"baNgul\" is a verb, attached to the object, indicating action on it.\n\nSo here: \"balan ñalNga baNgul [modifier]\" — so \"the something is making [quiet boy] [with modifier]\"\n\nBut what is the modifier? \"NumaNgu guniymuNagu bambunman\" — likely a noun phrase.\n\n\"NumaNgu\" = man who is always being followed \n\"guniymuNagu\" = stinging tree \n\"bambunman\" = fat → modifies \"guniymuNagu\"?\n\nNo — in 3, \"bambun\" = fat, and it's a property of the mother-in-law.\n\nIn 5: \"balan malayigara baNgu garandu biNgunman\" → \"smoke is making scorpion tired\" → \"biNgunman\" = tired\n\nSo adjectives are attached as postmodifiers.\n\nThus, \"bambunman\" = fat → applies to \"guniymuNagu\"?\n\nBut \"guniymuNagu\" likely = stinging tree → \"fat stinging tree\"?\n\nBut no such thing. More likely: \"bambunman\" applies to the man?\n\nBut \"NumaNgu\" is \"man that is always being followed\" — could be modified by \"bambunman\" → \"the man that is always being followed and is fat\"?\n\nBut \"bambunman\" is not directly attached to \"NumaNgu\" — the phrase is \"NumaNgu guniymuNagu bambunman\" → a chain.\n\nFrom examples: \n- 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" → \"strong man is blaming mother that is always following death adders\" \n→ \"guliNgu Nunéañu\" → \"that is always following death adders\" → \"guli\" = following, \"Nunéañu\" = death adders\n\nSo \"guli\" is verb, \"Nunéañu\" is object.\n\nSo \"NumaNgu\" = man that is always being followed? → \"Numa\" = always being followed → \"guli\" = following?\n\nBut \"guli\" is literal follow.\n\nSo pattern: [X] + [guli] + [N] = \"X that is following N\"\n\nSo \"NumaNgu\" → \"man that is always being followed\"? \n\"Numa\" + \"guli\"? → if \"Numa\" = \"always being followed\", \"guli\" = \"following\" → might be redundant.\n\nAlternatively, \"Numa\" = always being followed, so \"Numa\" alone can modify.\n\nBut in sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"the man that is always being followed is offending the strong father\"\n\nSo \"Numa\" = \"that is always being followed\"\n\nThus \"NumaNgu\" = \"man that is always being followed\" (the N changes from \"Numa\" to \"NumaNgu\" — likely nom. form)\n\nSimilarly, \"guliNgu\" = \"that is always following\" → \"guli\" = following, \"Ngu\" = possessive?\n\nNo: \"guliNgu \" → \"that is always following\"\n\nSo \"guli\" = following, \"Ngu\" = descriptive suffix?\n\nIn 2: \"guliNgu Nunéañu\" → \"that is always following death adders\"\n\nSo \"guli\" + \"Ngu\" → \"that is always following\"\n\nSo \"guli\" = verb stem (following), \"Ngu\" = relative clause marker?\n\nIn 15: \"biñéiriñ biNgun baNgul\" → \"quiet boy is looking at\"\n\n\"biNgun\" = looking at\n\nThus, derived:\n\n- \"baNgul\" = verb meaning \"is making\" or \"is carrying\" depending on context\n- \"guli\" = \"following\" (verb)\n- \"bambun\" = \"fat\"\n- \"ñalNga\" = \"quiet boy\"\n- \"Numa\" = \"that is always being followed\"\n\nSo back to 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n→ \"the [something] is making the quiet boy\" \n→ the \"something\" is \"NumaNgu guniymuNagu bambunman\"?\n\nBut from pattern, \"NumaNgu\" = man who is always being followed \n\"guniymuNagu\" = stinging tree? (from \"guniñu\" = stinging tree in 10) \n\"bambunman\" = fat → applies to \"guniymuNagu\"? → \"fat stinging tree\"?\n\nUnlikely.\n\nAlternatively, \"bambunman\" applies to the man → \"man who is always being followed and is fat\"?\n\nBut structure: \"NumaNgu guniymuNagu bambunman\" — likely a noun phrase: **the man that is always being followed, following the stinging tree, which is fat**?\n\nBut \"bambunman\" = fat → adjective.\n\nCould it mean \"the man who is always being followed and is fat, and is following the stinging tree\"?\n\nBut no verb link.\n\nWait — in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\" → \"biNgun\" = looking at, \"ñalNga\" = quiet boy, \"mugurugu\" = tired, \"buóan\" = lizard.\n\nSo \"biNgun\" = verb, \"baNgul\" = looking at? But it's \"biNgun\", not \"baNgul\"\n\nIn 17: \"baNgul\" is the verb.\n\nIn sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"man that is always being followed is offending the strong father\"\n\n\"baNgul\" = is offending\n\nSo \"baNgul\" = verb of action (offending, carrying, making)\n\nSo in 17: \"balan ñalNga baNgul\" = \"the something is carrying or making the quiet boy\"\n\nBut \"something\" = \"NumaNgu guniymuNagu bambunman\"\n\nSo \"the [man who is always being followed, following the stinging tree, which is fat] is making the quiet boy\"\n\nBut what does \"making\" imply? In other cases like sentence 1: \"booze is making the man tired\" — \"making\" = causing to be [tired]\n\nHere, if \"making the quiet boy\", then the result is on the quiet boy.\n\nBut no adjective on \"ñalNga\" — the quiet boy is not described as tired or fat.\n\nThus, likely \"is making\" = is causing the boy to become [something]\n\nBut no property.\n\nAlternatively, \"baNgul\" = \"is carrying\" — then \"carrying the quiet boy\"?\n\nBut the boy is not being carried.\n\nCompare to sentence 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"the fat doctor is pushing the big stone\" → \"baNgul\" = pushing → transitive\n\nIn 17: if \"balan\" = a substance (like booze), then it could \"make\" something tired.\n\nBut in 1, \"bayi\" = booze → \"is making\"\n\nIn 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → \"death adder that is always searching for scorpions is following the possum\" → \"bayi\" = death adder (subject) → so \"bayi\" is not always “booze”\n\n\"bayi\" appears in 1,8 — 1: \"booze is making\", 8: \"booze is making\"\n\nBut in 7: \"bayi midin\" — \"death adder that is always searching\" → so \"bayi\" is a noun for various animals.\n\nSimilarly, \"balan\" in 2: \"strong man\" — subject\n\nSo \"balan\" = \"the strong man\" or \"the [something]\" — base noun\n\nThus in 17: \"balan\" = the [something] that is making \n\"ñalNga\" = quiet boy → object \n\"baNgul\" = verb = making / carrying / causing\n\nSo \"the something is making the quiet boy\"\n\n\"NumaNgu guniymuNagu bambunman\" = describing the something\n\n\"NumaNgu\" = man that is always being followed \n\"guniymuNagu\" = stinging tree? (guniñu = stinging tree) \n\"bambunman\" = fat → applied to \"guniymuNagu\"? → fat stinging tree?\n\nUnlikely.\n\nMaybe \"bambunman\" modifies \"NumaNgu\" → man who is fat and always being followed?\n\n\"guniymuNagu\" = following the stinging tree?\n\nBut no \"following\" verb.\n\nPerhaps guli is missing — but not present.\n\nAlternative: look at sentence 18 and 19 for patterns.\n\n18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n\n\"bala\" → subject = the [something] \n\"diban\" → fat → \"fat doctor\" in 12 → \"diban\" = fat \n\"bilmbalmuNa\" → from sentence 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law that is always pushing stones is looking at smoke\" \n\"waymindu\" = pushing \n\"dibanbilmbalNaymuNagu\" → \"mother-in-law that is always pushing stones\" → \"diban\" = fat, \"bilmba\" = pushing, \"l\" = following? \nBut \"bilmbalNaymuNagu\" — likely compound.\n\nIn 13: \"dibanbilmbalNaymuNagu\" → \"fat mother-in-law that is always pushing stones\"\n\nSo \"bilmbalNaymuNagu\" = \"that is always pushing stones\"\n\nThus \"bilmbalmuNa\" → \"that is always pushing stones\" → likely same base.\n\nSo \"bala diban bilmbalmuNa\" = \"the fat thing that is always pushing stones\" → subject\n\n\"baNgun\" = verb — in sentence 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"tired wallaby is searching for little feather\" → \"baNgul\" = searching\n\nIn 9: \"bala garan baNgun biñéiriñéu banéan\" → \"lizard is following the smoke\" → \"baNgun\" = following\n\nSo \"baNgun\" = \"is following\"\n\n\"biñéiriñéu\" = the quiet one? → from 15: \"biñéiriñ\" = quiet → \"biñéiriñéu\" = the quiet one\n\n\"guniñu\" = the little feather\n\nSo \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\" → \"the fat thing that is always pushing stones is following the quiet one, the little feather?\"\n\nBut \"biñéiriñéu\" = quiet one → \"guniñu\" = little feather?\n\nIn 4: \"bargandu biNgundu guniñu\" → \"little feather\"\n\nSo \"guniñu\" = little feather\n\nSo this means: \"the fat thing that is always pushing stones is following the quiet little feather\"\n\nBut \"biñéiriñéu\" = the quiet one → if it's \"the quiet little feather\", then it makes sense.\n\nIn 15: \"quiet boy\" → so \"quiet\" is descriptive.\n\nSo \"biñéiriñéu\" = \"the quiet\" → describes the object.\n\nSo 18: \"the fat thing that is always pushing stones is following the quiet little feather\"\n\nBut what is \"diban", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12446.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "Unit id: b.1 — \"I begin to eat it\" \nLook for equivalents of \"begin to eat\". The form \"kekēskahtæq\" means \"we1+2 bite it through\" (bites into it). \"Begin to eat\" is similar to beginning to consume, which may involve biting or gnawing. The form \"ketāwahtæq\" means \"we1+2 bite, gnaw a hole in it\". The form \"ketǣnam\" is \"he takes it out by hand\", not directly eating. \"kewǣpeqtaq\" is \"we begin\", and \"wǣpohnæw\" is \"he begins walking\". \n\nBut \"ketāwahtæq\" involves gnawing, which is close to eating. However, \"begin to eat\" is more reflexive than just gnawing. \"KePtāwahtæq\" is a form for group eating. For \"I begin to eat\", we need a form where the subject is first person singular and the action is \"begin to eat\". \n\nLooking at \"kewǣpānæhkæq\" — \"we1+2 begin to dig\". The pattern of \"begin + to + verb\" is established. So \"begin to eat\" might follow a similar structure. \"I begin\" = \"I start\" → might use \"kewǣpeqtaq\" form, but with \"eat\" as the verb. \n\nBut in the list, \"kekēskahtæq\" = we1+2 bite through → not eating per se. \"ketāwahtæq\" = gnaw a hole in it → close, but not exactly \"begin to eat\". \n\nIs there a verb for \"begin eating\"? Possibly derived from \"begin\" + \"eat\". The form \"kewǣpeqtaq\" is \"we begin\", and \"kewǣpānæhkæq\" is \"we begin to dig\". The root structure is *kewǣp- + verb. So “begin to [verb]” uses the *kewǣp- prefix. \n\nSo \"begin to eat\" would use *kewǣp- + the verb for \"eat\". But that verb is not directly listed. Yet \"kepītahtæq\" = \"we1+2 come eating it\" — suggesting a form for eating. \"I begin to eat\" may be similar. \n\nHowever, \"kepītahtæq\" is \"we come eating it\", not \"begin\". \n\nBut consider: \"I begin to eat\" → subject is first person, verb is \"begin to eat\". \"begin\" is a verb. The form \"kewǣpānæhkæq\" is \"we begin to dig\" → so \"begin to [X]\" uses *kewǣp- + [X]. \n\nSo if \"eat\" is a verb, we need to find the root. \"ketāwahtæq\" = we bite, gnaw → perhaps \"eat\" is derived from that. But it's \"we\", not \"I\". \n\nIs there a form for \"begin to eat\" in first person? The list has no direct form. But \"kewǣpeqtaq\" = we begin (no verb after). So perhaps \"begin to eat\" is formed with *kewǣp- and the verb root for eat. \n\nLooking at \"nepītohnæm\" = \"I walk here\", and \"pekāsh\" might be a root. \n\nWait: \"kepītahtæq\" = \"we1+2 come eating it\" — the verb is \"came eating\", so eating is part of the meaning. But \"begin to eat\" is starting the action. \n\nCould \"kepītahtæq\" be used for \"I begin to eat\"? No, it's \"we come eating\", not \"start eating\". \n\nPossibility: the verb for eat is derived from \"bite\" or \"gnaw\". So \"begin to eat\" → begin to gnaw. The form for \"gnaw\" is in \"ketāwahtæq\" (we bite/gnaw). So \"I begin to gnaw\" might be the translation. But the task says \"I begin to eat\". \n\nEarlier, \"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\" — could be interpreted as \"begin to eat\" if \"bite\" is a verb of eating. So \"I begin to eat\" → \"I begin to bite\" → \"I begin to gnaw\". Since \"bite\" is a form of eating, it could be acceptable. \n\nBut better: is there a root form \"eat\"? Looking at \"kekēskahtæq\" — we bite through. \"ketāwahtæq\" — we bite/gnaw. So \"biting\" is the verb. So \"begin to eat\" = \"begin to bite\". \n\nSo the Menominee form might be \"kewǣpānæhkæq\" with \"biting\" → but that's \"begin to dig\". Structure is: *kewǣp- + verb. So if the verb is \"bite\", we need the form of \"bite\". But \"ketāwahtæq\" is \"we1+2 bite, gnaw\". No first person singular. \n\nSo is there a first person \"I begin to bite\"? No form given. \n\nAlternative: the verb \"eat\" might be part of a verb like \"kepītahtæq\" → which is \"we come eating it\" — perhaps \"begin to eat\" is not listed. \n\nBut the structure of \"kewǣpeqtaq\" is \"we begin\", so \"I begin\" would be \"I start\" → but no direct form. \n\nWait: \"nektāwāhpem\" = \"I fall over laughing\". \"nekāwāhpem\" = I fall over laughing. So \"I\" verbs are used with first person prefix. \n\nLooking at \"nektāwāhpem\" — first person. \"nepītohnæm\" — I walk here. \n\nCould \"I begin to eat\" be derived from \"kewǣpeqtaq\" with a change? Or a form like \"newāckesan\" = I cut around it. \n\nNot helping. \n\nBut: \"pāhkeqtaw\" = he opens up. \"pāhkaham\" = he opens by tool. \n\nStill not relevant. \n\nAnother idea: perhaps \"begin to eat\" is equivalent to \"begin to gnaw\", and gnaw is \"ketāwahtæq\" for we. But we need first person. \n\nIs there a form like \"nektāwahtæq\"? Not given. \n\nBut: \"nekāwāhpem\" = I fall over laughing. So the first person is marked with \"ne-\". \n\nSo perhaps \"I begin to eat\" → \"ne-kewǣp- + verb\". But no such form given. \n\nHowever, in the list, \"kewǣpānæhkæq\" = \"we1+2 begin to dig\" — this shows that \"kewǣp- + verb\" = begin to [verb]. \n\nSo \"begin to eat\" → kewǣp- + eat. But we don’t have \"eat\" as a verb root. \n\nBut \"ketāwahtæq\" = we bite, gnaw → so perhaps \"eat\" is a synonym for \"gnaw\". In that case, \"begin to eat\" = begin to gnaw → so verb root is from \"ketāwahtæq\". \n\nSo \"kewǣp- + keta-?\" → not found. \n\nWait: the form \"ketāwahtæq\" has root \"ketāw\". Could \"kewǣpaketāw\" be formed? Unlikely. \n\nBut is there a form directly meaning “I begin to eat”? \n\nLooking again: \"kepītahtæq\" = \"we1+2 come eating it\" → which is ongoing eating. \n\n\"begin to eat\" is initiation. \n\nPerhaps the only possible equivalent is a form like \"kewǣp- + gnaw\" — and since gnaw is used in eating, it might be acceptable. \n\nBut no first person. \n\nAlternative: maybe \"begin to eat\" = \"begin to bite\" = \"kewǣp- + bite\". \n\nBite is in \"ketāwahtæq\", so root is keta. \n\nSo form might be \"kewǣpaketāw\"? But that’s not in the list. \n\nBut in \"kewǣpānæhkæq\", \"kewǣp- + ānæhkæ\" = begin to dig. So verb is \"dig\". \n\nSo for \"eat\", we need a verb root. \n\nNo verb for \"eat\" is listed. The closest is \"gnaw\" or \"bite\". \n\nPerhaps in Menominee, \"begin to eat\" = \"begin to gnaw\" → and the verb is \"gnaw\". \n\nSo the translation might be \"kewǣpaketāw\"? But not in the data. \n\nWait — is there a form \"ne-kewǣp...\"? No. \n\nBut the verb \"eat\" might be \"kēskenam\" — \"he breaks it through by hand\" → not eating. \n\n\"pahkǣsam\" — he cuts it off → not eating. \n\nNo. \n\nConclusion: \"begin to eat\" is best approximated by \"begin to bite\" → so form is \"kewǣp- + the root for bite\". \n\nBite is in \"ketāwahtæq\" — so root \"ketāw\". Possible form: \"kewǣpaketāw\". But no such form. \n\nWait — look at \"kewǣpānæhkæq\" — \"we1+2 begin to dig\" → \"kewǣp- + ānæhkæ\". \n\nSo if \"eat\" is like \"bite\", and \"bite\" is in \"ketāwahtæq\", perhaps \"begin to eat\" = \"kewǣpaketāw\"? But this is not listed. \n\nBut in the list, \"newāckesan\" = I cut around it → so \"cut\" is with \"newāc\". \n\nNo verb for eat. \n\nAlternative: maybe \"I begin to eat\" uses \"kepītahtæq\" — but that's \"come eating\", not \"begin\". \n\nSo perhaps the intended solution is \"kewǣpaketāw\", but it's not in the dictionary. \n\nAnother possibility: \"begin to eat\" = \"come eating\" but that's not \"begin\". \n\nWait — perhaps there's no direct form. But we must derive from patterns. \n\nNote: \"nepītohnæm\" = I walk here → first person, 'I walk here'. \n\n\"nekāweqtam\" = I lie down → first person. \n\n\"nekāwāhpem\" = I fall over laughing. \n\nSo first person: starts with \"ne-\". \n\nSo \"I begin to eat\" → \"ne-kewǣp-...\"? \n\nBut \"kewǣp\" is \"we begin\", not \"I begin\". \n\nSo perhaps \"ne-kewǣp-\" is not standard. \n\nBut look at \"kekēskahtæq\" = we1+2 bite through → \"we bite through\". \n\n\"ketāwahtæq\" = we bite/gnaw. \n\nSo \"bite\" is used. \n\nSo \"I begin to eat\" → \"I begin to bite\" → \"ne-kewǣpaketāw\"? \n\nBut no such form. \n\nPerhaps \"begin to eat\" is just \"kewǣp- + eat\", and \"eat\" is not found, so must be inferred. \n\nBut no match. \n\nAlternative: could \"kepītahtæq\" be used? \"we come eating\" — not \"begin\". \n\nPerhaps the verb for \"eat\" is missing, but in context, \"begin to eat\" is equivalent to \"begin to gnaw\" → so verb is \"gnaw\". \n\nSo the Menominee form is \"kewǣpaketāw\" — but not in the list. \n\nWait — is there a form for \"lay it flat by hand\"? That might be clearer. \n\nUnit b.2: \"we1+2 lay it flat by hand\" \nLay flat — like \"place level\". \"walk here\" = \"nepītohnæm\" — I walk here. \"pāhkeh\" = open up. \n\n\"lay it flat\" — could be \"place it level\". \n\nIs there a verb for \"place\" or \"lay\"? \n\n\"pāhkeqtaw\" = he opens up → not flat. \n\n\"pāhkaham\" = he opens by tool → opening. \n\n\"nektāwāhpem\" = I fall over laughing. \n\nNo \"lay\". \n\nBut \"we1+2 walk out\" is given — \"kekǣtohnæq\" = we walk out. \n\nAnd \"we1+2 walk here\" is \"nepītohnæm\" → I walk here. \n\nSo \"walk\" is with \"ne-\" and \"kew-\" prefixes. \n\n\"lay it flat\" — not in list. \n\n\"pāhkaham\" = open by tool → maybe opening. \n\n\"pāhkeqtaw\" = open up. \n\n\"kepītahtæq\" = we come eating. \n\nNo \"lay flat\". \n\nBut \"nepītohnæm\" = I walk here → maybe \"walk\" is used for placement? Unlikely. \n\nPerhaps \"lay\" is not a verb here. \n\nAnother idea: \"lay it flat by hand\" → \"place it flat by hand\". Hand is part of it. \n\n\"break it\" = kēskenam. \"cut it\" = pahkǣsam. \n\n\"dig a hole\" = ? \n\nLook at unit b.3: \"he digs a hole\" — so verb for dig. \n\nIn list: \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is \"ānæhkæ\". \n\nSo \"he digs a hole\" → \"he begins to dig\"? But that's \"we\". \n\n\"he digs\" → could be \"he dig\" → in the list, \"kewǣpānæhkæq\" is we1+2 begin to dig → so for \"he\", it might be \"he dig\" without \"begin\"? \n\nBut the list has no standalone \"he dig\". \n\n\"pahkǣsam\" = he cuts it off → cutting. \n\n\"tawǣsam\" = he cuts a hole in it → cuts a hole. \n\n\"pāhkaham\" = he opens by tool. \n\n\"pahkǣsam\" = cut off. \n\n\"tawǣsam\" = cut a hole → so \"cut a hole\" = tawǣsam. \n\n\"dig a hole\" — different from cut. \n\n\"dig\" is not in list. \"begin to dig\" is in list: kewǣpānæhkæq. \n\nIs there a verb for \"dig\"? \n\nLooking at the form \"kewǣpānæhkæq\" — \"we1+2 begin to dig\" → so \"dig\" is \"ānæhkæ\". \n\nSo \"he digs\" would be \"he + dig\" → but no standalone form. \n\nBut \"dig a hole\" might be \"he begins to dig\"? But that's \"we\". \n\n\"he\" verb? \n\n\"pahkǣsam\" = he cuts it off — \"cut\" not \"dig\". \n\n\"tawǣsam\" = he cuts a hole → so \"cuts a hole\", not \"digs a hole\". \n\nSo \"dig a hole\" is not directly available. \n\nBut perhaps \"he digs a hole\" = \"he begins to dig\", and since the form for \"begin to dig\" is \"kewǣpānæhkæq\", and \"he\" could be used with \"kewǣp-\", but \"kew-\" is \"we\", not \"he\". \n\n\"he\" is in forms like \"kawāham\", \"kēskenam\", \"pahkǣsam\" — so the root verbs are in the third person. \n\nSo \"he digs\" must be a third person verb. \n\nIs there a verb like \"he digs\"? Not directly. \n\nBut \"he cuts a hole\" is \"tawǣsam\". \n\n\"dig a hole\" might be equivalent to \"cut a hole\"? Not likely. \n\nAlternative: \"dig a hole\" could be \"he begins to dig\", even if it's not in list. \n\nBut \"kewǣpānæhkæq\" is \"we begin to dig\", not \"he\". \n\nSo no. \n\nBut perhaps in Menominee, the verb \"dig\" is used in \"kewǣpānæhkæq\" and only has \"we\" form. \n\nSo not helpful. \n\nUnit b.4: \"he walks out\" → this is given in \"kekǣtohnæq\" = we1+2 walk out. \n\nSo \"we1+2 walk out\" → so \"he walks out\" would be missing. \n\nBut the only form is \"kekǣtohnæq\" for \"we1+2 walk out\". \n\nNo form for \"he walks out\". \n\nBack to b.1: \"I begin to eat\" — from the forms, the only verb close to \"eat\" is \"bite\" or \"gnaw\" in \"ketāwahtæq\". \n\nSo \"I begin to eat\" → likely \"kewǣpaketāw\" — but not in list. \n\nBut perhaps the verb root is from \"ketāw\", and \"begin\" is kewǣp. \n\nSo form is \"kewǣpaketāw\". \n\nBut that's not in list. \n\nAnother possibility: \"kepītahtæq\" = \"we come eating it\" — so eating is present. \n\n\"begin to eat\" might be \"start eating\" — no form. \n\nBut perhaps \"I begin to eat\" is the same as \"we begin to eat\" using \"kewǣp-\". \n\nBut for first person, it's not clear. \n\nNow, unit b.2: \"we1+2 lay it flat by hand\" \n\n\"lay it flat\" → level. \"by hand\" is \"by hand\" — so perhaps \"by hand\" indicates the manner. \n\nVerbs with \"by hand\" or \"by tool\" are: \n\n- kēskenam = he breaks it through by hand \n- pāhkaham = he opens it by tool \n- nekǣtahan = I pry it out by tool \n\nSo \"by", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11717.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "b.1: kewǣpānæhkæq \nb.2: kekǣtohnæq \nb.3: kewǣpeqtaq \nb.4: kekǣtohnæq \n\nScratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|------------------------------------|-----------------------------|---------|\n| b.1 | I begin to eat it | kewǣpānæhkæq | \"we1+2 begin to dig\" → \"begin\" + \"by hand\" or \"into\"; \"begin to eat\" likely uses \"begin\" + \"eat\" verb; \"kewǣpānæhkæq\" = \"we1+2 begin to dig\" → \"begin\" is core, \"to eat\" may be implied; but no direct \"eat\" verb. However, \"kekēskahtæq\" = \"we1+2 bite it through\", \"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\". \"I begin to eat it\" → \"begin\" + \"to eat\" → likely inflected as \"begin\" with intention of eating. But no \"eat\" form. But \"begin\" + \"bite\" = possible. However, \"kewǣpānæhkæq\" = begin to dig. \"begin to eat\" is not directly given. But \"begin\" stems from kewǣpeqtaq (we begin), kewǣpānæhkæq (we begin to dig), so kewǣpānæhkæq is \"begin to act with hand/tool\". So for \"I begin to eat it\", likely \"kewǣpānæhkæq\" with semantic shift? But no \"eat\" verb. Alternatively, \"kekēskahtæq\" = bite through, a small amount. Not eating. \"ketāwahtæq\" = bite/gnaw a hole. Still not eating. But \"kekāpeth\" not present. Perhaps \"begin to eat\" is not a direct verb. But \"begin\" is in kewǣpeqtaq, kewǣpānæhkæq. So \"begin\" = kewǣpā-? \"I begin to eat\" → likely uses \"begin\" + eating. But no forming. \"kepītahtæq\" = we come eating it. So \"eat\" is involved. But no verb for \"I begin to eat it\". No direct form. So best match: \"begin\" verb is used in kewǣpānæhkæq (we begin to dig), and \"to eat\" may be implied by \"bite\" or \"gnaw\". So perhaps \"ketāwahtæq\" (we bite/gnaw) but for \"I\". \"nekāwāhpem\" = I fall over laughing. No. Only candidate using \"begin\" with hand is kewǣpānæhkæq. But \"dig\" and \"eat\" are different. But \"begin to eat\" = possibly \"kewǣpeqtaq\" with eating? Not clear. However, in the given list, \"we1+2 come eating it\" = kepītahtæq. \"we1+2 bite\" = ketāwahtæq. So \"I begin to eat it\" — no direct form. But perhaps \"kewǣpeqtan\" not present. Only \"begin\" indicator is kewǣpeqtaq. So likely, \"begin to eat\" is represented by a form with \"begin\" and \"eat\" implied. But no such form. However, \"kewǣpānæhkæq\" = begin to dig — use of \"begin\" + instrumental. Perhaps minore use of same root. But no \"eat\". So perhaps the intended form is not available. But in Menominee, verbs are often compound or derived. Given the translation \"I begin to eat it\" → missing direct form. But \"begin\" = kewǣpeqtaq. So perhaps the verb must be derived from \"begin\" + \"eat\". But no. Alternatively, \"biting\" is eating in small way. \"I bite it\" = ketāwahtæq (we1+2). \"I bite\" = nekāwāhpem? No. \"I lay it flat\" = we1+2 lay flat → kekǣtohnæq (we1+2 walk out) — that's \"walk out\", not lay flat. \"we1+2 lay it flat by hand\" → \"lay\" not directly present. \"we1+2 walk out\" → kekǣtohnæq. \"he walks out\" → kekǣtohnæq. \"he digs a hole\" → \"dig\" = kewǣpānæhkæq (we1+2 begin to dig) — \"dig\" is in \"begin to dig\". \"he digs a hole\" → likely kewǣpānæhkæq? But \"we1+2\". \"he\" = singular. So need singular for \"he digs\". \"kewǣpānæhkæq\" is we1+2. \"he begins to dig\" — not given. Only \"we1+2 begin to dig\". So no \"he digs\". But \"he cuts it off\" = pahkǣsam. \"he cuts a hole\" = tawǣsam. \"he opens it by tool\" = pāhkaham. \"he breaks it through by hand\" = kēskenam. So digging a hole → \"dig\" might be \"kewǣpānæhkæq\", but only with \"we\". Need singular \"he digs\". No such form. But \"he begins to dig\" = kewǣpānæhkæq with subject he? Not given. But only \"we1+2 begin to dig\". So perhaps the form is the same? But no. So must derive. Is there a verb for \"dig\"? Yes, in \"begin to dig\" = kewǣpānæhkæq. So \"he digs\" may be an interpretation of that. But \"he walks out\" = kekǣtohnæq. \"we1+2 walk out\" = kekǣtohnæq. So \"we1+2 walk out\" = kekǣtohnæq. \"he walks out\" = same form? But different subject. Probably no. So need singular form for \"he walks out\". \"he walks out\" = kekǣtohnæq? But only we1+2 form. \"we1+2 walk out\" = kekǣtohnæq. So \"he walks out\" must be from same root. So likely kekǣtohnæq is for \"we1+2\", and singular form not given. So perhaps the form is the same. Or multiple forms. But no singular in list. So perhaps the translation assumes the same form. So \"he walks out\" = kekǣtohnæq. Similarly, \"he digs a hole\" = kewǣpānæhkæq — but \"we1+2\". Perhaps no singular, so use same stem. But \"lay it flat by hand\" → \"lay flat\" → no verb. \"we1+2 lay it flat by hand\" → \"lay\" not present. \"walk\" is in \"we1+2 walk out\" = kekǣtohnæq. \"begin\" = kewǣpeqtaq. \"begin to eat\" — only kewǣpānæhkæq has \"begin to dig\", not eat. \"begin to eat\" → perhaps from \"bite\" or \"gnaw\"? \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it. So \"I bite it\" = ? not given. \"I lay it flat\" → no \"lay\" verb. \"we1+2 walk out\" → kekǣtohnæq. So likely \"he walks out\" = kekǣtohnæq. \"he digs a hole\" → \"dig\" → likely kewǣpānæhkæq (begin to dig) — but only we1+2. But no singular. So perhaps all are derived from the root with subject omitted. So \"he digs a hole\" = kewǣpānæhkæq. \"I begin to eat it\" → \"begin to eat\" → no verb. But \"bite\" is used for eating. So \"I begin to eat it\" = something with \"begin\" and \"bite\". \"I bite it\" = nekāwāhpem? No. \"I cut around it\" = newāckesan. No. \"I begin to eat\" → only possible if \"begin\" + \"eat\" → no such form. But \"begin\" in kewǣpeqtaq. \"begin to eat\" → perhaps kewǣpānæhkæq with semantic shift? But \"dig\", not \"eat\". So likely, the intended answer is: \nb.1: kewǣpānæhkæq — because \"begin to eat\" may be equivalent to \"begin to act on it\", and the verb root is shared. But not justified. \nBut go back to list: \n\"we1+2 begin\" = kewǣpeqtaq \n\"we1+2 begin to dig\" = kewǣpānæhkæq \nSo \"begin\" is with various actions. \n\"I begin to eat it\" → likely the form with \"begin\" and \"eat\" or eating action. No such verb. \nBut \"kepītahtæq\" = we1+2 come eating it → eating is involved. \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → eating. \nSo perhaps \"begin to eat\" uses the \"begin\" verb with eating. \nBut form not given. \nAlternatively, \"begin to eat\" might be kewǣpānæhkæq — assume that \"eat\" is semantic equivalent to \"dig\"? No. \nAnother idea: \"lay it flat\" → \"lay\" → not present. \"we1+2 walk out\" = kekǣtohnæq. So \"he walks out\" = kekǣtohnæq. \n\"he digs a hole\" = kewǣpānæhkæq (we1+2) — only available form. \n\"we1+2 lay it flat by hand\" → \"lay flat\" — no verb. \n\"walk out\" = kekǣtohnæq. \n\"begin to eat\" — only \"begin\" verbs. \nBest matches: \n- \"he walks out\" → kekǣtohnæq (we1+2 walk out) — so likely the same form \n- \"he digs a hole\" → kewǣpānæhkæq (we1+2 begin to dig) — likely the only \"dig\" form \n- \"we1+2 lay it flat by hand\" → no direct. \"walk\" is in \"walk out\", but not \"lay flat\". \"lay flat\" might be from \"put down\"? No verb. \"break it through\" = kēskenam. \"cut it off\" = pahkǣsam. \"cut a hole\" = tawǣsam. \"break through\" = kēskenam. No \"lay flat\". \nBut \"we1+2 walk out\" = kekǣtohnæq. \nIs there a verb for \"lay\" or \"place\"? No. \n\"we1+2 come eating it\" = kepītahtæq. \nSo no \"lay\". \nPerhaps \"lay it flat\" is a translation error, or uses a root. \nBut in the list, \"we1+2 walk out\" is kekǣtohnæq. \nSo \"he walks out\" = kekǣtohnæq. \n\"he digs a hole\" = kewǣpānæhkæq (we1+2 begin to dig) — only verb with \"dig\". \n\"we1+2 lay it flat by hand\" → perhaps \"we1+2 walk out\" is not it. Or perhaps \"begin\" is used. \nAnother idea: \"begin to eat\" → could be kewǣpānæhkæq? But \"dig\" not \"eat\". \nBut \"begins to eat\" in Menominee might be with \"begin\" verb. \n\"we1+2 begin\" = kewǣpeqtaq. So \"I begin\" = kewǣpeqtaq with subject marker? Not given. \nSo all forms are in plural or mixed. \nOnly \"I\" forms: \"I walk here\" = nepītohnæm; \"I pry it out\" = nekǣtahan; \"I lie down\" = nekāweqtam; \"I fall over laughing\" = nekāwāhpem. \nSo \"I\" verbs are available. \n\"I begin to eat it\" → not present. \nBut \"I bite\" = nekāwāhpem? No, that's \"fall over laughing\". \n\"nektan\" not present. \nSo perhaps the verb is missing. But must derive from pattern. \nPerhaps \"begin to eat\" is derived from \"begin to dig\" via semantic equivalence? Unlikely. \nPerhaps the verb is \"kepītahtæq\" = come eating — but not \"begin to eat\". \nI suspect that \"I begin to eat it\" is intended to be \"kewǣpānæhkæq\" with subject \"I\" — even though it's \"we1+2\". \nSimilarly, \"he digs a hole\" = kewǣpānæhkæq. \nBut both use the same form. \nHowever, \"we1+2 lay it flat by hand\" — no verb. \n\"lay flat by hand\" — \"hand\" = by hand. \n\"we1+2 walk out\" = kekǣtohnæq. \nSo perhaps: \n- b.1: kewǣpānæhkæq (begin to eat it) — from \"begin to dig\" with semantic shift to eating \n- b.2: kekǣtohnæq (we1+2 lay it flat by hand) — but \"walk out\" not \"lay flat\" \nBut \"we1+2 lay it flat\" — no verb. \n\"we1+2 walk out\" = kekǣtohnæq. \nSo b.2 cannot be kekǣtohnæq. \n\"lay it flat by hand\" — perhaps from \"walk\" or \"move\"? No. \nAnother candidate: \"pahkǣsam\" = he cuts it off. \"tawǣsam\" = cuts a hole. \"pāhkaham\" = opens by tool. \nNo. \n\"kepītahtæq\" = we1+2 come eating it. \n\"ketāwahtæq\" = we1+2 bite, gnaw. \nSo no \"lay flat\". \nPerhaps \"lay it flat\" is a translation of \"we1+2 walk out\"? Unlikely. \nPerhaps the verb is missing, or we have to use existing forms. \nAnother idea: \"we1+2 lay it flat by hand\" might be analogous to \"walk out\" or \"begin\" verbs. \nBut no. \nPerhaps \"lay it flat\" is not a physical action, but a metaphor. \nBut unlikely. \nPerhaps \"we1+2 lay it flat by hand\" = a form with \"place\" or \"put\". \nNo verb. \nSo only possible forms are: \n- begin to eat = kewǣpānæhkæq (we1+2 begin to dig) — assume general \"begin to act\" \n- we1+2 lay it flat by hand = ? \n- he digs a hole = kewǣpānæhkæq \n- he walks out = kekǣtohnæq \n\nBut kewǣpānæhkæq used twice, not allowed. \nMust be distinct. \n\nSo revise: \n- \"he walks out\" = kekǣtohnæq — only form \n- \"he digs a hole\" = ? — only kewǣpānæhkæq available \n- \"we1+2 lay it flat by hand\" = ? \n- \"I begin to eat it\" = ? \n\n\"lay it flat\" — perhaps from \"walk out\"? No. \n\"by hand\" — \"by hand\" = \"through hand\" — kēskenam = breaks it through by hand; so \"by hand\" = through hand. \nSo perhaps a verb with \"through hand\" for laying. \nBut no verb. \nPerhaps \"break it through\" but not \"lay\". \nAnother possibility: \"we1+2 lay it flat\" might be \"we1+2 come eating it\" but not. \n\nPerhaps \"we1+2 lay it flat\" is not directly given. But in the list, \"we1+2 walk out\" = kekǣtohnæq. \n\"we1+2 begin\" = kewǣpeqtaq. \n\"we1+2 bite\" = ketāwahtæq. \nSo no. \n\nUnless \"begin to eat\" is kewǣpeqtaq. \nkewǣpeqtaq = \"we1+2 begin\". \nSo \"I begin to eat it\" = kewǣpeqtaq? With subject and object? But not specified. \n\nBut the only \"begin\" verb is kewǣpeqtaq (we1+2) and kewǣpānæhkæq (we1+2 begin to dig). \nSo \"begin\" root is in kewǣp- (we1+2 beginning). \n\nFor \"he digs a hole\" — only available is kewǣpānæhkæq (we1+2 begin to dig). \nNo singular. \n\nFor \"he walks out\" — only kekǣtohnæq (we1+2 walk out). \n\nFor \"we1+2 lay it flat by hand\" — no verb. \n\nPerhaps \"lay it flat\" is a translation error, or uses \"cut\", \"break\", or \"open\". \n\nBut \"cut a hole\" = tawǣsam. \n\"open it\" = pāhkaham. \n\"break it through\" = kēskenam. \n\"cut it off\" = pahkǣsam. \n\nNo verb for \"lay flat\". \n\nPerhaps in Menominee, \"lay\" is not a separate verb. \n\nAnother thought: \"we1+2 come eating it\" = kepītahtæq —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11187.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "Scratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|--------------------------------------|------------------------------|--------------------------------------------------------------------------|\n| b.1 | I begin to eat it | kewǣpānæhkæq | \"we1+2 begin to dig\" → \"begin\" + \"by hand\" → \"kewǣpānæhkæq\" has \"begin\" + \"by hand\" (digging) – but \"eat\"? Wait. Look for \"begin to eat\". No exact match. \"kepītahtæq\" = we1+2 come eating it; bring in mouth. \"I begin to eat\" → likely uses \"begin\" + eating. Is there a verb with \"begin\" and \"eat\"? No. But \"begin to\" (we1+2) is shared. \"kewǣpeqtaq\" = we1+2 begin. \"kewǣpānæhkæq\" = we1+2 begin to dig. So \"begin\" verbs are prefixed with kewǣ-. \"I begin to eat\" → must be \"I\" form of \"begin\" + \"eat\". Look for \"eat\" in the list. \"kepītahtæq\" = we1+2 come eating it; bring in mouth → contains eating. Is there \"begin to eat\"? Perhaps \"kewǣpānæhkæq\" is misaligned. What about \"kekǣtohnæq\"? we1+2 walk out. \"kēskenam\" = he breaks it through by hand. \"pītenam\" = he passes it here. \"nekāwāhpem\" = I fall over laughing. \"pāhkeqtaw\" = he opens up. Still missing. \"kewǣpānæhkæq\" = begin to dig. \"kekēskahtæq\" = we1+2 bite it through. \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it. So verb for \"begin to eat\"? None. But \"begin to eat\" → \"begin + eat\". \"eat\" is not directly listed. But \"come eating it\" implies eating. Is there a verb for \"begin to eat\"? Maybe formed from \"begin\" + \"bite\" or \"gnaw\"? \"bite\" appears in \"ketāwahtæq\" and \"kekēskahtæq\". \"begin to bite\"? Not available. However, \"begin\" verbs: kewǣ- (we1+2), and \"I\" forms? No \"I begin\" form. Only \"kewǣ-\" for \"we1+2 begin\". \"I begin\" would require \"I\" + begin. But no \"I begin\" form directly. Is there a \"begin\" verb in \"I\" form? \"kewǣpeqtaq\" is \"we1+2 begin\". No \"I begin\". But \"kewǣpānæhkæq\" is \"we1+2 begin to dig\". So \"begin\" + action. For \"I begin to eat\", perhaps no exact match. But look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it. \"bite\" may be used as \"eat\". In some contexts, bite = eat. So \"begin to bite\" = begin to eat? Possibly. No \"begin\" + \"bite\" for \"I\". But the form \"kewǣpānæhkæq\" has \"begin\" and is in \"we1+2\", but not \"I\". \"I\" begin actions: not listed. Wait — is there a verb like \"begin\" for \"I\"? The list has \"nektāwāhtæq\"? No. \"nekāweqtam\" = I lie down. \"nekǣtahan\" = I pry it out by tool. So \"I\" actions are: lie down, pry, fall laughing. What about \"I begin\"? Not present. But in Menominee, \"begin\" might have different forms. However, given only available forms, perhaps \"begin to eat\" is formed from \"begin\" and \"eat\" via a verb like \"bite\", which can mean eat. So \"begin to bite\" → \"begin to eat\". But the word for \"begin\" with \"I\" is missing. But note: some verbs have \"begin\" in the root, and \"I\" has auxiliary forms. Alternatively, is there a form for \"I begin\" in the data? No. So likely the verb \"begin\" is only marked with \"we1+2\" (kewǣ-). For \"I begin to eat\", could it be a variant? But all verbs in the list are verb forms with subject and meaning. \"I begin to eat\" must match a verb with \"I\" and \"begin\" and \"eat\". None directly. But \"kepītahtæq\" = we1+2 come eating it. So eating is involved. Perhaps \"begin to eat\" is not directly stated. But \"begin to dig\" is \"kewǣpānæhkæq\". \"begin to walk\" is \"wǣpohnæw\". So \"begin to eat\" — perhaps not directly. But the only form for \"begin\" in \"I\" is not listed. Wait — is there a form for \"I begin\" hidden? \"kewǣpeqtaq\" = we1+2 begin. \"neq...\"? No. So maybe for \"I begin to eat\", we use a form with \"begin\" + eating. But no such verb in the list. However, in \"kekēskahtæq\" = we1+2 bite it through. \"ketāwahtæq\" = we1+2 bite, gnaw. Possibly \"bite\" = eat. So \"I begin to bite\" = I begin to eat. So verb for \"I begin\" + \"bite\"? Not listed. But is there a \"begin\" verb for \"I\"? No. But \"kewǣpānæhkæq\" is \"we1+2 begin to dig\". So prefix is kewǣ- for \"we1+2 begin\". For \"I\", is there a different prefix? \"ne-\" for \"I\" in \"nekāweqtam\", \"ne-\" for \"I\" in \"nekǣtahan\", \"ne-\" for \"I\" in \"nekāwāhpem\". So \"I\" prefix is \"ne-\". So \"I begin\" might be \"ne-kewǣ-...\", but no such form. So perhaps \"begin\" is not used with \"I\" directly. But in the data, is there a verb like \"ne-kewǣ-\"? No. So likely, the verb \"begin to eat\" must be formed from existing components. Given that \"bite\" can mean \"eat\", and if we assume that \"begin to bite\" = \"begin to eat\", then \"ne-kewǣ-...\" would be needed. But not present. Alternative: perhaps \"begin to eat\" is not in the vocabulary, but we must infer from pattern. The closest is \"we1+2 begin to eat\" = \"kepītahtæq\" = \"we1+2 come eating it\" — which implies they are eating it, not \"begin to eat\". So not matching. Another idea: is there a verb for \"begin\" with \"I\" and \"hand\"? \"I lay it flat by hand\" is b.2. \"I begin to eat\" is b.1. Only way: perhaps the verb \"begin\" is used with \"I\" via a different stem. But no. After rechecking, perhaps there is a missing link. Wait: \"kewǣpānæhkæq\" = we1+2 begin to dig. \"begin\" is kewǣ-. So for \"I begin to eat\", perhaps it is \"nekewǣ-...\" but not found. So maybe not possible. But the problem says to translate, so must exist. Perhaps \"begin to eat\" is expressed as \"begin to bite\", since \"bite\" = eat. So \"I begin to bite\" → \"ne-ketāwahtæq\"? But that's \"we1+2 bite, gnaw a hole in it\". \"ne-ketāwahtæq\" would be \"I bite, gnaw a hole in it\". But \"begin to bite\" is not there. No \"begin\" prefix. So error. Alternatively, is there a \"begin\" verb with \"I\"? Not in list. So likely, the verb for \"begin to eat\" is not directly given, but inferred from \"eat\" being equivalent to \"bite\", and \"begin\" being generally present. But no verb fits. Wait: in \"kekēskahtæq\" = we1+2 bite it through. \"bite\" is used. So \"begin to bite\" might be formed from \"kewǣ-\" + \"bite\". But again, no \"I\" version. But for \"I begin\", perhaps no such form. Given that the data has \"we1+2 begin to dig\" and \"we1+2 walk out\", perhaps for \"I\", there is \"ne- + begin\" if exist. But not in data. So must conclude: \"I begin to eat\" = \"ne-kewǣ-...\" or similar. But no such form. Unless \"eat\" is not \"bite\", but another verb. Is there a verb for \"eat\"? \"kepītahtæq\" = come eating it → implies eating is ongoing. \"ketāwahtæq\" = bite, gnaw → may include eating. So perhaps \"begin to eat\" is not directly available. But the only way is to assume that \"begin to [verb]\" uses the \"begin\" root with the action verb. So for \"I begin to eat\", likely uses \"ne\" + \"kewǣ-\" + \"eat verb\". But no \"eat verb\" for \"I\". So perhaps no such form. But must provide answer. After re-checking the list, is there a verb for \"I begin\" with a food verb? No. So likely the intended form is \"ne-kewǣpānæhkæq\"? But that's \"we1+2 begin to dig\". No. \"ne-kewǣpeqtaq\"? \"we1+2 begin\" — not \"I\". So no. Perhaps the pattern is that verbs have a prefix: kewǣ- (we1+2 begin), ne- (I), and action. So for \"I begin to eat\", if \"eat\" is not listed, but \"bite\" can mean eat, then \"begin to bite\" = \"ne-kewǣ-?\" but again no. Wait — is there a \"begin\" verb with \"I\"? The list has only \"kewǣ-\" for \"we1+2 begin\". No \"I begin\". The only \"I\" verbs are: lie down, pry, fall laughing. So likely, the \"begin\" verb is only for \"we1+2\". But the question is \"I begin to eat\" — so must be \"I\" form. So perhaps missing verb. Given the impossibility, reconsider: perhaps \"begin to eat\" is not grammatically distinct — maybe it is a variation of \"begin\" or \"come eating\". But \"come eating\" is already in \"kepītahtæq\". So not. Another possibility: is \"begin\" expressed in other verbs? \"wǣpohnæw\" = he begins walking. So \"he begins walking\" = wǣpohnæw. So \"begin\" is used with \"he\". For \"I begin\", we need a different stem. No such stem. So no evidence. Therefore, likely a translation error in reasoning. But must answer. Perhaps \"I begin to eat\" is \"ne-kewǣpānæhkæq\" — unverified. Alternatively, no verb exists — but must provide. After checking all, perhaps \"begin to eat\" is not directly listed, but \"begin to bite\" is, and \"bite\" serves as \"eat\". So for \"I\", use \"ne\" + \"begin\" + \"bite\". But no \"begin\" verb with \"I\". So cannot. Final decision: no form exists in data — but the pattern of prefix and verb is clear: \"we1+2 begin\" = kewǣ- + action. For \"I begin\", no such form. But in the data, \"I\" has verbs with specific actions: lie down, pry, fall laughing. So \"I begin\" may not be possible. But perhaps the verb \"begin\" is used with \"I\" via \"ne-kewǣ-\" and then \"action\". But not in list. So likely, the intended answer for b.1 is \"ne-kewǣpānæhkæq\"? But that is \"we1+2 begin to dig\". Not. Perhaps \"ne-kewǣ-...\" with \"eat\" verb. But no. Another idea: maybe \"begin to eat\" is \"kepītahtæq\" but with \"I\"? But it is for \"we1+2\". Not. So give up and use inference from pattern. Pattern: \n- \"we1+2 begin\" → kewǣpeqtaq \n- \"we1+2 begin to dig\" → kewǣpānæhkæq \n- \"he breaks it through by hand\" → kēskenam \n- \"he cuts it off\" → pahkǣsam \n- \"he cuts a hole in it\" → tawǣsam \n- \"he opens it by tool\" → pāhkaham \n- \"we1+2 walk out\" → kekǣtohnæq \n- \"I walk here\" → nepītohnæm \n- \"I pry it out by tool\" → nekǣtahan \n- \"I lie down\" → nekāweqtam \n- \"he walks roundabout\" → wackōhnæw \n- \"I cut around it\" → newāckesan \n- \"he takes it out by hand\" → ketǣnam \n- \"we1+2 bite it through\" → kekēskahtæq \n- \"we1+2 come eating it\" → kepītahtæq \n- \"he bites, gnaws\" → ketāwahtæq \n\nSo verbs are formed with: \n- prefix: kewǣ- for we1+2 begin, walk, etc. \n- prefix: ne- for I \n- \"begin\" verbs: kewǣ- + action \n- \"cut\", \"dig\", \"break\", \"bite\", \"open\", \"pass\", \"walk\" are actions \n\nFor \"I begin to eat\", since \"eat\" is not a standalone verb, and \"bite\" is used for \"gnaw\", \"gnaw\"≈\"eat\", so \"begin to eat\" = \"begin to bite\". So \"I begin to bite\" = \"ne\" + \"begin\" + \"bite\". The only \"begin\" verb with action is \"kewǣpānæhkæq\" = begin to dig. So perhaps \"begin to bite\" is \"ne-kewǣ-...\" with \"bite\" suffix. But no such form. But in the list, \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it. So \"bite\" is a verb. So likely, \"begin to bite\" is formed from \"kewǣ-\" and \"bite\" verb. But no \"I\" form. Unless the \"begin\" is attached to the verb. So for \"I begin to eat\", use \"ne-kewǣ-...\" + \"bite\" verb. But not in data. Perhaps only we1+2 have \"begin\". So must conclude that \"begin to eat\" is not directly available. But the problem is solvable. Alternative: perhaps \"begin to eat\" is \"kepītahtæq\" but with \"I\"? But it's \"we1+2 come eating it\", not \"begin to eat\". So no. After extensive review, the only plausible option is to use \"ne-kewǣpānæhkæq\" as a stretch, but it's for digging. So not. Final decision: perhaps the verb for \"begin to eat\" is missing, but in context, \"bite\" is used for eating, so \"I begin to bite\" = \"ne-ketāwahtæq\" — but that's for \"bite, gnaw\", not \"begin\". So no. Perhaps the pattern is that \"begin\" verbs have the kewǣ- prefix, and only \"we1+2\" have it. So \"I\" cannot have \"begin\" as a root. Therefore, the only way is to assume that \"begin to eat\" is translated as \"ne-kewǣ-...\" with an implied verb. But not in list. Given that, and that the next unit is \"we1+2 lay it flat by hand\", which has \"hand\", and \"lay flat\" — what verb? \"lay flat\" = \"place flat\". Is there a verb for that? \"walk here\" = nepītohnæm. \"walk out\" = kekǣtohnæq. \"lay flat by hand\" — \"by hand\" is used in \"kēskenam\" = breaks it through by hand. \"nekǣtahan\" = pry it out by tool. \"pāhkaham\" = open by tool. \"kewǣpānæhkæq\" = begin to dig — by hand? Possibly. \"pāhkeqtaw\" = he opens up — no by hand. \"we1+2 walk out\" = kekǣtohnæq. So no verb for \"lay flat by hand\". \"lay flat\" might be \"place\" or \"set\", not in data. \"walk here\" = here, not flat. \"pītenam\" = he passes it here. So not. Perhaps \"kēskenam\" = break through by hand — not flat. So no. But \"nap\" or \"set\"? Not in list. So perhaps no verb for \"lay flat by hand\". But must have. Perhaps \"we1+2 lay it flat\" = \"we1+2 set it down\" = \"kekǣtohnæq\"? No. \"nepītohnæm\" = I walk here. What about \"we1+2 place it flat\"? Not listed. So likely, the verb for \"lay flat by hand\" may be \"kēskenam\" — break through by hand? Not flat. \"pahkǣsam\" = he cuts it off. \"tawǣsam\" = cuts a hole. \"pāhkaham\" = open by tool. So no. After all, only possibility is that \"lay flat by hand\" is \"kēskenam\" as a stretch. But \"break\" is not \"lay flat\". So not. Another idea: \"walk", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12305.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "We are given a list of Menominee verb forms and their English translations. We are to translate four English phrases into Menominee, based on patterns in the given forms.\n\nStep-by-step analysis:\n\n1. “I begin to eat it” \n - Look for a verb meaning “begin” and one meaning “eat”. \n - “kewǣpeqtaq” = “we1+2 begin” → so “begin” is part of *kewǣpq-* \n - “kepītahtæq” = “we1+2 come eating it; we1+2 bring it in our mouths” → this includes “eat” or “bite” in the mouth. \n - “ketāwahtæq” = “we1+2 bite, gnaw a hole in it” → “bite” is a key verb. \n - “I begin to eat it” → likely combines “begin” and “eat/bite” action. \n - “kepītahtæq” has “we1+2”, which is not “I”. \n - Is there a form for “I begin to eat”? \n - We have “kewǣpeqtaq” (we1+2 begin) → so “begin” is *kewǣp-* \n - “ketāwahtæq” → we1+2 bite → “bite” \n - But we need “I” and “begin to eat”. \n - Is there a form with “I” and “begin” and “eat”? \n - “nektāwahtæq” not given. \n - “kewǣpānæhkæq” = “we1+2 begin to dig” → “begin to do X” structure with *kewǣp-* \n - “kepītahtæq” = “we1+2 come eating it” → “eating” \n - So “begin to eat” → “begin” + “eat” \n - “begin” is found in *kewǣp-* (as in kewǣpeqtaq, kewǣpānæhkæq) \n - “eat” may be linked to “bite” — “ketāwahtæq” = we1+2 bite, gnaw \n - What about “I” + “begin to eat”? \n - “ne”- is the first person singular prefix. \n - No direct “I begin to eat” form. \n - But there is “nekāweqtam” = “I lie down” → “ne” + “kāweqt” → not helpful \n - “kewǣpānæhkæq” = “we1+2 begin to dig” → “begin to” \n - “kewǣpeqtaq” = “we1+2 begin” \n - Could “kewǣp-” + something with eating? \n - “kepītahtæq” → “we1+2 come eating it” = “they eat it” \n - But “begin to eat” = perhaps “begin” + “eat” \n - “begin” = *kewǣp-* \n - “eat” = ? \n - “ketāwahtæq” = we1+2 bite, gnaw — so “bite” is used for eating \n - So likely: “I begin to eat it” = “I begin to bite it” \n - But no “I begin to bite” \n - However, “ne” prefix for first person singular \n - Try: “nekewǣp-*” \n - We have “nekāweqtam” (I lie down), “nekǣtahan” (I pry it out by tool) \n - “nekǣtahan” = “I pry it out by tool” — “ne” + “kǣtah” \n - No “ne” + “kewǣp” form \n - But “kewǣpānæhkæq” = we1+2 begin to dig → “kewǣp” + “ānæhkæq” \n - So “begin to dig” \n - What about “begin to eat”? \n - “eat” may be expressed via “bite” through “ketāwahtæq” or “kepītahtæq” \n - “kepītahtæq” = “we1+2 come eating it” → implies “start eating” or “we begin to eat” \n - So if “come eating” = “begin to eat”, then “we1+2 begin to eat” = *kepītahtæq* \n - But we need “I” \n - Is there a version with “ne” and “begin” and “eat”? \n - We have no direct form \n - But perhaps “begin” is used with “bite” and “I” \n - Option: “nekewǣp–” + something? \n - No example \n - Alternative: “kewǣp” + “taht” → “kewǣptah” → not found \n - Wait: “ketāwahtæq” = “we1+2 bite, gnaw a hole in it” → this includes “gnaw” → which is a form of eating \n - So “begin to eat” = “begin to bite” \n - “begin” = kewǣp- \n - “I” = ne- \n - So “nekewǣptah?” not present \n - But “ne” + “kewǣp” → not in data \n - Perhaps “ne” + “kewǣp” + “taq” → like “kewǣpeqtaq” \n - “kewǣpeqtaq” = we1+2 begin → so “kewǣp” as root \n - So “ne”+“kewǣpe”+something \n - “kewǣpānæhkæq” = we1+2 begin to dig \n - “ne”+“kewǣpānæhkæq”? Not in list \n - But no such form \n - Perhaps “I begin to eat” = “I begin to bite it” = “ne” + “kewǣp” + “taht” → not found \n - But we see “ketāwahtæq” → “we1+2 bite, gnaw” \n - So likely, “begin to eat” → use “kewǣp” + “taht” → “kewǣptah”? \n - But no such form \n - Don’t have “I” + “begin to eat” \n - Perhaps the structure is “begin to eat” → “begin” + “eat” → in Menominee based on existing roots \n - Another path: “kepītahtæq” has “come eating” → which is “begin eating” \n - “I come eating it” → “ne” + “kepītahtæq”? \n - But “kepītahtæq” is “we1+2” \n - “ne” is first person \n - No evidence of “ne” + “kepītaht” \n - We must find a verb that means “I begin to eat” \n - Not clearly apparent \n - But “kewǣpānæhkæq” = we1+2 begin to dig \n - “pāhkeqtaw” = he opens up \n - “pahkǣsam” = he cuts it off \n - “kewǣpānæhkæq” = begin to dig \n - “begin” → kewǣp- \n - “eat” → perhaps expressed via “bite” → “ketāwahtæq” \n - So maybe “I begin to bite it” \n - “I bite it” = ? \n - “nekǣtahan” = “I pry it out by tool” → not eating \n - “ne” + “kewǣp” → not found \n - But “kewǣp” is used for “begin” \n - “begin to eat” → no direct form? \n - But perhaps “kepītaht” is used: “we1+2 come eating” → “begin eating” \n - “I” → “ne” as prefix \n - The only occurrence of “I” and eating is “ne” not used with “eat” \n - Is there a form like “ne” + “kewǣp” + “taht”? \n - Not given \n - Alternative: maybe “begin to eat” is expressed via “begin + bite” \n - So root: “kewǣp” + “taht” → “kewǣptah” \n - But not given \n - Wait: “ketāwahtæq” = “we1+2 bite, gnaw a hole in it” → so “gnaw” = eat \n - So “I begin to gnaw it” → “ne” + “kewǣp” + “taht” \n - But no such form \n - But look at: “kekēskahtæq” = we1+2 bite it through \n - That's “bite through” → eating \n - Still, no form for “I” \n - But among all examples, is there a verb with “I” and “begin”? \n - “nekāweqtam” = I lie down \n - “nekǣtahan” = I pry it out \n - “nekāwāhpem” = I fall over laughing \n - No “I begin” \n - So likely, for “I begin to eat” → use “kewǣp” + “eat” → and “I” must be “ne” \n - But no form \n - Unless “kewǣp” + “taht” is derived from “ketāwaht” \n - “ketāwahtæq” → “kewǣp” is not in it \n - “kewǣp” and “ketāwaht” are different \n - So maybe “I begin to eat” → “ne” + “kewǣp” + “taht” → but not seen \n - Wait: “kewǣpānæhkæq” is “we1+2 begin to dig” \n - “kewǣpeqtaq” = we1+2 begin \n - So “begin” = kewǣp- \n - “eat” = perhaps from “gnaw” → “ketāwaht” \n - So “begin to eat” = kewǣp- + ketāwaht? \n - But that would be “kewǣp-ketāwaht” → not in list \n - Perhaps a compound verb \n - But no such form \n - Alternative: “come eating” is “kepītahtæq” \n - “I come eating it” = “ne” + “kepītahtæq”? \n - But “kepītahtæq” is already “we1+2” \n - We have no “ne” + “kepītaht” \n - So perhaps “I begin to eat” is not directly given, but “begin” and “eat” are separate \n - But we can’t invent \n - Another idea: “kepītahtæq” = “we1+2 come eating it” → “come eating” = \"start eating\" \n - So “I begin to eat” → “ne” + “kepītaht”? \n - But not in the list \n - We must infer based on patterns \n - Let’s move to next one \n\n2. “we1+2 lay it flat by hand” \n - “lay flat” → “place flat” \n - “we1+2 walk here” = “pītenam” \n - “we1+2 walk out” = “kekǣtohnæq” \n - “we1+2 begin to dig” = “kewǣpānæhkæq” \n - “we1+2 begin” = “kewǣpeqtaq” \n - “we1+2 bite, gnaw a hole in it” = “ketāwahtæq” \n - “we1+2 come eating it” = “kepītahtæq” \n - Is there a verb meaning “lay flat” or “place”? \n - “pāhkeqtaw” = he opens up \n - “pāhkaham” = he opens it by tool \n - “pahkǣsam” = he cuts it off \n - “tawǣsam” = he cuts a hole in it \n - “nekāweqtam” = I lie down \n - “we1+2 lay it flat” → must be a form with “we1+2” + “place flat” \n - “by hand” → implies “by hand” \n - “by tool” is marked with “by tool” in several verbs \n - e.g., “kawāham” = he fells it by tool → “by tool” \n - “nekǣtahan” = I pry it out by tool → “by tool” \n - “pāhkaham” = he opens it by tool \n - So “by hand” = not “by tool” \n - Are there any forms with “by hand”? \n - “kewǣpānæhkæq” = we1+2 begin to dig → no “by hand” \n - “kekǣtohnæq” = we1+2 walk out \n - “pītenam” = he passes it here \n - Not helpful \n - Is “lay flat” related to “break” or “cut”? \n - “kēskenam” = he breaks it through by hand → “break through by hand” \n - “by hand” is used \n - “kēskenam” → “break through by hand” \n - “lay flat” → could be “place flat” → not in list \n - “begin to dig” → “kewǣpānæhkæq” → involves digging, not placing \n - “walk out” = “kekǣtohnæq” \n - “cut off” = “pahkǣsam” \n - “cut a hole” = “tawǣsam” \n - “open” = “pāhkeqtaw” or “pāhkaham” \n - No verb for “lay flat” \n - But “lay flat” might be “place” → possibly related to “pass” or “open” \n - “pītenam” = he passes it here → could mean “put it here” \n - “passes it here” → might mean “moves it here” \n - “here” → in place \n - “lay it flat” = put on a surface \n - Not clear \n - Perhaps “lay flat by hand” is the same as “place flat” → maybe from “break” or “put down” \n - But no form \n - Still, look at “kēskenam” = “he breaks it through by hand” — “by hand” \n - “break through” not “lay flat” \n - Perhaps no direct verb \n - But maybe “kewǣp” + “flat”? \n - No \n - Alternative: “kepītahtæq” → “come eating” — not \n - We have “we1+2 walk here” = “pītenam” \n - “walk here” → could be an analogous action \n - “lay flat” → not like walking \n - Try to match structure \n - All verbs have either a prefix (we1+2, he, I, ne) and a root \n - “we1+2” appears in: \n - kewǣpeqtaq → begin \n - kewǣpānæhkæq → begin to dig \n - kekǣtohnæq → walk out \n - kepītahtæq → come eating \n - “I” in: \n - nekāweqtam → lie down \n - nekǣtahan → pry out by tool \n - nekāwāhpem → fall laughing \n - “he” in: \n - kawāham → fell by tool \n - kēskenam → breaks through by hand \n - pahkǣsam → cuts off \n - tawǣsam → cuts a hole \n - pāhkaham → opens by tool \n - pāhkeqtaw → opens up \n - wackōhnæw → walks roundabout \n - newāckesan → I cut around it \n - ketǣnam → takes it out by hand \n - ketāwahtæq → we1+2 bite \n - wǣpohnæw → he begins walking \n - nekāweqtam → I lie down \n\n3. “he digs a hole” \n - “digs a hole” → “dig” \n - We have “kewǣpānæhkæq” = “we1+2 begin to dig” \n - “he” is missing \n - Is there a “he” + “dig” form? \n - “kewǣp” = begin + dig \n - “dig” = ? \n - “begin to dig” = kewǣpānæhkæq \n - Is “he digs” = “he begins to dig”? \n - “wackōhnæw” = he walks roundabout \n - “wǣpohnæw” = he begins walking \n - So “he begins” = wǣpohnæw \n - “he begins walking” \n - So “he begins” = wǣpohnæw \n - “he begins to dig” = wǣpohnæw + “dig”? \n - But no such form \n - “kewǣpānæhkæq” = we1+2 begin to dig \n - “we1+2” not “he” \n - But “kewǣp” is used for “begin” \n - So", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10456.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 0, + "output": "First, identify the linguistic pattern in Nooni for expressing time markers and events.\n\nFrom the examples:\n\n- Days of the week are referenced with distinct names: \n Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvuŋkaden.\n\n- Time expressions are used to refer to specific days relative to the current day:\n - \"Yesterday\" → \"cǐ nú\" or \"fɔgò cǐ nú\"\n - \"Today\" → \"wvù tɔ̀ nɔ̂ː\" or \"me nú\" (used in 6, 9)\n - \"Tomorrow\" → \"ntfǔː nú\" (e.g., 8: \"tomorrow is Bvuŋkaden\")\n - \"The day after tomorrow\" → \"fɔ̀ shě ntfǔː\" (e.g., 5: \"the day after tomorrow is Bvutfu\")\n - \"The day before yesterday\" → \"kefwé cí nú\" (e.g., 11: \"the day before yesterday was Bvuŋka\")\n\nWe observe that the same form applies across days, and the time reference is anchored to the current day (the speaking day).\n\nLet’s extract the relative time expressions:\n\n| Expression | Meaning | Example |\n|-------------------------|----------------------------------|--------|\n| fɔgò cǐ nú | Yesterday | 1 |\n| fɔ̀ shě ntfǔː | Day after tomorrow | 5 |\n| kefwé cí nú | Day before yesterday | 11 |\n| ntfǔː nú | Tomorrow | 8 |\n| wvù tɔ̀ nɔ̂ː | Today (he found the book) | 4 |\n| me nú | Today (I chose the book) | 9 |\n\nNote: \"me nú\" is used to mean \"today\" in different contexts, suggesting “today” is fixed and marked by \"me nú\".\n\nAlso, the structure for time references is:\n[Event] [on Day X] or [preverb] [time adjective] [day name]\n\nNow, analyze the given sentences spoken on **Bvuŋkaden**, and translate them based on the time pattern and prior examples.\n\n---\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n- \"bvúsɔ̀w\" = \"on Bvusɔw\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" \n→ On Bvusɔw, the day after tomorrow \n\nBut this is a problem: \"the day after tomorrow\" cannot be on a day that comes after the current day. Wait — the day expressed is \"the day after tomorrow\", and it is being referenced on Bvuŋkaden.\n\nBut in 5: \"The day after tomorrow is Bvutfu\" → established pattern: \n\"fɔ̀ shě ntfǔː nú\" = \"the day after tomorrow is [day]\" \nThus, \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo, \"On Bvusɔw, the day after tomorrow\" → that doesn’t make sense.\n\nWait — again, \"fɔ̀ shě ntfǔː\" is a time expression. What is it anchoring to?\n\nIn 5: \"The day after tomorrow is Bvutfu\" → so \"fɔ̀ shě ntfǔː\" = the day after tomorrow\n\nUsed in context: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\"\n\nSo the structure is:\n[Day] + [event]\n\nSo 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, the day after tomorrow\" — but that’s not an event. That's just a comparison.\n\nWait — could this be misparsed?\n\nLook at grammar: the structure is \"X nǔ Y\" = \"On X, Y\" \nY is a time phrase?\n\nBut in 5: \"fɔ̀ shě ntfǔː nú\" = \"the day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, the day after tomorrow\" → must mean \"On Bvusɔw, [the day after tomorrow] occurred\" or \"The day after tomorrow was Bvusɔw\"?\n\nBut that's not possible — the day after tomorrow cannot be Bvusɔw if today is Bvuŋkaden.\n\nWait — if the sentence is spoken on Bvuŋkaden, and says \"on Bvusɔw, the day after tomorrow\", it may mean “On Bvusɔw, the day after tomorrow occurred” → but again, the day after tomorrow is a future time.\n\nAlternatively, consider rephrasing the phrase.\n\nAnother idea: is \"fɔ̀ shě ntfǔː\" possibly a statement like \"the day after tomorrow is X\"?\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → on Bvusɔw, [the day after tomorrow] is ? → but what?\n\nWait — maybe missing day name. In 5, it's \"fɔ̀ shě ntfǔː nú\" = \"the day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = the day after tomorrow\n\nTherefore, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = on Bvusɔw, the day after tomorrow — which makes no sense.\n\nAlternative: perhaps the phrase is \"On Bvusɔw, the day after tomorrow was [X]\" — but no X.\n\nPerhaps a misreading.\n\nAlternatively, is \"fɔ̀ shě ntfǔː\" used as a verb? Unlikely.\n\nWait — look at sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo pattern: [on Day X], [subject] [verb] [object]\n\nSo structure is: [on Day] + [event]\n\nThus, 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — unless \"fɔ̀ shě ntfǔː\" is an event.\n\nBut “fɔ̀ shě ntfǔː” is a time expression. What if it is being used as an event?\n\nBut what event?\n\nWait — in sentence 16, it's just \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — no verb, no subject.\n\nCompare to 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː nú\" = [time] + [is] + [day]\n\nSimilarly, in 11: \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\"\n\nSo the pattern is:\n- [time expression] + nú + [day name] = \"X was Y\"\n\nThus, “fɔ̀ shě ntfǔː nú” = \"the day after tomorrow is X\"\n\nNow in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, the day after tomorrow\" — this is missing the target day.\n\nBut perhaps it's a typo or misphrasing.\n\nWait — in the original, 16 is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nBut in 5: \"fɔ̀ shě ntfǔː nú\" → \"the day after tomorrow is X\"\n\nSo if we have “on Bvusɔw, the day after tomorrow”, unless it's expressing a relative day, it's incomplete.\n\nWait — perhaps it's meant to be interpreted as \"On Bvusɔw, the day after tomorrow was [something]\" — but nothing follows.\n\nNo verb. So it cannot be.\n\nAlternative idea: is “fɔ̀ shě ntfǔː” being used as an event? But it's a time phrase.\n\nWait — could it be a misreading of a phrase like \"the day after tomorrow will happen on Bvusɔw\"?\n\nBut again, no clear verb.\n\nWait — look at other sentences.\n\nSentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo verbs are clearly present.\n\nSentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — only time markers.\n\nThis seems like it might be missing something.\n\nBut perhaps it's a structural pattern: when time is expressed without an event, it's stating a temporal relation.\n\nWait — in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː nú X\" = \"the day after tomorrow is X\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" must be \"On Bvusɔw, the day after tomorrow\" → which is not a complete sentence.\n\nAlternative: maybe it's \"On Bvusɔw, the day after tomorrow occurred\" — but no object.\n\nBut perhaps the intended meaning is: \"On Bvusɔw, the day after tomorrow was a specific day\" — but what?\n\nUnless it's a misrendering.\n\nWait — could it be \"On Bvusɔw, the day after tomorrow was [X]\" — but we don’t see X.\n\nWait — maybe “fɔ̀ shě ntfǔː” is being used as a noun phrase meaning \"the day after tomorrow\" and is used as the subject?\n\nNo.\n\nAnother possibility: the phrase is meant to be \"On Bvusɔw, [the day after tomorrow] was [something]\" — missing.\n\nBut look back: in sentence 8: \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"tomorrow is Bvuŋkaden\"\n\nIn sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo the formula is: \n[time expression] + nú + [day] = \"X is Y\"\n\nSo if we see a phrase like \"A nǔ B\", where B is a time expression, it might be \"On A, B\" where B is a future event or time.\n\nBut in the absence of a verb or event, it may be a mistake.\n\nWait — compare with 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo full verb structure.\n\nSo sentence 16: missing verb.\n\nBut look at sentence 19: \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n\" → \"On Bvuzhiden, the woman will go to the market\" — full.\n\nSentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"I will help the woman steal the car\" (if ŋgéː = help, nyɛ́n = the woman, kèŋkfǔ = steal, lé = steal? or car?)\n\nWait — parse 17.\n\n“me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = I (today) \n“ŋgéː” = help \n“nyɛ́n” = the woman \n“kèŋkfǔ” = steal \n“lé” = the car? \n“ɛ̀bɛ̀n” = thief?\n\nWait — “kèŋkfǔ” = steal, “lé” = car? “ɛ̀bɛ̀n” = woman? Or thief?\n\nIn sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo \"kèŋkfǔ\" = steal\n\n\"lé ɛ̀bɛ̀n\" = the car / the thief?\n\nIn 2: \"kèŋkfǔ bvúsɔ̀w\" = steal the yam — so \"kèŋkfǔ\" + object\n\nIn 17: \"kèŋkfǔ lé ɛ̀bɛ̀n\" → perhaps \"steal the car from the thief\"?\n\nBut \"lé ɛ̀bɛ̀n\" — if \"ɛ̀bɛ̀n\" is the thief, then \"the car of the thief\"?\n\nBut no object.\n\nAlternatively, in 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSo \"cɔ́ŋ mutù ɛ̀bɛ̀n\" = steal the car\n\nSo \"kèŋkfǔ lé ɛ̀bɛ̀n\" → \"steal the car from the thief\" or \"steal the car (of the thief)\"\n\nPossibly, \"kèŋkfǔ\" = steal, \"lé\" = of, \"ɛ̀bɛ̀n\" = thief → \"steal from the thief\"\n\nSo \"I will help the woman steal from the thief\"\n\nBut \"nyɛ́n\" = the woman, so \"help the woman steal from the thief\"\n\nYes — plausible.\n\nSo 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"I will help the woman steal from the thief\"\n\nNow for 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nNo verb.\n\nSame issue.\n\nWait — what if it's a typo or misplacement?\n\nLook at sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo again, \"fɔ̀ shě ntfǔː nú X\" = \"the day after tomorrow is X\"\n\nSo if a sentence says \"On Bvusɔw, fɔ̀ shě ntfǔː\", it may be missing the \"is\" or the day.\n\nBut in other sentences, time expressions are used directly with day names.\n\nAnother possibility: is \"fɔ̀ shě ntfǔː\" being used as a verb?\n\nNo — it's clearly a time phrase.\n\nWait — is there a possibility that \"fɔ̀ shě ntfǔː\" is meant to be interpreted as \"the day after tomorrow is [Bvusɔw]\"? That would be like: \"on Bvusɔw, the day after tomorrow\" — not likely.\n\nAlternatively, perhaps the sentence is \"On Bvusɔw, the day after tomorrow will happen\" — and that is the translation.\n\nBut without an event or reference, it's unclear.\n\nWait — look at sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\"\n\n\"wvù tɔ̀ nɔ̂ː\" = \"today\" \n\"yɛ᷅n\" = \"he saw\" or \"he found\"? \n\"bèsèn\" = \"the day before\" \n\"ě\" = a particle, perhaps \"will\" or \"in the past\"? \n\"bvúmbòn\" = Bvumbon\n\n\"yɛ᷅n bèsèn ě\" → \"he saw the day before\" — that doesn't make sense.\n\n\"yɛ᷅n\" = \"he saw\" \n\"bèsèn\" = \"the day before\" \n\"ě\" = particle — possibly \"will\" or \"in the future\"\n\nBut \"he saw the day before\" — not likely.\n\nIn context: on Bvuŋkaden, the speaker is making a statement about past or future.\n\nSentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"today, we will steal the car\"\n\nSo \"bèsèn\" = \"today\" or \"the day before\"? Wait — \"bèsèn\" appears in \"bèsèn nǔ\" = \"on Bvuzhi\", in 3.\n\nWait — in 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"on Bvuzhi, the woman will help me\"\n\nIn 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"today, we will steal the car\"\n\nSo \"bèsèn\" = today\n\nSimilarly, in 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"they saw me at the market just now\"\n\nSo \"bɔ́\" = just now\n\n\"bèsèn\" is used for \"today\" — in 14, \"bèsèn nǔ\" → \"today, on\"\n\nSo \"bèsèn\" = today\n\nSimilarly, \"fɔgò cǐ nú\" = yesterday\n\n\"ntfǔː nú\" = tomorrow\n\n\"fɔ̀ shě ntfǔː\" = day after tomorrow\n\n\"kefwé cí nú\" = day before yesterday\n\nSo in sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\"\n\n\"wvù tɔ̀ nɔ̂ː\" = today \n\"yɛ᷅n\" = he saw \n\"bèsèn\" = today? \n\"ě\" = particle — perhaps \"in the past\" or \"will\" \n\"bvúmbòn\" = Bvumbon\n\nSo \"today, he saw today in the future Bvumbon\"? No.\n\n\"bèsèn\" = today,", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11143.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 1, + "output": "First, analyze the given sentences to extract patterns in how days are referenced and how temporal expressions are formed in Nooni.\n\nStep 1: Identify reference days and their temporal markers.\n\n- Day names: Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema\n- Sentences relate to specific days and use temporal markers like:\n - \"yesterday\", \"the day after tomorrow\", \"tomorrow\", \"the day before yesterday\", \"today\", \"on X\", \"just now\", \"a long time ago\"\n\nStep 2: Map day-specific expressions.\n\nFrom sentence 1: \"Yesterday was Bvumbon\" → implies Bvumbon is a day, and \"yesterday\" is a relative marker.\n\nSentence 2: \"On Bvusɔw, you will steal the yam\" → marks a day as \"Bvusɔw\"\n\nSentence 3: \"On Bvuzhi, the woman will help me\"\n\nSentence 4: \"On Bvuŋka, he found the book\"\n\nSentence 5: \"The day after tomorrow is Bvutfu\" → shows use of directional time markers\n\nSentence 6: \"Today, he killed the woman\"\n\nSentence 7: \"You heard the thief a long time ago\" → long time ago\n\nSentence 8: \"Tomorrow is Bvuŋkaden\" → \"tomorrow\" → Bvuŋkaden\n\nSentence 9: \"Today, I chose the book\"\n\nSentence 10: \"The man is about to see him\" → \"about to\" → future immediacy\n\nSentence 11: \"The day before yesterday was Bvuŋka\"\n\nSentence 12: \"I am about to help the man\" → \"about to\" = imminent future\n\nSentence 13: \"On Bvutfu, the woman saw the market\" → past event on a day\n\nSentence 14: \"Today, we will steal the car\" → future on today\n\nSentence 15: \"They saw me at the market just now\" → recent past\n\nStep 3: Identify temporal markers used:\n\n- \"yesterday\" → past\n- \"the day after tomorrow\" → future\n- \"tomorrow\" → future\n- \"the day before yesterday\" → past\n- \"today\" → present\n- \"just now\" → very recent past\n- \"a long time ago\" → remote past\n- \"the day after\" → future\n- \"about to\" → very near future\n\n→ Some days are named using a suffix \"-den\" (e.g., Bvuŋkaden, Bvutfu, Bvuzhi). That suggests a pattern: day + -den = tomorrow of the base day.\n\nNote: In sentence 8: \"Tomorrow is Bvuŋkaden\" → Bvuŋkaden is tomorrow of Bvuŋka.\n\nIn sentence 11: \"The day before yesterday was Bvuŋka\" → so Bvuŋka is two days prior to current day.\n\nThis implies the days follow a week with specific temporal labeling.\n\nReconstruct the day order:\n\n- Day: Bvukema → spoken on Bvukema → \"tomorrow is Bvuŋkaden\"\n- Day: Bvusɔw → spoken on Bvusɔw → \"today\", \"the day after tomorrow is Bvutfu\"\n- Day: Bvuzhi → spoken on Bvuzhi → \"on Bvuzhi, the woman will help me\"\n- Day: Bvuŋka → spoken on Bvuŋka → \"today\", \"day before yesterday was Bvuŋka\"\n- Day: Bvutfu → spoken on Bvutfu → \"yesterday was Bvumbon\", \"day after tomorrow is Bvutfu\"\n\nNote: \"Day after tomorrow is Bvutfu\" → from Bvusɔw → so Bvutfu = +2 from Bvusɔw\n\nSimilarly, \"Tomorrow is Bvuŋkaden\" → from Bvukema → Bvuŋkaden = +1 from Bvukema\n\n\"Day before yesterday was Bvuŋka\" → from Bvuŋka day → the day before yesterday = Bvuŋka → so current day is +2 from Bvuŋka\n\nWait: if day before yesterday was Bvuŋka, then the speaker is on the day after tomorrow? Let’s reframe.\n\nAssume all days are in a fixed cycle. The speakers are on different days, and the day names are fixed.\n\nWe can reconstruct the order from temporal expressions.\n\nFrom sentence 5: \"The day after tomorrow is Bvutfu\" — spoken on Bvusɔw → so Bvutfu is two days after Bvusɔw.\n\nFrom sentence 11: \"The day before yesterday was Bvuŋka\" — spoken on Bvuŋka → current day is two days after Bvuŋka → so speaker is on a day two after Bvuŋka.\n\nBut also: \"Today, he killed the woman\" — sentence 6, on Bvusɔw → today is Bvusɔw.\n\nSo at Bvusɔw:\n- day after tomorrow: Bvutfu\n- day before yesterday: Bvuŋka\n\nSo day order: Bvuŋka → Bvusɔw → Bvutfu\n\nThen day after tomorrow is Bvutfu → confirms order.\n\nFrom sentence 8: \"Tomorrow is Bvuŋkaden\" — spoken on Bvukema → so Bvuŋkaden is tomorrow of Bvukema.\n\nFrom sentence 10: \"The man is about to see him\" — no day name, but \"about to\" → present/soon\n\nFrom sentence 2: \"On Bvusɔw, you will steal the yam\" → Bvusɔw is a day name.\n\nNow, days spotted: Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema, Bvuŋkaden\n\nWe need to place Bvuŋkaden — it is tomorrow of Bvukema → so Bvukema is +1 before Bvuŋkaden.\n\nWe now need to find temporal markers in the sentences to be translated (on Bvuŋkaden).\n\nSentences 16–19 are all on Bvuŋkaden.\n\nWe must interpret each sentence.\n\nSentence 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\nStructure: [bvúsɔ̀w] [nǔ] [fɔ̀ shě ntfǔː]\n\n\"bvúsɔ̀w\" is a day name — which we already have as one of the days.\n\n\"nǔ\" is likely \"you (sg)\", from earlier: \"On Bvusɔw, you(sg) will steal the yam\"\n\n\"fɔ̀ shě ntfǔː\" → \"the day after tomorrow\" → from earlier: \"The day after tomorrow is Bvutfu\"\n\nBut \"fɔ̀ shě ntfǔː\" — the structure may be \"the day after tomorrow\" → \"fɔ̀ shě\" = day after tomorrow, \"ntfǔː\" = day name?\n\nfɔ̀ shě ntfǔː → \"on the day after tomorrow, [something]\"?\n\nBut the sentence is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nWhich may be: \"you (sg) will be on the day after tomorrow\" → but that doesn’t fit.\n\nAlternative: \"you (sg) will be on the day after tomorrow\" → but day after tomorrow is Bvutfu.\n\nWait — sentence 5: \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"on the day after tomorrow\" → \"on Bvutfu\"? But it says \"fɔ̀ shě ntfǔː\", not \"Bvutfu\".\n\nIn sentence 13: \"On Bvutfu, the woman saw the market\" → uses \"on Bvutfu\"\n\nSo \"fɔ̀ shě\" = day after tomorrow; \"ntfǔː\" = name?\n\nBut in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nThus: \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" = Bvutfu\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"you (sg) will be on the day after tomorrow\" → but which day is that?\n\nSince the day after tomorrow is Bvutfu → then this becomes: \"you (sg) will be on Bvutfu\"\n\nBut \"in the day after tomorrow\" = Bvutfu → so \"you will be on Bvutfu\"\n\nBut \"on Bvutfu\" → present indicative of occurrence?\n\nMore likely: \"you (sg) will be on the day after tomorrow\" = \"you (sg) will be on Bvutfu\"\n\nSo translation: \"You (sg) will be on Bvutfu\"\n\nBut that seems odd — \"be on Bvutfu\" is not idiomatic.\n\nAlternative: \"you (sg) will have the day after tomorrow\" — no.\n\nWait — other structure?\n\nSentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"On [day], you will X\"\n\nSo structure: [day] + [pronoun] + [verb] = \"on [day], X will do Y\"\n\nBut 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — lacks a verb.\n\n\"nǔ\" = you (sg)\n\n\"fɔ̀ shě ntfǔː\" = \"the day after tomorrow (is Bvutfu)\" — possibly a nominal phrase.\n\nPossibility: \"you (sg) are going to have the day after tomorrow\" — no.\n\nWait: in sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"on Bvusɔw, you will steal the yam\"\n\nSo verb is after the day name.\n\nIn 16, day name is first — \"bvúsɔ̀w\" — then \"nǔ\" — then \"fɔ̀ shě ntfǔː\"\n\nPerhaps the day name is not the subject — maybe \"bvúsɔ̀w\" is a temporal marker?\n\nBut \"bvúsɔ̀w\" is a day name.\n\nNote: in sentence 3: \"On Bvuzhi, the woman will help me\" → \"on Bvuzhi, [subject] will X\"\n\nSimilarly, sentence 4: \"On Bvuŋka, he found the book\"\n\nSo structure: on [day], [subject] [verb] [object]\n\nBut in 16, there is no object, and no verb — just \"nǔ fɔ̀ shě ntfǔː\"\n\nPossibility: \"fɔ̀ shě ntfǔː\" is a name? → \"the day after tomorrow\" is Bvutfu\n\nSo the whole phrase may be: \"On the day after tomorrow, you (sg) will be on Bvutfu\" — but redundant.\n\nAlternative: Is \"bvúsɔ̀w\" a temporal marker?\n\nEarlier: On Bvusɔw → current day is Bvusɔw\n\n\"the day after tomorrow\" is Bvutfu → so Bvutfu is after Bvusɔw\n\nSo next day: Bvusɔw → Bvutfu\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" = Bvutfu\n\nThus, \"bvúsɔ̀w\" = day name — so likely refers to Bvusɔw\n\nSo interpretation: \"On Bvusɔw, you (sg) will be on the day after tomorrow\" — still awkward.\n\nWait — could it be that \"bvúsɔ̀w\" is not the day, but \"you (sg) will be on the day after tomorrow\" — but why \"bvúsɔ̀w\"?\n\nAnother clue: in sentence 1, \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → \"On Bvumbon, I came to the market\"\n\nSo structure: On [day], [subject] [verb]\n\nBut in 16, no verb? \"fɔ̀ shě ntfǔː\" may be a structure like \"will be on the day after tomorrow\"\n\nBut no subject?\n\nnǔ = you (sg)\n\nSo: \"you (sg) will be on the day after tomorrow\" → but what is the meaning?\n\nPerhaps \"be on\" means \"have\" or \"be present on\"?\n\nBut more likely: is \"fɔ̀ shě\" a verb? \"fɔ̀\" = day after, \"shě\" = tomorrow?\n\n\"shě\" = tomorrow? \"fɔ̀\" = the day after?\n\nIn sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" = day after tomorrow\n\nSo \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow\"\n\nSo the phrase is \"you (sg) will be on the day after tomorrow\" → i.e., \"you will be on Bvutfu\"\n\nBut that’s redundant.\n\nWait — sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo \"On [day], [subject] [verb] [object]\"\n\nIn sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — lacks verb and object.\n\nOnly \"nǔ\" — \"you\"\n\nSo maybe missing verb?\n\nUnless the verb is \"shě\"? But \"shě\" is not a verb.\n\nPossibility: It's a copy of sentence 2 — where \"on Bvusɔw, you will steal the yam\"\n\nSo perhaps \"bvúsɔ̀w\" is day, \"nǔ\" is you, and \"fɔ̀ shě ntfǔː\" is the verb phrase?\n\nBut \"fɔ̀ shě ntfǔː\" is \"the day after tomorrow\", not an action.\n\nWait — another possibility: \"fɔ̀ shě\" is a verb meaning \"will have\", and \"ntfǔː\" is the object? But \"ntfǔː\" is a day name.\n\nNo.\n\nBack to context: all sentences are on Bvuŋkaden.\n\nWe need to translate 16–19 from Bvuŋkaden.\n\nWe have observed:\n\n- \"fɔ̀ shě\" = day after tomorrow\n- \"ntfǔː\" = day name Bvutfu\n- \"yɛ᷅n\" = see\n- \"bèsèn\" = will\n- \"bɔ́\" = see\n- \"me\" = I\n- \"wvù\" = he\n- \"nɔ̂ː\" = to\n- \"kéː\" = steal\n- \"wáy\" = market\n- \"ɛ̀bɛ̀n\" = woman\n- \"bóy\" = woman\n- \"fí\" = help\n- \"lě\" = him\n- \"cɔ́ŋ\" = steal\n- \"mutù\" = car\n\nNow, sentence 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\n\nPossible translation: \"On Bvusɔw, you (sg) will be on the day after tomorrow\"\n\nBut \"be on\" is not idiomatic.\n\nAlternative: \"You (sg) will have the day after tomorrow\" → implies you will possess that day?\n\nUnlikely.\n\nAnother idea: in sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo \"on [day], you will X\"\n\nBut this sentence has no \"will\" or \"steal\".\n\nUnless \"fɔ̀ shě\" is a verb? But it's not.\n\nCould \"fɔ̀ shě\" be a verb meaning \"will become\" or \"will go\"?\n\nNo — \"fɔ̀ shě\" = the day after tomorrow.\n\nOnly possibility: typo or misreading?\n\nCheck original: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nPossibility: it's \"On Bvusɔw, you (sg) will steal the yam\" → same as sentence 2\n\nBut they used \"cɔ́ŋ\" — not \"fɔ̀ shě\"\n\n\"shě\" is not a verb.\n\nWait — could \"fɔ̀ shě\" be \"will have\" and \"ntfǔː\" is the object?\n\nBut \"ntfǔː\" = Bvutfu — a day.\n\n\"you will have Bvutfu\" — possible?\n\n\"have\" a day?\n\nIn English: \"you will have Bvutfu\" → meaning you will be in Bvutfu?\n\nLike \"you will be on Bvutfu\"?\n\nYes — \"have\" may be used in that sense.\n\nSo \"you will have the day after tomorrow\" → \"you will be on Bvutfu\"\n\nThus: \"You (sg) will have the day after tomorrow\" → \"you will be on Bvutfu\"\n\nSo translation: \"You (sg) will be on Bvutfu\"\n\nBut in context, spoken on Bvuŋkaden → so at this point, Bvutfu is in the future.\n\nSimilarly, check sentence 17: me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n\"me\" = I\n\n\"nú\" = on\n\n\"ŋgéː\" = will see? or \"will have\"?\n\n\"nyɛ́n\" = the market?\n\n\"kéː\" = steal\n\n\"lé\" = the\n\n\"ɛ̀bɛ̀n\" = woman\n\n\"ŋgéː\" = possibly \"will see\" or \"will have\"?\n\nIn sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\n\"nyɛ́n\" = the market\n\n\"kéː\" = steal → \"steal the woman\"?\n\n\"kéː nyɛ́n\" = steal the market? no.\n\n\"kéː\" = steal, \"nyɛ́n\" = the market → \"steal the market\"?\n\nBut in sentence 2: \"cɔ́ŋ kèŋkfǔ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11373.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 2, + "output": "First, analyze the known sentences to identify the pattern of time references in Nooni, especially how days are named and how temporal markers are used.\n\nKey observations from the examples:\n\n1. Days are named: Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema. These appear as standalone day names in sentences.\n2. Temporal markers used:\n - “Yesterday” = \"nú bvúmbòn\" → refers to the day before the current day.\n - “The day after tomorrow” = \"fɔ̀ shě ntfǔː\" → a future day.\n - “Tomorrow” = \"ntfǔː nú bvûŋka᷆ːde᷆n\" → in sentence 8.\n - “The day before yesterday” = “kefwé cí nú bvûŋka” → sentence 11.\n - “Today” = used with “me nú mbóy” (I chose), “wɔ̀ tɔ̀” (you heard), “wvù bɛ̂ː” (he killed).\n - “The day after tomorrow” = “fɔ̀ shě ntfǔː” (sentence 5).\n - “Tomorrow” = “ntfǔː nú bvûŋka᷆ːde᷆n” → sentence 8.\n - “On X” = used to refer to a specific day (e.g., “On Bvutfu, I came”).\n3. Time relative to the day of speaking:\n - If the sentence is spoken on Bvutfu, then:\n - “Yesterday” = Bvumbon (sentence 1)\n - “The day after tomorrow” = Bvutfu (sentence 5)\n - If spoken on Bvusɔw:\n - “Today” = present (sentence 6)\n - “You heard the thief a long time ago” = “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → past remote (sentence 7)\n - If spoken on Bvukema:\n - “Tomorrow” = “Bvuŋkaden” → sentence 8\n - “The day before yesterday” = Bvuŋka → sentence 11\n - If spoken on Bvuŋka:\n - “Today” = “bèsèn” → “Today, we will steal” → sentence 14\n\nNow, construct a temporal mapping. Let’s assign days to positions relative to the speaking day.\n\nLet the speaking day be D.\n\nWe use:\n- “Yesterday” → D − 1\n- “Tomorrow” → D + 1\n- “The day after tomorrow” → D + 2\n- “The day before yesterday” → D − 2\n- “Today” → D\n- “A long time ago” → very remote past (not timed directly)\n\nNow, check the named day shifts:\n\nFrom sentence 1 (spoken on Bvutfu):\n- \"Yesterday was Bvumbon\" → Bvumbon = Bvutfu − 1\n- \"On Bvusɔw, you will steal\" → Bvusɔw = Bvutfu + 1? Wait — Bvusɔw appears in multiple days.\n\nWait — better: find consistency.\n\nFrom sentence 1: spoken on Bvutfu → yesterday = Bvumbon → Bvumbon = Bvutfu − 1\n\nFrom sentence 5: spoken on Bvusɔw → \"The day after tomorrow is Bvutfu\" → so Bvutfu = Bvusɔw + 2\n\nSo:\n- Bvusɔw + 2 = Bvutfu\n→ Bvutfu = Bvusɔw + 2 → so Bvusɔw = Bvutfu − 2\n\nBut earlier, yesterday on Bvutfu = Bvumbon → so Bvutfu − 1 = Bvumbon\n\nSo:\n- Bvumbon = Bvutfu − 1\n- Bvusɔw = Bvutfu − 2\n\nNow, from sentence 8: spoken on Bvukema → \"Tomorrow is Bvuŋkaden\" → Bvuŋkaden = Bvukema + 1\n\nFrom sentence 11: spoken on Bvukema → \"The day before yesterday was Bvuŋka\" → Bvuŋka = Bvukema − 2\n\nSo:\n- Bvuŋkaden = Bvukema + 1\n- Bvuŋka = Bvukema − 2\n\nNow, we have day positions:\n\nSet Bvutfu = 0\n\nThen:\n- Bvutfu = 0\n- Bvumbon = −1 (yesterday)\n- Bvusɔw = −2 (since Bvusɔw = Bvutfu − 2)\n- Bvuŋka = ? → from sentence 11: Bvuŋka = Bvukema − 2\n- Bvukema = ? → from speech on Bvukema\n\nWe know: spoken on Bvukema → tomorrow = Bvuŋkaden → Bvuŋkaden = Bvukema + 1\n\nAlso, sentence 13: spoken on Bvuŋka → “On Bvutfu, the woman saw the market” → Bvutfu = 0 → so Bvutfu is referenced as a day in the past.\n\nNow, determine Bvukema.\n\nTry to see if we can link all days.\n\nWe have:\n- Bvutfu = 0\n- Bvumbon = −1\n- Bvusɔw = −2\n- Bvukema = X\n- Bvuŋka = X − 2\n- Bvuŋkaden = X + 1\n\nWe also have sentence 13 (spoken on Bvuŋka): “On Bvutfu, the woman saw the market” → so the speaker is on Bvuŋka, and refers to Bvutfu as a past day.\n\nSo Bvutfu = 0, and speaker is on Bvuŋka → so Bvuŋka < 0 or > 0?\n\nIf Bvutfu = 0 and speaker is on Bvuŋka, and refers to Bvutfu (a day) — that is possible only if Bvutfu is in the past or present.\n\nBut if Bvutfu is 0, and the speaker is on Bvuŋka, which is not 0, then Bvutfu is either past or future.\n\nIn sentence 13: “On Bvutfu, the woman saw the market” — clearly a past reference.\n\nSo speaker is on Bvuŋka, and Bvutfu is a day in the past → Bvutfu < Bvuŋka\n\nBut Bvutfu = 0 → so 0 < Bvuŋka → Bvuŋka > 0\n\nBut also from above: Bvuŋka = X − 2 → where X = Bvukema\n\nAnd Bvuŋkaden = X + 1\n\nNow, from sentence 14: “Today, we will steal the car” — spoken on Bvuŋka → so “today” is Bvuŋka\n\nWe don’t have a contradiction.\n\nNow go to the target: sentences spoken on Bvuŋkaden.\n\nSo we need the translation of 16–19, spoken on Bvuŋkaden.\n\nSo the speaking day is Bvuŋkaden.\n\nWe want to translate:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nWe now set the reference point: speaking on Bvuŋkaden.\n\nWe want to find what day this is relative to others, and use the pattern.\n\nWe have:\n- Bvutfu = 0 (assumed)\n- Bvusɔw = Bvutfu − 2 = −2\n- Bvumbon = Bvutfu − 1 = −1\n- Bvuŋka = X − 2 → where X = Bvukema\n- Bvukema = X\n- Bvuŋkaden = X + 1\n\nWe also have sentence 13: spoken on Bvuŋka → refers to “On Bvutfu” → so Bvutfu is a day in the past → so Bvuŋka > 0 → because Bvutfu = 0\n\nSo Bvuŋka > 0 → so X − 2 > 0 → X > 2 → so Bvukema > 2\n\nThus Bvuŋkaden = X + 1 > 3\n\nSo Bvuŋkaden is in the future (relative to Bvutfu = 0)\n\nNow verify other points.\n\nSentence 5: spoken on Bvusɔw → \"The day after tomorrow is Bvutfu\"\n\nBvusɔw = −2 → so day after tomorrow = −2 + 2 = 0 → which is Bvutfu → correct.\n\nSentence 8: spoken on Bvukema → \"Tomorrow is Bvuŋkaden\" → Bvuŋkaden = Bvukema + 1 → correct.\n\nSentence 11: \"The day before yesterday was Bvuŋka\" → Bvukema = X → day before yesterday = X − 2 → Bvuŋka → correct.\n\nAll consistent.\n\nNow, speaking on Bvuŋkaden → current day = D = Bvuŋkaden = X + 1\n\nWe now translate each sentence:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n- “bvúsɔ̀w” is a day name → from above, Bvusɔw = −2\n- “fɔ̀ shě ntfǔː” → “the day after tomorrow”\n- So: “On the day after tomorrow, Bvusɔw?”\n\nBut “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → is “On [day] [the day after tomorrow]”?\n\nWait — structure: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\n“nǔ” may be a preposition — like “on” or “in”\n\nBut in sentence 1: “me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn” → “On Bvumbon, I came to the market” — so “on” used with day name.\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” likely means “On Bvusɔw, the day after tomorrow” — but that doesn't make sense.\n\nAlternative: perhaps it's “On the day after tomorrow, Bvusɔw” → but that would be an event.\n\nWait — is “fɔ̀ shě” a time reference?\n\nFrom sentence 5: “fɔ̀ shě ntfǔː” = “The day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě” = “the day after tomorrow”\n\nSo the sentence says: “On Bvusɔw, the day after tomorrow”?\n\nThat seems grammatically odd.\n\nPossibility: “bvúsɔ̀w” is not the day, but a subject.\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam” → clearly “On Bvusɔw”\n\nIn sentence 3: “On Bvuzhi, the woman will help me”\n\nSo “X nǔ Y” = “On X, Y”\n\nSo 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → “On Bvusɔw, the day after tomorrow”\n\nBut “the day after tomorrow” is a time, not a place.\n\nAlternative: perhaps “fɔ̀ shě” is a verb or event?\n\nNo — “fɔ̀ shě” appears in “fɔ̀ shě ntfǔː” meaning “the day after tomorrow”\n\nSo likely a temporal phrase.\n\nThus, “On Bvusɔw, the day after tomorrow” — grammatically odd.\n\nWait — is it “On Bvusɔw, it is the day after tomorrow”? But no different expression.\n\nAlternative: perhaps the structure is “On [time], [event]” — but Bvusɔw is a day.\n\nPossibly a typo or misordering.\n\nWait — look at sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nSo in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — “On Bvusɔw, the day after tomorrow” — but that's redundant.\n\nCould it be “On the day after tomorrow, Bvusɔw”?\n\nBut again, Bvusɔw is a day name.\n\nMore plausible: the phrase “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” means “On Bvusɔw, the day after tomorrow is [something]” — but no complement.\n\nWait — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam” — so “on day, event”\n\nSo likely, “date nǔ event” = “On date, event”\n\nSo 16: “On Bvusɔw, the day after tomorrow” — but the day after tomorrow is not an event.\n\nUnless it's a misreading.\n\nWait — could “fɔ̀ shě” be a verb? But no verb in that context.\n\nAlternative: perhaps “fɔ̀ shě” is a noun meaning “that time”?\n\nNo — from sentence 5, it's clearly “the day after tomorrow”\n\nSo this sentence must be malformed.\n\nBut perhaps it's “On the day after tomorrow, Bvusɔw” — meaning “Bvusɔw occurs on the day after tomorrow”?\n\nBut Bvusɔw is a fixed day.\n\nWait — Bvusɔw = −2, and current day is Bvuŋkaden = X+1, which is >3 → so Bvusɔw is far in the past.\n\nBut the sentence says “On Bvusɔw, the day after tomorrow” — again, unclear.\n\nWait — in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nCompare to sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal yam”\n\nSo “event on day”\n\nStructure: [subject] + [preposition] + [day name]\n\nBut here: “day name” + “preposition” + “time phrase”\n\nNo logical fit.\n\nPerhaps a typo — maybe it's meant to be “On the day after tomorrow, Bvusɔw”?\n\nThat would be “fɔ̀ shě ntfǔː nǔ bvúsɔ̀w” — which is not the case.\n\nGiven the examples, the day name comes first when it's the reference point.\n\nSo likely, the sentence is “On Bvusɔw, [something]”\n\nBut what?\n\nCould it be that “fɔ̀ shě” is being used as a verb?\n\nNo — “fɔ̀ shě” is part of the future tense.\n\nAnother idea: in some languages, time markers can be used as events.\n\nWait — sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"On Bvutfu, the woman saw me at the market\" — clearly, “on day, action”\n\nSo structure is fixed: day + [event]\n\nSo sentence 16 must be: day + event\n\nBut “fɔ̀ shě ntfǔː” is not an event — it's a time.\n\nUnless “fɔ̀ shě ntfǔː” is the event? But that doesn't make sense.\n\nAlternative: could it be that “fɔ̀ shě” is “is”?\n\nNo — “fɔ̀ shě” appears with “ntfǔː” as “the day after tomorrow”\n\nSo it's a time phrase.\n\nPossibly, the sentence is “On Bvusɔw, the day after tomorrow occurs” — but that's redundant.\n\nAfter reconsidering, it's likely that the original sentence is misread.\n\nLook again: the sentence is \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nBut in the list, similar structures appear with time phrases.\n\nSentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\"\n\nSo “fɔ̀ shě ntfǔː” is the time expression.\n\nIn sentence 16, it might be the time expression, not the day.\n\nBut the structure is “day name preposition time expression” — not standard.\n\nUnless “nǔ” is not “on” but something else.\n\nBut in other sentences, “nǔ” is used with “Bvumbon”, so likely “on”.\n\nAnother possibility: “bvúsɔ̀w” is not a day name, but a verb?\n\nBut in all other uses, “bvúsɔ̀w” is used as a day name.\n\nIn sentence 2: “On Bvusɔw, you will steal the yam” — so “bvúsɔ̀w” is a day.\n\nSo must be a day.\n\nTherefore, likely the sentence is: “On Bvusɔw, the day after tomorrow” — which is grammatically incorrect.\n\nOr perhaps it's “On the day after tomorrow, Bvusɔw” — which would make sense if Bvusɔw is an event.\n\nBut Bvusɔw is a day.\n\nWait — in sentence 2: “you will steal the yam on Bvusɔw” — so Bvusɔw is the day.\n\nTherefore, it's not an event.\n\nSo subtraction: perhaps the", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10938.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 3, + "output": "First, identify the pattern of time references in Nooni based on the given sentences.\n\nWe observe time expressions in relation to the current day (the day of speech). The days in the week are named: Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema, and Bvuŋkaden (implied). From the sentences:\n\n- On Bvutfu: \"Yesterday was Bvumbon\" (1), \"The day after tomorrow is Bvutfu\" (5), so Bvutfu is not today, and \"day after tomorrow\" = Bvutfu.\n- On Bvusɔw: \"Today, he killed the woman\" (6), \"The day after tomorrow is Bvutfu\" (5), so Bvutfu is two days after Bvusɔw.\n- On Bvukema: \"Tomorrow is Bvuŋkaden\" (8), so Bvuŋkaden = tomorrow.\n- On Bvuŋka: \"Today, we will steal the car\" (14), and \"The day before yesterday was Bvuŋka\" (11), meaning the day before yesterday = Bvuŋka.\n\nThus, current day = Bvukema (sentence 9: \"Today, I chose the book\").\n\nSo, the days are ordered as:\n- Bvutfu → 2 days before Bvusɔw (since on Bvusɔw, \"day after tomorrow is Bvutfu\") → so Bvutfu = Bvusɔw − 2\n- Bvusɔw → one day after Bvutfu → Bvusɔw = Bvutfu + 1\n- Bvuzhi → on day 3 (sentence 3: \"On Bvuzhi, the woman will help me\")\n- Bvuŋka → on day 4\n- Bvukema → day 5 (current day)\n- Bvuŋkaden → tomorrow → day 6\n\nSo the days in order: \n1. Bvutfu \n2. Bvusɔw \n3. Bvuzhi \n4. Bvuŋka \n5. Bvukema \n6. Bvuŋkaden\n\nThis ordering confirms the time structure where each day refers to a fixed point, and time expressions involve offsets relative to the day of speech.\n\nKey markers:\n- “Yesterday” → −1 \n- “Tomorrow” → +1 \n- “The day after tomorrow” → +2 \n- “The day before yesterday” → −2 \n- “On X” = referring to X day, which is a named day\n\nNow, examine the time expressions in the target sentences spoken on Bvuŋkaden (day 6):\n\n---\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \nLit: \"On Bvusɔw, [you] will have [the day after tomorrow]\" → \"On Bvusɔw, you will have the day after tomorrow\" \n→ Bvusɔw is 3 days before Bvuŋkaden (Bvuŋkaden = day 6, Bvusɔw = day 3) \nThus, \"the day after tomorrow\" from Bvusɔw = day 5 (Bvukema) \nBut the structure is “on Bvusɔw, you will have the day after tomorrow” — likely misphrased.\n\nWait — “fɔ̀ shě ntfǔː” = “the day after tomorrow” \nBut spoken on Bvuŋkaden — so “on Bvusɔw, you will have the day after tomorrow” in reference to Bvuŋkaden? Unlikely.\n\nAlternative: in Nooni, time adverbials in clauses like “on X, [you] will have [Y]” may mean that Y occurs on X.\n\nBut examples:\nSentence 1: “Yesterday was Bvumbon” — \"was\" = past, reference to yesterday\n\nSentence 5: “The day after tomorrow is Bvutfu” — refers to a future day.\n\nSentence 8: “Tomorrow is Bvuŋkaden”\n\nSentence 11: “The day before yesterday was Bvuŋka” — past.\n\nSentence 13: “On Bvutfu, the woman saw the market” — event on Bvutfu.\n\nSo “on X, [someone] will do Y” means Y happens on X.\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow” — doesn’t make sense.\n\nWait — perhaps “fɔ̀ shě ntfǔː” is not “the day after tomorrow”?\n\nCheck meaning of “fɔ̀ shě ntfǔː”\n\nIn sentence 5: “The day after tomorrow is Bvutfu” → “fɔ̀ shě ntfǔː” = \"the day after tomorrow\"\n\nSo “fɔ̀ shě” = “the day after tomorrow”\n\nSo “On Bvusɔw, you will have the day after tomorrow” — clearly wrong.\n\nAlternative: perhaps it's “you will have [the day after tomorrow]” in a different sense?\n\nBut no such structure.\n\nAnother idea: grammatical structure. \n\"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → perhaps “on Bvusɔw, you will see (the day after tomorrow)”? But \"see\" is not implied.\n\nWait — in sentence 7: “You(sg) heard the thief a long time ago.” — so \"heard\" = past, a long time ago.\n\nIn sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → \"I will see the yam thief (or steal the car?)\"\n\nNo direct link.\n\nAlternative: is \"fɔ̀ shě\" a time expression?\n\nYes — from sentence 5: “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nBut in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → “On Bvusɔw, you will have the day after tomorrow” — still odd.\n\nWait — perhaps it's \"On Bvusɔw, you will have [a day] that is the day after tomorrow\" — meaning the event happens on a day that is the day after tomorrow, relative to some point?\n\nBut that makes no sense.\n\nAlternative: perhaps \"fɔ̀ shě\" is not a day, but a verb?\n\nBut “fɔ̀ shě” is not a verb — “fɔ̀” is a particle. “shě” = “to be” or “to have”? Not found.\n\nContext: sentence 15: “They saw me at the market just now” — “saw” = verb.\n\nSentence 13: “On Bvutfu, the woman saw the market” — \"saw\" is a past event.\n\nSo verbs in time clauses refer to events.\n\nBut in 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — no verb.\n\nWait — “fɔ̀ shě” may be a nominal phrase: “the day after tomorrow” = fɔ̀ shě ntfǔː\n\nSo “on Bvusɔw, you will have the day after tomorrow” — still bad syntax.\n\nAnother possibility: it’s a typo or misreading.\n\nWait — look at sentence 3: “On Bvuzhi, the woman will help me” → “will help”\n\nSentence 2: “On Bvusɔw, you(sg) will steal the yam” → “will steal”\n\nSentence 4: “On Bvᵤŋka, he found the book” → “found”\n\nSo verbs are used with \"on X, subject will do something\"\n\nBut in 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — no verb.\n\nUnless “fɔ̀ shě” is a verb. But no known verb.\n\nAlternative: look at form: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCompare to sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “On Bvutfu, the woman saw me at the market” → so “saw” is “yɛ᷅n me lé”\n\nSimilarly, in sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “I will see the yam thief”\n\n“nyɛ́n” = “the” → \"nyɛ́n kèŋkfǔ\" = \"the yam thief\"\n\n“ŋgéː” = verb “to see” (from “ŋgéː nyɛ́n”)\n\nSimilarly, “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn” = “he found the thief”\n\nSo “ŋgéː” = “see” or “find”\n\nThus, “fɔ̀ shě” may be a verb?\n\nBut “fɔ̀ shě” doesn’t appear elsewhere.\n\nIn sentence 5: “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nBut in 16, it's used as a verb-object?\n\nNo — structure: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nNo copula or verb.\n\nPerhaps it's “On Bvusɔw, you will have (the day after tomorrow)” — meaning “you will experience the day after tomorrow” — but that doesn't make sense.\n\nWait — look at sentence 11: “The day before yesterday was Bvuŋka” → past\n\nSo pattern: time expressions like “the day after tomorrow” are used to name days, like “the day after tomorrow is X”.\n\nThus, “On Bvusɔw, you will have the day after tomorrow” may be a misreading.\n\nBut in sentence 19: “bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n” → “Today, the woman will go to the market Bvuzhiden”\n\n“bèsèn” = today \n“nǔ” = the woman \n“bóy” = will go \n“tɔ́” = to \n“fɔ̀wǎy” = market \n“bvúzhı᷇ːde᷆n” = Bvuzhiden — future day?\n\nBut “bvúzhı᷇ːde᷆n” → likely “after Bvuzhi” or “after Bvuzhi” → Bvuzhi is day 3, so Bvuzhiden = day 4?\n\nNo — in sentence 8: “Tomorrow is Bvuŋkaden” → so tomorrow = Bvuŋkaden\n\nIn sentence 11: “The day before yesterday was Bvuŋka” — so Bvuŋka = day 4\n\nSo timeline:\n\n- Day 1: Bvutfu \n- Day 2: Bvusɔw \n- Day 3: Bvuzhi \n- Day 4: Bvuŋka \n- Day 5: Bvukema (current day) \n- Day 6: Bvuŋkaden (speaking day)\n\nSo:\n\n- “Tomorrow” = day +1 \n- “Yesterday” = day −1 \n- “The day after tomorrow” = day +2 \n- “The day before yesterday” = day −2\n\nNow:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ \"On Bvusɔw, you will have the day after tomorrow\" \n\"the day after tomorrow\" from what? From the day of speech? Or from Bvusɔw?\n\nBut the structure is \"on X, you will have Y\" — Y is a day.\n\nBut Bvusɔw is day 3, day after tomorrow (day +2) = day 5 → Bvukema\n\nSo “you will have Bvukema”?\n\nNo — “have” is not a verb used.\n\nPerhaps “fɔ̀ shě” is a verb? No.\n\nAlternative: is “fɔ̀ shě ntfǔː” a time indicator?\n\nOnly appears in sentence 5: “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nSo likely, “on Bvusɔw, you will have [the day after tomorrow]” is a syntactic error.\n\nBut in sentence 13: “On Bvutfu, the woman saw the market” → so on a day, someone sees something.\n\nIn sentence 2: “on Bvusɔw, you will steal the yam” → on day, future action.\n\nSo when the sentence has “on X, subject will do Y” → action on X.\n\nBut here, it is “on Bvusɔw, you will have [the day after tomorrow]” — no action.\n\nBut “have” is not in the verb list.\n\nWait — look at 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” \n→ “I will see the yam thief”\n\n“ŋgéː” is “see”, “nyɛ́n” = “the”, “kèŋkfǔ” = “yam thief”\n\nSo verb = “see”\n\nIn 18: “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn” \n→ “he found the thief [on the day of] Bvumbon”?\n\n“wvù” = he \n“tɔ̀” = found \n“nɔ̂ː” = the \n“yɛ᷅n” = thief \n“bèsèn” = today \n“ě” = on? \n“bvúmbòn” = Bvumbon\n\n“bèsèn ě” = “on today” → “on the day that is today”\n\nSo “he found the thief on Bvumbon”\n\nBut the day of speech is Bvuŋkaden → so Bvumbon must be a past day.\n\nWhat day is Bvumbon?\n\nFrom sentence 1: “Yesterday was Bvumbon” → when spoken on Bvutfu.\n\nOn Bvutfu → yesterday = Bvumbon \nBvutfu = day 1 → yesterday = day 0 → so Bvumbon = day 0 → before day 1.\n\nBut earlier we had a cycle of 6 days.\n\nFrom sentence 1: “Yesterday was Bvumbon” → so if today is Bvutfu, then yesterday = Bvumbon.\n\nBvutfu = day 1 → yesterday = day 0 → Bvumbon = day 0\n\nThen on Bvusɔw (day 2): “the day after tomorrow is Bvutfu” → day 2 +2 = day 4 — but Bvutfu is day 1 → contradiction.\n\nWait — that can't be.\n\nEarlier assumption: Bvutfu is day 1?\n\nBut on Bvusɔw (day 2): “the day after tomorrow is Bvutfu” → day 2 +2 = day 4 → so Bvutfu = day 4\n\nBut on Bvutfu (day 1): “yesterday was Bvumbon” → day 1 −1 = day 0 → Bvumbon = day 0\n\nThen on Bvuzhi (day 3): “On Bvuzhi, the woman will help me” → Bvuzhi = day 3\n\nOn Bvuŋka (day 4): “The day before yesterday was Bvuŋka” → day 4 −2 = day 2 → so Bvuŋka = day 2? But day 4 = Bvuŋka? Contradiction.\n\nSo the cycle must be different.\n\nLet's fix the timeline.\n\nLet day of speech be D.\n\nOn Bvutfu (speech day D): \n1. \"Yesterday was Bvumbon\" → D−1 = Bvumbon \n2. \"The day after tomorrow is Bvutfu\" → D+2 = Bvutfu → Bvutfu = D+2 → so Bvutfu is D+2 → so speech is not on Bvutfu\n\nThus, speech is not on Bvutfu.\n\nOn Bvusɔw (speech day D): \n5. \"The day after tomorrow is Bvutfu\" → D+2 = Bvutfu → so Bvutfu = D+2 \n6. \"Today, he killed the woman\" \n7. \"You(sg) heard the thief a long time ago\" → long time ago → past, distant\n\nOn Bvukema (speech day D): \n8. \"Tomorrow is Bvuŋkaden\" → D+1 = Bvuŋkaden \n11. \"The day before yesterday was Bvuŋka\" → D−2 = Bvuŋka\n\nOn Bvuŋka (speech day D): \n12. \"I am about to help the man\" \n13. \"On Bvutfu, the woman saw the market\" → so Bvutfu is a named day \n14. \"Today, we will steal the car\" \n15. \"They saw me at the market just now\"\n\nSo now we have:\n\nFrom Bvusɔw (speech day D): \n- D+2 = Bvutfu → (1)\n\nFrom Bvukema (D): \n- D+1 = Bvuŋkaden → (2) \n- D−2 = Bvuŋka → (3)\n\nFrom Bvuŋka (speech day D): \n- Bvutfu is a past day → for sentence 13: \"On Bvutfu, the woman saw the market\" → so Bvutfu exists and is before Bvuŋka\n\nBut from (1): Bvutfu = D+2\n\nBut Bvuŋka is on a day — when is it spoken? The sentence is \"spoken on Bvuŋka\" → so speech day = Bvuŋka\n\nSo on day D = Bvuŋka, we have information about Bvutfu.\n\nSo \"On Bvutfu, the woman saw the market\" → Bvutfu is a day in the past or future?\n\nSince it's spoken on Bvuŋka, and \"on Bvutfu\" is an event from the past, B", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10922.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "Scratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|----------------------------------|------------------------------|---------|\n| b.1 / 19. | The shaman hurt you. | Angatkuq aanniqtanga | Inuktitut has \"Angatkuq\" for shaman (e.g., 6: \"The shaman cured a doctor\"), \"aanniqtanga\" = hurt yourself (3: \"You hurt yourself\") → \"hurt you\" is \"aanniqtanga\" with dative |\n| b.2 / 20. | The teacher saw the boy. | Qingmiq iluaqhaijivit | \"Qingmiq\" = dog (1: \"Your dog saw you\"), \"iluaqhaijivit\" = saw (1: \"your dog saw you\") → \"saw\" in past tense, \"teacher\" not directly present; but \"Qingmiq\" may be a loan or substitute; look for \"teacher\" → no direct match; but \"teacher\" not in examples. Wait — \"Qingmivit\" = dog saw; \"Qingmiq\" = dog; \"iluaqhaijivit\" = saw. No \"teacher\" in examples. Possibly \"Iluaqhaiji\" is doctor, not teacher. Teacher not present. Alternative: \"qaq\" or \"iquq\"? Not in list. Is \"teacher\" a missing word? But 10: \"your teacher\" is mentioned → \"ilinniaqtitsijiit\" = teacher (10: \"The dog hurt your teacher\"). So \"ilinniaqtitsijiit\" = teacher. Then \"teacher saw boy\" = \"ilinniaqtitsijiit iluaqhaijivit\" → but \"iluaqhaijivit\" = saw. So \"ilinniaqtitsijiit iluaqhaijivit\" = teacher saw → but no object? Wait — saw the boy → must include boy. \"iluaqhaijivit\" = saw (past), but object missing. So must be \"ilinniaqtitsijiit iluaqhaijivit iluq\" → no. Look at 1: \"Qingmivit takujaatit\" = dog saw you → verb is \"takujaatit\" = saw. So \"iluaqhaijivit\" is not \"saw\", it's \"cured\" (4: cured you). Wait: 4: \"Iluaqhaijiup aarqijaatit\" = doctor cured you. 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" = boy shot doctor. 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" = your doctor cured your boy. So \"iluaqhaijivit\" = cured. That changes everything. So \"iluaqhaijivit\" = cured, not saw. So \"saw\" = ? Not in list. Only \"takujaatit\" = saw (1). So \"takujaatit\" is saw. Where is \"saw\" in the list? 1: \"Qingmivit takujaatit\" = your dog saw you. So \"takujaatit\" = saw. So past tense verb for \"see\" = takujaatit. So \"teacher saw boy\" = ilinniaqtitsijiit takujaatit iluq? But \"iluq\" for boy? Boy is \"inuuhuktuup\" (2). Where is boy? 20. \"teacher saw boy\" → so need: ilinniaqtitsijiit + takujaatit + object (boy). Object must be \"inuuhuktuup\" or something. Is \"inuuhuktuup\" a boy? Yes (2: \"the boy\"). So \"ilinniaqtitsijiit takujaatit inuuhuktuup\". But is \"inuuhuktuup\" the boy? Possibly. Also, in 8: \"your doctor cured your boy\" → \"inuuhuktuit\" = your boy. So \"inuuhuktuup\" = boy. So \"teacher saw boy\" = ilinniaqtitsijiit takujaatit inuuhuktuup. But is the verb order correct? \"takujaatit\" is saw, takes a dative or accusative? In example 1: \"Qingmivit takujaatit\" → your dog saw you → \"you\" is dative? Or object? \"takujaatit\" likely takes object. In 1: \"your dog saw you\" → you is object. So \"takujaatit\" takes direct object. So \"ilinniaqtitsijiit takujaatit inuuhuktuup\" = teacher saw the boy. But is \"teacher\" itself written? In 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" = the dog hurt your teacher → \"ilinniaqtitsijiit\" = teacher. So \"ilinniaqtitsijiit\" is teacher. So good. So b.2 = ilinniaqtitsijiit takujaatit inuuhuktuup. |\n| b.3 / 21. | Your wolf fell. | Iluq unuqaq takujaatit? Or: Angunahukti upuq? Wait — \"fell\" = ? Not in examples. 11: \"Ukiakhaqtutit\" = you fell. So \"Ukiakhaqtutit\" = you fell. So \"you fell\" = \"ukiaqhaqtutit\". So \"your wolf\" = \"iluq\" (wolf) + possessive? \"iluq\" = wolf. Possessive: \"your\" = \"qanuuq\" or \"qanuka\"? Not clear. In 9: \"Angunahukti nanurmik qukiqsijuq\" = hunter shot a polar bear. 7: \"Nanuq qaijuq\" = polar bear came. 12: \"Angunahukti nanurmik qukiqsijuq\" = hunter shot a polar bear. \"nanurmik\" = a polar bear. So \"iluq\" = wolf. \"Your wolf\" = \"iluq qanuka\" or \"iluq qanuuq\"? In 11: \"Ukiakhaqtutit\" = you fell. So \"you fell\" = \"ukiaqhaqtutit\". So \"your wolf fell\" = iluq qanuka ukiakhaqtutit? But no \"your\" marker. In 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" = dog hurt your teacher — \"your teacher\" = ilinniaqtitsijiit aanniqtanga? That seems to be the structure. So \"your\" is attached to noun, possibly via possessive prefix. In example 1: \"Qingmivit takujaatit\" = your dog saw you → \"Qingmivit\" = your dog. So \"Qingmi\" = dog, \"Qingmivit\" = your dog. So \"v\" = possessive. So \"qanu\" or \"qanu\" → \"your\" = \"qanua\" or \"qanu\" + suffix. In Inuktitut, possessive is often suffix. So \"iluq\" + \"qanu\" = your wolf? Not likely. \"iluq\" is wolf, \"qanu\" is your — so \"qanu iluq\" = your wolf? But in 1: \"Qingmivit takujaatit\" = \"your dog\" + \"saw you\". So \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" → \"v\" = possessive suffix. So \"v\" = your. So for \"your wolf\" = \"iluq\" + \"v\" = iluqiv? But not in examples. No \"wolf\" directly. In 9: \"Angunahukti nanurmik qukiqsijuq\" = hunter shot a polar bear → \"nanurmik\" = polar bear. So \"iluq\" = wolf, so \"your wolf\" = iluqiv? But need to verify. In 11: \"Ukiakhaqtutit\" = you fell. So \"your wolf fell\" = iluqiv ukiakhaqtutit. But is \"v\" the correct possessive? In 1: \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" → yes. So \"iluq\" + \"v\" → \"iluqiv\" = your wolf. Then \"fell\" = \"ukiaqhaqtutit\" (11). So \"iluqiv ukiakhaqtutit\". |\n| b.4 / 22. | You shot a dog. | Ukiakhaqtutit? No — \"you shot\" = ? In 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" = boy shot doctor → \"qukiqtanga\" = shot. So \"qukiqtanga\" = shot. In 9: \"Angunahukti nanurmik qukiqsijuq\" = hunter shot a polar bear → \"qukiqsijuq\" = shot. So \"qukiq\" + suffix = shot. So \"qukiqtanga\" = shot. So \"you shot a dog\" = you + shot + dog. \"you\" = you → may be \"qanu\" or nothing? In 1: \"Qingmivit takujaatit\" = your dog saw you → \"you\" is object. So \"you\" as subject? In 11: \"Ukiakhaqtutit\" = you fell → \"you\" as subject. So \"you\" = subject. So \"you shot a dog\" = ukiakhaqtutit? No — \"ukiaqhaqtutit\" = fell. So not. \"you shot\" = \"you\" + \"shot\". So subject + verb + object. So \"you\" = root? In 11: \"you fell\" = ukiakhaqtutit → so \"ukiaqhaqtutit\" is the verb for \"fell\". So \"shot\" = \"qukiqtanga\" or \"qukiqsijuq\"? In 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" = boy shot doctor → \"qukiqtanga\" = shot. So \"qukiqtanga\" = shot. So \"you shot a dog\" = you + qukiqtanga + dog. \"you\" = no possessive? Since \"you\" is not possessive. So \"qanu\" or stem. In Inuktitut, subject markers may be absent. In example 1: \"Qingmivit takujaatit\" — no \"you\" subject marker. So likely, \"you\" is implied. So verb for \"shot\" = qukiqtanga. Object = dog. Dog = \"Qingmiq\" (5: \"Qingmiq iputujait\" = you speared the dog). So \"Qingmiq\" = dog. So \"you shot a dog\" = qukiqtanga qingmiq? But no subject. In 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" = the dog hurt your teacher — \"Qingmiup\" = your dog? \"Qingmiup\" = your dog? So \"Qingmi\" + \"up\" = your dog. So possessive suffix. In 1: \"Qingmivit\" = your dog → \"v\" = your. So \"up\" or \"v\" — likely different. In 1: \"Qingmivit\" → \"v\" is possessive. In 5: \"Qingmiq iputujait\" = you speared the dog → \"Qingmiq\" = dog, no possessive. So \"Qingmiq\" = dog. So object = \"Qingmiq\". So \"you shot a dog\" = ukiakhaqtutit? No. Verb is \"qukiqtanga\". So \"qukiqtanga qingmiq\". But is \"you\" needed? In 11: \"Ukiakhaqtutit\" = you fell → has subject \"you\"? No — it's \"Ukiakhaqtutit\" = you fell. So \"you\" is subject. So in \"you shot a dog\", subject is \"you\" → so no explicit marker. In the absence of a possessive prefix, subject may be implied. So \"qukiqtanga qingmiq\" = you shot a dog. But \"you\" is not marked; in 11, \"you fell\" uses \"Ukiakhaqtutit\" — so perhaps the subject is implied. So likely \"qukiqtanga qingmiq\". |\n| b.5 / 23. | Your dog hurt a teacher. | Qingmivit aanniqtanga ilinniaqtitsijiit? In 1: \"Qingmivit takujaatit\" = your dog saw you → \"Qingmivit\" = your dog. So \"Qingmivit\" = your dog. \"hurt\" = \"aanniqtanga\" — in 3: \"Aanniqtutit\" = you hurt yourself → \"aanniqtutit\" = you hurt yourself. So \"aanniqtanga\" = hurt (someone). Object = teacher → \"ilinniaqtitsijiit\" = teacher (10). So \"Qingmivit aanniqtanga ilinniaqtitsijiit\" = your dog hurt a teacher. |\n\nFinal answers:\n\n- 19. The shaman hurt you → Angatkuq aanniqtanga\n- 20. The teacher saw the boy → ilinniaqtitsijiit takujaatit inuuhuktuup\n- 21. Your wolf fell → iluqiv ukiakhaqtutit\n- 22. You shot a dog → qukiqtanga qingmiq\n- 23. Your dog hurt a teacher → Qingmivit aanniqtanga ilinniaqtitsijiit\n\nNow verify all derivations:\n\n- 19: shaman = Angatkuq (6: shaman cured a doctor), hurt = aanniqtanga (3: you hurt yourself) → \"Angatkuq aanniqtanga\" = shaman hurt you → yes\n- 20: teacher = ilinniaqtitsijiit (10: dog hurt your teacher), saw = takujaatit (1: your dog saw you), boy = inuuhuktuup (2: the boy) → ilinniaqtitsijiit takujaatit inuuhuktuup → correct\n- 21: your wolf → iluqiv (iluq + v = your wolf; v from \"Qingmivit\" = your dog), fell = ukiakhaqtutit (11: you fell) → iluqiv ukiakhaqtutit → correct\n- 22: you shot a dog → you = implicit, shot = qukiqtanga (2 and 9), dog = qingmiq (5: you speared the dog) → qukiqtanga qingmiq → correct\n- 23: your dog = Qingmivit (1: your dog saw you), hurt = aanniqtanga (3), teacher = ilinniaqtitsijiit (10) → Qingmivit aanniqtanga ilinniaqtitsijiit → correct\n\nAll units are derived from direct evidence and consistent patterns in verb forms, possessives, and noun forms.\n\n\\boxed{b.1: Angatkuq aanniqtanga; b.2: ilinniaqtitsijiit takujaatit inuuhuktuup; b.3: iluqiv ukiakhaqtutit; b.4: qukiqtanga qingmiq; b.5: Qingmivit aanniqtanga ilinniaqtitsijiit}", + "generated_tokens": 3610, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: Angatkuq aanniqtanga; b.2: ilinniaqtitsijiit takujaatit inuuhuktuup; b.3: iluqiv ukiakhaqtutit; b.4: qukiqtanga qingmiq; b.5: Qingmivit aanniqtanga ilinniaqtitsijiit", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9359.0, + "ioling_final_answer_chars": 170.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "Scratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|----------------------------------|----------------------------------|--------------------------------------------------------------------------|\n| b.1 / 19 | The shaman hurt you | Angatkuq aanniqtanga | Sentence 6: \"The shaman cured a doctor\" → \"Angatkuq iluaqhaijimik aarqisijuq\" → cured → aarqisijuq; hurt → aanniqtanga; subject \"Angatkuq\" |\n| b.2 / 20 | The teacher saw the boy | Iqiniq iputujait | Sentence 1: \"Your dog saw you\" → \"Qingmivit takujaatit\" → \"q + noun + verb\" → \"saw\" = takujaatit; \"teacher\" = iqiniq; \"boy\" = inuuhuktuit |\n| b.3 / 21 | Your wolf fell | Qulikunatukhaqtutit | Sentence 11: \"You fell\" → \"Ukiakhaqtutit\"; \"your wolf\" → qulikuni + (object) → qulikunatukhaqtutit |\n| b.4 / 22 | You shot a dog | Qingmivit qukiqtanga | Sentence 2: \"The boy shot the doctor\" → \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"shot\" = qukiqtanga; subject = you = \"iputujait\" → \"iputujait qukiqtanga\" → \"You shot a dog\" → q = dog → \"qukiqtanga\" |\n| b.5 / 23 | Your dog hurt a teacher | Qingmivit aanniqtanga ijaniq | Sentence 10: \"The dog hurt your teacher\" → \"Qingmiq iputujait\" → hurt = aanniqtanga; \"your teacher\" = ijaniq → \"Qingmivit aanniqtanga ijaniq\" |\n\nDerivation:\n\n- Inuktitut verbs are often marked with case and person in suffixes. The key pattern is that:\n - \"hurt\" = aanniqtanga (e.g., sentence 3: \"Aanniqtutit\" → \"You hurt yourself\")\n - \"shot\" = qukiqtanga (e.g., sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\")\n - \"saw\" = takujaatit (e.g., sentence 1: \"Qingmivit takujaatit\")\n - \"fell\" = ukiakhaqtutit (sentence 11: \"Ukiakhaqtutit\" → you fell)\n\n- Possession and objects:\n - \"your\" = \"your\" prefix or case marker; \"your dog\" = \"Qingmivit\"\n - \"teacher\" = ijaniq (inferred from \"your teacher\" in sentence 10)\n - \"boy\" = inuuhuktuit (used in sentence 8: \"your boy\" → \"inuuhuktuit\")\n\n- 19. \"The shaman hurt you\": \"Angatkuq\" (shaman) + \"aanniqtanga\" (hurt) + \"you\" → \"Angatkuq aanniqtanga (you)\" → \"Angatkuq aanniqtanga\" (you is implied)\n\n- 20. \"The teacher saw the boy\": \"Iqiniq\" (teacher) + \"takujait\" (saw) + \"inuuhuktuit\" (boy) → \"Iqiniq takujaatit inuuhuktuit\"\n\n- 21. \"Your wolf fell\": \"Qulikunatukhaqtutit\" → \"your wolf\" + \"fell\" → \"qulikuni\" (wolf) + \"tukhaqtutit\" (fell) → \"Qulikunatukhaqtutit\"\n\n- 22. \"You shot a dog\": \"iputujait\" (you) + \"qukiqtanga\" (shot) + \"qingmivit\" (dog) → \"iputujait qukiqtanga qingmivit\"? But in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" = \"the boy shot the doctor\" → object is marked. To match, likely \"iputujait qukiqtanga qingmivit\" → \"you shot a dog\"\n\n- 23. \"Your dog hurt a teacher\": \"Qingmivit\" (your dog) + \"aanniqtanga\" (hurt) + \"ijaniq\" (teacher) → \"Qingmivit aanniqtanga ijaniq\"\n\nFinal answers:\n\n\\boxed{b.1: Angatkuq aanniqtanga; b.2: Iqiniq takujaatit inuuhuktuit; b.3: Qulikunatukhaqtutit; b.4: iputujait qukiqtanga qingmivit; b.5: Qingmivit aanniqtanga ijaniq}", + "generated_tokens": 1153, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: Angatkuq aanniqtanga; b.2: Iqiniq takujaatit inuuhuktuit; b.3: Qulikunatukhaqtutit; b.4: iputujait qukiqtanga qingmivit; b.5: Qingmivit aanniqtanga ijaniq", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 3125.0, + "ioling_final_answer_chars": 159.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "First, analyze the given examples to extract the verb patterns and structure in Inuktitut.\n\n1. Qingmivit takujaatit. → Your dog saw you. \n → \"saw\" is \"takujaatit\" (past tense, 3rd person, marked with -vit for agent, -atit for patient, \"you\" as patient) \n → \"saw\" = takujaatit → verb stem \"takuj\" + past suffix -a- + -atit (patient focus)\n\n2. Inuuhuktuup iluaqhaiji qukiqtanga. → The boy shot the doctor. \n → \"shot\" = qukiqtanga → \"qukiqt\" (stem) + -anga (past tense) + -tanga (patient?) \n → \"qukiq\" may be the verb root for \"shoot\", and -tanga is past tense with patient (doctor)\n\n3. Aanniqtutit. → You hurt yourself. \n → \"hurt\" = aanniqtutit → verb stem \"aanniqt\" + -utit (past tense, patient is self)\n\n4. Iluaqhaijiup aarqijaatit. → The doctor cured you. \n → \"cured\" = aarqijaatit → stem \"aarqij\" + -a- + -atit → patient is you\n\n5. Qingmiq iputujait. → You speared the dog. \n → \"speared\" = iputujait → stem \"iputuj\" + -ait → past tense with patient (dog)\n\n6. Angatkuq iluaqhaijimik aarqisijuq. → The shaman cured a doctor. \n → \"cured\" = aarqisijuq → stem \"aarqis\" + -ijuq → patient is \"a doctor\"\n\n7. Nanuq qaijuq. → The polar bear came. \n → \"came\" = qaijuq → verb stem \"qaij\" + -uq → simple past, no patient (intransitive)\n\n8. Iluaqhaijivit inuuhuktuit aarqijanga. → Your doctor cured your boy. \n → \"cured\" = aarqijanga → stem \"aarqij\" + -anga (past) + \"your boy\" (agent) \n → \"aarqijanga\" shows past tense with patient \"your boy\"\n\n9. Angunahuktiup amaruq iputujanga. → The hunter speared the wolf. \n → \"speared\" = iputujanga → stem \"iputuj\" + -anga → past tense, patient is wolf\n\n10. Qingmiup ilinniaqtitsijiit aanniqtanga. → The dog hurt your teacher. \n → \"hurt\" = aanniqtanga → stem \"aanniqt\" + -anga → past tense with patient (teacher)\n\n11. Ukiakhaqtutit. → You fell. \n → \"fell\" = ukiakhaqtutit → stem \"ukiakhaq\" + -utit → past tense, patient is self\n\n12. Angunahukti nanurmik qukiqsijuq. → The hunter shot a polar bear. \n → \"shot\" = qukiqsijuq → stem \"qukiqs\" + -ijuq → past tense, patient = polar bear\n\nNow, identify patterns:\n\n- Verbs: \n - \"see\" → takujaatit \n - \"shoot\" → qukiqtanga / qukiqsijuq \n - \"hurt\" → aanniqtutit / aanniqtanga \n - \"cure\" → aarqijaatit / aarqisijuq / aarqijanga \n - \"fall\" → ukiakhaqtutit \n\n- Verb suffixes: \n - Past tense: -vit, -utit, -anga, -ijuq \n - Patient marking: -atit, -anga, -ijuq \n - Possession or focus: \"your\", \"your\" → typically marked via prefix or possessive particle \n\n- Agent vs patient: \n - Active voice: agent + verb + patient \n - For \"you hurt yourself\": aanniqtutit → patient is self \n - For \"the doctor cured you\": aarqijaatit → patient = you \n\n- \"Your\" = inuuhuk (in example 8: \"your doctor\") or prefix like \"inuuhuk\" or \"iluaqhaijivit\" (in 8: \"your doctor\")\n\nNow, build translations for required items:\n\n19. The shaman hurt you. \n- \"hurt\" = aanniqt (base) → with patient \"you\" → aanniqtanga? \n- Example 10: \"The dog hurt your teacher\" → aanniqtanga \n- So \"hurt\" = aanniqtanga → but with subject \"the shaman\" and patient \"you\" \n- \"The shaman\" = Angatkuq (from 6: \"The shaman cured a doctor\") \n- So: Angatkuq aanniqtanga → \"the shaman hurt you\" \n→ But check 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ So Angatkuq is \"the shaman\" \n→ \"hurt\" = aanniqtanga (from 10: \"The dog hurt your teacher\" → aanniqtanga) \n→ So \"The shaman hurt you\" = Angatkuq aanniqtanga\n\n20. The teacher saw the boy. \n- \"saw\" = takujaatit (from 1) \n- \"the boy\" = inuuhuk (from 2: \"the boy\") → more likely \"inuuhuk\" or \"inuuhukti\" \n- Example 8: \"your doctor cured your boy\" → \"your boy\" = \"inuuhuktuit\" \n- So \"boy\" = inuuhuk \n- So: \"the teacher\" = ? \n- No direct \"teacher\" in examples \n- Example 10: \"The dog hurt your teacher\" → \"your teacher\" = \"ilinniaqtitsijiit\" → \"ilinniaq\" + \"titsijiit\" → \"teacher\" \n- So \"teacher\" = ilinniaq (likely) \n- So \"the teacher saw the boy\" = ilinniaq takujaatit inuuhuk \n- Need to check grammar: agent (teacher) + verb (saw) + patient (boy) \n- In 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → agent + verb + patient \n→ So same pattern \n→ So: ilinniaq takujaatit inuuhuk → \"the teacher saw the boy\"\n\n21. Your wolf fell. \n- \"fall\" = ukiakhaqtutit (from 11: \"You fell\" → ukiakhaqtutit) \n- \"your wolf\" = ? \n- \"your dog\" = qingmivit (example 1) \n- \"your doctor\" = iluaqhaijivit (example 8) \n→ \"your wolf\" = iluaqhaijivit? No — wolf is not mentioned. \n- Example 9: \"The hunter speared the wolf\" → \"the wolf\" = patient → no possessive \n- \"your wolf\" = likely \"iluaqhaiji aarqijaatit\"? No \n- From 1 and 8: \"your dog\" = qingmivit \n- So \"your wolf\" = qingmivit? No \n→ Must use a possessive prefix. In example 8: \"your doctor\" = \"iluaqhaijivit\" → \"iluaqhaiji\" + \"vit\" → marked as \"your\" \n→ So \"your wolf\" = iluaqhaijivit? But \"wolf\" is not in examples \n→ Wait: example 11: \"You fell\" = ukiakhaqtutit \n→ \"your wolf fell\" = inuuhuk? \n→ More likely: \"inuuhuk\" is \"boy\", not wolf \n→ Alternative: inuit grammar may use \"inuuhuk\" for boy; \"qay\" for wolf? Not found \n→ But in example 9: \"The hunter speared the wolf\" → \"the wolf\" = no marker \n→ So \"your wolf\" = qay (wolf) with possessive = ? \n→ No direct example \n→ But pattern from 1: \"your dog\" = qingmivit \n→ So \"your wolf\" = qingmivit? No — wolf ≠ dog \n→ But \"your\" is marked with \"inuuhuk\" or \"iluaqhaijivit\"? \n→ In example 8: \"your doctor cured your boy\" → \"your doctor\" = iluaqhaijivit → agent \n→ So \"your\" = attached to noun? \n→ \"your\" = inuuhuk in some cases? \n→ From 1: \"your dog\" = qingmivit → qingmivit = \"your dog\" \n→ So for \"your wolf\", it would be \"qayivit\"? Not in examples. \n→ But \"your\" may be marked as -ivit or -vit \n→ Example 1: \"your dog\" = qingmivit → qingmi + vit \n→ So \"your\" + noun → noun + vit \n→ Similarly: \"your doctor\" = iluaqhaijivit — yes \n→ So \"your wolf\" = qayivit? \n→ But \"wolf\" is not in examples — so is \"qay\" the word for wolf? Not given. \n→ Example 9: \"the hunter speared the wolf\" → \"the wolf\" = patient → no possessive \n→ So \"your wolf\" = qayivit \n→ Then \"your wolf fell\" = qayivit ukiakhaqtutit \n→ But check: example 11: \"You fell\" = ukiakhaqtutit → subject \"you\" \n→ So \"your wolf\" = qayivit → agent or patient? \n→ \"your wolf fell\" → subject = your wolf → so verb is intransitive \n→ So: qayivit ukiakhaqtutit → \"your wolf fell\"\n\n22. You shot a dog. \n- \"shot\" = qukiqtanga (example 2) or qukiqsijuq (example 12) \n- Example 2: \"The boy shot the doctor\" → the doctor → patient, shot = qukiqtanga \n- Example 12: \"The hunter shot a polar bear\" → qukiqsijuq → patient = polar bear \n- So \"shot\" = qukiqsijuq → stem + -ijuq \n- \"a dog\" = qingmi (example 5: \"you speared the dog\" → qingmi) \n- \"a dog\" → not possessive → \"qingmi\" \n- \"you\" → subject \n- So \"you shot a dog\" = ukiakhaqtutit? No — \"you\" is subject \n- \"You shot\" → in 5: \"You speared the dog\" = Qingmiq iputujait → subject = you, verb = iputujait \n- In 12: \"The hunter shot a polar bear\" = Angunahukti nanurmik qukiqsijuq → subject = hunter, verb = qukiqsijuq \n- So \"you\" = ukiakhaqtutit? No → \"you\" is subject \n- So verb form for \"you shot\" → likely a form like \"qukiqsijaat\" or something? \n- But in 12: \"The hunter shot a polar bear\" = Angunahukti nanurmik qukiqsijuq \n→ Subject: Angunahukti → \"the hunter\" \n→ Patient: nanurmik → \"a polar bear\" \n→ Verb: qukiqsijuq \n→ So \"you shot a dog\" = you + shot + dog \n→ \"you\" = ? \n→ Not explicit \n→ But from 5: \"You speared the dog\" = Qingmiq iputujait → \"Qingmiq\" = you speared \n→ So \"you speared\" = Qingmiq iputujait \n→ \"spearing\" = iputuj \n→ \"shooting\" = qukiq? \n→ So \"you shot a dog\" = ukiakhaqtutit? No \n→ No direct \"you shot\" \n→ But 12: \"The hunter shot a polar bear\" → qukiqsijuq \n→ So for \"you\", it may be qayivit? No \n→ But in 10: \"The dog hurt your teacher\" → agent = dog, patient = your teacher \n→ No subject verb form \n→ Perhaps verb takes patient suffix \n→ \"you shot a dog\" → subject \"you\", patient = dog → verb = qukiqsijuq → modified to match subject? \n→ But not in examples \n→ Alternative: in 5: \"You speared\" = Qingmiq iputujait → subject = you = Qingmiq \n→ verb = iputujait → patient = dog (implied) \n→ So for \"you shot\", could be ukiakhaqtutit? No \n→ So likely: \"you shot a dog\" = ukiakhaqtutit? No \n→ But in 12: \"The hunter shot a polar bear\" = Angunahukti nanurmik qukiqsijuq \n→ Subject = Angunahukti → \"the hunter\" \n→ Patient = nanurmik → \"a polar bear\" \n→ So \"you shot a dog\" = ukiakhaqtutit? No — no \"you\" marker \n→ From 1: \"your dog saw you\" = qingmivit takujaatit → agent = \"your dog\" \n→ So \"you\" as subject is not used in verbs? \n→ But in 5: \"You speared the dog\" = Qingmiq iputujait → \"Qingmiq\" = you \n→ So subject \"you\" = Qingmiq \n→ So verb = iputujait \n→ So \"you shot a dog\" → verb = qukiqsijuq → with subject = you? \n→ But \"you\" = Qingmi? Not seen \n→ \"you\" appears as subject in form: Qingmiq in example 5 \n→ So \"you shot\" = Qingmiq qukiqsijuq? \n→ \"a dog\" = qingmi \n→ So \"you shot a dog\" = Qingmiq qukiqsijuq qingmi? \n→ But in 12: \"The hunter shot a polar bear\" = Angunahukti nanurmik qukiqsijuq → subject, patient, verb \n→ So likely \"you shot a dog\" = Qingmiq qukiqsijuq qingmi \n→ But is \"you\" = Qingmiq? Yes, from 5: \"You speared the dog\" = Qingmiq iputujait \n→ So verb \"iputujait\" = \"you speared\" \n→ So \"qukiqsijuq\" = \"you shot\" → possible \n→ So \"you shot a dog\" = Qingmiq qukiqsijuq qingmi \n→ But is \"q\" used for k-like sound? Yes — in \"qukiqtanga\", \"qukiqsijuq\" \n→ So acceptable\n\nBut in example 12: \"The hunter shot a polar bear\" → subject + patient + verb → verb has -ijuq \n→ So \"you shot a dog\" = subject (you) + verb (qukiqsijuq) + patient (a dog) \n→ So use Qingmiq qukiqsijuq qingmi\n\n23. Your dog hurt a teacher. \n- \"your dog\" = qingmivit (from 1) \n- \"hurt\" = aanniqtanga (from 10: \"The dog hurt your teacher\" = aanniqtanga) \n- \"a teacher\" = ilinniaqtitsijiit (from 10: \"The dog hurt your teacher\" → ilinniaqtitsijiit) \n- So \"your dog hurt a teacher\" = qingmivit aanniqtanga ilinniaqtitsijiit \n\nNow verify all:\n\n19. The shaman hurt you → Angatkuq aanniqtanga \n→ \"The shaman\" = Angatkuq (example 6) \n→ \"hurt\" = aanniqtanga (example 10) \n→ patient = you → correct\n\n20. The teacher saw the boy → ilinniaq takujaatit inuuhuk \n→ \"teacher\" = ilinniaq (from 10) \n→ \"saw\" = takujaatit \n→ \"boy\" = inuuhuk (from 8: \"your boy\") \n→ correct\n\n21. Your wolf fell → qayivit ukiakhaqtutit \n→ \"your wolf\" = qayivit (pattern: \"your dog\" = qingmivit → \"your wolf\" = qayivit) \n→ \"fell\" = ukiakhaqtutit (example 11) \n→ acceptable\n\n22. You shot a dog → Qingmiq qukiqsijuq qingmi \n→ \"you\" = Qingmiq (from 5: \"You speared the dog\" = Qingmiq iputujait) \n→ \"shot\" = qukiqsijuq (from 12: \"The hunter shot a polar bear\" = qukiqsijuq) \n→ \"a dog\" = qingmi \n→ correct\n\n23. Your dog hurt a teacher → qingmivit aanniqtanga ilinniaqtitsijiit \n→ \"your dog\" = qingmivit (example 1) \n→ \"hurt\" = aanniqtanga (example 10) \n→ \"a teacher\" = ilinniaqtitsijiit (example 10) \n→ correct\n\nFinal answers:\n\nb.1 / 19.: Angatkuq aanniqtanga \nb.2 / 20.: ilinniaq takujaatit inuuhuk \nb.3 / 21.: qay", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11064.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "Scratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|---------|------------------------------------|------------------------------|--------------------------------------------------------------------------|\n| b.1 / 19 | The shaman hurt you | Angatkuq aanniqtanga | Sentence 6: \"The shaman cured a doctor\" → \"Angatkuq iluaqhaijimik aarqisijuq\"; \"cured\" = aarqisijuq; \"hurt\" = aanniqtanga; \"shaman\" = Angatkuq → pattern: Angatkuq + aanniqtanga → \"The shaman hurt you\" |\n| b.2 / 20 | The teacher saw the boy | Ilinniaqtaq qaijuq iluaqhaiji | Sentence 1: \"Your dog saw you\" → \"Qingmivit takujaatit\"; \"saw\" = takujaatit; \"dog\" = Qingmi; \"you\" = takujaatit → \"teacher\" likely = ilinniaqtaq (from 10: \"dog hurt your teacher\" = Qingmiq iputujait aanniqtanga); \"boy\" = iluaqhaiji → \"teacher saw boy\" = ilinniaqtaq qaijuq iluaqhaiji? But \"saw\" is takujaatit → ilinniaqtaq takujaatit iluaqhaiji → better: ilinniaqtaq takujaatit iluaqhaiji |\n| b.3 / 21 | Your wolf fell | Qaariq qukiqtanga | Sentence 11: \"You fell\" = Ukiakhaqtutit → \"fell\" = Ukiakhaqtutit; \"wolf\" = qaariq → \"your wolf fell\" = Ukiakhaqtutit → \"your wolf\" = qaariq + inu? → \"your wolf\" = qaariq up → \"your wolf fell\" = qaariq up ukiakhaqtutit → check: sentence 9: \"The hunter speared the wolf\" = Angunahuktiup amaruq iputujanga → \"wolf\" = amaruq → so amaruq = wolf → so qaariq = wolf → thus qaariq up ukiakhaqtutit → \"your wolf fell\" |\n| b.4 / 22 | You shot a dog | Qingmivit qukiqtanga | Sentence 2: \"The boy shot the doctor\" = Inuuhuktuup iluaqhaiji qukiqtanga → \"shot\" = qukiqtanga → \"doctor\" = iluaqhaiji → so \"you shot a dog\" → \"you\" = takujaatit → \"dog\" = qingmi → so takujaatit qukiqtanga qingmi? But sentence 5: \"You speared the dog\" = Qingmiq iputujait → \"speared\" = iputujait → so \"shot\" = qukiqtanga → sentence 10: \"The dog hurt your teacher\" → Qingmiup ilinniaqtitsijiit aanniqtanga → \"hurt\" = aanniqtanga → \"dog\" = Qingmi → \"your teacher\" = ilinniaqtitsijiit → so \"you shot a dog\" = takujaatit qukiqtanga qingmi |\n| b.5 / 23 | Your dog hurt a teacher | Qingmivit aanniqtanga ilinniaqtaq | Sentence 1: \"Your dog saw you\" = Qingmivit takujaatit → \"saw\" = takujaatit → \"hurt\" = aanniqtanga → \"dog\" = Qingmi → \"teacher\" = ilinniaqtaq → so \"your dog hurt a teacher\" = Qingmivit aanniqtanga ilinniaqtaq |\n\nFinal derivation:\n\n- 19. \"The shaman hurt you\" → from sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"cured\" = aarqisijuq, \"hurt\" = aanniqtanga → \"Angatkuq aanniqtanga\" = shaman hurt → \"you\" = takujaatit → but no \"you\" in that sentence? → better: sentence 3: \"Aanniqtutit\" = \"You hurt yourself\" → \"aanniqtutit\" = you hurt yourself → so \"aanniqtanga\" = hurt (intransitive, to oneself) → \"hurt someone\" = aanniqtanga + noun → so \"Angatkuq aanniqtanga takujaatit\" = shaman hurt you → yes → confirmed with 19: the shaman hurt you → Angatkuq aanniqtanga takujaatit \n- 20. \"The teacher saw the boy\" → sentence 1: \"Qingmivit takujaatit\" = your dog saw you → \"saw\" = takujaatit → \"teacher\" = ilinniaqtaq (from sentence 10: \"The dog hurt your teacher\" = Qingmiup ilinniaqtitsijiit aanniqtanga → \"teacher\" = ilinniaqtaq) → \"boy\" = iluaqhaiji (sentence 2) → so \"ilinniaqtaq takujaatit iluaqhaiji\" = teacher saw boy → no article → correct → \"ilinniaqtaq takujaatit iluaqhaiji\" \n- 21. \"Your wolf fell\" → sentence 11: \"Ukiakhaqtutit\" = you fell → \"fell\" = ukiakhaqtutit → \"your wolf\" = qaariq up → from sentence 9: \"The hunter speared the wolf\" = Angunahuktiup amaruq iputujanga → \"wolf\" = amaruq → amaruq = wolf → so qaariq = wolf (common noun) → thus \"qaariq up ukiakhaqtutit\" → \"your wolf fell\" \n- 22. \"You shot a dog\" → sentence 2: \"The boy shot the doctor\" = Inuuhuktuup iluaqhaiji qukiqtanga → \"shot\" = qukiqtanga → \"doctor\" = iluaqhaiji → so \"you shot a dog\" = takujaatit qukiqtanga qingmi → confirmed from sentence 5: \"You speared the dog\" = Qingmiq iputujait → so \"qukiqtanga\" = shot → \"dog\" = qingmi → thus takujaatit qukiqtanga qingmi \n- 23. \"Your dog hurt a teacher\" → sentence 1: \"Your dog saw you\" = Qingmivit takujaatit → \"saw\" = takujaatit → \"hurt\" = aanniqtanga → \"your dog\" = Qingmivit → \"teacher\" = ilinniaqtaq → so Qingmivit aanniqtanga ilinniaqtaq \n\nAll patterns match the verb roots and possessive markers in the original sentences.\n\n\\boxed{b.1: Angatkuq aanniqtanga takujaatit; b.2: ilinniaqtaq takujaatit iluaqhaiji; b.3: qaariq up ukiakhaqtutit; b.4: takujaatit qukiqtanga qingmi; b.5: Qingmivit aanniqtanga ilinniaqtaq}", + "generated_tokens": 1682, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: Angatkuq aanniqtanga takujaatit; b.2: ilinniaqtaq takujaatit iluaqhaiji; b.3: qaariq up ukiakhaqtutit; b.4: takujaatit qukiqtanga qingmi; b.5: Qingmivit aanniqtanga ilinniaqtaq", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 4620.0, + "ioling_final_answer_chars": 181.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "unit_audit", + "sample_index": 0, + "output": "We are given a set of Nooni sentences from different days of the Nooni “week” and asked to translate five sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical and temporal patterns from the provided examples, focusing on time references, verb forms, and expressions like “just now,” “today,” “on X,” “will,” “heard,” “helped,” etc.\n\n---\n\n### Step 1: Identify time expressions in the data\n\nWe observe that time expressions in Nooni are built around specific days (like Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvuŋkaden) and use temporal markers:\n\n- **\"On X\"** → a specific day (e.g., On Bvusɔw)\n- **\"Tomorrow\"** → (noted in sentence 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n”)\n- **\"The day after tomorrow\"** → sentence 5: “The day after tomorrow is Bvutfu” → “fɔ̀ shě ntfǔː nú bvútfu᷅”\n- **\"Today\"** → used directly (e.g., sentence 6: \"Today, he killed the woman\" → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n”)\n- **\"Just now\"** → sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy”\n- **\"A long time ago\"** → sentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ”\n\nThus, we can see:\n\n- **\"just now\"** = present, immediate past (likely a specific temporal particle: *yɛ᷅n* or *nɔ̂ː yɛ᷅n*)\n- **\"today\"** = current day, with specific particle (e.g., *wvù bɛ̂ː*, *me mbɛ̂ː*)\n- **\"on X\"** = a specific day, with “On X” structure implied\n- Future: “will” → future tense marker (e.g., *nú*, *cǐ*, *bɛ̂ː*, etc.)\n\n---\n\n### Step 2: Verb patterns and tense marking\n\nLooking at sentences:\n\n- (1): “Yesterday was Bvumbon” → past fact, stated as is\n- (2): “On Bvusɔw, you(sg) will steal the yam” → future: “will steal” → *cɔ́ŋ* used with future construction\n- (3): “On Bvuzhi, the woman will help me” → “bóy fí me” → “will help”\n- (4): “On Bvuŋka, he found the book” → past: *wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà*\n- (5): “The day after tomorrow is Bvutfu” → not a direct verb, but temporal statement\n- (6): “Today, he killed the woman” → present tense? “bɛ̂ː” → particle used with past action\n- (7): “You(sg) heard the thief a long time ago” → past with time reference: “a long time ago”\n\nKey verbs:\n\n- **\"help\"** → “fí” (e.g., “bóy fí me”)\n- **\"steal\"** → “cɔ́ŋ” (e.g., “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ”)\n- **\"find\"** → “tɔ̀” (e.g., “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà”)\n- **\"hear\"** → “cɔ̌ŋ” (e.g., “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” — heard the thief)\n- **\"see\"** → “wvù” (e.g., “dìɛ̀msɛ̌n nú yɛ́n wvù lě” — “the man is about to see him”)\n\n---\n\n### Step 3: Identify temporal markers\n\n| Meaning | Expression in given data | Notes |\n|-------------------|-------------------------------------------------------|-------|\n| Today | “Today, he killed” → “wvù bɛ̂ː” or “me mbɛ̂ː” | particle *bɛ̂ː* marks today |\n| Just now | “just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” | *yɛ᷅n* appears in immediate past |\n| Tomorrow | “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n” | *ntfǔː* = tomorrow |\n| Day after tomorrow| “The day after tomorrow is Bvutfu” → “fɔ̀ shě ntfǔː” | *shě* = “day after tomorrow” |\n| A long time ago | “heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w” | time reference with *tɔ̀* or *nɔ̂ː* |\n| Will (future) | “will steal”, “will help” → appears with *cɔ́ŋ*, *fí* | future marker attached to verb |\n| About to (imminent) | “is about to see” → “dìɛ̀msɛ̌n nú yɛ́n wvù lě” | *dìɛ̀msɛ̌n* = about to; *wvù* = see |\n\n---\n\n### Step 4: Derive translations for each unit (all spoken on Bvumbon)\n\nWe translate each sentence into Nooni, using patterns from the corpus.\n\n---\n\n**20. On Bvusɔw, I helped the man.**\n\n- “On Bvusɔw” → “nú bvúsɔ̀w” (as in sentence 2: “On Bvusɔw, you will steal”)\n- “I helped” → “me fí” → from “the woman will help me” → “bóy fí me”\n- So, “me fí dìɛ̀msɛ̌n” → but wait: “help” is “fí”, so “I helped” = “me fí dìɛ̀msɛ̌n”\n- But is “help” expressed as “fí”? Yes, used in “bóy fí me” → “helped me”\n\nSo: “On Bvusɔw, I helped the man” → “me fí dìɛ̀msɛ̌n nú bvúsɔ̀w”\n\nBut verify: in sentence 2: “On Bvusɔw, you will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → structure: [pronoun] [verb] [object] [day]\n\nSo:\n- “On Bvusɔw, I helped the man” → “me fí dìɛ̀msɛ̌n nú bvúsɔ̀w”\n\n→ **me fí dìɛ̀msɛ̌n nú bvúsɔ̀w**\n\n---\n\n**21. The thief stole the yam just now.**\n\n- “The thief” → “yo᷅kwɔ᷆ːn” (from sentence 6: “he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “yo᷅kwɔ᷆ːn” = woman/thief)\n- “stole” → “cɔ́ŋ” (from sentence 2: “you will steal the yam” → “cɔ́ŋ kèŋkfǔ”)\n- “just now” → present immediate past → sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → uses *bɔ́ nɔ̂ː yɛ᷅n* → “just now”\n\nTherefore: “yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ bɔ́ nɔ̂ː yɛ᷅n”\n\n→ **yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ bɔ́ nɔ̂ː yɛ᷅n**\n\n---\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- “On Bvuŋkaden” → from sentence 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n” → “bvûŋka᷆ːde᷆n” = Bvuŋkaden\n- “I will hear” → “I will hear” = future of “hear”\n- “hear” → “cɔ̌ŋ” (sentence 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → *cɔ̌ŋ* = hear)\n- Future marker: “will” → from sentence 2: “you will steal” → “cɔ́ŋ” with future context → but “will” in Nooni may not be a separate verb, may be constructed with tense particle\n\nBut in sentence 3: “on Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “fí” is used with “will”\n\nSo “will” may be encoded via contextual structure or tense marker.\n\nBut in sentence 5: “The day after tomorrow is Bvutfu” → no future verb, just statement.\n\nIn sentence 8: “On Bvuŋkaden, the thief will find us” → “cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n” → “cɔ̌ŋ” = hear/find?\n\nWait: sentence 8: “cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n” → “the thief will find us”\n\n→ So “will find” is expressed with “cɔ̌ŋ” (“find”) and “nú” or implied structure.\n\nBut in sentence 7: “you heard” — past, with *nɔ̂ː*\n\nIn sentence 6: “he killed” — past\n\nSo what about future?\n\nSentence 3: “will help” → “bóy fí me” — “fí” = help, with “will” encoded in context?\n\nBut in sentence 2: “will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → present?\n\nNo: “On Bvusɔw” — future day.\n\nSo seems that future tense is marked by the time reference, not a verb suffix.\n\nBut we have: “will hear” — must be future.\n\nFrom sentence 8: “On Bvuŋkaden, the thief will find us” → “cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n”\n\nSo “cɔ̌ŋ” = find/locate, used with future day → “will find”\n\nSimilarly, “hear” is a verb that appears in past form (sentence 7: “heard”), so future form may be inferred.\n\nIs there a future form of “hear”?\n\nNo direct example. But only past and present are given.\n\nHowever, sentence 3: “will help” → “bóy fí me” → “fí” appears without future particle\n\nBut in that case, “will” is encoded via time reference (on Bvuzhi).\n\nSimilarly, we need “on Bvuŋkaden” — future day → so “will” is implicitly marked by the time reference.\n\nThus, “I will hear the car” = “me cɔ̌ŋ mutù bvútfu᷅” but wait: “the car” = “mutù”?\n\nIn sentence 5: “I will choose the car” → “me nú mbóy ncáw mutù bvútfu᷅”\n\nSo “car” = “mutù”\n\nThus: “I will hear the car” → “me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n”\n\nBut is “hear” expressed with *cɔ̌ŋ* in future?\n\nIn past: “heard the thief” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “cɔ̌ŋ” with past tense\n\nBut no example of future “hear”.\n\nHowever, the only form of “hear” is “cɔ̌ŋ” → likely used in both tenses.\n\nAlso, in sentence 8: “the thief will find us” → “cɔ̌ŋ nú bóy bɔ́ŋ bèsèn” → future action with verb *cɔ̌ŋ*\n\nSo likely: future “hear” = “me cɔ̌ŋ mutù”\n\nAnd time reference: “on Bvuŋkaden” = “nú bvûŋka᷆ːde᷆n”\n\nThus: **me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n**\n\n---\n\n**23. Today, the woman will kill the man.**\n\n- “Today” → marked by *bɛ̂ː* (sentence 6: “Today, he killed” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n”)\n- “the woman” → “kwɔ᷆ːn” (sentence 6: “he” is “wvù”, “woman” is “yo᷅kwɔ᷆ːn”)\n- “will kill” → “kill” = “ɛ̀bɛ̀n” (from sentence 6: “he killed the woman” → “ɛ̀bɛ̀n”)\n- So “the woman will kill the man” → “kwɔ᷆ːn ɛ̀bɛ̀n me”\n- With “today” → “kwɔ᷆ːn ɛ̀bɛ̀n me bɛ̂ː”\n\nOrder: in sentence 6: “he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → subject + time + verb + object\n\nSo “the woman will kill the man” → “kwɔ᷆ːn ɛ̀bɛ̀n me bɛ̂ː”\n\n→ **kwɔ᷆ːn ɛ̀bɛ̀n me bɛ̂ː**\n\n---\n\n**24. Today, the man saw you(sg).**\n\n- “Today” → *bɛ̂ː*\n- “the man” → “dìɛ̀msɛ̌n” (sentence 12: “I am about to help the man” → “me nú nfí dìɛ̀msɛ̌n”)\n- “saw” → “wvù” (sentence 15: “they saw me” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” — “saw” = “wvù”)\n- “you(sg)” → “nǔ”\n- So: “dìɛ̀msɛ̌n wvù nǔ bɛ̂ː”\n\nCheck order: in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → they saw me → “bɔ́ nɔ̂ː yɛ᷅n me lé” → “wvù” is used with object\n\nSo “the man saw you” → “dìɛ̀msɛ̌n wvù nǔ”\n\nWith “today” → “dìɛ̀msɛ̌n wvù nǔ bɛ̂ː”\n\n→ **dìɛ̀msɛ̌n wvù nǔ bɛ̂ː**\n\n---\n\n### Final Check: Evidence Table\n\n| unit | meaning | candidate | evidence |\n|------|--------|----------|---------|\n| c.1 / 20 | On Bvusɔw, I helped the man | me fí dìɛ̀msɛ̌n nú bvúsɔ̀w | sentence 2: “On Bvusɔw, you will steal” → structure; sentence 3: “the woman will help me” → “fí” |\n| c.2 / 21 | The thief stole the yam just now | yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ bɔ́ nɔ̂ː yɛ᷅n | sentence 2: “you will steal” → “cɔ́ŋ” + object; sentence 15: “saw just now” → “bɔ́ nɔ̂ː yɛ᷅n” |\n| c.3 / 22 | On Bvuŋkaden, I will hear the car | me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n | sentence 8: “the thief will find us” → “cɔ̌ŋ” with future day; “car” = “mutù” as in sentence 5 |\n| c.4 / 23 | Today, the woman will kill the man | kwɔ᷆ːn ɛ̀bɛ̀n me bɛ̂ː | sentence 6: “Today, he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9552.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "unit_audit", + "sample_index": 1, + "output": "First, identify the key linguistic pattern in the given Nooni sentences, particularly regarding time expressions and verb usage.\n\nStep 1: Analyze time expressions and their forms across days.\n\n- \"Yesterday was X\" → sentence 1: \"fɔgò cǐ nú bvúmbòn\" → past day reference.\n- \"On X, I came to the market\" → sentence 2: \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\"\n- \"On Bvusɔw, you will steal the yam\" → sentence 2\n- \"The day after tomorrow is Bvutfu\" → sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → future day\n- \"Tomorrow is Bvuŋkaden\" → sentence 8: \"ntfǔː nú bvûŋka᷆ːde᷆n\" → future day\n- \"The day before yesterday was Bvuŋka\" → sentence 11 → past day\n\nObservation: Time expressions are marked by specific days (e.g., Bvutfu, Bvusɔw), and each has a corresponding grammatical structure.\n\nStep 2: Identify past/future time markers.\n\n- \"Yesterday\" → fɔgò cǐ\n- \"The day after tomorrow\" → fɔ̀ shě ntfǔː → comes before \"is X\"\n- \"Tomorrow\" → ntfǔː nú [day]\n- \"The day before yesterday\" → kefwé cí\n\nSo:\n- \"yesterday\" → fɔgò cǐ\n- \"the day after tomorrow\" → fɔ̀ shě\n- \"tomorrow\" → ntfǔː nú\n- \"the day before yesterday\" → kefwé cí\n\nNote: In sentence 11: \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\" → so \"kefwé cí\" = day before yesterday.\n\nSimilarly:\n- \"today\" → no explicit marker, e.g., \"Today, he killed the woman\" → sentence 6\n- \"just now\" → sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n\"just now\" is used in finite present or immediate past.\n\nStep 3: Identify verb form and aspect.\n\n- \"will\" → future: \"you(sg) will steal\" → sentence 2 → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"will help\" → sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\n\"will\" is expressed with a future verb form.\n\n- \"heard\" in sentence 7 → \"You(sg) heard the thief a long time ago\" → past with distance: \"a long time ago\"\n\nSo past with long time ago → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"you(sg) heard the thief a long time ago\"\n\n\"just now\" → immediate past → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nSo:\n- \"just now\" = present perfect or immediate past → marked by specific verb form (e.g., bɔ́ nɔ̂ː yɛ᷅n)\n\nStep 4: Analyze verb forms for \"help\", \"kill\", \"steal\", \"hear\", etc.\n\n- \"help\" → sentence 3: kwɔ᷆ːn nǔ bóy fí me → \"the woman will help me\" → \"fí\" is the verb\n- \"steal\" → \"cɔ́ŋ\" in multiple cases\n- \"kill\" → \"ɛ̀bɛ̀n\" is used in \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n- \"hear\" → \"cɔ̌ŋ\" used in \"you heard the thief\"\n\nSo:\n- Steal → cɔ́ŋ\n- Kill → ɛ̀bɛ̀n\n- Help → fí\n- Hear → cɔ̌ŋ (used in both \"heard\" and \"will hear\")\n\nThus:\n- \"the thief stole the yam\" → \"yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ\" (thief + stole + yam)\n\nStep 5: \"just now\" usage.\n\nIn sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo \"saw\" → yɛ᷅n me lé → \"saw me at the market\"\n\n\"just now\" = \"bɔ́\" (a present or immediate past marker)\n\nSimilarly, in sentence 21: \"The thief stole the yam just now\"\n\n→ verb form should be immediate past, using \"bɔ́\" form?\n\nBut in sentence 2, \"will steal\" is \"cɔ́ŋ\", so \"future\" → cɔ́ŋ\n\n\"just now\" → immediate past → likely uses the same verb form but with present tense marker.\n\nIn sentence 15: \"They saw me at the market just now\" → uses \"bɔ́ nɔ̂ː yɛ᷅n me lé\"\n\nSo \"bɔ́\" likely marks immediate past.\n\nSo \"just now\" → bɔ́ + verb base\n\nThus:\n- \"thief stole the yam just now\" → yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ\n\nBut \"cɔ́ŋ\" is the base, and with \"bɔ́\" it may become a present/past tense.\n\nAlternatively, \"just now\" may not require a separate marker; perhaps the verb itself is used in present/immediate past.\n\nBut the only sentence with \"just now\" is sentence 15 → it is marked with \"bɔ́ nɔ̂ː yɛ᷅n\" → so \"bɔ́\" applies to the verb.\n\nSo verb form with \"bɔ́\" = just now / immediately past\n\nSo in 21: \"The thief stole the yam just now\" → yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ\n\nStep 6: \"On Bvuŋkaden, I will hear the car\"\n\n- Bvuŋkaden = tomorrow → from sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n\n\nSo \"today\" = no explicit day tag → sentence 9: \"Today, I chose the book\" → me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\n\nSo time markers:\n- today → no marker (directly stated)\n- \"on X\" → used when referring to a day (X) with preposition \"nú\"\n- \"tomorrow\" → ntfǔː nú\n- \"yesterday\" → fɔgò cǐ\n- \"day after tomorrow\" → fɔ̀ shě\n- \"day before yesterday\" → kefwé cí\n\nSo: \"On Bvuŋkaden, I will hear the car\"\n\n→ \"nú bvûŋka᷆ːde᷆n\" + \"me cɔ̌ŋ mutù\" → \"hear the car\"\n\nBut \"will\" is needed → so present/future form of \"hear\"\n\n\"will\" → in future: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\" → used as future\n\nSo \"will hear\" → cɔ̌ŋ with future marker?\n\nBut in sentence 14: \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"we will steal\"\n\nSo \"cɔ́ŋ\" is used with \"future\" = will\n\nSo \"will hear\" → cɔ̌ŋ\n\nSo: \"me cɔ̌ŋ mutù\" → \"I will hear the car\"\n\nBut with \"on Bvuŋkaden\" → \"nú bvûŋka᷆ːde᷆n\"\n\nSo full: \"me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\"\n\nBut in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\" → so \"nú\" + day\n\nSo format: [time marker] + [verb] → but \"on X\" = \"nú X\"\n\nSo \"On Bvuŋkaden, I will hear the car\" → \"me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\"\n\nBut do we need a future marker? \"will\" → future → so must use future verb form.\n\nIn previous: \"will steal\" = cɔ́ŋ → so cɔ̌ŋ = \"steal\", \"hear\"? → verb base is cɔ̌ŋ\n\nYes, \"hear\" = cɔ̌ŋ → same as \"steal\" in sentence 2 and 14\n\nSo: \"me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\"\n\nNow check sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\nSo \"help\" → fí\n\nSo \"will\" is not attached to the verb — the verb itself is in future form.\n\nSo future → inherent in verb form.\n\nSo \"I will hear\" → me cɔ̌ŋ mutù\n\nNo separate future marker.\n\nSo on Bvuŋkaden → \"nú bvûŋka᷆ːde᷆n\"\n\nThus: \"me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\"\n\nStep 7: \"Today, the woman will kill the man\"\n\n- \"today\" → no marker → \"Today, we will steal\" → sentence 14 → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\nSo \"will kill\" → ɛ̀bɛ̀n → used in \"killed the woman\"\n\nIn sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n\nSo \"kill\" → ɛ̀bɛ̀n\n\nSo \"the woman will kill the man\" → \"nǔ ɛ̀bɛ̀n me\"\n\nNow, \"today\" → optional marker? But in all cases, it is stated with \"Today, X\"\n\nSo → \"nǔ ɛ̀bɛ̀n me\"\n\nBut is there an indicator for time? In the list, days like \"on Bvutfu\" only use \"nú\" for future days.\n\nToday → directly said.\n\nSo → \"nǔ ɛ̀bɛ̀n me\"\n\nBut in the sentence: \"Today, the woman will kill the man\" → so subject is \"the woman\", verb is \"will kill\"\n\nSo: \"nǔ ɛ̀bɛ̀n me\"\n\nNo \"on\" or day reference → just \"today\"\n\nStep 8: \"Today, the man saw you(sg)\"\n\n- \"saw\" → from sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nSo \"saw\" → yɛ᷅n\n\nSo \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n\"\n\nBut \"today\" → no marker → just \"today\"\n\nSo → \"dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n\"\n\nNow, \"just now\" is already used elsewhere.\n\nIn this sentence, no \"just now\" → so simple past.\n\nSo final translations:\n\n20. On Bvusɔw, I helped the man.\n\n→ \"On Bvusɔw, I helped\" → \"me fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nUse: \"help\" → fí (from sentence 3)\n\n\"on Bvusɔw\" → \"nú bvúsɔ̀w\"\n\n\"I\" → me\n\nSo → \"me fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\n21. The thief stole the yam just now.\n\n→ \"yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ\"\n\n\"the thief\" → yo᷅kwɔ᷆ːn\n\n\"stole\" → cɔ́ŋ\n\n\"yam\" → kèŋkfǔ\n\n\"just now\" → bɔ́\n\nSo → \"yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ\"\n\n22. On Bvuŋkaden, I will hear the car.\n\n→ \"me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\"\n\n\"hear\" → cɔ̌ŋ\n\n\"the car\" → mutù\n\n\"on Bvuŋkaden\" → nú bvûŋka᷆ːde᷆n\n\n\"will\" → inherent in cɔ̌ŋ → no marker needed\n\n23. Today, the woman will kill the man.\n\n→ \"nǔ ɛ̀bɛ̀n me\"\n\n\"the woman\" → nǔ\n\n\"will kill\" → ɛ̀bɛ̀n\n\n\"the man\" → me\n\n\"today\" → implied by \"today\"\n\n24. Today, the man saw you(sg).\n\n→ \"dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n\"\n\n\"the man\" → dìɛ̀msɛ̌n\n\n\"saw\" → yɛ᷅n\n\n\"you(sg)\" → ɛ̀bɛ̀n\n\n\"today\" → implied\n\nNow verify with source language patterns.\n\nSentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → so \"nǔ bóy fí me\" = woman helps me\n\nSo \"help\" = fí → correct.\n\nSentence 14: \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → so \"cɔ́ŋ\" = steal → so \"hear\" = cɔ̌ŋ → correct.\n\nSentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw → correct.\n\nSo all verb forms match.\n\nFinal answers:\n\nc.1 (20): me fí dìɛ̀msɛ̌n nú bvúsɔ̀w \nc.2 (21): yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ \nc.3 (22): me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n \nc.4 (23): nǔ ɛ̀bɛ̀n me \nc.5 (24): dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n\n\nScratch table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|--------|--------------------------|-------------------|---------|\n| c.1 / 20 | On Bvusɔw, I helped the man | me fí dìɛ̀msɛ̌n nú bvúsɔ̀w | Sentence 3: \"on Bvuzhi, woman will help me\" → fí; sentence 2: \"on Bvusɔw\" structure |\n| c.2 / 21 | The thief stole the yam just now | yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ | Sentence 15: \"saw just now\" = bɔ́ + yɛ᷅n; sentence 2: \"you will steal\" = cɔ́ŋ |\n| c.3 / 22 | On Bvuŋkaden, I will hear the car | me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n | Sentence 8: \"tomorrow is Bvuŋkaden\" → ntfǔː nú; sentence 14: \"will steal\" = cɔ́ŋ |\n| c.4 / 23 | Today, the woman will kill the man | nǔ ɛ̀bɛ̀n me | Sentence 6: \"Today, he killed the woman\" → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n |\n| c.5 / 24 | Today, the man saw you(sg) | dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n | Sentence 15: \"they saw me\" → yɛ᷅n me |\n\nAll units present, no duplication, consistent with grammar and examples.\n\n\\boxed{c.1: me fí dìɛ̀msɛ̌n nú bvúsɔ̀w; c.2: yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ; c.3: me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n; c.4: nǔ ɛ̀bɛ̀n me; c.5: dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n}", + "generated_tokens": 4058, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: me fí dìɛ̀msɛ̌n nú bvúsɔ̀w; c.2: yo᷅kwɔ᷆ːn bɔ́ cɔ́ŋ kèŋkfǔ; c.3: me cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n; c.4: nǔ ɛ̀bɛ̀n me; c.5: dìɛ̀msɛ̌n yɛ᷅n ɛ̀bɛ̀n", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9409.0, + "ioling_final_answer_chars": 145.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "unit_audit", + "sample_index": 2, + "output": "We are given various sentences in Nooni from different days of the week, and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical and temporal patterns from the given examples.\n\n---\n\n### Step 1: Identify temporal markers and their meanings\n\nFrom the examples:\n\n- **\"On Bvumbon\"** appears in sentences 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. \n These are all specified days in the Nooni week.\n\n- Events are grouped by day: \n - Bvutfu: yesterday, day after tomorrow, tomorrow? \n - Bvusɔw: today, “the day after tomorrow” \n - Bvuzhi: “on Bvuzhi” — future \n - Bvuŋka: today, “the day before yesterday” \n - Bvuŋkaden: tomorrow \n\nWe need to determine how temporal markers are formed and how verbs are conjugated for tense and aspect.\n\n---\n\n### Step 2: Look at time expressions\n\nFrom sentence 1: \n> fɔgò cǐ nú bvúmbòn. → Yesterday was Bvumbon. \nSo: **\"yesterday was [day]\"**\n\nSentence 5: \n> fɔ̀ shě ntfǔː nú bvútfu᷅. → The day after tomorrow is Bvutfu. \nSo: **\"day after tomorrow is [day]\"**\n\nSentence 8: \n> ntfǔː nú bvûŋka᷆ːde᷆n. → Tomorrow is Bvuŋkaden. \nNotice \"ntfǔː\" = tomorrow, \"bvûŋka᷆ːde᷆n\" = a shifted day (Bvuŋka + \"de\"?) — likely a suffix indicating future.\n\nSentence 11: \n> kefwé cí nú bvûŋka. → The day before yesterday was Bvuŋka. \n\"day before yesterday\" = **kefwé cí nú** → \"day before yesterday was\"\n\nSo chain of time markers:\n\n- **day before yesterday** → kefwé cí nú \n- **yesterday** → fɔgò cǐ nú \n- **today** → (no explicit marker in example, but used as context) \n- **tomorrow** → ntfǔː nú \n- **day after tomorrow** → fɔ̀ shě ntfǔː nú \n\nNow, the days themselves are not necessarily in a fixed order; they are named with context.\n\nBut crucially: in sentence 8, \"Tomorrow is Bvuŋkaden\", and earlier \"Tomorrow is Bvuŋka\" is not present — so “Bvuŋkaden” is a day that comes after Bvuŋka.\n\nSo: \n- Bvumbon → (first day) \n- Bvusɔw → next \n- Bvuzhi → next \n- Bvuŋka → next \n- Bvuŋkaden → next day after Bvuŋka\n\nThus, the week is: \nBvumbon → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden\n\nThis is confirmed by other references.\n\n---\n\n### Step 3: Identify verb forms and aspect\n\nSentences use verbs like:\n\n- “came” → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn \n- “will help” → kwɔ᷆ːn nǔ bóy fí me bvúzhí \n- “found” → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː \n- “heard” → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ \n- “will steal” → bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n \n- “killed” → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n \n- “will help” → me nú nfí dìɛ̀msɛ̌n \n- “saw” → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy → they saw me at market just now\n\nWe see that:\n\n- **Present/future: \"nú\"** as in “On Bvusɔw, I came” → \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → past tense with time marker \n- “will” → future tense → often indicated by **\"bèsèn\"** or **\"nú\"** in context \n\nBut look at sentence 9: *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n* → Today, I chose the book → past tense, but “today”? How?\n\nSentence 12: *me nú nfí dìɛ̀msɛ̌n* → I am about to help → “nú” suggests present or future.\n\nSentence 10: *dìɛ̀msɛ̌n nú yɛ́n wvù lě* → The man is about to see him → \"nú yɛ́n\" → “is about to”\n\nSentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → They saw me at the market just now → past tense, “just now” → “fɔ̀wǎy” is used in past.\n\nSo **“just now”** → fɔ̀wǎy? \nIn sentence 15: “saw me at the market just now” → “fɔ̀wǎy” → this is likely a past tense with aspect: **just now**\n\nSimilarly:\n\nSentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “heard the thief a long time ago” → “a long time ago” — no marker, but implies past duration\n\nNow sentence 13: *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* → On Bvutfu, the woman saw the market. → “saw” with time marker → “yɛ᷅n” → past tense?\n\nBut “just now” is likely signaled by “fɔ̀wǎy”\n\nSo:\n\n- **past tense with recent aspect** → fɔ̀wǎy \n- **past tense with distant past** → no marker \n- **future tense** → “will” marker like “bèsèn” or “nú” with future day \n- **present/proximity** → “nú” = on [day] or “today”?\n\nBut in sentence 20: *On Bvusɔw, I helped the man.*\n\nWe see that past tense is used regularly.\n\nAlso, the noun “man” appears as dìɛ̀msɛ̌n → “the man” \n“woman” → nǔ bóy \n“thief” → yo᷅w \n“market” → fɔ̀wǎy \n“car” → mutù \n“book” → ŋwà \n“yam” → cɔ́ŋ\n\nSo common nouns:\n\n- man → dìɛ̀msɛ̌n \n- woman → nǔ bóy \n- thief → yo᷅w \n- market → fɔ̀wǎy \n- car → mutù \n- book → ŋwà \n- yam → cɔ́ŋ\n\n---\n\n### Step 4: Translate each required sentence\n\nWe are to translate into Nooni, **spoken on Bvumbon**\n\nSo all sentences are in present context — Bvumbon is the reference day.\n\n---\n\n#### 20. On Bvusɔw, I helped the man.\n\n“On Bvusɔw” → *nú bvúsɔ̀w* \n“I helped” → “me nú nfí” → from sentence 12: *me nú nfí dìɛ̀msɛ̌n* → “I am about to help the man” — but “helped” = past?\n\nBut sentence 20 says “I helped” — past.\n\nBut in other cases, like sentence 4: “he found” → “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà” — present/past? “found” is past.\n\nSentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “will help” → future\n\nSo “helped” → past → must use past tense verb.\n\nWhat is the past tense of “help”? In sentence 12: “I am about to help” → “me nú nfí” → present/future.\n\nNo explicit past form.\n\nBut in sentence 2: “On Bvusɔw, you(sg) will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “will steal”\n\nSo “will” = future → “yúː” is the verb (possibly stem)\n\nSo “help” → where is it?\n\nIn sentence 13: “the woman saw the market” → “yɛ᷅n” → past\n\nWe need a verb for “help”.\n\nFrom sentence 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “will help me”\n\nSo verb “fí” → “to help”\n\nSo past form? — no direct example.\n\nBut in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw”\n\nSo “saw” = yɛ᷅n\n\nBut “help” stem = fí\n\nCan it be “me fí dìɛ̀msɛ̌n”?\n\nNo example.\n\nBut in sentence 12: “me nú nfí dìɛ̀msɛ̌n” → “I am about to help the man”\n\nBut that’s **present/future**, not past.\n\nHowever, in other contexts: “I helped” must be past.\n\nIs there a past tense marker?\n\nSentence 9: “Today, I chose the book” → “me mbɛ̂ː nca᷅w ŋwà” → “chose” — past?\n\n“mbɛ̂ː” = past tense? → possible\n\nSentence 14: “Today, we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù” → “will steal”\n\nSo verb “cɔ́ŋ” → steal\n\nSo “will steal” → “bèsèn cɔ́ŋ” or “bèsèn nǔ géː cɔ́ŋ”\n\nSo past verb? No direct form.\n\nBut in context, when we say “I helped”, it must be something like:\n\n→ “me fí dìɛ̀msɛ̌n” — but not with aspect?\n\nWait — sentence 15: “They saw me at the market just now” → used “fɔ̀wǎy” → just now → present/past with recent time.\n\nBut in 20, it says “on Bvusɔw” — not “just now”.\n\nSo temporal context is **past**.\n\nSo likely, the verb is past tense, and likely the stem is “fí” for help.\n\nAlso, in sentence 3: “kwɔ᷆ːn nǔ bóy fí me” → future (with “kwɔ᷆ːn”)\n\nSo “fí” is the verb.\n\nWe may need to assume that “helped” = “me fí dìɛ̀msɛ̌n” — but without a past tense marker?\n\nBut look back — in sentence 1: “fɔgò cǐ nú bvúmbòn” → “yesterday was Bvumbon” — uses “fɔgò” — past\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is” — future\n\nBut “I came” in 2: *me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy* → “came to market” — with “ncí” = verb?\n\nBut “ncí” is past? or present?\n\nSentence 2: “On Bvumbon, I came to the market” → past\n\nSo “came” = “ncí”?\n\nSo past tense → uses verb stem with tone?\n\nWe don’t have “helped” explicitly.\n\nBut we can assume that “fí” is used with past context.\n\nSo likely: “me fí dìɛ̀msɛ̌n” — “I helped the man”\n\nWith time: “nú bvúsɔ̀w”\n\nSo full sentence: **nú bvúsɔ̀w me fí dìɛ̀msɛ̌n**\n\nBut “helped” may require a past particle.\n\nAlternatively, is “help” in past form?\n\nIs “fí” used in past with “ncí”?\n\nBut “ncí” is for “came” — different verb.\n\nThus, no direct evidence.\n\nBut look at sentence 1: “fɔgò cǐ nú” — “yesterday was” \nSentence 11: “kefwé cí nú” — “day before yesterday was”\n\nSo “was” → “cǐ” or “cí”?\n\nIn 20, “on Bvusɔw” — so “nú bvúsɔ̀w” is the time.\n\nSo verb is “helped” → likely **me fí dìɛ̀msɛ̌n**\n\nBut in sentence 12, “me nú nfí dìɛ̀msɛ̌n” → “I am about to help” → present\n\nBut “helped” is past → must use past form.\n\nWait — is there an auxiliary?\n\nNo.\n\nPerhaps in Nooni, past tense is implied by context, or the verb stem is used.\n\nBut the pattern seems to be that tense is often marked by time reference or aspect.\n\nSince “on Bvusɔw” is a completed past, and no “just now” or “today”, “helped” must be past.\n\nThus, we use **me fí dìɛ̀msɛ̌n** — though no clear past particle, and no other example.\n\nBut sentence 3: “will help” → future → “kwɔ᷆ːn nǔ bóy fí me” → so “fí” is used in future in version with “kwɔ᷆ːn”\n\nSo “fí” is the base verb, and tense is contextually marked — so in past, it can be used with time marker.\n\nThus, **nú bvúsɔ̀w me fí dìɛ̀msɛ̌n**\n\n---\n\n#### 21. The thief stole the yam just now.\n\n“the thief” → yo᷅w \n“stole” → from sentence 2: “you will steal” → “yúː cɔ́ŋ” → so “cɔ́ŋ” = steal \n“just now” → fɔ̀wǎy (as in sentence 15: “saw me at the market just now” → “fɔ̀wǎy”)\n\nSo: “yo᷅w cɔ́ŋ fɔ̀wǎy” — but without subject?\n\n“the thief stole” → “yo᷅w cɔ́ŋ”\n\n“just now” → “fɔ̀wǎy”\n\nSo full: **yo᷅w cɔ́ŋ fɔ̀wǎy**\n\nBut is “fɔ̀wǎy” attached to the verb?\n\nYes — as in sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw me at market just now” → verb + fɔ̀wǎy\n\nSo “yo᷅w cɔ́ŋ fɔ̀wǎy” — consistent.\n\n---\n\n#### 22. On Bvuŋkaden, I will hear the car.\n\n“On Bvuŋkaden” → “nú bvûŋka᷆ːde᷆n” — from sentence 8 → “tomorrow is Bvuŋkaden” \nSo “on Bvuŋkaden” → “nú bvûŋka᷆ːde᷆n”\n\n“I will hear” → “hear” → from sentence 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “heard”\n\nSo “heard” = “nɔ̂ː yo᷅w cɔ̌ŋ”\n\n“will” → future → “bèsèn” — from sentence 14: “we will steal” → “bèsèn nǔ géː cɔ́ŋ mutù”\n\nSo “will hear” = “bèsèn nɔ̂ː yo᷅w cɔ̌ŋ”?\n\nBut “hear” = “nɔ̂ː yo᷅w cɔ̌ŋ” — yes\n\nSo: “bèsèn nɔ̂ː yo᷅w cɔ̌ŋ” → “will hear”\n\nBut “the car” → “mutù”\n\nSo: “bèsèn nɔ̂ː yo᷅w cɔ̌ŋ mutù”\n\nBut is “mutù” the object?\n\nYes — in sentence 14: “steal the car” → “cɔ́ŋ mutù”\n\nSo “hear the car” → “nɔ̂ː yo᷅w cɔ̌ŋ mutù” → verb + object\n\nSo future: “bèsèn” → “will”\n\nSo full: **nú bvûŋka᷆ːde᷆n bèsèn nɔ̂ː yo᷅w cɔ̌ŋ mutù**\n\n---\n\n#### 23. Today, the woman will kill the man.\n\n“Today” → in sentence 9: “Today, I chose the book", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10111.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "unit_audit", + "sample_index": 3, + "output": "We are translating into Nooni sentences spoken on Bvumbon, based on the provided examples and patterns in the data.\n\nFirst, observe the structure of time expressions and verb forms across the examples.\n\n---\n\n**Step 1: Time expressions and their Nooni equivalents**\n\nWe see time references like:\n- \"Yesterday\" → \"fɔgò cǐ nú bvúmbòn\" → “Yesterday was Bvumbon”\n- \"The day after tomorrow\" → “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n- \"Tomorrow\" → “ntfǔː nú bvûŋka᷆ːde᷆n” → “Tomorrow is Bvuŋkaden”\n- \"The day before yesterday\" → “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nFrom this, we infer:\n- \"Yesterday\" = fɔgò cǐ\n- \"Tomorrow\" = ntfǔː nú\n- \"The day after tomorrow\" = fɔ̀ shě ntfǔː nú\n- \"The day before yesterday\" = kefwé cí nú\n\nAdditionally, \"On X\" structure is common: \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → “On Bvumbon, I came to the market”\n\nSo, the construction:\n- [Subject] [verb] [object] on [day] \nis common.\n\nBut also:\n- \"Today\" appears in sentences: e.g. “Today, he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n”\n\nAlso:\n- \"just now\" appears: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “They saw me at the market just now”\n\nThis indicates that:\n- \"just now\" = bɔ́ nɔ̂ː yɛ᷅n (e.g., in 15)\n\nSimilarly, \"a long time ago\" → “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ”\n\nSo:\n- “a long time ago” = tɔ̀ nɔ̂ː yo᷅w\n- “just now” = bɔ́ nɔ̂ː yɛ᷅n\n\n---\n\n**Step 2: Verb forms and tense**\n\nWe see:\n- Future: “will” → “cǐ” or “nú” with \"will\" implied (e.g. “the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí”)\n- Past (completed): “came”, “killed”, “heard”, “saw” — often with tense markers\n\nIn sentence 14: “Today, we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → verb \"géː cɔ́ŋ\" = “will steal”\n\nIn sentence 2: “On Bvusɔw, you(sg) will steal the yam” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w”\n\nHere, the verb form \"cɔ́ŋ\" is used — clearly a future or intention verb.\n\nAlso, \"will hear\" → “bɛ̂ː” as in “Today, I chose the book” → “me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n”\n\n\"chose\" = mbɛ̂ː\n\n\"helped\" → “nú nfí” → in 12: “I am about to help the man” → “me nú nfí dìɛ̀msɛ̌n”\n\nSo “about to” = nú\n\n\"hear\" → possibly from \"bɛ̂ː\" (as in \"I chose\" — \"mbɛ̂ː\") or \"bɛ̂ː\" for \"hearing\"?\n\nBut in 22: “On Bvuŋkaden, I will hear the car” → we need \"hear the car\"\n\n\"hear\" = ? \nIn sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw me” → “yɛ᷅n me”\n\nSo \"see\" = yɛ᷅n (someone) → \"saw me\" = yɛ᷅n me\n\nNow, \"hear\" might be a different verb — possibly \"yɛ᷅n\" is used for both? But \"hear\" is not equivalent to \"see\".\n\nLook at sentence 21: “The thief stole the yam just now” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” is \"heard the thief a long time ago\"\n\nBut sentence 21: “The thief stole the yam just now” — so “stole” = cɔ̌ŋ?\n\nYes — in sentence 2: “you will steal the yam” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ”\n\nSo “cɔ́ŋ” = “steal”\n\nThen “stole” is past of cɔ́ŋ → so “cɔ̌ŋ” with tone and time marker.\n\n“just now” is bɔ́ nɔ̂ː yɛ᷅n → as in sentence 15\n\nSo “stole just now” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n cɔ̌ŋ” → “the thief, just now, stole the yam”\n\nThis matches: 21 → “The thief stole the yam just now”\n\nSo structure:\n- [Agent] [past tense verb] [object] [time marker]\n- past tense of \"steal\" = cɔ̌ŋ (with tone)\n\nSimilarly, “hear” is not directly present, but in 22: “On Bvuŋkaden, I will hear the car” — so “will hear”\n\n\"hear the car\" — what is the word?\n\nWe don’t have a direct translation, but in sentence 13: “On Bvutfu, the woman saw the market” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅”\n\n“saw the market” → “yɛ᷅n wáy”\n\nSo “see” = yɛ᷅n (object → wáy)\n\nSo “hear” might be a separate verb.\n\nBut in sentence 14: “Today, we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n”\n\n\"steal the car\" → “géː cɔ́ŋ mutù”\n\nSo verb + object.\n\nWe need \"hear the car\" → so likely “bɛ̂ː” for \"hear\" (as in \"chose the book\" → \"me mbɛ̂ː nca᷅w ŋwà\")\n\nIn sentence 9: “Today, I chose the book” → “me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n”\n\n“chose” = mbɛ̂ː\n\nSo “hear” might be “bɛ̂ː” as well? Possible.\n\nBut “bɛ̂ː” appears with “chose” — not “hear”.\n\nAlso, in sentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → [you] [heard] [thief]\n\nBut “heard” is already present — “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ”\n\nSo “heard” = tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → complete phrase\n\nSo “heard” = tɔ̀ nɔ̂ː yo᷅w (a long time ago) + cɔ̌ŋ (action)\n\nThus, “hear” = cɔ̌ŋ? But that is \"steal\"\n\nNo — “cɔ̌ŋ” is \"steal\"\n\nSo “hear” must be a different verb.\n\nPossibility: “bɛ̂ː” might mean “hear” — it appears in both “chose” and “hear”?\n\nBut in both instances, it's used in a transitive way:\n\n- “I chose the book” → “me mbɛ̂ː nca᷅w ŋwà”\n- “I will hear the car” → “me bɛ̂ː nɔ̂ː yɛ᷅n mutù” → no, “yɛ᷅n” is \"see\", not \"hear\"\n\nWe do not have a clear word for “hear”.\n\nBut look at sentence 13: “On Bvutfu, the woman saw the market” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅”\n\nSo “saw the market” = “yɛ᷅n wáy”\n\nSimilarly, “hear the car” = possibly “yɛ᷅n mutù”?\n\nBut \"yɛ᷅n\" = \"see\", not \"hear\".\n\nUnless \"hear\" and \"see\" are treated as the same — unlikely.\n\nAlternative: is \"bɛ̂ː\" used for hearing?\n\nIn sentence 9: “Today, I chose the book” → me mbɛ̂ː nca᷅w ŋwà\n\nIn sentence 14: “Today, we will steal the car” → bèsèn nǔ géː cɔ́ŋ mutù\n\nNo \"hear\".\n\nOnly one sentence has \"hear\" — 7: “you heard the thief a long time ago” → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\nSo “heard” = tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\nSo the verb “cɔ̌ŋ” is used in both \"steal\" and \"hear\"?\n\nThis suggests that in this language, \"hear\" is marked with time expression, and \"cɔ̌ŋ\" is the verb.\n\nBut \"cɔ̌ŋ\" clearly means \"steal\" in “you will steal the yam” — so it cannot mean both.\n\nTherefore, likely \"hear\" is a different verb.\n\nBut no such word appears.\n\nWait — in sentence 21: “The thief stole the yam just now” → must use a verb.\n\nSo unless \"hear\" is another form of \"see\", or a synonym.\n\nBut \"see\" = yɛ᷅n, and \"hear\" is not equivalent.\n\nPossibility: the word “yɛ᷅n” can mean both “see” and “hear” in some contexts?\n\nBut in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → clearly “saw” = yɛ᷅n\n\nIn sentence 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → this must be “heard” = verb + time + object\n\nSo again, “cɔ̌ŋ” is used for “heard” — contradiction.\n\nThus, the only possibility is that in Nooni, “hear” is expressed by a full construction with time expression — or possibly “bɛ̂ː” is the verb.\n\nBut in “chose the book” = mbɛ̂ː\n\nAnd “heard” = wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\nSo verb “cɔ̌ŋ” for stealing and hearing? Not possible.\n\nUnless the time marker covers the action.\n\nThis suggests that “cɔ̌ŋ” is not the only verb — or the environment is restricting.\n\nAlternative: maybe \"hear\" is expressed via “yɛ᷅n” with object?\n\nBut that would be “see”.\n\nUnless in Nooni, “hear” is used interchangeably with “see” — not supported.\n\nBut check sentence 13: “the woman saw the market” → “yɛ᷅n wáy”\n\nSentence 15: “They saw me” → “yɛ᷅n me”\n\nSo “see” = yɛ᷅n\n\nTherefore, “hear” is not “yɛ᷅n”\n\nWe must conclude that “hear the car” must be rendered using a verb like “bɛ̂ː” (as in “choose”) or “cɔ̌ŋ” — but cɔ̌ŋ is steal.\n\nAnother possibility: the verb “bɛ̂ː” may be used for both “hear” and “choose” — due to semantic overlap?\n\nUnlikely.\n\nBut look: in sentence 2, “you will steal the yam” → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ → cɔ́ŋ = steal\n\nIn sentence 7: “you heard the thief” → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → cɔ̌ŋ = hear?\n\nImpossible — so either the verb is different or there is a morphological error.\n\nMore likely: the translation “you heard the thief” uses a different verb.\n\nBut the only verb used is “cɔ̌ŋ”.\n\nPerhaps in Nooni, “cɔ̌ŋ” means both “steal” and “hear” by context?\n\nThis is unlikely.\n\nAlternative: perhaps the verb for “hear” is “yɛ᷅n” → e.g., “hear the car” = “yɛ᷅n mutù”\n\nBut in sentence 15: “saw me” = yɛ᷅n me → so if “hear” is “yɛ᷅n”, then “hear me” = yɛ᷅n me — same form.\n\nSo maybe “yɛ᷅n” can mean both “see” and “hear”?\n\nBut in sentence 7, “you heard the thief” cannot be “yɛ᷅n yo᷅w” — that would be “you saw the thief” — different.\n\nSo no.\n\nThus, only possible conclusion is that “hear” is expressed via “bɛ̂ː” — as in “chose” — but that lacks evidence.\n\nWait — sentence 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n” — future day\n\nSentence 22: “On Bvuŋkaden, I will hear the car” → need future marking.\n\n“will” = in examples, “will steal” = “cɔ́ŋ”, “will help” = “fí”, “will kill” = “géː” (in 14)\n\nSo future tense verbs are:\n- steal → cɔ́ŋ\n- help → fí\n- steal → géː (in 14)\n\nSo “will hear” → no such verb.\n\nBut in sentence 14: “we will steal” → “bèsèn nǔ géː cɔ́ŋ” → so “géː” is a form of “will”\n\n“ge” might be “will” — as auxiliary.\n\nSimilarly, in 2: “you will steal” → “wɔ̀ nǔ yúː cɔ́ŋ” — no auxiliary.\n\nIn 12: “I am about to help” → “me nú nfí” → “nú” = about to\n\nSo “nú” = future/aspect\n\nIn 22: “On Bvuŋkaden, I will hear the car” → likely “me bɛ̂ː nɔ̂ː yɛ᷅n mutù” or similar.\n\nWe have no example of “hear” — but we have “hear the thief a long time ago” — only in sentence 7: “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ”\n\nSo cɔ̌ŋ = hear?\n\nBut in context, “you heard the thief” → if “cɔ̌ŋ” means “heard”, then “cɔ̌ŋ” must be “hear” — not “steal”.\n\nBut in sentence 2: “will steal” → “cɔ́ŋ” — same verb.\n\nSo tension.\n\nTherefore, only possible conclusion: the verb “cɔ̌ŋ” means both “steal” and “hear” in this language — by context.\n\nBut that seems extreme.\n\nAlternatively, perhaps the time expression is attached differently.\n\nIn sentence 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ”\n\nIf “cɔ̌ŋ” means “heard”, then it is used for hearing.\n\nIf not, the verb must be missing.\n\nBut there is no other verb.\n\nThus, we must accept that “cɔ̌ŋ” can be used for both “steal” and “hear” — likely due to semantic or phonological borrowing.\n\nBut that contradicts dictionary.\n\nAlternative: in Nooni, verbs are marked by time and context.\n\nBut in sentence 21: “The thief stole the yam just now” — should be a past tense.\n\n\"just now\" = bɔ́ nɔ̂ː yɛ᷅n\n\nSo “the thief stole the yam just now” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n cɔ̌ŋ kèŋkfǔ”\n\nYes — matches pattern.\n\nSimilarly, for “hear the car” — if “hear” = cɔ̌ŋ, then “me cɔ̌ŋ mutù” — but with time?\n\n\"On Bvuŋkaden, I will hear the car\" → future.\n\nFuture → “nú” or “bèsèn”?\n\nIn sentence 14: “Today, we will steal” → “bèsèn nǔ géː cɔ́ŋ”\n\nSo “bès", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10255.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "Start by analyzing the given pairings to detect patterns in Jaqaru.\n\nGiven:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- ishinhna → in my bed \n- markstxi → is it our1+2 town? \n- ishma → your bed \n- utamt”a → from your house \n- utnha → my house \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nNow, identify markers of grammatical constructions.\n\nLook at possessive markers:\n\n- “our1+2” appears in: \n - qucxst”psa → from our1+2 lake too \n - markstxi → is it our1+2 town? \n - yapsanpsa → in our1+2 field too \n\n→ So \"our1+2\" is marked by the suffix or root “st” in “markstxi” and “qucxst”psa.\n\nSimilarly:\n- “his” → chushp”a \n- “your” → ishma (your bed), utamt”a (from your house)\n\nIn “ishma” = your bed, “utamt”a” = from your house → “your” appears as in root with marker\n\nNow, the suffix “-t” or “-nt” appears in:\n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- utamt”a → from your house \n- p”ak”unhpsa → my pot too \n\n\"Too\" appears in:\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\n\"Too\" often comes after the base, with a suffix like -psa or -nha, or attached directly.\n\nNow, match each requested translation:\n\n4. our1+2 cliff \n→ From qaqat”a = from the cliff \n→ So “our1+2 cliff” = from our1+2 cliff → should be like qucxst”psa → from our1+2 lake too \n→ So pattern: [from] + [our1+2] + [noun] \n→ Base: qaqat”a → from the cliff \n→ So “from our1+2 cliff” = qaqat”a with “our1+2” marker → like qucxst”psa = from our1+2 lake too \n→ \"lake\" becomes “qucx” → “cliff” becomes “qqa”? → qaqat”a → “cliff” is qaqat”a \n→ So “from our1+2 cliff” → qaqat”a with our1+2 → likely qaqast”psa? \nBut look at qucxst”psa = from our1+2 lake too → “qucx” = lake, “st” = our1+2, “psa” = too \nSo “st” marks “our1+2”, and “psa” marks “too”\n\nThus: \n- Base: qaqat”a → from the cliff \n- So “from our1+2 cliff” → qaqast”a? or qaqast”psa?\n\nCompare: \n- qucxst”psa → from our1+2 lake too → “qucx” + “st” + “psa” \n- qaqat”a → from the cliff → no modifying elements \n→ So “our1+2 cliff” = qqa + st + psa? But \"cliff\" is qqa, not qqa?\n\nActually, “cliff” is “qaqat”a → root qaqat → so base: qaqat \n\n“our1+2” appears with “st” in “qucxst”psa (lake), “markstxi” (town), “utamt”a (from your house) \n→ “st” = our1+2 \n→ But “utamt”a” = from your house → “your” not “our” → so not consistent?\n\nWait: \n- qucxst”psa → from our1+2 lake too → “st” = our1+2 \n- markstxi → is it our1+2 town? → “st” = our1+2 \n- qaqat”a → from the cliff → no “st” \n→ So “our1+2” is marked by suffix “st” in nouns with possession\n\nBut in “utamt”a” = from your house → “your” is marked in a different way\n\nSo likely “our1+2” = marker “st” added to noun\n\nSo “our1+2 cliff” = qaqat + st → qaqatst?\n\nBut the base is \"qaqat\", so qaqatst?\n\nBut “qucxst”psa” → qucx + st + psa → so pattern is [noun] + st + [suffix]\n\n“too” appears in: \n- aq”ipsa → the cave too → “ipsa” → with “psa” at end \n- p”ak”unhpsa → my pot too → “unhpsa” \n- qucxst”psa → from our1+2 lake too → “stpsa” → suffix “psa” \n\nSo “psa” seems to mean “too” or “also”\n\nThus: \n4. our1+2 cliff → likely qaqast”psa → “from our1+2 cliff” → actually, the question says “our1+2 cliff”, not “from”\n\nSo it's just “our1+2 cliff” → not a locative or derived form\n\nNow, what is “in your corner”? \n→ “your corner” = ? \nWe have: \n- chushp”a → his corner \n→ “his” = chush \n→ So “your” likely = “ish” or “ish-”?\n\nWe have: \n- ishma → your bed \n→ so “your” = ish? \n- ishinhna → in my bed → “in my” \n→ “your bed” = ishma \n→ thus “your” = ish \n\nSo “in your corner” → in + your corner → “in” + ish + corner \n\n“corner” is chushp”a → his corner → so base chush → “corner” \n\nSo “in your corner” = ish + chush → ishchush? \n\nBut is there a “in” marker? \n“in the cave” = aq”na → aq” + na → “aq” = cave, “na” = in? \n\n“in my bed” = ishinhna → “ishin” + “hna”? → “inh” = in, “hna” = bed? \n\n“in the cave” = aq”na → “na” = in? \n\n“in our1+2 town” = markstxi → “is it our1+2 town?” → “in” not present \n\nBut “in your corner” → similar to “in my bed” → “ishinhna” → “ishin” + “hna” → “ishin” = in + my? \n\nBut “my” = “in”? No — “ishinhna” = in my bed\n\nSo “in” appears as a prefix or suffix?\n\n“in the cave” = aq”na → aq” + na → “na” = in? \n\n“in my bed” = ishinhna → ishi + n + hna? → “inhna” → “inh” = in, “hna” = bed? \n\n“in our1+2 town” = markstxi → not “in” — it's a yes/no question \n\nSo perhaps “in” is marked by the suffix -nha or -na?\n\nWe have: \n- aq”na → in the cave \n- ishinhna → in my bed \n→ “na” and “hna” → both might mean “in”\n\nSo perhaps “in” is marked by a suffix ending in -na or -hna?\n\nNow “corner” → chushp”a → so base “chush” + “p”a → “p”a = corner?\n\nSo “in your corner” = [in] + [your] + [corner] → with “in” suffix\n\nPossibility: “inh” + chush → in your corner?\n\nBut “in my bed” is “ishinhna” → contains “inh” and “hna” → “inh” + “hna”\n\nSo “in your corner” → could be “ischna”? or “ishchush”?\n\nBut “your” = ish, “corner” = chush → so “ishchush”?\n\nNow test with others:\n\n5. in your corner → → candidate: ishchush? or ishchusha?\n\nBut we have no word for “in your corner” — idea: use “inh” + “ish” + “chush”?\n\nBut “ishinhna” = in my bed → so “in” + “my” + “bed”\n\n→ “my” = in? → “ish” = your → not mine\n\nIn “ishinhna” → “ish” = your, “inh” = in? → but it's “ishinhna” → could be “ishin” + “hna”\n\nSo perhaps “in” is not a separate word — maybe attached to the root\n\nAgain: \n- aq”na → in the cave → “aq” + “na” → “na” = in \n- ishinhna → in my bed → “ishin” + “hna” → “in” = “ishin”? → or “inh”?\n\n“na” and “inh” appear in different words but both involved in “in” meaning.\n\nPerhaps “in” is marked by suffix -na or -hna.\n\nSo “in X” = X + na or X + hna?\n\n“in the cave” = aq”na → cave + na \n“in my bed” = ishinhna → my bed + hna? → “hna” = bed\n\nSo “bed” = hna → so “in my bed” = ishin + hna → so “ishin” = in my?\n\nNo → likely, “in” is a prefix or infix.\n\nAlternative: \n- “in your corner” → like “in our1+2 town” → which is “markstxi” → “is it our1+2 town?” → so not a location\n\nBut “in” appears in:\n- aq”na \n- ishinhna \n- probably also in “in your corner”\n\nSo likely structure: [possessive] + [noun] + [in suffix]\n\nLook at all location phrases:\n\n- aq”na → in the cave \n- ishinhna → in my bed \n- ishma → your bed → not “in” \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- utamt”a → from your house \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\n→ So “in” is marked by suffix -na or -hna?\n\n“in the cave” = aq”na → suffix -na \n“in my bed” = ishinhna → suffix -hna → so -hna = in? \nBut “a” ≠ “h”, so different.\n\nWait: \nWhen “in” is with “bed”, it’s “inhna” → in + bed? \nWhen with “cave”, it’s “na” → cave + na?\n\n“cave” = aq” → aq”na → cave + na \n“bed” = hna → in my bed = ishinhna → ishin + hna → so likely “in” is attached as “ishin” → not a fixed suffix\n\nBut “ish” = your, so “ishin” = in + your? → meaning in your bed?\n\nYes. So “in your bed” = ishinhna → can be parsed as “ishin” + “hna” → “ishin” = in your?\n\nThis suggests that “in” is fused with possessive.\n\nSo “in X” = (possessive prefix) + “in” + X?\n\nBut “in the cave” is aq”na → no possessive — “a” = cave, “na” = in?\n\nSo “in” is a suffix attached to the noun.\n\nThus, general rule: \n- “in” = suffix -na or -hna (depending on noun) \n- “in X” = root + na or hna \n\nBut no consistent suffix.\n\nNow, for “in your corner” → corner = chushp”a → root chush?\n\nSo “in your corner” → use “ish” (your) + chush → ishchush? → with “na” or “hna”?\n\nBut “in” is the locative mark.\n\nSo likely: ishchushna? or ishchushhna?\n\nBut no such word.\n\nAlternatively, compare to “in my bed” = ishinhna → “ishin” + “hna”\n\nSo “in” = “in” → “in” → “in” is “ishin” for “your”? → so “ishin” = in your?\n\nBut “ishin” is not a standalone word.\n\nNotice: in “ishinhna” → “inh” = in, “hna” = bed → “inh” might be the locative marker\n\nIn “aq”na → “na” = locative marker\n\nSo the locative suffix is -na or variants.\n\nIn “yapsanpsa” = in our1+2 field too → so “yapsanpsa” → “yap” + “san” + “psa” → “san” = field? — but “field” → yaputxi = is it the field?\n\nSo “field” = yap → yaputxi\n\nSo “in our1+2 field too” = yapsanpsa → “yap” + “san” + “psa” → “san” = our1+2 field? → no\n\nActually, “yapsanpsa” → likely “yap” + “san” + “psa” → “yap” = field, “san” = our1+2, “psa” = too\n\nSo pattern: [noun] + [our1+2] + [too]\n\nSimilarly, “qucxst”psa” → qucx + st + psa → qucx = lake, st = our1+2, psa = too\n\nSo “too” is marked by -psa\n\n“in” may be marked by -na or -hna\n\nNow, back to:\n\n5. in your corner → → same as “in my bed” → aq”na or ishinhna\n\n“in my bed” = ishinhna → root ishin + hna → hna = bed? → so corner = chush → maybe chushna?\n\nBut “corner” is chushp”a → so likely chusha → chushna?\n\nSo “in your corner” = ishchushna?\n\nBut “ish” = your → “ishchushna”\n\nIs there a word like that?\n\nWe have “marka” = the town → no in\n\nSo try to build:\n\n4. our1+2 cliff \n→ from qaqat”a → so “our1+2 cliff” → qaqat with st? → qaqast”a or qaqast”psa?\n\nWe have qucxst”psa → from our1+2 lake too → so “st” = our1+2, “psa” = too\n\nSo “our1+2” = suffix “st”\n\nSo “our1+2 cliff” = qaqat”st” → qaqat”st”?\n\nBut “cliff” = qaqat”a → so qaqat”st”\n\n6. in your corner too \n→ “in your corner” + “too” \n→ “in your corner” = ? \n“in my bed” = ishinhna \n→ “in your corner” → likely ishchushna \n→ “too” = psa → so ishchushna + psa → ishchushnapsa?\n\nBut “p”a may be root — chushp”a = his corner → so “chushp”a” → so “p”a is part of corner\n\nSo “corner” = chushp”a → so perhaps “in your corner” = ishchushna → but “na” = in?\n\nSo in your corner = ishchushna\n\nThen “too” = psa → ishchushnap”sa” or ishchushnapsa?\n\n7. from your corner too \n“from your corner” → “from” is marker\n\nWe have:\n- from his town = markp”t”a → mark + p”t”a → p”t”a = from his town \n- from your house = utamt”a → uta + mt”a → mt”a = from your house? \n- from the cliff = qaqat”a → qaqat”a\n\nSo “from” is marked by suffix or prefix?\n\nmarkp”t”a → marka (town) + p”t”a → “p”t”a” = from his town\n\n“his” = chush → so “p”t”a” = from his town?\n\n“your” = ish → possible: from your town = i sh + t”a? — not evident\n\n“from your house” = utamt”a → uta + mt”a → “mt”a = from your house?\n\nSo “from” = suffix -t”a or -mt”a?\n\nIn markp”t”a → “p”t”a” → “p” = his?\n\nIn utamt”a → “mt”a → “m” = your?\n\nSo “from X”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10504.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "Start by analyzing the given Jaqaru words and their translations to identify patterns in structure and affixation.\n\nGiven data:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nNote: Presence of \"our1+2\" = \"mine and yours\", used as a group possessive.\n\nObserve that:\n\n- \"in\" often appears as a preposition, marked by a suffix or stem like \"na\", \"stxi\", or \"hna\".\n- \"too\" is often marked by a suffix \"-psa\" or \"-hpsa\" (e.g., aq”ipsa, p”ak”unhpsa, qucxst”psa, yapsanpsa).\n- \"from\" appears with a stem like \"qucx\", \"markp”, \"qqa\" → \"qqa\" = from the cliff.\n- \"is it\" is a question form using \"untxi\".\n\nNow go to the target questions.\n\n4. our1+2 cliff \n→ “from the cliff” is qaqat”a, so “our1+2 cliff” should be “from our1+2 cliff”? Wait — no. \nWe need “our1+2 cliff”, not from. \nSo what is the base for “cliff”? \nqaqat”a = from the cliff → base \"qaqat\" → likely \"q”aqa”t”a\" or \"q”aqa”t”a\"? \nBut note: \"our1+2 lake\" → qucxst”psa → qucx = lake, st”psa = from our1+2 \nSo pattern: [noun] + [ending] → from our1+2 [noun] → [-st”psa] \nBut for \"our1+2 cliff\", not “from”.\n\nWhich word has \"our1+2 cliff\"? \nDirect translation: “our1+2 cliff” → likely the stem of the noun with possessive.\n\nWe see: \n- \"in the cave\" = aq”na → “in” + “cave” \n- “in my bed” = ishinhna → “in” + “my bed” \n- “in your corner” → ? \n- “is it in the corner?” → chushuntxi \nSo “in the corner” = chushuntxi → but that's a question.\n\nWhat about the suffix? \nLook at \"chushp”a\" = his corner \n\"marka\" = the town \n\"markp”t”a\" = from his town \n\"markstxi\" = is it our1+2 town? \n\"markstxi\" = is it our1+2 town → so \"our1+2 town\" is expressed in \"markstxi\" (is it...)\n\nSo: \n\"from his town\" → markp”t”a \n\"from our1+2 town\" → not directly given → markstxi is “is it our1+2 town?” → not “from”\n\nBut look: qucxst”psa = from our1+2 lake too \nqucx = lake → qucxst”psa = from our1+2 lake \nBut lake is used as a noun.\n\nSimilarly, qaqat”a = from the cliff → basic form.\n\nSo “from” + noun → qaqat”a → qqa + at”a = from the cliff \nSo “from our1+2 cliff” = ? → likely qaqat”a with possessive → qaqast”psa?\n\nBut in qucxst”psa → lake becomes qucxst”psa → from our1+2 lake → so affix -st”psa = from our1+2\n\nSo “our1+2 cliff” → base “qaqat”a → modify with -st”psa → qaqast”psa?\n\nBut qaqat”a is from the cliff → so “from the cliff” = qaqat”a → so without possessive.\n\nTo get “our1+2 cliff”, it must be the noun with possessive.\n\nWe see: \n- our1+2 lake → in qucxst”psa → which is “from our1+2 lake” \nBut “our1+2 lake” is not directly stated.\n\nFrom: qucxap”a = through the lake \nqucxst”psa = from our1+2 lake too → so “our1+2 lake” is used in a locative construction.\n\nBut no word for \"our1+2 lake\" directly.\n\nSimilarly, look for patterns in other places.\n\nWe have:\n- chushp”a = his corner\n- chushuntxi = is it in the corner?\n\nSo: “in your corner” → likely “ishma” is “your bed”, so “your corner”?\n\nNo direct word.\n\nBut “in my bed” = ishinhna → ishina + hna \n\"ishma\" = your bed → ishma → so “in your bed” would be ? \nNot directly given.\n\nBut “is it in the corner?” → chushuntxi → so “in the corner” is expressed as a question.\n\nSo, “in your corner” → likely a form like “ish” + “chush”?\n\n“chush” = corner → “his” \nSo “your” = ? \nWe have “your bed” = ishma\n\n“your” → ish?\n\nSo yes, “your corner” = ish + chush → ishchush?\n\nBut no word.\n\nBut note: “is it in the corner?” → chushuntxi → so “in the corner” → chushuntxi → so “in + corner” → chushuntxi\n\nSo “in your corner” → ishchushuntxi?\n\nSimilarly, “in my bed” = ishinhna → “in + my bed” → so “in + (my bed)” → ishinhna\n\nSo “in your corner” → likely ishchushuntxi\n\nSo unit 5: in your corner → ishchushuntxi\n\nNow unit 6: in your corner too → “too” suffix → -psa → so ishchushuntxi + psa → ishchushuntxi psa\n\nBut in the examples: \n- aq”ipsa = the cave too → “the cave” + too → so “cave” + psa? aq”ipsa → “the cave too” \n- p”ak”unhpsa = my pot too → p”ak”u (the pot) + unhpsa → so -unhpsa = my pot too\n\nSimilarly, yapsanpsa = in our1+2 field too → yapsa (in the field) + npsa → -npsa = too?\n\nBut in yapsanpsa → “in our1+2 field too” → so this is “in + field” + too\n\nUse case: “too” → suffix -psa or -hpsa?\n\nIn aq”ipsa → “the cave too” → so likely -psa is attached to the word stem.\n\nSimilarly, qucxst”psa → from our1+2 lake too → so -st”psa\n\nWait — qucxst”psa = from our1+2 lake too → so “too” is marked by -st”psa?\n\nBut in qucxap”a = through the lake → no “too” \nqucxst”psa = from our1+2 lake too → so -st”psa is “from our1+2” + “too”?\n\nBut in aq”ipsa = the cave too → so “the cave” + “too” → aq”ipsa\n\nSo the “too” suffix appears as -psa or part of the word.\n\nIn qucxst”psa → “from our1+2 lake too” → so the “too” is part of the suffix.\n\nBut also in p”ak”unhpsa → my pot too → so “my” + pot + too → -unhpsa?\n\np”ak”u → the pot \np”ak”unhpsa → my pot too → so “my” + “pot” + “too” → gives a suffix -unhpsa?\n\nBut in aq”ipsa → “the cave too” → “the” + “cave” → “cave too” = aq”ipsa → so suffix -psa?\n\nBut in yapsanpsa → “in our1+2 field too” → yapsanpsa → “in” + “our1+2 field” + “too” → so likely -npsa?\n\nThe pattern is that “too” is marked by a suffix that appears after the base.\n\nFor “our1+2 cliff” → noun: cliff → in qaqat”a → from the cliff\n\nSo “cliff” base → qqa?\n\nSo “our1+2 cliff” → ? \nIf “our1+2 lake” appears in “qucxst”psa → from our1+2 lake → so “our1+2” appears with a suffix -st”psa\n\nSo “our1+2 cliff” → qaqast”psa?\n\nBut qaqat”a = from the cliff → so if we drop “from”, we get “the cliff”?\n\nBut we want “our1+2 cliff”.\n\nIs there a noun for “cliff”? Yes — qaqat”a → from the cliff → so the cliff is the object.\n\nSo “the cliff” → qaqat”a (without “from”) → but this is “from the cliff”, so qaqat”a = from the cliff → so the stem is “cliff”.\n\nTo get “our1+2 cliff” → likely qaqast”psa → from our1+2 cliff? But we want “our1+2 cliff”, not “from”.\n\nWait — “our1+2 lake” is not directly given, but in qucxst”psa, we have “from our1+2 lake” → so “our1+2 lake” is a noun.\n\nIn fact, “our1+2 lake” = qucxst”psa → “from” is attached.\n\nSo likely, the possessive is attached with a suffix like -st”psa.\n\nBut in the examples:\n\n- qucxst”psa = from our1+2 lake too → so the suffix -st”psa = from our1+2\n\nSimilarly, markstxi = is it our1+2 town? → “our1+2 town”\n\nSo: -st”psa = from our1+2 (in locative) \n- markstxi = is it our1+2 town?\n\nSo “our1+2” appears via the suffix -st”psa or -stxi\n\nSo for “our1+2 cliff” → use the cliff base with -st”psa → qaqast”psa\n\nBut qaqat”a = from the cliff → so if qaqast”psa = from our1+2 cliff → that’s “from”, not “our1+2 cliff”\n\nWe are missing the form for “our1+2 cliff” directly.\n\nBut in the examples: \n- “our1+2 lake” → appears in “qucxst”psa → so the structure is [noun stem] + st”psa = from our1+2 [noun]?\n\nSo “from our1+2 [X]” → [X stem] + st”psa\n\nThen “our1+2 [X]” → would be [X stem] + st”psa? But only used in “from”.\n\nNo direct word for “our1+2 lake” alone.\n\nUnless the possessive applies to the noun directly.\n\nWe have: \n- “in our1+2 field” → yapsanpsa → “in our1+2 field too” → so “in” + “our1+2 field” → so “our1+2 field” = yapsa? or yapsan?\n\nyapsa → in the field \nyapsanpsa → in our1+2 field too → so “our1+2 field” = yapsan → with -n?\n\nBut “n” appears in “npsa”\n\nSimilarly, “our1+2 lake” → not directly given.\n\nBut “our1+2 town” → markstxi → “is it our1+2 town?”\n\nSo “our1+2 town” is a phrase.\n\nSo to get “our1+2 cliff” → likely qaqast”psa → but that would be “from our1+2 cliff”\n\nBut we want “our1+2 cliff”, not “from”.\n\nPossibly, the possessive is in the noun.\n\nBut in chushp”a = his corner → “his” corner\n\nSo “his” is marked by chush?\n\n“our1+2” → not directly in stem.\n\nIn qucxst”psa = from our1+2 lake → so “our1+2” is attached via the suffix -st”psa\n\nSo “our1+2 X” → X stem + st”psa\n\nThus, “our1+2 cliff” → qaqast”psa\n\nBut again, qaqat”a is “from the cliff” → so qaqast”psa would be “from our1+2 cliff” — the “from” is part of the stem.\n\nSo perhaps the base is “cliff” = q”aqa”t”a → from the cliff\n\nIf we remove “from”, we get “the cliff” → q”aqa”t”a without “from”?\n\nImpossible.\n\nAll forms include a preposition or question.\n\nBut “our1+2 cliff” is just a noun phrase.\n\nLooking back: “the cave” → aq”ipsa \na”q”ipsa → “the cave too” — so “the cave” is aq”ipsa, with “too” in suffix.\n\nSo perhaps when possessive is added, it’s attached via the same suffix.\n\nSo “our1+2 lake” → not directly given.\n\nBut we have: \n- “in our1+2 field too” → yapsanpsa → so “in our1+2 field” → yapsan → with -n?\n\n- “is it our1+2 town?” → markstxi → so “our1+2 town”\n\nThus, “our1+2” appears with a suffix or directly in the stem.\n\nFor “cliff”, no such form.\n\nBut qaqat”a = from the cliff → so “cliff” is in the base.\n\nSo “our1+2 cliff” → qaqast”psa — even if it means “from our1+2 cliff”, perhaps this is how it's expressed.\n\nBut that seems inconsistent.\n\nAlternatively, the possessive is marked by a suffix like -st”psa for “our1+2” in the context of location.\n\nBut let's try to derive each.\n\nUnit 4: our1+2 cliff \n→ We have no direct form. \nBut in “our1+2 lake” → in qucxst”psa → and the stem is qucx + st”psa → so st”psa = from our1+2 \nSo the suffix -st”psa = from our1+2 \nSo to get “our1+2 cliff” → cliff base + st”psa = qaqast”psa \nSo qaqast”psa\n\nBut this is “from our1+2 cliff” — a prepositional phrase.\n\nBut the request is “our1+2 cliff” — a noun phrase.\n\nNo word given for “cliff” directly.\n\nUnless the base is q”aqa”, and “our1+2” is attached.\n\nAnother idea: in “chushp”a = his corner → so “his” is attached to corner → chush + p”a\n\nSimilarly, “his town” = markp”t”a → mark + p”t”a\n\nSo \"his\" = p”? → no, chush = corner, mark = town.\n\nFor “your” → ish?\n\nSo “your corner” → ishchush?\n\nBut “in your corner” → ishchushuntxi?\n\nYes.\n\n“in your corner too” → ishchushuntxi + psa → ishchushuntxi psa\n\n“from your corner too” → “from + your corner”?\n\n“from his corner” → markp”t”a? No — markp”t”a = from his town\n\n“from his corner” → not given.\n\nBut “from the corner”? Not given.\n\nBut “is it in the corner?” → chushuntxi\n\nSo “in the corner” = chushuntxi\n\nSo “in your corner” = ishchushuntxi\n\n“in your corner too” = ishchushuntxi psa\n\n“from your corner too” → “from” must be added.\n\n“from” appears in qaqat”a = from the cliff\n\nSimilarly, from the lake → qucxap”a? No — qucxap”a = through the lake → not from.\n\nqucxst”psa = from our1+2 lake → so “from” is with “our1+2 lake”\n\nSo “from your corner” → likely a stem like “chush” + “from”?\n\nBut “from” is not a separate stem.\n\nqqa = from the cliff\n\nSo “from your corner” = q”aqa”t”a? No.\n\nPerhaps the base is from the [noun], so [noun] with possessive.\n\nBut options:\n\n- qaqat”a = from the cliff\n- so from your corner = q”aqa”t”a with “your” → q”aqa”t”a with ish?\n\nBut “his” is chush → so “your” = ish?\n\nSo “from your corner” = ish + q”aqa”t”a? Unlikely.\n\nPerhaps the structure is: [possessive] + [noun] or [noun] + [possessive]\n\nFrom the pattern:\n\n- in the cave = aq”na → aq", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11150.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by examining the given translations and identifying patterns in the structure of Jaqaru.\n\nFirst, list the given pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- ishinhna → in my bed \n- markstxi → is it our1+2 town? \n- ishma → your bed \n- utamt”a → from your house \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nNow observe the pattern of possession:\n\n- “our1+2” appears in: qucxst”psa (from our1+2 lake too), markstxi (is it our1+2 town?), yapsanpsa (in our1+2 field too)\n\n- “your” appears in: ishma (your bed), utamt”a (from your house)\n\n- “his” appears in: chushp”a (his corner), markp”t”a (from his town)\n\nNow, look at the affixes:\n\n- Possession with “our” is marked by adding a suffix with a form of “our1+2” in location or source. For example:\n\n - qucxst”psa = from our1+2 lake too → “from” + “our1+2” + “lake” + “too”\n\n - markstxi = is it our1+2 town? → “is it” + “our1+2” + “town”\n\n - yapsanpsa = in our1+2 field too → “in” + “our1+2” + “field” + “too”\n\nSimilarly, for “your”:\n\n- utamt”a = from your house \n- ishma = your bed \n\nSo, “your” is marked by a basic form of “your” in the noun, with no added possessive suffix.\n\nNow for the questions:\n\n8. is it from the cave? \n→ The pattern for “is it from X?” is seen in: “chushuntxi” = is it in the corner? \n→ So “is it from X?” would follow a similar structure, with “from” + noun.\n\n\"from the cave\" → qaqat”a = from the cliff → so likely from the cave = qaqat”a with possessive?\n\nBut “from the cave” should be “from” + “the cave”\n\nWe have: aq”na = in the cave \nSo “from the cave” → likely “aq”na with “from” prefix?\n\nBut look at: qaqat”a = from the cliff → so “from” + [noun]\n\nSo “from the cave” = qaqat”a with “cave” substituted?\n\n→ So “from the cave” = qaqata → but the word is qaqat”a → so no change.\n\nThus, “is it from the cave?” → should be: “ishuntxi” + “from the cave”?\n\nCompare with: chushuntxi = is it in the corner?\n\nSo “is it in the corner?” → chushuntxi\n\nSimilarly, “is it from the cave?” → likely “aq”na + “untxi” → “aqnauntxi”?\n\nBut is there a pattern?\n\nWe have:\n\n- chushuntxi = is it in the corner?\n\n→ “in” seems to be a morpheme.\n\nBut “in” is not directly used. \"in my bed\" is ishinhna → so “in” is already encoded in “ishinhna”\n\nWait: ishinhna → in my bed → so “in” is part of “ishin”?\n\nSimilarly, markstxi → is it our1+2 town? → “is it” + “our1+2” + “town”\n\nchushuntxi → is it in the corner? → “is it” + “in” + “corner”?\n\nSo the structure for “is it in X?” is “untxi” + noun?\n\n“chushuntxi” → corner + untxi → “chush” + “untxi”\n\nBut “chushp”a = his corner → so “chush” = his corner → so untxi is the “is it” suffix?\n\nYes: chushuntxi = is it in the corner?\n\nSo “is it in X?” = [X] + “untxi”\n\nSimilarly, “is it from X?” = [X] + “untxi”?\n\nBut from the cave → qaqat”a = from the cliff → so “from the cave” = qaqat”a?\n\nBut the cliff word is qaqat”a — so “cave” is likely a cognate.\n\nSo “from the cave” → qaqat”a?\n\nBut “the cave” is aq”ipsa — so from the cave → \"aq”ipsa\" with “from” prefix?\n\nBut no such form.\n\nPossibility: the word for from the lake is qucxst”psa → from our1+2 lake too\n\nSo “from” + “our1+2” + “lake” + “too”\n\nSo “from the cave” → with “our1+2” or “your”?\n\nBut question 8 is “is it from the cave?” → not possessing.\n\nSo it may just be “aq”na + untxi → “aqnauntxi”?\n\nBut the pattern is: “in X” = [X] + untxi? → chushuntxi = corner + untxi\n\nSo “in the cave” = aq”na → which is already a term.\n\nWait — ishinhna = in my bed → so “in” is embedded.\n\nBut “in” is not a surface morpheme.\n\nLook at: “chushuntxi” = is it in the corner?\n\nSo “untxi” = is it in?\n\nThus, “is it from X” → likely “untxi” + “from X”?\n\nBut no word with “from” in front.\n\nAlternatively, the “from” is encoded in a noun form.\n\nFrom the list:\n\n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a\n\nSo “from the cave” → must be a similar noun → likely qaqat”a with “cave” instead of cliff?\n\nSo only if cave has a similar form.\n\nBut the cliff is qaqat”a → so the base is qaqat”a for “from the cliff”\n\nSo “from the cave” = qaqat”a after substitution?\n\nBut we don’t have a word for “cave”.\n\nWait — we do: aq”ipsa = the cave too\n\nSo the base for “the cave” is aq”ipsa\n\nSo “from the cave” = derived from aq”ipsa\n\nBut no direct form.\n\nAnother possibility: the default “is it from X” = [X] + untxi?\n\nLike “chushuntxi” = is it in the corner?\n\nSo “is it from the cave?” = aq”ipsa + untxi → “aq”ipsauntxi”\n\nSimilarly, “is it the house?” = utamt”a = from your house — so “the house” = utamt”a without “from”?\n\nBut we have ishma = your bed, p”ak”u = the pot, utamt”a = from your house\n\nSo “the house” is not directly given.\n\nBut “utamt”a = from your house → so “your house” = utamt”a\n\nThus, “the house” is likely not directly given — but “my house” is p”ak”unhpsa = my pot too\n\nWait — p”ak”u = the pot → p”ak”unhpsa = my pot too\n\nSo possessive suffix is “unhpsa” — but only with “my”\n\nWe have:\n\n- p”ak”unhpsa = my pot too → so “my” + pot + “too”\n\nSimilarly, aq”ipsa = the cave too → “the cave too”\n\nSo “too” is marked by a suffix.\n\nThus, “in your corner” → corner is chushp”a → “your”?\n\nWe have: chushp”a = his corner\n\nSo “his” → chush\n\nFor “your” → ? We have “your bed” = ishma → so “isha” = your?\n\nSo “is” + “ha” → your?\n\nThen “your corner” → likely “chush” with “your”?\n\nBut “his corner” → chushp”a → so perhaps all corners have “chush” as root?\n\nSo “your corner” → would be ishchush? Or chushisha?\n\nBut “your” = ish (in ishma)\n\nSo “your corner” = ish + chush → ishchush?\n\nBut is that plausible?\n\nCompare: “marka” = the town → “mark”?\n\n“markp”t”a = from his town → mark + p + t”a\n\n“markstxi” = is it our1+2 town? → mark + stxi → so “town” + stxi (is it)\n\nSo “town” is marked by “mark”\n\nSimilarly, “corner” is marked by “chush”\n\nSo “your corner” → “ish” + “chush” → ishchush?\n\nNow, “in your corner too” → in + your corner + too\n\nWe have: aq”na = in the cave → so “in” is part of it.\n\nBut also, “in our1+2 field too” = yapsanpsa → in + our1+2 + field + too\n\nSo “in X too” = [base] + “anpsa” → almost identical: yapsanpsa\n\nSimilarly, “in the cave too” = aq”ipsa — wait, aq”ipsa = the cave too → so “the cave too” not “in the cave too”\n\nBut “the cave” = aq”ipsa, “in the cave” = aq”na\n\nSo different.\n\nSo “in your corner too” → might be “ishchush” + “anpsa”?\n\nSimilarly, “from your corner too” → “from” + “your corner” + “too”\n\nWe have: “from his town” = markp”t”a → mark + p + t”a\n\nSo “from” + “your corner” → ishchush + p”t”a?\n\nBut “your” is ish → so ishchushp”t”a?\n\nOr ishchush + p”t”a?\n\nPossibly.\n\nBut we have “from our1+2 lake too” = qucxst”psa → qucx + st + psa\n\nSo pattern: [noun] + st + psa → but st + psa may be “from our1+2”?\n\nNo: qucxst”psa = from our1+2 lake too\n\nSo “qucx” = through, “st” = from our1+2?\n\nPossibility: the suffix “st” = from our1+2?\n\nBut then “in our1+2 field too” = yapsanpsa — “anpsa” = in our1+2 too?\n\nWait: “in our1+2 field too” = yapsanpsa → so “anpsa” = in our1+2 too?\n\nSimilarly, “the cave too” = aq”ipsa → “ipsa” = too?\n\nSo “too” is marked by “ipsa” or “anpsa”?\n\n- aq”ipsa → the cave too → ends in “ipsa”\n- yapsanpsa → in our1+2 field too → ends in “anpsa”\n- p”ak”unhpsa → my pot too → ends in “unhpsa”\n\nSo “too” is marked by a suffix: ipsa, anpsa, unhpsa\n\nSo in “in your corner too” → likely structure: “in” + “your corner” + “too”\n\nWhat is “in”? In “ishinhna = in my bed” → so “ishin”?\n\nSo in with “ishin”?\n\nSimilarly, “in the corner” → ? We don’t have it directly.\n\nBut “in the corner” → might be chushp”a with “in” prefix?\n\nWe have “is it in the corner?” = chushuntxi\n\nSo “in the corner” → chushuntxi without “is it”?\n\nBut not given.\n\nSo perhaps “in your corner” = “ish” + “chush” → ishchush?\n\nThen “in your corner too” = ishchush + “anpsa” → ishchushanpsa?\n\nSimilarly, “from your corner too” = “from” + your corner + too → we have “from his town” = markp”t”a → so “p”t”a” = from?\n\nAnd “from our1+2 lake too” = qucxst”psa → st”psa = from our1+2 too?\n\nBut “p”t”a” = from his?\n\nSo “from your” → might be “ish” + “p”t”a” → ishp”t”a?\n\nThen “from your corner too” = ishp”t”a + “anpsa”? Or with “chush”?\n\n“from your corner” = from + your + corner → likely ishchushp”t”a?\n\nThen “too” = anpsa → ishchushp”t”a + anpsa → ishchushp”t”aanpsa?\n\nBut that’s long.\n\nBut in “from our1+2 lake too” = qucxst”psa — so “st” might be the possessive “our1+2”, and “psa” = too?\n\nSo “st” + “psa” = from + our1+2 + too?\n\nBut “from your” is not possessive — it’s “your”.\n\nFor “from your corner” → “p”t”a” = from + ? → “p”t”a” is used with “his town” → markp”t”a\n\nSo “p”t”a” = from + his?\n\nSo for “your”, perhaps “p”t”a” is modified.\n\nBut “your” is ish → so ishp”t”a?\n\nAnd for “too” — the suffix varies.\n\nIn “a cave too” = aq”ipsa → “ipsa” = too\n\nIn “field too” = yapsanpsa → “anpsa” = too\n\nIn “my pot too” = p”ak”unhpsa → “unhpsa” = too\n\nSo the “too” suffix differs by the “root” — it’s a thematic suffix.\n\nSo “in your corner too” → in + your corner + too → likely ishchush + “anpsa” → ishchushanpsa\n\nSimilarly, “from your corner too” → from + your corner + too → ishchushp”t”a → ishchushp”t”a + anpsa → ishchushp”t”aanpsa?\n\nBut is there a structure like “p”t”a” for from?\n\nWe have:\n\n- markp”t”a = from his town → so “p”t”a” = from his?\n\n- so from your = ishp”t”a?\n\nThen from your corner = ishchushp”t”a?\n\nAnd from your corner too = ishchushp”t”a + anpsa → ishchushp”t”aanpsa?\n\nBut “anpsa” is used in “in our1+2 field too” — so “anpsa” = too?\n\nBut we don’t have a form for “from your corner too”.\n\nAlternatively, “too” is attached to the whole phrase.\n\nNow for 4. our1+2 cliff\n\nWe have “from the cliff” = qaqat”a\n\nSo “our1+2 cliff” → should be qaqat”a with “our1+2”?\n\nLook at “from our1+2 lake too” = qucxst”psa → so “st” = from our1+2?\n\nSo “st” is the possessive.\n\nIn “from our1+2 lake” = qucxst”psa\n\nSo “st” = from our1+2\n\nThus, “our1+2 cliff” = qaqat”a with “st” → qaqat”ast”?\n\nBut we don’t have such a form.\n\nAlternatively, “cliff” = qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut is there alternation?\n\nIn “our1+2 lake” → must be “qucxst”psa → qucx + st + psa\n\n“our1+2 field too” → yapsanpsa → so “anpsa” = in our1+2 too?\n\nSo “in” may be encoded by “anpsa”?\n\nWait — “in our1+2 field too” = yapsanpsa → so pattern: noun + anpsa\n\nBut “from our1+2 lake too” = qucxst”psa → noun + st + psa?\n\nNo — both have “psa”.\n\nBut “psa” = too?\n\nSo for “our1+2 cliff” → would be qaqat”ast”?\n\nBut “st” = from our1+2?\n\nSimilarly, “our1+2 field” → field is not given.\n\nBut only “cliff” and “lake” given.\n\nWe have qaqat”a = from the cliff → so cliff = qaqat”a\n\nSo “our1+2 cliff” → likely qaqat”a with possessive?\n\nPossibly with “st” → qaqat”ast”?\n\nBut is there something like that?\n\nAlternatively, since “in our1+2 field too” = yapsanpsa → “anpsa” = in our1+2 too?\n\nBut “our1+2” is not directly attached — “anpsa” may be the suffix.\n\nBut in “from our1+2 lake” = qucxst”psa → st is possessive.\n\nSo for “our1+2 cliff”, it would be qaqat”ast”?\n\nSo qaq", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11069.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "Start by identifying the patterns in the given Jaqaru words and their translations.\n\nGiven data:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishma = your bed \n- utamt”a = from your house \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- qaqat”a = from the cliff \n- yapsanpsa = in our1+2 field too \n\nObserve the structural patterns:\n\n1. \"our1+2\" appears in: \n - qucxst”psa → from our1+2 lake too \n - markstxi → is it our1+2 town? \n - yapsanpsa → in our1+2 field too \n So: \"our1+2\" is used with a locative modifier.\n\n2. \"your\" appears in: \n - ishma = your bed \n - utamt”a = from your house \n - chushp”a = his corner → \"his\" (not \"your\") \n → So \"your\" is marked by a prefix; \"your bed\" = ishma\n\n3. \"in\" = aq”na (in the cave), and \"in our1+2 field too\" = yapsanpsa → \"in\" is marked by a prefix like \"na\" or \"san\"? \n But: aq”na = in the cave → \"na\" is the locative suffix \n yapsanpsa = in our1+2 field too → \"sanpsa\" → “san” + “psa” \n Compare to: aq”ipsa = the cave too → “ipsa” → “psa” is a noun root \n qucxst”psa = from our1+2 lake too → “st” + “psa” → st”psa → from + (our1+2 lake) + too \n So: “too” is marked by “psa” → “ipsa”, “st”psa, “npsa”?\n\nNow, consider:\n\n4. \"our1+2 cliff\" \n→ \"from the cliff\" is qaqat”a \n→ So \"from\" is \"qaqat”a\" \n→ \"our1+2\" + \"cliff\" = likely \"qaqat”a\" with \"our1+2\" attached → like qucxst”psa \n→ qucxst”psa = from our1+2 lake too → structure: from + ours+lake + too \n→ So: from + our1+2 + noun → [from] + [our1+2] + [noun] \n→ For \"our1+2 cliff\" = ? \n→ If \"from the cliff\" = qaqat”a → then \"our1+2 cliff\" might be “our1+2” + “cliff” → similar to “our1+2 lake” → qucxst”psa → which is “from our1+2 lake too” \nBut “our1+2 cliff” is not “from” — it is just location. \n→ So \"in our1+2 cliff\"? No. \"our1+2 cliff\" = a location → recall:\n\n“in the cave” = aq”na \n“in our1+2 field too” = yapsanpsa → so \"in\" + our1+2 + field → → “in” + our1+2 + noun → “yapsanpsa” → so “san” might be “in” → “san” + “psa”? \nWait: yapsanpsa = in our1+2 field too → so root might be “psa” = field → “yapsanpsa” = in + our1+2 + field? \nBut yapsanpsa = in our1+2 field too → so “in” is marked by “yap”? “yap” = in? \nCompare: \n- aq”na → in the cave → “na” → in \n- aq”ipsa → the cave too → “ipsa” → cave \n- yapsanpsa → in our1+2 field too → “yap” + “san” + “psa” → maybe “yap” = in, “san” = our1+2?\n\nBut “chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nSo root: \n- chushp”a = his corner → corner = p”a \n- marka = the town → town = “marka” \n- utamt”a = from your house → “utam” + “t”a → from + your + house \n- qaqat”a = from the cliff → “qaqat”a → from + the cliff\n\nSo, “from” appears in both \"from your house\" and \"from the cliff\"\n\nThus, “from the cliff” = qaqat”a \n→ So “from the cliff” = qaqat”a → meaning hq → “from” + “cliff” \nSo “our1+2 cliff” = ? \nWe don’t have “our1+2 cliff” directly.\n\nBut we have: \n- qucxst”psa = from our1+2 lake too → “from” + “our1+2” + “lake” → so “our1+2” is attached to a noun with “st” for lake? \nqucxst”psa = from our1+2 lake too → “qucx” = lake → “st” might be locative? \nBut “from our1+2 lake” → “st”psa?\n\nAlternatively, look at “our1+2 field too” = yapsanpsa \n→ “yapsa” = in our1+2 field → “yap” = in, “san” = our1+2, “psa” = field?\n\nWait: “psa” appears in: \n- aq”ipsa → the cave too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n→ So “psa” is a noun root: cave, lake, field\n\nSo: \n- cave = ipsa \n- lake = qucxst”psa → but lake is “qucx” → so “qucx” is lake \n- field = psa → \"yapsanpsa\" → field = \"psa\" \n→ So: \n- aq”ipsa = the cave too → “ipsa” = cave \n- qucxst”psa = from our1+2 lake too → “qucx” = lake, “st” = from? \nBut “qucxap”a = through the lake → “ap” = through → so “ap” = through, “st” = from?\n\nLet’s tabulate:\n\n| English | Jaqaru | Observation |\n|--------|--------|------------|\n| the cave too | aq”ipsa | “ipsa” = cave (root) |\n| in the cave | aq”na | “na” = in the cave |\n| from our1+2 lake too | qucxst”psa | “st” = from? “qucx” = lake, “psa” = ‘lake’? |\n| his corner | chushp”a | “chush” = his, “p”a = corner |\n| is it in the corner? | chushuntxi | “untxi” = is it? |\n| the town | marka | “marka” = town |\n| from his town | markp”t”a | “p”t”a = his town? → “p”t”a” → “t”a = town, “p” = his? |\n| is it our1+2 town? | markstxi | “st” = our1+2? “markstxi” = is it our1+2 town? |\n| your bed | ishma | “ish” = your, “ma” = bed |\n| from your house | utamt”a | “utam” = from your house → “utam” = from your? |\n| the pot | p”ak”u | “p”ak”u” = pot |\n| my pot too | p”ak”unhpsa | “unhpsa” = my pot too → “unh” = my? |\n| from the cliff | qaqat”a | “qaqat”a = from the cliff |\n| in our1+2 field too | yapsanpsa | “yap” = in, “san” = our1+2, “psa” = field |\n\nNow, pattern:\n\n- For “our1+2” + noun: \n - lake → qucxst”psa → “from our1+2 lake” \n - town → markstxi → “is it our1+2 town?” → so “our1+2 town” in question \n - field → yapsanpsa → “in our1+2 field too” → so “our1+2 field” is part of “in our1+2 field”\n\n→ So “our1+2” is marked by “san” (in yapsanpsa) or “st” (in markstxi, qucxst”psa)\n\n\"qucxst”psa\" = from our1+2 lake too → uses “st” \n\"markstxi\" = is it our1+2 town? → uses “st” \n\"yapsanpsa\" = in our1+2 field too → uses “san”\n\nInconsistent? But \"st\" and \"san\" may be different markers.\n\nMaybe “st” = “from”, “san” = “in”?\n\nBut “in our1+2 field” = yapsanpsa → so “yap” = in, “san” = our1+2 → so “san” = our1+2\n\n“from our1+2 lake” = qucxst”psa → “st” = from? → possibly “st” = from, “san” = our1+2?\n\nBut in “chushp”a = his corner → “chush” = his \nSimilarly, “markp”t”a” = from his town → “p”t”a = his town → “p” = his \n“ishma” = your bed → “ish” = your \n“utamt”a = from your house → “utam” = from your → “utam” = from your house → so “utam” contains “your”\n\nThus: \n- “his” = chush \n- “your” = ish \n- “our1+2” = appears in: \n - qucxst”psa → with “st” \n - markstxi → with “st” \n - yapsanpsa → with “san”\n\n→ So “our1+2” may be marked by “st” when used with “from” or “is it?” and “san” when used with “in”\n\nBut for “our1+2 cliff” — what is the base?\n\n“from the cliff” = qaqat”a \nSo “cliff” = “qaqat”a → “qaqat” = cliff\n\nSo what is “our1+2 cliff”?\n\n→ If “from” is used, we can generalize from “from our1+2 lake” = qucxst”psa \n→ So “our1+2 cliff” = qaqat”a with “our1+2” added → likely qaqat”a with “st” → but “qucxst”psa” = from our1+2 lake → uses “st” + “qucx” + “psa”\n\nSo: \n→ “our1+2 cliff” = qaqat”st”a? → qaqat”st”a → from our1+2 cliff? \nBut target is not “from” — it is “our1+2 cliff” → location?\n\n→ We have “in the cave” = aq”na \n→ So “in” + noun → aq”na → “na” → in\n\nSimilarly, “in your corner” → ?\n\nWe have “is it in the corner?” = chushuntxi → “untxi” = is it?\n\n“chushp”a = his corner → so “corner” = “p”a\n\nThus: \n- “in your corner” = ? → “your” + “in” + “corner” \n→ “your” = ish → so “ish” + ? + “p”a\n\nDo we have “in”?\n\n“in” appears in aq”na (in the cave) → “na” = in \n“in our1+2 field” → yapsanpsa → uses “yap” → not “na”\n\nSo “in” may be marked by “na” or “yap”?\n\na q”na → in the cave \nyapsanpsa → in our1+2 field → so “yap” = in?\n\nBut “yap” is only in yapsanpsa → so “yap” might be “in” with suffix?\n\n“chushuntxi” = is it in the corner? → “untxi” = is it?\n\nSo “in the corner” = chushuntxi? → no, chushuntxi = is it in? → it's a question\n\nBut “in your corner” → needs to be a statement.\n\nWe have: \n- ishma = your bed \n- so “your” = ish \n- “p”a = corner\n\nSo “in your corner” = ? + “p”a → with “in”?\n\na q”na → “na” = in the cave \n→ Could “in” be “na”?\n\nSo “in your corner” → “ish” + “na” + “p”a → ish”na”p”a?\n\nBut we don’t have such a word.\n\nBetter: is there a pattern for “in” + noun?\n\na q”na = in the cave → noun = “cave” = “ipsa” → so “na” = in, “ipsa” = cave → so “na” is in?\n\nBut in yapsanpsa → in + our1+2 + field → “yap” is used → not “na”\n\nContradiction?\n\nAlternative: “in” is marked by “na” when direct, but with “our1+2” it uses “yap”?\n\nBut “yap” appears only in yapsanpsa.\n\nWait: yapsanpsa = in our1+2 field too → “yap” = in\n\n→ So perhaps:\n- “in” = “na” for singular or direct?\n- “in” = “yap” when with “our1+2”?\n\nBut “in our1+2” is common in several words.\n\nBut “in your corner” — “your” is ish, so perhaps “ish” + “na” + “p”a = ish”na”p”a?\n\nWe don’t have a word, but it is plausible.\n\nBut can we use the pattern from chushuntxi?\n\nchushuntxi = is it in the corner? → “untxi” = is it?\n\nSo “in the corner” is embedded in “is it in the corner?”\n\nSo location phrase: “in the corner” = “p”a → “chushp”a = his corner → so “p”a” = corner\n\nSo for “in your corner” → “ish” + “na” + “p”a → ish”na”p”a\n\nSimilarly, “in your corner too” → “too” is marked by “psa” → in aq”ipsa = the cave too → “ipsa” = cave too\n\nQucxst”psa = from our1+2 lake too → “too” = “psa”\n\nYapsanpsa = in our1+2 field too → “too” = “psa”\n\nSo “too” = “psa” → at end\n\nThus: “in your corner too” = ish”na”p”a”psa\n\nSimilarly, “from your corner too” → “from” + “your corner” + “too”\n\n“from” is marked in: \n- from your house → utamt”a \n- from the cliff → qaqat”a \n- from our1+2 lake → qucxst”psa\n\nSo “from” is marked by “t” or “qa”?\n\n“utamt”a = from your house → “utam” = from your? \n“qaqat”a = from the cliff → “qaqat” = from the\n\nSo may be “t” + “your”?\n\n“ut” → from? → “utam” → ut + am?\n\n“t” → from? “utamt”a → “utam” = from\n\nBut no clear suffix.\n\n“from your corner” → missing?\n\nBut “his corner” = chushp”a → so “corner” = “p”a\n\n“your” = ish\n\nSo “from your corner” = ? + “ish” + “p”a\n\nFrom “from your house” = utamt”a → so “utam” = from your house\n\nSo perhaps “utam” + “p”a = from your corner?\n\n→ utam”p”a?\n\nBut “utam” = from your house → so it may be “utam” + “p”a = from your corner?\n\nSimilarly, “from your corner too” → add “psa” → utam”p”apsa\n\nSimilarly, for 8. “is it from the cave?”\n\n→ “is it from the cave?” → similar to “is it in the corner?” = chushuntxi\n\n“chushuntxi” = is it in the corner?\n\nSo pattern: “is it from X?” = “untxi” + X?\n\n“untxi” = is it?\n\nSo “is it from the cave?” = untxi + from + cave\n\nCave = “ipsa” → from = ? → “from the cave” = qaqat”a? But that's from the cliff.\n\nWe have: “from the cave”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10219.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 0, + "output": "Start by analyzing the given Inuktitut sentences and their English translations to identify patterns in verb forms, possession, subject, and modification.\n\nLook at sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (possessed, marked with \"your\" in possessive) \n- \"takujaatit\" = saw you (past tense, active, causative or perception verb)\n\nSentence 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor \n- \"qukiqtanga\" = shot (past tense, causative verb)\n\nSentence 3: \n\"Aanniqtutit\" → \"You hurt yourself.\" \n- \"aanniqtutit\" = you hurt (yourself) \n- subject is \"you\", object is \"yourself\"\n\nSentence 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor \n- \"aarqijaatit\" = cured you \n- \"aarqijaatit\" = cured, passive or active with benefit to subject\n\nSentence 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"Qingmiq\" = you \n- \"iputujait\" = speared (action) \n- object is \"the dog\" (implied)\n\nSentence 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman \n- \"iluaqhaijimik\" = a doctor (possessed, nominative) \n- \"aarqisijuq\" = cured (past tense)\n\nSentence 7: \n\"Nanuq qaijuq\" → \"The polar bear came.\" \n- \"Nanuq\" = the polar bear \n- \"qaijuq\" = came (simple past)\n\nSentence 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"Iluaqhaijivit\" = your doctor \n- \"inuuhuktuit\" = your boy \n- \"aarqijanga\" = cured\n\nSentence 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter \n- \"amaruq\" = the wolf \n- \"iputujanga\" = speared\n\nSentence 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog \n- \"ilinniaqtitsijiit\" = your teacher \n- \"aanniqtanga\" = hurt\n\nSentence 11: \n\"Ukiakhaqtutit\" → \"You fell.\" \n- \"Ukiakhaqtutit\" = you fell (you injured yourself)\n\nSentence 12: \n\"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter \n- \"nanurmik\" = a polar bear \n- \"qukiqsijuq\" = shot\n\nNow, observe the verb forms:\n\nCommon structures:\n- Verbs end in -it (past), -anga (past), -aqtit (past)\n- Possession: \"your\" → \"your-...\" → e.g., \"Qingmivit\" (your dog), \"iluaqhaijivit\" (your doctor)\n- The verb is often marked with a specific suffix to show the object or recipient\n- For injuries: \"aanniqtutit\" = you hurt yourself → \"aanniqtanga\" = hurt (with \"a\" marking object)\n- \"iputujait\" = speared, \"qukiqtanga\" = shot, \"aarqijaatit\" = cured\n\nNow, analyze each target:\n\n13. Amaruup angatkuit takujanga \nBreak down:\n- \"Amaruup\" = the wolf \n- \"angatkuit\" = came? → from \"angatkuq\" in sentence 7 → \"angatkuq\" = came → \"angatkuit\" = came (past tense)\n- \"takujanga\" → \"takujaatit\" = saw → \"takujanga\" = saw (or perhaps saw the subject?) \nBut \"takujanga\" = saw (a past action) \nBut who did it see? \nPossibly: \"the wolf saw someone\" \nBut \"angatkuit\" = came → so \"the wolf came and saw [someone]\" → but structure?\n\nWait: \"Amaruup angatkuit takujanga\" → final verb: \"takujanga\" \n\"takujanga\" = saw → past tense \n\"angatkuit\" = came (past) \nSo: \"the wolf came and saw [someone]\" → but [someone] missing?\n\nBut in English, indirect meaning: perhaps \"the wolf came and saw you\"?\n\nBut based on translations, \"takujanga\" = saw (active perception)\n\nBut in sentence 1: \"Qingmivit takujaatit\" = your dog saw you → \"saw\" → \"takujaatit\"\n\nSo \"takujanga\" → saw → past\n\nBut passively? No.\n\nSo \"Amaruup\" → the wolf \n\"angatkuit\" → came \n\"takujanga\" → saw → likely saw someone (implied subject)\n\nBut no object — maybe it's \"the wolf came and saw you\" (the implication of the person speaking)\n\nBut no mention of \"you\" — so maybe it's missing?\n\nHowever, in sentence 3: \"You hurt yourself\" — closed reflexive.\n\nSo likely: \"The wolf came and saw you.\" \nSeems plausible.\n\n14. Nanuit inuuhukturmik aanniqsijuq \n- \"Nanuit\" = the polar bear \n- \"inuuhukturmik\" = your boy? → \"inuuhuktuit\" = your boy (sentence 8) → so \"inuuhukturmik\" = your boy \n- \"aanniqsijuq\" → from \"aanniqtutit\" → \"hurt\" → \"aanniqtanga\" → so \"aanniqsijuq\" = hurt (past, causative)\n\nSo: \"the polar bear hurt your boy\"\n\n15. Angunahuktiit aarqijuq \n- \"Angunahuktiit\" = the hunter (with -it suffix) → past tense of \"angunahukti\" → \"the hunter\" \n- \"aarqijuq\" → from \"aarqijaatit\" = cured → \"aarqiji\" + \"a\" → \"aarqijuq\" = cured \nSo: \"the hunter cured\"\n\nBut is it \"cured someone\"? No object mentioned.\n\nBut from earlier: \"cured\" action → in multiple cases with object.\n\nIn sentence 4: \"iluaqhaijiup aarqijaatit\" → the doctor cured you → object is \"you\"\n\nHere: only \"the hunter cured\" — so missing object? But likely context implies \"you\" or \"someone\"\n\nBut in sentence 5: \"You speared the dog\" → object exists\n\nIn sentence 6: \"The shaman cured a doctor\" → object exists\n\nSo \"the hunter cured\" → possibly \"cured you\"?\n\nBut no object — could be \"cured himself\"?\n\nBut \"aarqijuq\" = cured — past\n\nPossibility: \"the hunter cured himself\" or \"the hunter cured you\"?\n\nBut no object. However, look back at sentence 8: \"your doctor cured your boy\" → object is marked.\n\nIn this sentence, no object. Maybe reflexive?\n\nBut \"aarqijuq\" — from \"aarqijaatit\", which had \"you\" → perhaps it's missing?\n\nBut in sentence 15: \"Angunahuktiit aarqijuq\" — no object → maybe \"cured himself\"?\n\nBut no marker for reflexive.\n\nAlternatively, in sentence 9: \"the hunter speared the wolf\" → object marked.\n\nSo without object, it might be assumed to be the subject → reflexive.\n\nIn Inuktitut, reflexive forms often use \"self\" or internal object.\n\nCompare to sentence 3: \"You hurt yourself\" → \"aanniqtutit\" → reflexive.\n\nSo \"aarqijuq\" — might be \"cured himself\"?\n\nBut \"aarqijaatit\" has object — only when object noun is present.\n\nBut here, no object.\n\nSo perhaps \"the hunter cured himself\"?\n\n16. Ilinniaqtitsiji qukiqtait \n- \"Ilinniaqtitsiji\" = your teacher? → from sentence 10: \"ilinniaqtitsijiit\" = your teacher \nSo \"Ilinniaqtitsiji\" = your teacher \n- \"qukiqtait\" = shot? → from \"qukiqtanga\" = shot → \"qukiqtait\" = shot (past tense)\n\nSo: \"your teacher shot\"\n\nLikely: \"your teacher shot you\"?\n\nBut no object.\n\n\"qukiqtait\" → shot — active verb\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → object present\n\nHere: object missing → so likely \"your teacher shot you\"?\n\nBut no \"you\" in structure.\n\nBut in sentence 5: \"You speared the dog\" → object present\n\nSo if object is missing, it may be reflexive → \"your teacher shot himself\"?\n\nBut \"shot\" is violent → unlikely.\n\nAlternatively, could \"qukiqtait\" = shot someone else?\n\nBut without object → probably active action on someone.\n\nIn consistent pattern, when object is missing, it may be implied to be the listener.\n\nBut no example of someone hitting themselves.\n\nCompare: sentence 5: \"You speared the dog\" → object is dog\n\nSentence 9: \"The hunter speared the wolf\" → object is wolf\n\nSo object is always present in active causative verbs.\n\nThus, in 16, object is missing → likely error? Or missing pronoun.\n\nBut pattern: perhaps \"your teacher shot you\"?\n\nBut why?\n\nLook at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"your teacher\" is object of hurt.\n\nSo when \"your teacher\" is subject, and verb \"hurt\", object is implied? No — object is \"your teacher\" of hurt? No — \"The dog hurt your teacher\" → so \"your teacher\" is object.\n\nSimilarly, in 16: \"Ilinniaqtitsiji qukiqtait\" → \"your teacher shot [someone]\" → if no object, maybe \"you\"?\n\nBut no.\n\nAlternative: \"qukiqtait\" could be \"was shot\" — passive?\n\nBut \"qukiqtait\" in sentence 2: \"qukiqtanga\" = shot (active) — so \"qukiqtait\" = shot (active)\n\nSo active → must have object.\n\nThus, missing object → likely implies \"you\" — the speaker.\n\nSo: \"your teacher shot you\"\n\nSimilarly, in sentence 3: \"You hurt yourself\" → reflexive.\n\n17. Qaijutit \n- \"Qaijutit\" → from \"qaijuq\" = came (sentence 7) → \"qaijutit\" = came \nSo: \"came\" → \"you came\" or \"it came\"? \nBut no subject — main verb: \"Qaijutit\" \nSo likely: \"You came\" → implied subject is \"you\"\n\nBut no marker — in sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\" \nSo \"qaijuq\" = came → only object present.\n\nHere: no object → so \"you came\"?\n\nYes — this seems to be a reflexive or self-action? No.\n\n\"Qaijutit\" → same as \"qaijuq\" → came \nSo \"you came\" — grammatically, without subject, likely \"you came\"\n\nLike \"Ukiakhaqtutit\" = \"you fell\" (sentence 11)\n\nSo \"Qaijutit\" = \"you came\"\n\n18. Angunahuktimik aarqisijutit \n- \"Angunahuktimik\" = the hunter (with object marker) → \"angunahuktii\" = hunter, with -mik → marking object? \nWait: in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter\" + \"the wolf\" → so \"up\" = possessive or definite \n\"Angunahuktimik\" → may be \"the hunter\" + object marker → \"mik\" → for object?\n\nBut \"aarqisijutit\" → from \"aarqijaatit\" = cured → \"aarqisijuq\" = cured → \"aarqisijutit\" = cured (past tense)\n\nSo: \"the hunter cured\" → again, object missing?\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object is marked\n\nSo here: \"Angunahuktimik aarqisijutit\" → \"mik\" = object marked → so object is present? But no noun.\n\n\"Angunahuktimik\" = the hunter (with object marker) → perhaps marks object? But no object noun.\n\nAlternatively, \"mik\" is a possessive or object marker → may imply \"the hunter cured the boy\" or \"the hunter cured you\"?\n\nBut no possessive.\n\nHowever, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" — both possession and action\n\nHere: only \"hunter\" and \"cured\"\n\nPossibly: \"the hunter cured you\"\n\nBut structure: \"Angunahuktimik\" → may be acting on object\n\nBut no object noun.\n\nTherefore, likely the object is missing — so only action is \"cured\"\n\nMust infer based on pattern.\n\nRe-express all:\n\n13. Amaruup angatkuit takujanga → the wolf came and saw you \n14. Nanuit inuuhukturmik aanniqsijuq → the polar bear hurt your boy \n15. Angunahuktiit aarqijuq → the hunter cured himself? \nBut reflexive not supported. \nIn sentence 3: \"you hurt yourself\" → reflexive \nSo \"cured yourself\"? \nBut \"aarqijuq\" — not marked for reflexive.\n\n\"aarqijaatit\" = cured you → object marked \n\"aarqisijuq\" = cured (someone)\n\n\"aarqisijutit\" = cured (with past tense)\n\nNo reflexive form in examples.\n\nBut sentence 3: \"you hurt yourself\" → uses reflexive form in verb? Yes — \"aanniqtutit\" — no object, so reflexive.\n\nSimilarly, is \"aarqijuq\" reflexive?\n\n\"aarqijuq\" = cured → but without object → possibly \"cured himself\"\n\nPossibility: in absence of object, it's reflexive.\n\nSimilarly, \"Qaijutit\" = \"you came\" → no object → subject is implied.\n\nSo for 15: \"Angunahuktiit aarqijuq\" → the hunter cured himself.\n\nFor 18: \"Angunahuktimik aarqisijutit\" → hunt + object marker + cured → object missing → so \"cured you\"?\n\nBut no object — so like 16?\n\n16: \"Ilinniaqtitsiji qukiqtait\" → your teacher shot → likely \"your teacher shot you\"\n\n18: similarly → \"the hunter cured you\"\n\nBut \"Angunahuktimik\" — what does it mean?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter\" + \"the wolf\"\n\nSo \"up\" marks possession or definiteness.\n\nHere, \"mik\" — could be object marker.\n\nIn Inuktitut, object markers like -mik, -it, -uit, etc. are used to mark direct objects.\n\nSo \"Angunahuktimik\" → the hunter + object marker → so object is marked — but no noun → so object is missing.\n\nBut in full sentence: \"Angunahuktimik aarqisijutit\" — the hunter (object marker) cured?\n\nSo verb is \"aarqisijutit\" — cured\n\nSo likely: \"the hunter cured [someone]\" — object missing.\n\nMissing noun implies: \"you\" or \"himself\"?\n\nNo sufficient evidence.\n\nBut in 14: \"inuuhukturmik\" = your boy → object marked \nIn 15: \"aarqijuq\" — no object → reflexive?\n\nSimilarly, in 16: \"qukiqtait\" — no object → so likely \"you\" as object.\n\nSo pattern: when object is missing, it's \"you\" (the listener).\n\nSo:\n\n13: the wolf came and saw you \n14: the polar bear hurt your boy \n15: the hunter cured yourself → but \"cured\" as in \"he cured himself\"? \nBut no such example.\n\nSentence 3: \"you hurt yourself\" → reflexive.\n\nSo verb form suggests self-action.\n\n\"aarqijuq\" — in absence of object — similar to \"aanniqtutit\" → reflexive.\n\nSo likely: \"the hunter cured himself\"\n\n16: your teacher shot you \n17: you came \n18: the hunter cured you → because \"mik\" marks object, so \"cured you\"\n\nBut \"mik\" → object marker → so object is present — but not named → so likely \"you\"\n\nSo:\n\n13: the wolf came and saw you \n14: the polar bear hurt your boy \n15: the hunter cured himself \n16: your teacher shot you \n17: you came \n18: the hunter cured you\n\nWait — inconsistency: 15 and 18 both involve \"hunter\" and \"cured\", but different objects.\n\nIs reflexive", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12688.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 1, + "output": "We are given a set of Inuktitut sentences and their English translations. Our task is to translate six new sentences (13–18) into English, based on the linguistic patterns observed in the given examples.\n\nStep 1: Identify key syntactic and morphological patterns.\n\nLook at the verbs and their constructions:\n\n- \"takujanga\" → \"saw\" → in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\"\n → \"takujaatit\" → third person saw (you), with subject \"Qingmivit\" (your dog). \n → \"takujanga\" is likely the base verb form \"to see\" in a different inflection.\n\nIn sentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\"\n→ \"aarqijaatit\" = cured you\n\nIn sentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\"\n→ \"iputujait\" = speared\n\nIn sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\"\n→ \"aaruqisijuq\" = cured, with object \"a doctor\"\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\"\n→ \"iputujanga\" = speared (third person)\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\"\n→ \"aanniqtanga\" = hurt oneself → \"aanniqtang\" (hurt) + -a (1st person?) → but subject is \"the dog\", so \"aanniqtanga\" = hurt someone (teacher)\n\nNow observe verb patterns:\n\nMany verbs are in suffix-based forms that indicate:\n- Voice (active/passive)\n- Person (first, second, third)\n- Object (you, him, them, etc.)\n\nLook at the verb root and suffixes:\n\n1. \"takuj\" → to see → takujaatit = saw you → root: takuj, suffix: -a- + -it → indicates third person, accusative, past\n → takujanga → likely \"you saw me\" or \"you saw\" → but in 13: \"Amaruup angatkuit takujanga\"\n → \"angatkuit\" = came, \"takujanga\" = saw?\n\nWait: sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\"\n→ \"qaijuq\" = came → root: qaij, past tense → \"qaijuq\"\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\"\n→ \"qukiqsijuq\" = shot → \"qukiq\" = shoot → \"qukiq\" + -sijuq = past tense, third person, transitive\n\nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\"\n→ \"qukiqtanga\" = shot (active, third person)\n\nSo: verbs often have roots with suffixes indicating:\n- Person (e.g., -it, -it, -uq, -up)\n- Object (e.g., -ji, -jiit, -mik)\n- Voice (active/passive)\n\nRefine verbs:\n\n- \"takuj\" → see → takujanga → sees (someone), possibly active?\n- \"iputuj\" → spear → iputujait → spears (you), iputujanga → speared (someone)\n- \"aarq\" → cure → aarqijaatit → cured you → aarqisijuq → cured someone\n- \"iluaqhaiji\" → doctor → iluaqhaiji \"doctor\"\n- \"angunahukti\" → hunter → angunahukti \"hunter\"\n- \"amaruq\" → wolf? But in 9: \"angunahuktiup amaruq iputujanga\" → hunter speared wolf → \"amaruq\" = wolf?\n→ In 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear → \"nanurmik\" = polar bear? → \"nanur\" = polar bear → nanurmik = a polar bear\n\nSo verb patterns:\n- The verb root + suffix shows tense, person, object.\n\nNow, look at 13: Amaruup angatkuit takujanga.\n\n\"Amaruup\" → likely \"a wolf\" or \"a hunter\"? \"Amaruq\" = wolf → \"Amaruup\" = ? (likely a possessive or object form? or just \"wolf\" as subject)\n\nBut in 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\"\n→ \"Amaruq\" = wolf (object), \"angunahuktiup\" = the hunter (subject), \"iputujanga\" = speared (active)\n\nSo \"amaruq\" = wolf\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"Amaruup\" is likely \"the wolf\"? or \"a wolf\"?\n\nBut the structure: \"Amaruup angatkuit takujanga\"\n\nCompare to sentence 7: \"Nanuq qaijuq\" → \"polar bear came\"\n\nSo \"angatkuit\" = came → \"angatkuq\" (in sentence 6) = shaman cured? No.\n\nWait: sentence 7: \"Nanuq qaijuq\" → \"polar bear came\"\n\n\"angatkuit\" may be related → but \"angat\" → bear? \"angat\" is sometimes used for bear? In sentence 6: \"Angatkuq\" → shaman cured?\n\nNo, \"Angatkuq\" → \"shaman\", not bear.\n\nBut sentence 7: \"Nanuq qaijuq\" → polar bear came → \"nanuq\" = polar bear\n\nSo \"angatkuit\" → may be a different verb?\n\nCompare to sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy\"\n→ \"inuuhuktuit\" = your boy → \"inuuhuktuup\" = the boy (subject)\n\nIn 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n→ \"nanuit\" = ? possibly \"the polar bear\"?\n→ \"inuuhukturmik\" → \"your boy\" or \"your boy\"? \"inuuhuktu\" = boy → inuuhukturmik = your boy (with object suffix)\n\n\"aanniqsijuq\" = hurt → aanniqtanga = hurt (in 10)\n\nSo \"aanniqsijuq\" = hurt someone\n\nLikewise, sentence 15: \"Angunahuktiit aarqijuq\" → the hunter cured?\n\n\"angunahuktiit\" = the hunter (third person) + -it → past?\n\"aarqijuq\" = cured → aarqisijuq = cured someone → aarqijuq = cured?\n\nBut correct form: in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → aarqijaatit → cured you\n→ So aarq + i + j + aat = cured you\n\nSo aarqijuq → could be cured someone?\n\nIn 15: \"Angunahuktiit aarqijuq\" → hunter cured someone?\n\nLikely: \"the hunter cured someone\"\n\nBut who? Not specified → so \"the hunter cured [someone]\"\n\nNow 16: \"Ilinniaqtitsiji qukiqtait\"\n\n\"Ilinniaqtitsiji\" → from sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher\n→ ilinniaqtitsijiit = your teacher → so ilinniaqtitsiji → your teacher?\n\nThen \"qukiqtait\" → shot? qukiqtanga → shot in sentence 2 → qukiqtait → perhaps past tense = shot?\n\n→ so \"your teacher was shot\"?\n\nSo \"Ilinniaqtitsiji qukiqtait\" → your teacher was shot\n\nNow 17: \"Qaijutit\" → from sentence 7: \"Nanuq qaijuq\" → polar bear came\n\n\"qaij\" → came → qaijut → what? qaijut → past tense of \"to come\"?\n→ qaijuq in 7 → past → so qaijut might be past \"came\"\n\nBut qaijut → possibly \"came\" with some form?\n\nIn sentence 7: \"Nanuq qaijuq\" → polar bear came → so \"qaijuq\" = came\n\n\"qaijut\" → maybe same root? → could be \"came\"?\n\nBut in 17: \"Qaijutit\" → \"you came\"? or \"it came\"?\n\n\"it\" → subject?\n\nBut form: \"qaijutit\" → could be third person past?\n\nCompare to \"takujanga\" → saw (you)\n\nSo for \"qaijutit\" → it could be \"it came\" → \"came\"\n\nBut in English: \"you came\" or \"it came\"?\n\n\"Qaijutit\" → possibly \"you came\" or \"it came\"?\n\nBut in sentence 7: \"nanuq qaijuq\" → \"polar bear came\" → so \"qaijuq\" = came (third person)\n\nSo \"qaijut\" → possibly the same → \"came\" (past tense)\n\n\"qaijut\" → missing a suffix?\n\nIn 17: \"Qaijutit\" → likely \"it came\" → \"it came\" in English?\n\nBut with \"it\" as subject → so \"it came\"\n\nWait – if \"qaijuq\" is \"came\", then \"qaijut\" might be a variant.\n\nBut in 17: \"Qaijutit\" → no subject → so might be \"it came\" or \"you came\"?\n\nBut no object.\n\nPossibly: \"it came\"\n\nNow 18: \"Angunahuktimik aarqisijutit\" → the hunter cured someone?\n\n\"angunahuktimik\" = hunter + object suffix → \"a doctor\"? or \"a person\"?\n\n\"aarqisijutit\" = cured (past, third person) → aarqisijuq → cured → aarqisijutit → cured someone?\n\nYes → so \"the hunter cured someone\"\n\nNow go back to 13: \"Amaruup angatkuit takujanga\"\n\n\"Amaruup\" → likely \"the wolf\" (as \"amaruq\" = wolf)\n\n\"angatkuit\" → from sentence 7: \"qaijuq\" = came → so \"angatkuit\" may not be \"came\"\n\nBut in 9: \"angunahuktiup amaruq iputujanga\" → \"hunter speared the wolf\"\n\nSo \"amaruq\" = wolf\n\nSo \"angatkuit\" → not wolf?\n\n\"angatkuq\" → in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\"\n\n\"angatkuq\" → \"shaman\" — so \"angat\" = shaman?\n\nPerhaps \"angat\" = bear?\n\nBut in sentence 7: \"Nanuq qaijuq\" → polar bear came → so \"nanuq\" = polar bear\n\nSo \"angatkuit\" → not bear?\n\nCould be a verb?\n\nPossibility: \"angat\" + \"kuit\" → could be a verb?\n\nCompare to: \"inuuhuktuup\" → \"the boy\" → root \"inuuhuk\" = boy\n\n\"qaijuq\" = came\n\n\"angatkuit\" — perhaps a verb meaning \"came\"?\n\nBut no match.\n\nAnother idea: many verbs have root + -it for past → so \"takujit\" = saw?\n\nBut in sentence 1: \"takujaatit\" → saw you\n\nSo \"takujit\" → saw? → \"takujit\" might be saw\n\nBut \"takujanga\" → not a form we see directly.\n\nIn 13: \"Amaruup angatkuit takujanga\"\n\nPossibility: structure is [subject] [verb] [object]\n\n\"Amaruup\" = wolf (object or subject?)\n\n\"angatkuit\" = verb?\n\n\"takujanga\" = object?\n\nBut \"takujanga\" = saw?\n\nBut \"saw whom\"?\n\nSo if \"angatkuit\" = \"saw\", then \"Amaruup angatkuit takujanga\" = wolf saw [someone]? But \"takujanga\" is the verb?\n\nNo → likely the structure is: subject + verb + object\n\nSo test: \"Amaruup\" = subject → wolf → then \"angatkuit\" = verb → came? → \"angatkuit\" = came?\n\nThen \"takujanga\" = object → saw?\n\nBut \"takujanga\" = saw → so \"wolf came\" and \"saw\"?\n\nNo.\n\nAlternative: \"angatkuit\" = verb, \"takujanga\" = object → wolf saw [someone]\n\nBut \"takujanga\" → saw who?\n\nIn sentence 1: \"Qingmivit takujaatit\" → dog saw you → \"takujaatit\" → saw you\n\nSo verb form is \"takuj\" + suffix → to see → so \"takujanga\" = saw (someone)\n\nSo if \"angatkuit\" is the verb, \"takujanga\" is object → but that would be \"wolf angatkuit saw X\" — not grammatical.\n\nStructure: subject + verb + object\n\nIn 9: \"Angunahuktiup amaruq iputujanga\" → subject (hunter) + object (wolf) + verb (speared)\n\nSo order: subject + object + verb → is that the case?\n\nNo: it's \"Angunahuktiup amaruq iputujanga\" → hunter + wolf + speared → so it's likely: [subject] + [object] + [verb]\n\nThe verb is at the end.\n\nSimilarly, in 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy + doctor + shot → so subject + object + verb\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog + your teacher + hurt\n\nIn 4: \"Iluaqhaijiup aarqijaatit\" → doctor + you → cured → so \"doctor cured you\" → so here, it's subject + verb + object? Not consistent.\n\nBut in 4: \"Iluaqhaijiup\" = doctor (subject), \"aarqijaatit\" = cured you → so verb is at end → verb in complex form\n\nBut in 4, the object \"you\" is not separate — \"aarqijaatit\" = cured you → so the verb has inflection for object.\n\nIn 2: \"qukiqtanga\" = shot → so \"qukiqtanga\" = shot, with object \"doctor\"\n\nSo \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → verb at end → \"qukiqtanga\" = shot\n\nSimilarly, in 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf → \"iputujanga\" = speared\n\nSo all have: [subject] [object] [verb]\n\nThus, structure: Subject + Object + Verb (with verb being past tense of action)\n\nTherefore, in 13: \"Amaruup angatkuit takujanga\"\n\n→ subject = \"Amaruup\" → wolf? or \"a wolf\"?\n\n→ object = \"angatkuit\"? → but that's a verb → not possible\n\n\"angatkuit\" → must be a noun?\n\nBut \"angatkuq\" is in sentence 6 → \"shaman\" → so \"angat\" likely not bear.\n\nPerhaps \"angatkuit\" is the verb?\n\nSo: \"Amaruup\" = subject, \"angatkuit\" = verb, \"takujanga\" = object?\n\nBut \"takujanga\" = saw?\n\nSo \"wolf angatkuit saw someone\" → but no \"someone\"\n\nBut in English: \"the wolf came and saw [someone]\"?\n\nBut only one verb.\n\nMore likely: the verb is \"takujanga\" → saw → and \"angatkuit\" is object?\n\nBut \"angatkuit\" is not a noun.\n\nUnless \"angatkuit\" is a noun. But no other example.\n\nBack: in sentence 7: \"Nanuq qaijuq\" → polar bear came → verb is at end\n\nSo \"qaijuq\" = came\n\nIn 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\n→ \"nanuit\" = polar bear?\n→ \"inuuhukturmik\" = your boy?\n→ \"aanniqsijuq\" = hurt\n\nSo \"the polar bear hurt your boy\"\n\nSimilarly, 15: \"Angunahuktiit aarqijuq\" → the hunter cured someone → \"aarqijuq\" = cured?\n\nYes: in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → aarqijaatit\n\nSo aarq + suffix → cured\n\n\"aarqijuq\" → cured → likely same root\n\nSo 15: \"The hunter cured [someone]\"\n\n16: \"Ilinniaqtitsiji qukiqtait\"\n\n→ ilinniaqtitsiji = your teacher\n→ qukiqtait = shot (past tense)\n\nSo \"your teacher was shot\"\n\n17: \"Qaijutit\" → qaijut → came → past tense → \"it came\" or \"you came\"?\n\nNo subject → likely \"it came\" → \"came\"\n\n18: \"Angunahuktimik aarqisijutit\" → hunter cured → \"aarqisijutit\" = cured → \"the hunter cured someone\"\n\nNow, back to 13: \"Amaruup angatkuit takujanga\"\n\nStructure: subject", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11402.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by analyzing the given Inuktitut sentences and their translations to detect patterns in verb forms and case markers, especially focusing on the agent, patient, and direction of action.\n\nLook at sentence 1: \n1. Qingmivit takujaatit → \"Your dog saw you.\" \n- \"Qingmivit\" = dog (agent), \"takujaatit\" = saw (verb), \"you\" = patient. \n→ \"Qingmivit\" is agent; \"takujaatit\" is active verb with marked patient.\n\nSentence 2: \n2. Inuuhuktuup iluaqhaiji qukiqtanga → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = boy (agent), \"iluaqhaiji\" = doctor (patient), \"qukiqtanga\" = shot. \n→ \"qukiqtanga\" is the verb (to shoot), with patient marked.\n\nSentence 3: \n3. Aanniqtutit → \"You hurt yourself.\" \n- \"aanniqtutit\" = you hurt yourself → reflexive. \n- Subject and object are the same (yourself). \n→ Reflexive verb with subject and object coordinated.\n\nSentence 4: \n4. Iluaqhaijiup aarqijaatit → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = doctor, \"aarqijaatit\" = cured (past), \"you\" = patient. \n→ Verb \"aarqijaatit\" = cured, patient marked.\n\nSentence 5: \n5. Qingmiq iputujait → \"You speared the dog.\" \n- \"iputujait\" = speared, \"Qingmiq\" = the dog (patient). \n→ Subject is \"you\", patient is dog.\n\nSentence 6: \n6. Angatkuq iluaqhaijimik aarqisijuq → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = shaman (agent), \"iluaqhaijimik\" = a doctor (patient), \"aarqisijuq\" = cured. \n→ Verb \"aarqisijuq\" = cured, patient marked.\n\nSentence 7: \n7. Nanuq qaijuq → \"The polar bear came.\" \n→ Simple verb \"qaijuq\" = came. No marked object.\n\nSentence 8: \n8. Iluaqhaijivit inuuhuktuit aarqijanga → \"Your doctor cured your boy.\" \n- \"iluaqhaijivit\" = your doctor (agent), \"inuuhuktuit\" = your boy (patient), \"aarqijanga\" = cured. \n→ Verb \"aarqijanga\" = cured, patient marked.\n\nSentence 9: \n9. Angunahuktiup amaruq iputujanga → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = hunter (agent), \"amaruq\" = wolf (patient), \"iputujanga\" = speared. \n→ Verb \"iputujanga\" = speared, patient marked.\n\nSentence 10: \n10. Qingmiup ilinniaqtitsijiit aanniqtanga → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog (agent), \"ilinniaqtitsijiit\" = your teacher (patient), \"aanniqtanga\" = hurt. \n→ Verb \"aanniqtanga\" = hurt, patient marked.\n\nSentence 11: \n11. Ukiakhaqtutit → \"You fell.\" \n→ Reflexive or self-caused action. Subject is \"you\", no object.\n\nSentence 12: \n12. Angunahukti nanurmik qukiqsijuq → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = hunter, \"nanurmik\" = a polar bear, \"qukiqsijuq\" = shot. \n→ Verb \"qukiqsijuq\" = shot, patient marked.\n\nNow observe the verb forms and their suffixes:\n\nAll verbs end in -it or -anga, and the suffix indicates the verb class or transitivity.\n\nLook at the suffix patterns:\n\n- -vit, -up, -it, -anga → all appear as verb forms with patient or agent marker.\n- The verb root remains consistent: \n - \"takujaat\" = see \n - \"qukiqt\" = shoot \n - \"aarqis\" = cure \n - \"iputuj\" = spear \n - \"aanniqt\" = hurt \n - \"qaijuq\" = come \n - \"angatkuq\" = shaman (noun), \"angunahukti\" = hunter \n\nNow look at inflections:\n\nAll verbs appear to be transitive with a marked object (patient) in the genitive or accusative form.\n\nBut the key pattern is:\n\n- When the patient is marked with a suffix, the verb ends in -it, -anga, -janga, etc., and the patient is expressed in a genitive or accusative form.\n\nLook at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"Qingmiq\" = the dog — patient \n- \"iputujait\" = speared\n\nContrast with sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (agent) \n- \"takujaatit\" = saw you (patient) \n\nHere, \"takujaatit\" = saw + patient (you). \n→ The verb ends in -it, the patient is marked.\n\nSimilarly, in sentence 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you \n\"aarqijaatit\" = cured + patient (you)\n\nSo, verb form = verb root + suffix (-it, -anga, -janga) → indicates transitive verb with patient.\n\nBut when no object is present, like sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" \n→ no patient, verb ends in -q → not a transitive verb.\n\nIn reflexive cases: \nsentence 3: \"Aanniqtutit\" → \"you hurt yourself\" → verb root \"aanniqt\" + -utit → reflexive \nsentence 11: \"Ukiakhaqtutit\" → \"you fell\" → reflexive\n\nSo the verb suffix indicates:\n\n- -utit → reflexive \n- -it → patient marked, transitive \n- -anga → patient marked, transitive (e.g., cured) \n- -janga → patient marked \n- -up → agent (possibly) \n- -vit → agent (e.g., dog) \n\nNow analyze the target sentences.\n\n13. Amaruup angatkuit takujanga \nBreak down: \n- \"Amaruup\" → likely \"a wolf\" (from 9: \"amaruq\" = wolf) → \"Amaruup\" = agent \n- \"angatkuit\" → \"angatkuq\" in 6 → shaman? But \"angatk\" is not clearly a verb. \nActually, \"angatkuit\" — likely verb: \"angatk\" + -uit? But \"angatkuq\" is noun (shaman). \nWait — in 6: \"Angatkuq\" is shaman. \nIn 12: \"Angunahukti\" = hunter \nSo likely \"angatkuit\" is a verb? But no such form. \n\nPossibly a misreading.\n\n\"angatkuit\" — compare with sentence 1: \"takujat\" — verb \"takuj\" = see \n\"angatkuit\" → \"angat\" + \"kuit\"? Possibly derived from a verb.\n\nLook for \"takuj\" form.\n\nIn 1: \"takujaatit\" → saw you \nIn 5: \"iputujait\" → speared \nSo verb is root + suffix: \n- takuj → see \n- iputuj → spear \n- aarqij → cure \n- qaijuq → come \n\nSo \"takuj\" + -a- it? → \"takujaatit\" — \"takuj\" + \"-aati\" → \"saw\" \nSimilarly, \"angatkuit\" → \"angat\" + \"kuit\"? But \"angatkuq\" = shaman — noun.\n\nBut sentence 13: \"Amaruup angatkuit takujanga\" \n→ subject: \"Amaruup\" — \"a wolf\" (wolf) \n→ verb: \"angatkuit\"? \n→ object: \"takujanga\" → \"see\" (takuj) + -anga → verb \"to see\" with patient marked.\n\n\"takujanga\" = saw (patient marked)\n\nSo verb is \"takujanga\" → saw someone\n\nSo \"Amaruup angatkuit takujanga\" → \"The wolf saw [someone]\" — but who?\n\n\"angatkuit\" — if it's a verb, what does it mean?\n\nWait — \"angatkuq\" = shaman — noun \n\"angunahukti\" = hunter — noun \nSo \"angatkuit\" — could be a verb form? \n\nBut in 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear \nSo \"qukiqsijuq\" = shot (verb)\n\nIn 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared the wolf\n\nSo \"iputujanga\" = speared\n\nSo verbs: \n- takuj → see \n- qukiq → shoot \n- iputuj → spear \n- aarqij → cure \n- aanniqt → hurt \n- qaijuq → come \n\nSo \"takujanga\" = saw (patient) — object marked\n\nThen \"angatkuit\" — perhaps a mistake? Or is it a verb?\n\nCompare with sentence 3: \"Aanniqtutit\" → you hurt yourself → reflexive\n\nBut \"angatkuit\" — could it be a variant?\n\nWait — look at sentence 1: \"Qingmivit takujaatit\" → your dog saw you → agent + verb + patient\n\nIn 13: \"Amaruup angatkuit takujanga\"\n\nCould \"angatkuit\" be the patient? But no — \"Amaruup\" is likely the subject.\n\nPossibly misparsed.\n\nAlternative: perhaps \"angatkuit\" = saw → verb?\n\nLike \"takujanga\" = saw, but \"angatkuit\" is a different verb?\n\nBut no such verb.\n\nWait — in sentence 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you\n\n\"iluaqhaijiup\" = doctor (agent)\n\nIn 13: \"Amaruup angatkuit takujanga\"\n\nIf \"angatkuit\" is the verb, and \"takujanga\" is the object?\n\nBut there is no \"takujanga\" in the verb list as agent.\n\nAll verb forms seem to have patient marking.\n\nAnother possibility: \"angatkuit\" = saw — verb \n\"takujanga\" = object — but in what form?\n\nNo, verbs are marked with suffix.\n\nBest analysis:\n\n- All transitive verbs have a patient marked with a suffix indicating direction of action.\n\nSo \"takujanga\" → saw (patient marked)\n\n\"angatkuit\" → perhaps not a verb? But in context, perhaps \"the wolf\" (Amaruup) did something.\n\nCould \"angatkuit\" be a verb meaning \"saw\"?\n\nBut no such form.\n\nAlternatively, compare with sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared the wolf\n\nSo subject (hunter), patient (wolf), verb (spear)\n\nSo sentence 13: Amaruup angatkuit takujanga\n\n→ Subject: Amaruup = wolf \n→ Verb: angatkuit \n→ Object: takujanga → which must be the patient\n\nBut \"takujanga\" = saw — patient\n\nSo: \"the wolf saw [someone]\" → object is \"someone\"\n\nNow, is \"angatkuit\" a verb?\n\nLook at sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor\n\nSo subject (agent), patient (doctor), verb (shot)\n\nSimilarly, sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor\n\nSubject: shaman (Angatkuq) \nPatient: a doctor (iluaqhaijimik) \nVerb: aarqisijuq\n\nSo the verb structure is: [agent] [patient] [verb]\n\nBut when the patient is marked, it's always with a suffix like -it, -anga, -janga.\n\nNow in 13: \"Amaruup angatkuit takujanga\"\n\nPossibly:\n\n- Amaruup → agent (wolf) \n- angatkuit → verb? (but verb form is missing) \n- takujanga → object (saw someone)\n\nBut \"angatkuit\" might be the verb, like \"takujanga\" = saw someone — so \"angatkuit\" must be a verb root.\n\nBut there is no \"angatkuit\" in the given. \"angatkuq\" is noun.\n\nWait — perhaps a typo in transcription.\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy \nSo \"inuuhuktuit\" = your boy (patient)\n\nSo patient is marked.\n\nSimilarly, sentence 9: \"Amaruq\" = wolf → patient\n\nIn 13: \"Amaruup\" → wolf (agent), \"angatkuit\" — verb? → perhaps \"takuj\" = see → verb\n\nBut \"angatkuit\" — if \"angat\" is a root, perhaps it means \"saw\"?\n\nNo match.\n\nAnother idea: in sentence 5: \"Qingmiq iputujait\" → you speared the dog → \"iputujait\" = verb\n\nSo verb root + -ait = transitive verb\n\n- takujaatit = saw you \n- aarqijaatit = cured you \n- iputujait = speared the dog\n\nSo pattern: \nVerb root + -it → verb with patient marking\n\nSo \"takujanga\" → \"takuj\" + \"anga\" → saw → past form with patient\n\nSimilarly, \"aanniqtutit\" → reflexive with -utit\n\nNow in sentence 13: \"Amaruup angatkuit takujanga\"\n\nPossibly:\n- Amaruup = agent (wolf) \n- angatkuit = verb? \nBut \"angatkuq\" is noun (shaman)\n\nPerhaps it's a misreading: \"angatkuit\" should be \"takujanga\" — but no.\n\nAlternative: \"angatkuit\" = \"saw\" (verb), \"takujanga\" = object?\n\nBut \"takujanga\" = saw → verb?\n\nNo.\n\nPerhaps \"takujanga\" is the patient.\n\nSo: \"the wolf saw [someone]\" → \"someone\" = takujanga? But \"takujanga\" is a verb form.\n\nThis is inconsistent.\n\nUnless \"takujanga\" is a noun? But it's not.\n\nAnother clue: sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"iluaqhaijimik\" = a doctor\n\nIn sentence 13: \"Amaruup angatkuit takujanga\" → perhaps \"takujanga\" = a person who was seen?\n\nBut no such noun.\n\nAlternatively, perhaps \"angatkuit\" is a noun, and \"takujanga\" is verb?\n\nBut \"takujanga\" is clearly a verb (from others).\n\nCheck if \"takujanga\" appears elsewhere.\n\nIn sentence 1: \"takujaatit\" → saw you → verb\n\nNo other \"takujanga\"\n\nSo concluded: \"takujanga\" must be a verb meaning \"saw\" with patient marked.\n\nThen \"angatkuit\" — if \"angat\" is a root, perhaps the verb \"to see\" in a different form?\n\nBut no.\n\nWait — in sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared the wolf\n\nSo agent (hunter), patient (wolf), verb (spear)\n\nSo in sentence 13: Amaruup (wolf) — agent, verb, patient\n\nSo must be: wolf [verb] [patient]\n\nSo verb = angatkuit? But \"angatkuit\" might be a typo for \"takujanga\"?\n\nBut sentence 1 has \"takujat\" with \"takujaatit\"\n\nNo.\n\nPerhaps \"angatkuit\" = \"saw\" — verb\n\nThen: \"the wolf saw [someone]\"\n\nBut who? The patient is \"takujanga\"? But \"takujanga\" is a verb.\n\nUnless \"takujanga\" is a noun — not found.\n\nAnother possibility: in sentence 3: \"Aanniqtutit\" → you hurt yourself\n\nIn sentence 11: \"Ukiakhaqtutit\" → you fell\n\nSo reflexive verbs end in -utit\n\nSomething like \"takujanga\" — does it have -it?\n\nYes: -anga is a patient-marked verb.\n\nCompare with \"aarqisijuq\" — verb with patient marked.\n\nSo \"takujanga\" = saw someone\n\nSo \"Amaruup angatkuit takujanga\" → wolf sees someone?\n\n\"angatkuit\" must be a verb.\n\nBut no verb with root \"angat\".\n\nHowever, in sentence 12: \"Angunahukti nanurmik qukiqsijuq\" — hunter shot a polar bear\n\n\"qukiqsijuq\" = shot\n\n\"angunahukti\" = hunter\n\nPresent tense?\n\nAll verbs in these sentences are past tense.\n\nSo \"angatkuit\" may be a verb form meaning \"saw\" — derived from \"angat\"?\n\nBut not found.\n\nPerhaps \"angatkuit\" is the object.\n\nBut \"Amaruup\" is before it — likely subject.\n\nOnly possible if \"Amaruup\" is object.\n\nBut \"Amaruup\" is a noun — likely subject.\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12081.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "unit_audit", + "sample_index": 3, + "output": "Start by analyzing the given Inuktitut sentences and their English translations to identify patterns in verb morphology, object marking, and possession or reference.\n\nFirst, note that many verbs are marked with suffixes indicating:\n- Agent (subject)\n- Patient (object)\n- Reciprocity or reflexivity\n- Possession (e.g., \"your\", \"your doctor\")\n- Tense or aspect (e.g., -it = past; -up = present; -mik = possessor)\n\nLook at sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n→ \"Qingmivit\" (your dog saw) + \"takujanga\" (you) → \"takujatit\" is likely \"saw\" (verb) + \"it\" = past tense. \n\"Qingmivit\" = \"your dog saw\" → stem \"qingmi\" + \"v\" (indicating possession and verb) + \"it\" (past). \n\"Qingmivit\" = your dog saw → verb \"takuj\" (see) + \"it\" (past) → \"takujatit\"\n\nSimilarly, sentence 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"Qingmiq\" (you) + \"iputujait\" (speared the dog) → \"iputuj\" = \"to spear\", \"ait\" = past tense, object unmarked. \nSo \"iputuj\" = spear, \"ait\" = past, object implied.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n→ \"Inuuhuktuup\" = the boy shot? \"Inuuhuk\" = boy, \"tuup\" = past tense. \n\"iluaqhaiji\" = the doctor → noun phrase. \n\"qukiqtanga\" → \"shot\" (\"qukiqt\" = shoot, \"anga\" = past). \n\nSo we see:\n- Agent: first element (subject)\n- Object: second noun phrase\n- Verb: third component (past tense of action)\n\nAlso note that:\n- \"aanniqtanga\" = \"you hurt yourself\" → reflexive\n- \"iluaqhaijiup\" → \"the doctor\" (noun) + \"up\" → present? → but \"iluaqhaijiup aarqijaatit\" = \"the doctor cured you\" → \"aarqijaatit\" = cured (past)\n\nPattern: verbs with prefix or suffix indicate:\n- Agent: noun (subject) + verbal stem\n- Object: noun phrase, marked by a suffix or context\n- Tense: often -it, -anga, -up, -mik\n\nKey pattern:\nWhen the verb has a suffix indicating object (e.g., -ji, -mik), it may indicate direction or target.\n\nNow, analyze each sentence:\n\n1. Qingmivit takujaatit → your dog saw you → \"takuj\" = see, \"atit\" = past, saw you\n2. Inuuhuktuup iluaqhaiji qukiqtanga → boy shot doctor → \"qukiqt\" = shoot, \"anga\" = past\n3. Aanniqtutit → you hurt yourself → \"aanniqt\" = hurt, \"utit\" = past, self-object\n4. Iluaqhaijiup aarqijaatit → doctor cured you → \"aarqijaatit\" = cured (past)\n5. Qingmiq iputujait → you speared the dog → \"iputuj\" = spear, \"ait\" = past\n6. Angatkuq iluaqhaijimik aarqisijuq → shaman cured a doctor → \"aarqisijuq\" = cured (past), \"iluaqhaijimik\" = a doctor (possessive: -mik)\n7. Nanuq qaijuq → polar bear came → \"qaij\" = come, \"uq\" = past?\n8. Iluaqhaijivit inuuhuktuit aarqijanga → your doctor cured your boy → \"aarqijanga\" = cured (past), \"inuuhuktuit\" = your boy (object)\n9. Angunahuktiup amaruq iputujanga → hunter speared the wolf → \"iputujanga\" = speared (past)\n10. Qingmiup ilinniaqtitsijiit aanniqtanga → dog hurt your teacher → \"aanniqtanga\" = hurt (past), object \"ilinniaqtitsijiit\" = \"your teacher\"\n11. Ukiakhaqtutit → you fell → \"ukiak\" = fall, \"qtutit\" = past\n12. Angunahukti nanurmik qukiqsijuq → hunter shot a polar bear → \"qukiqsijuq\" = shot (past), \"nanurmik\" = a polar bear\n\nNow, the pattern in the verb forms:\n- Base verb stem + tense suffix (-it, -anga, -up)\n- Possessive suffix: -mik (possessive), -up (present), -it (past)\n- Reflexive: -self (e.g., aanniqtanga)\n\nObserve that:\n- \"Aanniqt\" = hurt (base)\n- \"Takuj\" = see\n- \"Iputuj\" = spear\n- \"Qukiqt\" = shoot\n- \"Aarqij\" = cure\n\nTense:\n- -it: past\n- -up: present\n- -anga: past\n- -mik: possession\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga \n→ \"Amaruup\" = the wolf? \"Amaru\" = wolf → \"up\" = present tense? \n→ \"angatkuit\" = past of \"angatkuq\"? \"angatkuq\" = polar bear came → \"angatkuit\" = came? \n→ \"takujanga\" = saw? → \"takuj\" + \"anga\" = past of \"see\" \nSo: \"Amaruup\" = the wolf (subject) \n\"angatkuit\" = came? \n\"takujanga\" = saw\n\nBut \"angatkuit\" → likely \"angatkuq\" = polar bear came → so \"angatkuit\" = came (past)\n\nSo \"the wolf came and saw...\" → but structure suggests \"wolf came and saw...\"\n\nBut all verbs are in past form. \n\"angatkuit\" = came → past \n\"takujanga\" → saw → past \nSo: the wolf came and saw?\n\nBut what did it see? No object → but possible that it saw someone.\n\nBut in the original, \"takua\" = see, \"anga\" = past → but no object.\n\nCompare to sentence 1: \"Qingmivit takujaatit\" → your dog saw you → object \"you\"\n\nHere, \"takujanga\" → no object → so maybe \"the wolf came and saw\" (what?) → incomplete?\n\nBut no object → so perhaps just \"the wolf came and saw\".\n\nBut is there a reflexive or self?\n\nNo. So it's a simple past with two verbs.\n\nStructure: Agent + verb1 + verb2 (in sequence, both past)\n\nLikely: \"The wolf came and saw.\"\n\nSo 13 → The wolf came and saw.\n\n14. Nanuit inuuhukturmik aanniqsijuq \n\"nanuit\" = the boy? \"Nanu\" = boy → \"uit\" = past? \n\"inuuhukturmik\" = a boy? → \"inuuhuk\" = boy → \"turmik\" = possessor? → \"turmik\" = possessed by someone? \n\n\"inuuhuk\" is boy. \"turmik\" = has? → \"inuuhukturmik\" = the boy has? → or \"the boy\" with -mik?\n\nBut \"inuuhuktuit\" = your boy → \"uit\" = past? \n\nWait: sentence 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"inuuhuktuit\" = your boy\n\nSo \"inuuhuktuit\" = your boy (possessive)\n\n\"inuuhukturmik\" → \"turmik\" = possessive? → \"inuuhukturmik\" = the boy's? → \"mik\" = of? → \"inuuhuk\" = boy → \"turmik\" = the boy’s? → so \"a boy\" with possessive?\n\nBut this is \"inuuhukturmik\" as object of \"aanniqsijuq\"\n\n\"aanniqsijuq\" = hurt → base \"aanniqt\" = hurt, \"sijuq\" = past?\n\nCompare to sentence 3: \"Aanniqtutit\" → you hurt yourself → \"utit\" = past\n\n\"aanniqsijuq\" → hurt (past)\n\nSo \"Nanuit\" = the boy (subject, past tense? \"uit\" = past) \n\"inuuhukturmik\" = the boy's? → or \"a boy\" → but \"inuuhuk\" = boy → \"turmik\" = possessive → object of \"hurt\"\n\nBut \"aanniqsijuq\" = hurt → so \"the boy hurt the boy’s?\"\n\nThat would be reflexive with possessive.\n\nBut better: \"the boy hurt the boy's [something]\"\n\nWait — \"aanniqsijuq\" = hurt → but in sentence 10, \"ilinniaqtitsijiit\" = your teacher → so possessive objects exist.\n\nBut \"inuuhukturmik\" = \"the boy's\" → so \"the boy hurt the boy’s [who?]\"\n\nNo object → meaning incomplete?\n\nWait — compare to sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher\n\nSo \"ilinniaqtitsijiit\" = your teacher (with \"siji\" → possessive? or marking?)\n\n\"inuuhukturmik\" → base \"inuuhuk\" = boy → \"turmik\" = of → so \"the boy’s\" → but missing something\n\nPossibility: \"Nanuit\" = the boy (subject) \n\"inuuhukturmik\" = the boy’s (object) → but object of what?\n\n\"aanniqsijuq\" = hurt\n\nSo \"the boy hurt the boy’s [what]?\" → no\n\nBut look at sentence 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\nIs it possible \"inuuhukturmik\" is possessive for one of the noun phrases?\n\nAnother idea: perhaps \"inuuhukturmik\" = \"your boy\" (but \"turmik\" is not \"your\", it is \"his\")\n\n\"turmik\" = possessive of the agent → \"the boy’s\"\n\nBut no object to hurt → so likely a typo or misreading.\n\nWait — \"aanniqsijuq\" → \"aanniqt\" = hurt, \"sijuq\" = past → so \"hurt\"\n\n\"inuuhukturmik\" → \"inuuhuk\" = boy → \"turmik\" = his → the boy’s?\n\nBut what is the object? Missing?\n\nWait — is it possible that \"inuuhukturmik\" is the object of \"aanniqsijuq\"?\n\nBut in sentence 3: \"Aanniqtutit\" = you hurt yourself → reflexive.\n\nSo \"inuuhukturmik\" → \"the boy\" → but marked as his?\n\nBut no object.\n\nAlternative: perhaps \"turmik\" is a possessive suffix on a noun, but here it’s on the verb?\n\nNo — structure is: [subject] + [object] + [verb]\n\nSo likely:\n- subject: nanuit → the boy\n- object: inuuhukturmik → the boy's [something] → but what?\n- verb: aanniqsijuq → hurt\n\nSo incomplete.\n\nBut in sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher → \"ilinniaqtitsijiit\" = your teacher → possessive\n\nSo \"inuuhukturmik\" → may be \"the boy’s\" → but missing the possessor?\n\nUnless \"inuuhukturmik\" = \"the boy\" (with possessive) and we interpret as \"the boy hurt himself\" → but \"turmik\" is not reflexive.\n\nReflexive is implied only when \"self\" is marked — like in \"aanniqtanga\"\n\nNo such marking here.\n\nBut \"inuuhukturmik\" → if it's the boy’s, then \"the boy hurt the boy’s [something]\" → but no something.\n\nWait — perhaps \"inuuhukturmik\" is a misanalysis.\n\n\"turmik\" → standard Inuktitut possessive suffix.\n\n\"inuuhuk\" → boy → \"inuuhukturmik\" → the boy's\n\nBut object of hurt must be a person or thing.\n\nNo object in original (only two nouns). So perhaps it's \"the boy hurt his own\" → but not marked.\n\nAlternatively, maybe the verb is \"hurt\" and the object is \"the boy’s\" → so \"the boy hurt the boy’s teacher\"? But no teacher.\n\nWait — another idea: perhaps \"inuuhukturmik\" is a possessive for a noun not present.\n\nBut the sentence has only three components.\n\nPerhaps a mistake in analysis.\n\nCheck sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy (subject) shot doctor (object)\n\nSo subject + object + verb\n\nSimilarly, sentence 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object is \"you\" → but not marked with -mik\n\n\"up\" = present? → \"aariqijaatit\" = cured (past)\n\nSo likely: subject + object (noun) + verb (past)\n\nIn 14: \"Nanuit inuuhukturmik aanniqsijuq\"\n\nSo:\n- Nanuit = the boy (subject)\n- inuuhukturmik = the boy's (object) → what? → not specified\n- aanniqsijuq = hurt\n\nSo \"the boy hurt the boy's [what]?\"\n\nBut no — it may be that \"inuuhukturmik\" = the boy's (reflexive or self), but not supported.\n\nAlternative: perhaps \"inuuhukturmik\" is \"your boy\" — but \"turmik\" is not \"your\"\n\n\"your\" is \"inuuhuk\" + \"uit\" — as in \"inuuhuktuit\" → your boy\n\n\"turmik\" → his\n\nNo.\n\nPossibility: typo — \"inuuhukturmik\" should be \"inuuhuktuit\" → your boy?\n\nBut \"turmik\" vs \"uit\" — different.\n\nAnother possibility: \"aanniqsijuq\" = \"hurt (himself)\" → but no self-marking.\n\nOnly reflexive in sentence 3: \"aanniqtutit\" → you hurt yourself → \"utit\" = past, self-object.\n\nNo other reflexive.\n\nSo in 14, it may be \"the boy hurt himself\" — but no marking.\n\nBut perhaps \"inuuhukturmik\" is a noun phrase where \"mik\" marks possession, and the possessor is missing.\n\nNo.\n\nBack to pattern: many verbs are built from:\n- Stem + (object suffix) + (tense)\n\nBut here, object is \"inuuhukturmik\" — a boy’s something.\n\nWe may have to accept that \"the boy hurt the boy’s [object]\" — but no object.\n\nWait — perhaps the object is implied — or the word is \"inuuhuk\" = boy → so \"the boy hurt himself\"? But \"turmik\" is not \"self\".\n\n\"self\" is not indicated.\n\nBut in sentence 10: \"ilinniaqtitsijiit\" = your teacher → resolved.\n\nAll object nouns are marked with suffixes.\n\nSo likely, the object is \"the boy’s (someone)\" — but missing.\n\nUnless \"inuuhukturmik\" is a mistake.\n\nBut let's try another sentence.\n\n15. Angunahuktiit aarqijuq \n\"Angunahuktiit\" = the hunter came? \"Angunahuk\" = hunter → \"tiit\" = past? \n\"aarqijuq\" = cured (past) — \"aarqij\" = cure, \"uq\" = past \nSo: \"the hunter came and cured\"? \nBut structure: agent + verb \n\"aarqijuq\" = cured → so \"the hunter came and cured\" → but what?\n\n\"Angunahuktiit\" = hunter came (past) \n\"aarqijuq\" = cured (past) → no object → so \"the hunter came and cured [someone]? – missing object\n\nBut no object — so likely \"the hunter came and cured\" — but what?\n\nBut in sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared the wolf → subject + object + verb\n\nSo in 15, object missing → so probably not.\n\nContrast with 18: \"Angunahuktimik aarqisijutit\" → hunter + object + verb\n\nSo in 15: \"Angunahuktiit aarqijuq\" → hunter came (past) + cured (past)\n\nNo object → so \"the hunter came and cured\" → but without object?\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object marked with -mik\n\nSo missing object? But here \"aarqijuq\" — no marking → so object not specified.\n\nBut \"aarqijuq\" alone → cured? → so \"the hunter came and cured\" — but who?\n\nLikely, meaning: the hunter came and cured (someone) — but not specified.\n\nBut in context, perhaps the object is implied from previous or general.\n\nBut in 16: \"Ilinniaqtitsiji qukiqtait\" \n\"Ilinniaqtitsiji\" = your teacher? → \"ilinniaqtitsiji\" = your teacher (with -siji?) \n\"qukiqtait\" = shot (past) — \"qukiqt\" = shoot, \"ait\" = past \nSo: \"your", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11976.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "We are given two linguistic systems: Nahuatl and Arammba, with various equations showing how numbers and operations are formed. Our task is to **write out in Nahuatl: 42; 494**.\n\nWe need to infer the pattern of number formation in Nahuatl from the given equations, especially focusing on how numbers like 42 and 494 are represented.\n\n---\n\nStep 1: Identify the components.\n\nIn the equations, we find:\n\n- \"mahtlactli\" appears in several expressions; likely represents a basic unit (possibly 1).\n- \"pöhualli\" and \"caxtölli\" appear frequently — may represent cycles or units of time.\n- \"öme\" appears in combinations; may represent a unit (e.g., 7 or 14).\n- \"cë\" may be a suffix or marker.\n- \"mäcuïl\" and \"mäcuïlli\" — possibly 20 or 120.\n- \"cem\" — may be 1 or a composite.\n\nLook at (2): \ncems-pöhualli × öme = öm-pöhualli \n→ This resembles a multiplication: possibly cem = 1, öme = 7, and pöhualli = 20, since 1×7 = 7, and 7 = öm.\n\nBut in (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Suggests addition of two units involving pöhualli and chicöme.\n\nBut equation (4): \nmäcuïlli + öme = chicöme \n→ Suggests a sum: if mäcuïlli is 20, then 20 + 7 = 27 → chicöme = 27.\n\nBut wait: is mäcuïlli = 20? Possibly — known in Nahuatl that 20 is a base unit.\n\nAlso, (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (X × X) = mäcuïl-pöhualli-om-X \nIf mahtlactli = 1, then 1×1 = 1 → but the right side is mäcuïl-pöhualli-om-1 → would be 20×20 = 400 plus 1? Seems off.\n\nBut mäcuïl-pöhualli might be 20×20 = 400.\n\nSo perhaps mahtlactli = 1 → 1×1 = 1 → doesn’t work.\n\nBut equation (1): (mahtlactli-on-cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nIf mahtlactli-on-cë = x, then x × 1 = result.\n\nRight side: mäcuïl-pöhualli-om-mahtlactli → could be 20×20 + 1 = 401? Unlikely.\n\nAlternative idea: \"mahtlactli-on-cë\" is 1 + something.\n\nBut let's look at equation (6): \nmäcuïlli × ëyi = caxtölli \n→ If mäcuïlli = 20, then 20×ëyi = caxtölli.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (1 + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ Which would be (1 + x)×x = x² + x\n\nLeft side: (1 + x) × x = x² + x \nRight side: cem-pöhualli-on-caxtölli-on-nähui\n\ncaxtölli = 20x from (6)\n\nSo suppose x = ëyi → then x² + x = cem-pöhualli-on-caxtölli-on-nähui\n\nBut if x is 7, 7×7 = 49, 7×8 = 56 → already in ranges.\n\nBut back to the core: we need to express 42 and 494.\n\nCheck if there’s a clear numeric pattern.\n\nTry equation (2): \ncem-pöhualli × öme = öm-pöhualli \nNow, cem-pöhualli: if cem = 1, pöhualli = 20 → 1×20 = 20 \nöme × 20 = öm-pöhualli → öme × 20 = 20 → so öme = 1 → contradiction.\n\nAlternatively: perhaps cem-pöhualli is a compound number.\n\nTry interpreting \"pöhualli\" as 20.\n\nCommon in Nahuatl: base units: 1, 20, 120 (20×6), etc.\n\nEquation (4): mäcuïlli + öme = chicöme \nIf mäcuïlli = 20, and öme = 7 → chicöme = 27.\n\nEquation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Adds two terms: one involving pöhualli and chicöme, one involving nähui.\n\nBut we might not need all.\n\nNow look at equation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe’ll come back to this.\n\nEquation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n→ This is forming a compound number.\n\nBut we don’t have \"ndamno\" in the list, so perhaps \"ndamno\" is a known number.\n\nWe need to relate 42 and 494 to Nahuatl expressions.\n\nFirst: What is 42?\n\nIn base 20: 42 = 2×20 + 2 → 2·20 + 2\n\nIn Nahuatl, numbers are often composed of multiples of 20 and a remainder.\n\nSimilarly, 494: 494 ÷ 20 = 24.7 → 24×20 = 480 → remainder 14 → so 24×20 + 14.\n\nNow, is there a multiplication pattern?\n\nEquation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n→ (1 + ëyi) × ëyi = result\n\n→ ëyi² + ëyi\n\nSo if ëyi = 6, then 6² + 6 = 36 + 6 = 42 → ah! 42.\n\nSo this suggests: 42 = (1 + 6) × 6\n\nSo if cem-pöhualli-on-caxtölli-on-nähui represents this product, then for ëyi = 6, it gives 42.\n\nNow, in equation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe know from (6): mäcuïlli × ëyi = caxtölli → 20×ëyi = caxtölli → so caxtölli = 20×ëyi\n\nSo the product result is: cem-pöhualli-on-caxtölli-on-nähui = cem-pöhualli-on-(20×ëyi)-on-nähui\n\nBut from (5), it's (1 + ëyi) × ëyi → which is ëyi² + ëyi\n\nFor ëyi = 6 → 36 + 6 = 42\n\nSo the Nahuatl form of 42 is: cem-pöhualli-on-caxtölli-on-nähui, with ëyi = 6.\n\nBut what is the value of ëyi? We need to find the unit.\n\nNow, in (4): mäcuïlli + öme = chicöme → 20 + öme = chicöme\n\nSuppose öme = 7 → chicöme = 27\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli\n\nIf pöhualli = 20 → 1×20 = 20 → so 20×öme = öm-pöhualli → 20×7 = 140 → 140 = ? → but 140 = 7×20 = 70? No.\n\nWait — equation (2): cem-pöhualli × öme = öm-pöhualli \nIf cem-pöhualli = 1×20 = 20 → 20 × öme = öm-pöhualli\n\nIf öme = 7, then 20×7 = 140 → öm-pöhualli → but öm-pöhualli = 7×20 = 140\n\nSo this is consistent: right side is öm-pöhualli → 7×20 = 140 → so öme = 7\n\nSo öme = 7\n\nSimilarly, in (4): mäcuïlli = 20 → 20 + 7 = 27 = chicöme\n\nNow, in equation (5): (1 + ëyi) × ëyi = 42 → ëyi = 6\n\nSo we can set ëyi = 6\n\nThen, from (6): mäcuïlli × ëyi = caxtölli → 20 × 6 = 120 → caxtölli = 120\n\nAnd (5) gives: (1 + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSo when ëyi = 6 → 42 = cem-pöhualli-on-120-on-nähui\n\nSo the Nahuatl form of 42 is:\n\ncem-pöhualli-on-caxtölli-on-nähui\n\nwith caxtölli = 120\n\nBut this expression appears exactly in equation (5) — it's the result of the multiplication.\n\nSo **42 = cem-pöhualli-on-caxtölli-on-nähui**, where caxtölli = 120, which corresponds to 20×6.\n\nSo we write 42 as: **cem-pöhualli-on-caxtölli-on-nähui**\n\nBut in the system, \"caxtölli\" is 20×ëyi, and \"nähui\" is a unit.\n\nWait — does \"on\" mean \"plus\"? Possibly.\n\nWe must confirm if this form is standard.\n\nNow, what about 494?\n\nTry to express 494.\n\n494 ÷ 20 = 24.7 → 24×20 = 480 → remainder 14\n\nSo 494 = 24×20 + 14\n\nNow, in Nahuatl, such numbers are formed by adding multiples of 20 and units.\n\nNow, is 24×20 + 14 present?\n\nWe have equations that show multiplication and addition.\n\nLook at equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nAssume mahtlactli = 1\n\nThen left: (1-on-cë) × 1 = 1-on-cë\n\nRight: mäcuïl-pöhualli-om-1\n\nmäcuïl-pöhualli = 20×20 = 400\n\nSo 400 + 1 → 401\n\nSo (1 + x) × 1 = 1 + x → not matching.\n\nBut earlier (5) with ëyi = 6 gives 42 → so perhaps a general multiplication pattern.\n\nAlternatively, can we build 494 as sum?\n\n494 = 400 + 94\n\n400 = 20×20 → mäcuïl-pöhualli = 400\n\nSo 400 + 94\n\nNow, 94 = 4×20 + 14 → 4×20 = 80 + 14 = 94\n\nSo 94 = mäcuïlli×4 + öme×? → öme = 7\n\nSo 4×20 + 14 = 4×20 + 2×7\n\nSo 494 = 20×20 + 4×20 + 2×7 = (24×20) + 14\n\nSo 494 = mäcuïl-pöhualli + (4×mäcuïlli) + (2×öme)\n\nBut do we have additive forms?\n\nLook at (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\npöhualli = 20 → yë-pöhualli-on-chicöme → seems like “yë” + 20×chicöme?\n\nBut (4): mäcuïlli + öme = chicöme → 20 + 7 = 27 → so chicöme = 27\n\nSo \"on\" may be a combining element.\n\nBut in (3), left side: yë-pöhualli-on-chicöme → might be a compound like \"yë\" (a number) plus a \"unit on something\"\n\nAlternatively, in the absence of a direct additive format, maybe 494 is built from known components.\n\nAnother idea: look at equations (13) and (14) to find established forms.\n\n(13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n(14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nBut we don’t have values of these.\n\nHowever, in (2) and (4), we have:\n\n- öme = 7\n- mäcuïlli = 20\n- pöhualli = 20\n\nNow, from (5): (1 + ëyi) × ëyi = 42 → ëyi = 6 → so 6×6 + 6 = 42\n\n→ So 42 = (1 + 6) × 6 → in Nahuatl: cem-pöhualli-on-caxtölli-on-nähui with caxtölli = 120\n\nSo 42 = cem-pöhualli-on-caxtölli-on-nähui\n\nNow, for 494 → try to build from known base numbers.\n\n494 = 400 + 94\n\n400 = 20×20 = mäcuïl-pöhualli\n\n94 = 4×20 + 14 = 4×mäcuïlli + 2×öme (since 14 = 2×7)\n\nSo 494 = mäcuïl-pöhualli + 4×mäcuïlli + 2×öme\n\nBut do we have a way to combine?\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui → this is addition of two terms.\n\nCould this be the form?\n\nFor example, if we take:\n\n- First term: yë-pöhualli-on-chicöme\n- Second term: mahtlactli-on-nähui\n\nBut we need to define yë.\n\nBut in (4): mäcuïlli + öme = chicöme → so chicöme is defined as 20 + 7 = 27\n\nSo is there a way to build 4×20 + 2×7?\n\nWe don’t have a multiplication unit in addition.\n\nBut equation (16): cen-xiquipilli = weremeke tarumba nimbo yànparo — not helpful.\n\nAnother idea: is there a pattern that 494 = (something) × something?\n\nWe can consider a pre-existing known number.\n\nBut in the absence of a direct pattern, we go with additive construction.\n\nBut note: in equation (5), we have only one multiplicative form.\n\nPerhaps 494 is formed using the standard pattern.\n\nAlternatively, try: 494 = 24×20 + 14 = (24)×20 + (14)\n\n24 can be formed as (1+6)× something? Not directly.\n\nBut we know 6×6 + 6 = 42 → so 6 is a number.\n\nNow, 24 = 6×4 → but no chain.\n\nBut logically, for 494, if we have to write it in Nahuatl using the same components, we must use known forms.\n\nSo: 494 = 20×24 + 14 = 20×(20+4) + 14 → not helpful.\n\nBut 20×24 = 480 → 14 remains.\n\nSo 494 = mäcuïl-pöhualli + (4 × mäcuïlli) + (2 × öme)\n\nCan this be written in a compound form?\n\nIn equation (3), we have addition: A + B =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9465.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to deduce how numbers are formed in Nahuatl, specifically to write out **42** and **494**.\n\nWe need to figure out a pattern based on the operations and derived forms.\n\n---\n\nFirst, examine the Nahuatl equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nAlso, we have direct mappings:\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo \n\nNote that the Arammba system provides some known values and operations, and the equations may reflect structural parallels.\n\nLet’s first identify key components and patterns.\n\nFrom (1): \nmahtlactli-on-cë × mahtlactli → mäcuïl-pöhualli-om-mahtlactli\n\nThis looks like multiplication involving a compound and something like \"mahtlactli\".\n\nNote: \"mahtlactli\" may mean \"10\", as in Mesoamerican base-20 systems.\n\n\"pöhualli\" is likely a \"day count\" or \"cycle\", and \"cë\" might be a unit. \"cë\" may be \"1\" or \"unit\".\n\nLet’s look for base-20 patterns.\n\nAssume:\n\n- mahtlactli = 20 \n- pöhualli = 1 day (unit of time) \n- cem = 1 (small unit) \n- öme = 1? \n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × 1 = öm-pöhualli \nSo likely, cem is 1, öme is 1, and multiplication by 1 leaves unchanged.\n\nFrom (4): mäcuïlli + öme = chicöme \nSo mäcuïlli + 1 = chicöme → suggests mäcuïlli = chicöme - 1 \n\n(6): mäcuïlli × ëyi = caxtölli \n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\nTry to interpret:\n\nLet’s suppose:\n\n- mahtlactli = 20 \n- ëyi = 1 → then mahtlactli × 1 = 20 \nBut in (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\nIf ëyi = 1, then mahtlactli-om-1 × 1 → likely a compound meaning 20. \n\nBut product is cem-pöhualli-on-caxtölli-on-nähui → long form.\n\nNow look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nNote: in (5), the product has caxtölli-on-nähui — similar to caxtölli-on-nähui in (13).\n\nFrom (6): mäcuïlli × ëyi = caxtölli → suggests caxtölli = mäcuïlli × ëyi\n\nFrom (4): mäcuïlli + öme = chicöme → so if öme = 1, then mäcuïlli = chicöme - 1 \n\nNow, in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\n\"ndamno\" appears as a value here.\n\nBut in (15): cen-tzontli = tarumba tambaroy fete asàr \n\nIn Arammba, (8): ngámbi + asàr = tambaroy \n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nNow (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n\nTàxwo may mean \"times\" or \"multiplied by\".\n\nAlso, (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ suggests some distributive or cancellation.\n\n(11): nimbo × fete = tarumba → so nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nThis looks like addition and multiplication.\n\nNow, in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\n(15): cen-tzontli = tarumba tambaroy fete asàr \n\nSo cen-tzontli appears in two forms.\n\nIn (14): cen-tzontli-on-something = yànparo tarumba \nIn (15): cen-tzontli = tarumba tambaroy fete asàr \n\nIt's likely that cen-tzontli is a number, and adding a compound gives a different value.\n\nCompare units:\n\nIn Arammba:\n- ngámbi + ngámbi = ngámbi × yànparo → so ngámbi + ngámbi = ngámbi × yànparo \n→ This suggests: 2 × ngámbi = ngámbi × yànparo → implies yànparo = 2 \n\nSo: yànparo = 2 \n\nThen from (8): ngámbi + asàr = tambaroy \n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nBut also (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ So (yenówe) × (yenówe tàxwo) = (fete) × (yenówe tàxwo) → implies yenówe = fete \n\nSo fete = yenówe \n\nThen (10): yenówe × yenówe tàxwo = yenówe × yenówe tàxwo → consistent.\n\nNow (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba \n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nWe already have yànparo = 2 \n\nSo (12): nimbo + 2 = yenówe tàxwo \n\nBut fete = yenówe, so yenówe tàxwo = yenówe × (tès) → maybe \"tès\" is 1, or \"tæ\" = 1 \n\nSo yenówe tàxwo = yànparo × yànparo? No.\n\nAlternatively, maybe \"tàxwo\" means multiplication.\n\nSo \"A + B tàxwo\" = A + (B × ...) \n\nBut (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (yànparo × something) + (fete × something else) = yànparo fete \n\nIf we suppose multiplication is \"×\", and \"tæ\" or \"tàxwo\" is just a modifier, then:\n\n(9): yànparo × x + fete × y = yànparo × fete → only holds if x=1 and y=1 → so multiplication is associative and distributive?\n\nBut later in (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → so (yenówe) × (yenówe) = fete × (yenówe) → implies yenówe = fete \n\nSo fete = yenówe \n\nThen from (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba \n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nIf \"tàxwo\" means \"×\", then:\n\nnimbo + 2 = yenówe × (yenówe) = (fete) × (fete) = fete² → since fete = yenówe \n\nSo nimbo + 2 = fete² \n\nBut from (11): tarumba = nimbo × fete \n\nSo we now have two expressions:\n\n- nimbo + 2 = fete² \n- tarumba = nimbo × fete \n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr \n\nBut from (8): ngámbi + asàr = tambaroy → can we assign values?\n\nWait — in Arammba, we deduced yànparo = 2 \n\nWe can now assign:\n\n- yànparo = 2 \n- fete = yenówe \n- nimbo + 2 = fete² \n\nBut we need to link to the Nahuatl side.\n\nNow look at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nFrom (6): mäcuïlli × ëyi = caxtölli → so caxtölli is a product of two units \n\nFrom (4): mäcuïlli + öme = chicöme → suggesting mäcuïlli is not a unit but a count \n\nFrom (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\nSuppose that:\n\n- mahtlactli = 20 \n- ëyi = 1 \n\nThen left side: 20 (20) × 1 = 20 \nProduct is cem-pöhualli-on-caxtölli-on-nähui \n\nSo 20 → cem-pöhualli-on-caxtölli-on-nähui \n\nMeanwhile, in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nThe structure is similar: yë-tzontli-on-... on-caxtölli-on-cë \n\nSo perhaps this represents 1 × (something involving caxtölli) = ndamno \n\nAnd in (5) we have a product with caxtölli-on-nähui → so caxtölli may be a component of multiplication.\n\nBut the key is in (15): cen-tzontli = tarumba tambaroy fete asàr \n\nWe know from Arammba:\n\n- tarumba = nimbo × fete \n- tambaroy = ngámbi + asàr \n- fete = yenówe \n- yànparo = 2 \n- nimbo + 2 = fete² \n\nWe can solve this system.\n\nSet fete = x \nThen nimbo + 2 = x² → nimbo = x² - 2 \ntarumba = nimbo × x = (x² - 2)x = x³ - 2x \n\nNow, in (15): cen-tzontli = tarumba tambaroy fete asàr \n\nBut what does this mean? Is it sum? Product?\n\nThe structure suggests that \"A B C D\" may mean A + B + C + D — but listed as a compound.\n\nIn (14): cen-tzontli-on-... = yànparo tarumba \n\nSo cen-tzontli plus something equals something else.\n\nBut in (15), cen-tzontli = multiple terms.\n\nLikely, cen-tzontli is a number composed of parts.\n\nSo if cen-tzontli = tarumba + tambaroy + fete + asàr → then we can compute.\n\nBut arithmetically, we have:\n\ntarumba = x³ - 2x \ntambaroy = ngámbi + asàr — we don’t know their values yet.\n\nWe need more.\n\nBut look at (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × ngámbi = ngámbi × 2 → always true → does not help \n\n(8): ngámbi + asàr = tambaroy — so tambaroy is a sum \n\n(11): nimbo × fete = tarumba → already used \n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr \n\nBut we don’t have values.\n\nAlternate idea: perhaps \"cen-tzontli\" is a standard number (e.g., 100), and in Nahuatl, numbers are built using positional values.\n\nGiven that in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nLet’s suppose:\n\n- mahtlactli = 20 \n- cë = 1 → so \"mahtlactli-on-cë\" = 20×1 = 20? \nBut 20 × 20 = 400 → in the right hand side: mäcuïl-pöhualli-om-mahtlactli \n\nIf pöhualli = 1 day → perhaps represents 1, and \"mäcuïl\" = 40, or 10? \n\n20 × 20 = 400 → 400 = 20 × 20 → might be a positional number.\n\nBut 400 = 2 × 200 → not clear.\n\nFrom (4): mäcuïlli + öme = chicöme → so mäcuïlli = chicöme - 1 \n\nFrom (6): mäcuïlli × ëyi = caxtölli \n\nSuppose ëyi = 1 → then caxtölli = mäcuïlli → contradicts if mäcuïlli = chicöme - 1 \n\nSuppose ëyi = 4 → then caxtölli = 4 × mäcuïlli \n\nBut from (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n\nThis might represent addition: A + B = C \n\n\"on\" may mean \"plus\"\n\nSo yë-pöhualli-on-chicöme = yë-pöhualli + chicöme \n+ mahtlactli-on-nähui = mahtlactli + nähui \n= näuh-pöhualli-on-cë → näuh-pöhualli + cë \n\nSo: (yë-pöhualli + chicöme) + (mahtlactli + nähui) = näuh-pöhualli + cë \n\nThis seems messy.\n\nBut go back to (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nCompare with (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\nBoth have caxtölli-on-... \n\nIn (5), left: mahtlactli-om-ëyi × ëyi → a product \nRight: cem-pöhualli-on-caxtölli-on-nähui \n\nIn (13), left: yë-tzontli-on-... → a sum? on might mean addition.\n\nSo perhaps:\n\nIn (5): (A - B) × B = C \nIn (13): A + B = D \n\nBut maybe the base system uses multiplication in a positional way.\n\nNotice that in (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nIf \"mahtlactli-on-cë\" means (20 + 1) = 21, then 21 × 20 = 420 → is that significant?\n\nThen right side: mäcuïl-pöhualli-om-mahtlactli \n\nCould \"mäcuïl\" be 40? (common in Nahuatl numerals)\n\n40 is 2×20\n\nSo mäcuïl = 40? \n\nThen 40 + pöhualli (1) + 20 = 61 → not 420 → no.\n\nIf \"mahtlactli-on-cë\" = 20 × 1 = 20 → 20×20 = 400 \n\nRight side: mäcuïl-pöhualli-om-mahtlactli \n\nIf mäcuïl = 40, pöhualli = 1, mahtlactli = 20 → 40+1+20 = 61 — not 400.\n\nAlternatively, \"pöhualli\" might be a multiplier.\n\nBut look at (4): mäcuïlli + öme = chicöme\n\n(6): mäcuïlli × ëyi = caxtölli\n\nSo from (4): mäcuïlli =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9963.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "We are given several equations in Nahuatl and Arammba, and we are to solve (b): write out in Nahuatl the numbers 42 and 494.\n\nWe must derive the linguistic pattern — likely a numeral system — from the equations.\n\n---\n\nStep 1: Look for patterns in the given equations.\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLeft: (A × A) \nRight: B-om-A \nThis suggests multiplication of a quantity by itself yields a compound structure involving a modified form.\n\nBut notice: \nmahtlactli is likely a base (like 1 or 10), and \"on-cë\" may be a preposition or suffix.\n\nBut equation (2): \ncem-pöhualli × öme = öm-pöhualli \nThis looks like: X × Y = Z\n\nNote: cem-pöhualli and öm-pöhualli – phonologically similar. cem vs. om? \nAlso, it is not symmetric. If cem-pöhualli × öme = öm-pöhualli → a possible symmetry if öme is 1?\n\nBut equation (4): \nmäcuïlli + öme = chicöme \nSo sum: A + B = C\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nThis looks complex. But note: \"on\" seems to link terms.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nAgain: (X × Y) = Z\n\nEquation (6): \nmäcuïlli × ëyi = caxtölli \nSo product of mäcuïlli and ëyi gives caxtölli.\n\nNow from (6): mäcuïlli × ëyi = caxtölli \nFrom (4): mäcuïlli + öme = chicöme \nSo we have additive and multiplicative forms.\n\nCheck if one of them is a unit.\n\nTry to identify base units.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSuppose öme = 1 → then cem-pöhualli × 1 = öm-pöhualli \nSo if öme = 1, then cem-pöhualli = öm-pöhualli \nBut cem and om differ → difference in pronunciation. \nBut perhaps öme = 1?\n\nAlso in (8): ngámbi + asàr = tambaroy → addition\n\nIn (7): ngámbi + ngámbi = ngámbi × yànparo → ngámbi × 2 = ngámbi × yànparo → so 2 = yànparo?\n\nSo ngámbi × yànparo = 2 × ngámbi → therefore, yànparo = 2\n\nThus, in Arammba:\nyànparo = 2\n\nSimilarly, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nNote: \"tàxwo\" likely means \"times\"? Or \"in\" or \"by\"?\n\n\"yenówe × yenówe tàxwo\" → possibly (x × x) = fete (x) → if x = 1, then 1×1 = fete(1)? \nBut (11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nTry: yànparo = 2\n\nSo (12): nimbo + (2) = yenówe \n(11): nimbo × fete = tarumba \n(10): (yenówe) × (yenówe) = fete (yenówe) → so (x)^2 = fete(x)\n\nSo x^2 = fete(x) → implies fete(x) = x^2\n\nThen from (10): x² = fete(x) → consistent\n\nFrom (11): nimbo × fete = tarumba → nimbo × (fete) = tarumba → but fete(x) = x² → so nimbo × x² = tarumba\n\nBut (12): nimbo + 2 = x (yenówe)\n\nLet x = yenówe\n\nSo nimbo + 2 = x → nimbo = x - 2\n\nThen (11): (x - 2) × x² = tarumba\n\nBut no direct value.\n\nNow (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nWhy is this structured?\n\n\"yànparo tàxwo\" likely means \"2 times\" → so \"2 ×\" \n\"fete asàr\" → \"fete × asàr\" → possibly \"fete\" is a multiplier? \nLeft: 2×A + (fete × asàr) → equals 2×fete?\n\nNot clear.\n\nBut go back to Nahuatl.\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose mahtlactli is 1.\n\nThen left: 1 × 1 = 1 → but result is mäcuïl-pöhualli-om-1 → so 1×1 = compound form.\n\nEquation (4): mäcuïlli + öme = chicöme → addition\n\nEquation (6): mäcuïlli × ëyi = caxtölli → multiplication\n\nSo if mäcuïlli = 10, and ëyi = 7 → 10×7 = 70 → caxtölli = 70? But why?\n\nEquation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli-om-ëyi = (1 × ëyi)? Or is it a compound?\n\nAssume mahtlactli = 1 → so mahtlactli-om-ëyi = 1 - om - ëyi → could be (1 + ëyi)? Or (1 × ëyi)?\n\nNote: such compound forms may be used in multiplication.\n\nBut equation (1): (a × a) = b-om-a → like a² = b-om-a → suggests a² = b × a → so b = a → only if a = 1?\n\nNot likely.\n\nWait: (a × a) = b-om-a → perhaps b-om-a = b × (a) → so a² = b × a → b = a\n\nThen a² = a × a → true → so consistent only if b = a\n\nBut in (1): left: mahtlactli × mahtlactli → right: mäcuïl-pöhualli-om-mahtlactli\n\nSo if mahtlactli = a, then a×a = mäcuïl-pöhualli × a → so a² = (mäcuïl-pöhualli) × a → so mäcuïl-pöhualli = a → so mäcuïl-pöhualli = a\n\nBut a = mahtlactli? So if mahtlactli = 1 → mäcuïl-pöhualli = 1?\n\nBut we don’t know values.\n\nIn (4): mäcuïlli + öme = chicöme\n\nIn (6): mäcuïlli × ëyi = caxtölli\n\nSo mäcuïlli is a base unit.\n\nIn Arammba: yànparo = 2 (from ngámbi + ngámbi = ngámbi × yànparo → 2 = yànparo)\n\nNow go to (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nWe now analyze (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis seems to define a value.\n\nSimilarly, (14): cen-tzontli-on-... = yànparo tarumba\n\nSo cen-tzontli appears in both — likely represents a value.\n\nAlso, in Arammba: (11) nimbo × fete = tarumba\n\n(12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe\n\nNow, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nfete is a multiplier? → (x) × (x) = fete(x)\n\nSo x² = fete(x)\n\nThen from (12): nimbo = x - 2\n\n(11): nimbo × fete = tarumba → (x - 2) × x² = tarumba\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo tarumba is part of a compound → perhaps a unit value.\n\nWe are to write 42 and 494 in Nahuatl.\n\nTry to find a known base.\n\nFrom (4): mäcuïlli + öme = chicöme → addition\n\nFrom (6): mäcuïlli × ëyi = caxtölli → multiplication\n\nSo mäcuïlli may be 10.\n\nAssume mäcuïlli = 10 → then 10 × ëyi = caxtölli\n\nAlso, in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis could be a compound structure like a × b × c → 42?\n\nSimilarly, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nyànparo = 2 → so 2 × tarumba\n\nBut also, from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = tarumba × tambaroy × fete × asàr (by implication of compound structure)\n\nBut if we assume \"on\" or \"om\" means \"times\", then:\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1, then cem-pöhualli = om-pöhualli → so value is preserved → suggests öme = 1?\n\nLikely öme = 1.\n\nThen from (4): mäcuïlli + 1 = chicöme → so if mäcuïlli = 10 → chicöme = 11\n\nBut (6): mäcuïlli × ëyi = caxtölli → so 10 × ëyi = caxtölli\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSuppose mahtlactli = 1 → so mahtlactli-om-ëyi = (1 × ëyi) or (1 + ëyi)? Or (1-om-ëyi) = a compound meaning 1 × ëyi?\n\nAssume multiplication → so (1 × ëyi) × ëyi = 1 × ëyi²\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui → which may be cem-pöhualli × caxtölli × nähui\n\nIf öme = 1, and cem-pöhualli = om-pöhualli (from (2)), then perhaps cem-pöhualli is a unit of 1.\n\nSo if 1 × ëyi² = (1) × caxtölli × nähui → so ëyi² = caxtölli × nähui\n\nBut from (6): caxtölli = 10 × ëyi\n\n→ so ëyi² = (10 × ëyi) × nähui → ëyi² = 10 × ëyi × nähui → ëyi = 10 × nähui → nähui = ëyi / 10\n\nBut ëyi = 7 → nähui = 0.7? Not integer.\n\nTry ëyi = 7 → caxtölli = 70 → then from (5): left = 1 × 7 = 7 → × 7 = 49 → right = cem-pöhualli × 70 × nähui\n\nSo 49 = (1) × 70 × nähui → nähui = 49/70 = 0.7 → not good.\n\nTry ëyi = 7, mäcuïlli = 10 → caxtölli = 70\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSuppose \"on\" = \"times\" or \"a compound of\"\n\nTry: yë-tzontli × näuh-pöhualli × caxtölli × cë = ndamno\n\nWhat is the value?\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nFrom (14): cen-tzontli-on-... = yànparo tarumba\n\nSuppose \"on\" means multiplication → so cen-tzontli × (something) = 2 × tarumba\n\nBut also cen-tzontli = tarumba × tambaroy × fete × asàr\n\nSo let T = tarumba\n\nThen cen-tzontli = T × t × f × a\n\nThen T × (something) = 2 × T → so (something) = 2\n\nSo the \"something\" is 2.\n\nWhat is that something?\n\nIn (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nSo it is: cen-tzontli × (cem-pöhualli × mahtlactli × öme)\n\nWe know öme = 1 → so this is × (cem-pöhualli × mahtlactli)\n\nThis equals yànparo tarumba = 2 × T\n\nBut cen-tzontli = T × t × f × a\n\nSo: (T × t × f × a) × (cem-pöhualli × mahtlactli) = 2 × T\n\nDivide both sides by T: (t × f × a) × (cem-pöhualli × mahtlactli) = 2\n\nWe need integer values.\n\nFrom (2): cem-pöhualli × 1 = om-pöhualli → so cem-pöhualli = om-pöhualli → value unchanged → perhaps cem-pöhualli = 1?\n\nThen (t × f × a) × 1 × mahtlactli = 2 → so (t × f × a) × mahtlactli = 2\n\nNow suppose mahtlactli = 1 → then t × f × a = 2\n\nBut t, f, a are units like tambaroy, fete, asàr → we have from (8): ngámbi + asàr = tambaroy → so asàr = tambaroy - ngámbi\n\nBut ngámbi = ? → in (7): ngámbi + ngámbi = ngámbi × yànparo → 2×ngámbi = ngámbi × 2 → consistent, no new info.\n\nWe have no value.\n\nBut now recall: in (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf we assume that “on” means “times”, and this equals 42, then perhaps:\n\nyë-tzontli × näuh-pöhualli × caxtölli × cë = 42\n\nSimilarly, (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThis may be a value.\n\nBut we need 42 and 494.\n\nTry to guess that in Nahuatl, the number 42 is represented as: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nAnd from (13), that equals ndamno → so 42 = ndamno\n\nThus, 42 = ndamno\n\nThen 494 = ?\n\nWe need to find a structure that gives 494.\n\nLook at equation (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose mahtlactli = 1 → then left: 1 × 1 = 1 → right: mäcuïl-pöhualli × 1 → so mäcuïl-pöhualli = 1\n\nNot helpful.\n\nEquation (4): mäcuïlli + öme = chicöme → mäcuïlli + 1 = chicöme → so if mäcuïlli = 10, then chicöme = 11\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 10 × ëyi = caxtölli\n\nSuppose ëyi = 7 → caxtölli = 70\n\nThen from (13):", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9541.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "We are given several equations in Nahuatl and Arammba, and we are to solve (b): write out in Nahuatl: 42; 494.\n\nWe must deduce the linguistic pattern, especially how numbers are formed.\n\n---\n\n### Step 1: Analyze the equations to find number patterns\n\nLook at the equations involving multiplication, addition, and the structure of number phrases.\n\n#### Equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLet’s suppose: \n- \"mahtlactli\" = 1 \n- \"cë\" = some function \n- \"mäcuïl-pöhualli\" = 1 × 2 = 2? \nBut the product is \"mäcuïl-pöhualli-om-mahtlactli\" → possibly 2 × 1 = 2? \nBut why would multiplication produce \"mäcuïl-pöhualli\"?\n\nFrom (4): \nmäcuïlli + öme = chicöme \n→ possibly \"mäcuïlli\" = 1, \"öme\" = 1 → \"chicöme\" = 2?\n\nFrom (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ possibly a sum of two numbers → leading to a composite.\n\nBut (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ if \"ëyi\" = 1, then left side is (1 × 1) = 1 → right is \"cem-pöhualli-on-caxtölli-on-nähui\" \nThat suggests \"cem-pöhualli\" = 12, \"caxtölli\" = something else?\n\nWait — known fact in Nahuatl: numbers are built from base 20. The system is in vigesimal (base 20).\n\nTry to map known elements:\n\nFrom (4): mäcuïlli + öme = chicöme → 1 + 1 = 2 → so chicöme = 2 \nFrom (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-2 → possibly denotes number 3?\n\nNote: “pöhualli” is a known Nahuatl term for “calendar day” or “20” and is associated with base 20 numbers.\n\nBut from (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nSuppose: \n- \"mahtlactli\" = 1 \n- Thus, 1 × 1 = 1 → but product is mäcuïl-pöhualli-om-1 → mäcuïl-pöhualli = 20? \n\nThus, the product is \"mäcuïl-pöhualli-om-mahtlactli\" = 20 + 1 = 21?\n\nBut 1 × 1 = 1 → doesn't make sense.\n\nAlternatively, maybe the expression \"A-on-B\" means A × B, or A + B?\n\nBut in (1): \"mahtlactli-on-cë × mahtlactli\" → the × is just marking multiplication, so that suggests \"mahtlactli-on-cë\" × \"mahtlactli\"\n\nSo: (A-on-B) × C\n\nSo let’s interpret:\n- \"mahtlactli-on-cë\" might mean (mahtlactli) × (cë) \n- then multiplied by mahtlactli → total product is (mahtlactli × cë) × mahtlactli = mahtlactli² × cë\n\nBut result is mäcuïl-pöhualli-om-mahtlactli\n\nSuppose \"mäcuïl\" means 20, \"pöhualli\" = 1 → no, pöhualli is related to 20.\n\nBetter: in Nahuatl, numbers are constructed as:\n- Units of 20s (1–19), then tens (20, 40, etc.)\n\nIn Arammba, we have:\n\nEquation (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 1 + 1 = 1 × yànparo → implies 2 = yànparo → yànparo = 2? \nBut also: ngámbi + ngámbi = ngámbi × yànparo → so 2 = yànparo? As if all are equal under operation.\n\nEquation (8): ngámbi + asàr = tambaroy \n→ 1 + x = y → maybe asàr = 1, tambaroy = 2?\n\nBut (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (yànparo + fete) with some indexing → (2 + fete) with suffix → becomes yànparo fete → suggests fete serves as a multiplication or addition?\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (x × y) = fete x \n→ if x = 1, then 1 × 1 = fete → fete = 1? \nBut result is \"fete yenówe tàxwo\" → so result is fete × yenówe?\n\nPossibly: \"A × B\" → equals C — with some compound form.\n\nFrom (11): nimbo × fete = tarumba → if fete = 1, then nimbo = tarumba?\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe? → if yenówe = 3?\n\nSo possible mappings:\n\n- ngámbi = 1 \n- yànparo = 2 \n- asàr = 1 \n- fete = 1 \n- tambaroy = 1 + 1 = 2 \n- nimbo = 2? \nFrom (11): nimbo × fete = tarumba → 2 × 1 = tarumba → tarumba = 2 \nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo → 2 + 2 = 4 → yenówe = 4?\n\nBut (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ 4 × 4 = 1 × 4 → 16 = 4 → contradiction.\n\nSo likely not arithmetic with integers.\n\nAlternative: use structure of equations to build number forms.\n\nLook at (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\nAssume \"on\" = \"of\", so \"A-on-B\" = A × B? \nThen left: (mahtlactli × cë) × mahtlactli = mahtlactli² × cë \n\nRight: mäcuïl-pöhualli-om-mahtlactli \n\nSuppose \"pöhualli\" = 20 \nSo mäcuïl-pöhualli = 20? \nThen \"mäcuïl\" may mean 20, and \"pöhualli\" also 20 → so 20×20?\n\nBut that’s 400.\n\nAlternatively: \"mäcuïl\" = 20, \"pöhualli\" = 1 → meaning 20 + 1 = 21?\n\nBut then \"mäcuïl-pöhualli-om-mahtlactli\" = 20 + 1 + 1 = 22?\n\nBut left: mahtlactli × cë × mahtlactli = (1 × cë × 1) = cë → so cë = 22?\n\nThen in (3): yë-pöhualli-on-chicöme \nIf \"yë-pöhualli\" = 1, \"chicöme\" = 2 → then product might be 1 × 2 = 2?\n\nBut equation (3): sum? \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nAssume “on” means “multiplied by” → \n(1 × 2) + (1 × n) = n - something?\n\nResult is näuh-pöhualli-on-cë → possibly 20 + 14 or something?\n\nBack to (4): mäcuïlli + öme = chicöme \nLikely: 1 + 1 = 2 → chicöme = 2\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nSuppose “mahtlactli-om-ëyi” = mahtlactli × ëyi → so (1 × x) × x = x² \nResult: cem-pöhualli-on-caxtölli-on-nähui → could be 12 + 10 + 1 = 23? Or is it 20 + 10 + 1?\n\n\"cem\" = 12? \"pöhualli\" = 20 → cem-pöhualli = 12 + 20 = 32 → then on caxtölli = 32 + 10 = 42? On nähui = +1 → 43?\n\nx² = 43 → nonsense.\n\nAlternatively, \"cem-pöhualli\" = 12, \"caxtölli\" = 20, \"nähui\" = 1 → 12 + 20 + 1 = 33 → x² = 33 → no.\n\nBut from (6): mäcuïlli × ëyi = caxtölli \nLikely: 1 × x = x → so caxtölli = x → so x = caxtölli → so \"ëyi\" = caxtölli?\n\nThen (5): (1 × ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ so (ëyi)² = cem-pöhualli-on-caxtölli-on-nähui \n→ implies squaring a number gives a compound expression.\n\nSuppose:\n- ëyi = 1 → 1² = 1 → not matching \n- ëyi = 2 → 4 → cem-pöhualli-on-caxtölli-on-nähui → 12 + 20 + 1 = 33 → no \n- ëyi = 3 → 9 → 12 + 20 + 1 = 33 → no \n- ëyi = 4 → 16 → still no \n- ëyi = 5 → 25 → 12 + 20 + 1 = 33 → no \n- ëyi = 10 → 100 → 12 + 20 + 1 = 33 → no\n\nNo clear match.\n\nBut look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWhat is “yë-tzontli”? \nCould yë = 1, tzontli = 1 → so (1 × tzontli) on (näuh-pöhualli-on-caxtölli-on-cë) = 1 × (something)?\n\n\"ndamno\" is a number — what is it?\n\nTry to see if the numbers match known Nahuatl numerals.\n\nKnown: \n- 1 = mahtlactli \n- 2 = chicöme \n- 3 = yë-pöhualli? \n- 4 = kahú \n- etc.\n\nFrom (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nLeft: cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme \nIs \"on\" = multiplication? → cen-tzontli × (cem-pöhualli) × (mahtlactli) × (öme)? \n\nBut \"om\" = \"and\" — so \"A-om-B\" = A + B? \nSo cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme \n= (cen-tzontli × cem-pöhualli) + mahtlactli + öme \n\nAssume:\n- mahtlactli = 1 \n- öme = 1 \n- cem-pöhualli = 12 \n- cen-tzontli = ?\n\nSo (cen × 12) + 1 + 1 = yànparo tarumba\n\nyànparo ≈ 2 in Arammba → yànparo tarumba = 2 × tarumba?\n\nFrom (11): nimbo × fete = tarumba → tarumba = nimbo × fete\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr \n→ so cen-tzontli = tarumba + tambaroy + fete + asàr? \n→ or as compound?\n\n\"tarumba tambaroy fete asàr\" → likely a sum or concatenation.\n\nIn (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n→ again, compound list?\n\nBut from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nIn Arammba: \n(8): ngámbi + asàr = tambaroy → 1 + x = y → if asàr = 1, tambaroy = 2 \n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo → 2 + x = y \n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies upgrading?\n\nTry assignments:\n\nSet: \n- ngámbi = 1 \n- asàr = 1 \n- tambaroy = 2 \n- yànparo = 2 \n- fete = 1 \n- nimbo = 1 → then (11): 1 × 1 = tarumba → tarumba = 1 \n- (12): 1 + 2 = 3 → yenówe = 3 \n\n(10): 3 × 3 = 1 × 3 → 9 = 3 → contradiction.\n\nTry nimbo = 3, fete = 1 → tarumba = 3 \n(12): 3 + 2 = 5 → yenówe = 5 \n(10): 5 × 5 = 1 × 5 → 25 = 5 → no.\n\nn = 20 → 20 × 20 = 1 × 20 → 400 = 20 → no.\n\nMust be different interpretation.\n\nAlternate: \"A on B\" = A + B \nIn (1): mahtlactli-on-cë + mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nSo (1 + cë) + 1 = (mäcuïl-pöhualli-om-mahtlactli) \n→ 2 + cë = 20 + 1 = 21 → cë = 19?\n\nThen in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nAssume \"on\" = addition \nSo (yë + chicöme) + (mahtlactli + nähui) = näuh-pöhualli + cë \n\nFrom (4): mäcuïlli + öme = chicöme → 1 + 1 = 2 → chicöme = 2 \nSo yë = 1 → 1 + 2 = 3 \nmahtlactli = 1 → 1 + nähui → total sum: 3 + 1 + nähui = 4 + nähui \nRight: näuh-pöhualli + cë → cë = 19 → so 4 + nähui = pöhualli + 19 \nSo pöhualli = 4 + nähui - 19 = nähui - 15 \n\nPossible if nähui = 20 → pöhualli = 5 — not likely.\n\nnähui = 19 → pöhualli = 4 → possible.\n\nBut pöhualli is a base-20 unit — so 20 likely.\n\nSo not matching.\n\nBack to (4): mäcuïlli + öme = chicöme → likely 1 + 1 = 2 — so chicöme = 2\n\n(6): mäcuïlli × ëyi = caxtölli → 1 × x = x → caxtölli = x\n\n(5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\"mahtlactli-om-ëyi\" = mahtlactli + ëyi = 1 + x \nThen (1 + x) × x = cem-pöhualli-on-caxtölli-on-nähui → gives final compound\n\nIf x = 2 → (1+2)×2 = 6 → output = cem-pö", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9050.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "unit_audit", + "sample_index": 0, + "output": "We are given several equations in Nahuatl and Arammba, and we are to derive how to write the numbers 43 and 569 in Arammba.\n\nWe need to find a pattern that connects numerical expressions in the equations. The key is to identify how numbers are built from compound terms in both languages and see how they relate via syntactic or semantic rules.\n\nLet’s go through the equations step by step, focusing on patterns in arithmetic and structure.\n\n---\n\n**Step 1: Look at Nahuatl equations**\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nThis resembles a square operation. The left side is mahtlactli-on-cë × mahtlactli. \n\"on-cë\" may be a preposition or suffix indicating multiplication or unity.\n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n→ (A × B) = C\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ (A + B) = C \nAddition with compound terms.\n\nEquation (4): \nmäcuïlli + öme = chicöme \n→ Simple addition\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (A × B) = C\n\nEquation (6): \nmäcuïlli × ëyi = caxtölli \n→ (A × B) = C\n\nNow, in Nahuatl, compound terms seem to follow the pattern:\n- A + B → C (e.g., (yë-pöhualli-on-chicöme) + (mahtlactli-on-nähui) → näuh-pöhualli-on-cë)\n- A × B → C (e.g., mahtlactli-on-cë × mahtlactli → mäcuïl-pöhualli-om-mahtlactli)\n\nFocusing on equations (1), (4), (6): \n(1): A × A → compound \n(4): A + B → new term \n(6): A × B → compound\n\nBut equation (6): mäcuïlli × ëyi = caxtölli \n→ This may represent 1 × 1 = 1? Not clear.\n\nNow, look at equation (4): mäcuïlli + öme = chicöme \n→ Likely: 1 + 1 = 2? Possibly.\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli \n→ Possibly: 2 × 1 = 2? Or 2 × x = x?\n\nBut let’s try to assign values.\n\nLet’s try to assign values:\n- Let mahtlactli = 1 → from equation (1): (mahtlactli-on-cë) × mahtlactli → product involving 1\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nIf mahtlactli = 1, then mahtlactli-on-cë = 1, so product = 1?\n\nBut the right side is mäcuïl-pöhualli-om-mahtlactli – that’s not simple.\n\nAlternatively, maybe \"on\" means \"plus\", and \"×\" means multiplication.\n\nBut look at (13) and (14), which link to the target.\n\nEquation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nEquation (15): \ncen-tzontli = tarumba tambaroy fete asàr \n\nEquation (16): \ncen-xiquipilli = weremeke tarumba nimbo yànparo \n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr \nThis means \"cen-tzontli\" equals a compound form of tarumba, tambaroy, fete, asàr.\n\nFrom (11): nimbo × fete = tarumba \n→ So tarumba = nimbo × fete\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ (nimbo + yànparo) = yenówe \nIn terms of operation, addition.\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (A × B) = C \nIf yenówe = A, then A × A = fete A → suggests fete A = A × A\n\nThen, fete = (yenówe) × (yenówe) / (yenówe) → not helping.\n\nBut from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo if Y × Y = fete Y → then fete = Y\n\nSo fete = yenówe? \nThen Y × Y = Y → only if Y = 1? Not likely.\n\nAlternatively, Y × Y = fete Y → so fete = Y → then Y × Y = Y → implies Y = 1.\n\nBut (11): nimbo × fete = tarumba \nIf fete = Y, then nimbo × Y = tarumba\n\nAlso, (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + yànparo = yenówe\n\nBut (11): nimbo × fete = tarumba\n\nAnd from (15): cen-tzontli = tarumba tambaroy fete asàr \nSo cen-tzontli = (nimbo × fete) + tambaroy + fete + asàr? Or concatenated?\n\nMaybe \"tarumba tambaroy fete asàr\" is just a list of terms with value 1 each?\n\nTry assigning values.\n\nLet’s suppose in Arammba, the basic units:\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × ngámbi = ngámbi × yànparo \nLet ngámbi = a, then 2a = a × yànparo \n→ if a ≠ 0, then 2 = yànparo \nSo yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ a + b = tambaroy → value?\n\nFrom (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2) + (fete) = 2 + fete → left side has \"tàxwo\", which may be a marker.\n\nIn (9): \"yànparo tàxwo + fete asàr tàxwo\" = \"yànparo fete\" \nSo (yànparo + fete) with suffix tàxwo → equals yànparo fete (without tàxwo)\n\nSo (2 + fete) with suffix → gives 2 + fete without suffix → suggests that \"tàxwo\" is a suffix that, when added, gets removed or acts as a multiplier?\n\nBut more likely: \"tàxwo\" means \"times\" or \"multiplication\".\n\nTry: yànparo tàxwo = yànparo × something\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo: Y × (Y tàxwo) = fete Y tàxwo\n\nIf tàxwo means \"times\", then Y × (Y) = fete × Y \nSo Y² = fete × Y \n→ If Y ≠ 0, then Y = fete\n\nSo fete = Y\n\nThen (10): Y × Y = fete × Y → Y² = Y × fete → if fete = Y → Y² = Y² → holds.\n\nSo fete = yenówe\n\nNow (11): nimbo × fete = tarumba \n→ nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (yànparo × ?) = yenówe × ?\n\nBut yànparo = 2 from earlier.\n\nLet’s suppose that \"tàxwo\" is multiplication.\n\nThen (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 × ?) + (fete × ?) = 2 + fete\n\nBut it equals \"yànparo fete\" — which may be just the sum without the marker.\n\nSo if the marker \"tàxwo\" marks multiplication, then term with \"tàxwo\" is value × something.\n\nMaybe the operation is: term1 + term2 → value, but in structural form.\n\nBut in (9): yànparo tàxwo + fete asàr tàxwo → becomes yànparo fete \nSo the suffix \"tàxwo\" is removed — suggesting that it is a temporary modifier.\n\nBut in (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ so multiplication gives a compound term.\n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \nSo nimbo + (2 × ?) = (yenówe × ?)\n\nBut we know that yenówe = fete, from (10)\n\nSo nimbo + 2 × x = fete × x \nBut from (10), fete = yenówe, so this becomes:\n\nnimbo + 2x = yenówe × x\n\nBut this must hold for some x — perhaps x is a unit of 1.\n\nSuppose x = 1 → then nimbo + 2 = yenówe \nBut yenówe = fete → so fete = nimbo + 2\n\nBut from (11): nimbo × fete = tarumba\n\nSo far:\n\n- yànparo = 2\n- fete = yenówe\n- fete = nimbo + 2 → from above\n\nThen nimbo = fete – 2\n\nThen from (11): nimbo × fete = tarumba \n→ (fete – 2) × fete = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nBut we don't have values yet.\n\nNow look at (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nNote that in Nahuatl, “cem-pöhualli” appears — from equation (2): cem-pöhualli × öme = öm-pöhualli \nSo (A × B) = C\n\nPossibly A = 2, B = 1 → gives 2? Or same?\n\nAlso, from the mapping in (13) and (14), the right-hand side in Nahuatl is translated to Arammba.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nTranslation to Arammba: ndamno\n\nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \nThis means this complex term equals \"yànparo tarumba\" in Arammba.\n\nFrom earlier, yànparo = 2 \nSo \"yànparo tarumba\" = 2 × tarumba\n\nSo the left side of (14) must represent 2 × tarumba\n\nNow, left side: cen-tzontli-on-... \n\nBut (15): cen-tzontli = tarumba tambaroy fete asàr \nSo if tarumba tambaroy fete asàr is a compound value, and cen-tzontli is equal to that, then this suggests that cer-tzontli is a value equivalent to the sum or product of those terms.\n\nBut “tarumba tambaroy fete asàr” — listed, likely with value 1 each?\n\nThus, cen-tzontli = tarumba + tambaroy + fete + asàr\n\nFrom (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n→ Synonym for something?\n\nWe know yànparo = 2\n\nWe have:\n\n- yànparo = 2\n- fete = nimbo + 2\n- tarumba = (nimbo) × (fete)\n\nLet H = nimbo\n\nThen fete = H + 2\n\ntarumba = H × (H + 2)\n\nThen cen-tzontli = tarumba + tambaroy + fete + asàr\n\nWe don’t know tambaroy or asàr.\n\nBut from (8): ngámbi + asàr = tambaroy \nAnd from (7): ngámbi + ngámbi = ngámbi × yànparo \nWe already used that to get yànparo = 2\n\nLet ngámbi = a\n\nThen a + a = a × 2 → 2a = 2a → identity\n\n(8): a + asàr = tambaroy → asàr = tambaroy – a\n\nThen from (15): cen-tzontli = tarumba + tambaroy + fete + asàr \nSubstitute:\n\n= [H(H+2)] + tambaroy + (H+2) + (tambaroy – a) \n= H² + 2H + tambaroy + H + 2 + tambaroy – a \n= H² + 3H + 2 + 2 tambaroy – a\n\nBut from (14): cen-tzontli-on-... = yànparo tarumba = 2 × tarumba = 2 × H(H+2) = 2H² + 4H\n\nThe left side is cen-tzontli-on-... — which may mean cen-tzontli × something?\n\nIn (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nCompare to equation (2): cem-pöhualli × öme = öm-pöhualli\n\nPossibly \"on\" means multiplication.\n\nSo \"cen-tzontli-on-...\" may mean cen-tzontli × (something)\n\nBut what is \"cem-pöhualli-om-mahtlactli-om-öme\"?\n\nWe don’t have its value.\n\nBut from (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1, then cem-pöhualli × 1 = cem-pöhualli → so no change.\n\nPossibly \"om\" means \"and\" or \"plus\"?\n\nHard to say.\n\nAlternative idea: in Nahuatl, numbers are built from compound terms.\n\nIn equation (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose that \"on\" is addition. Then mahtlactli + cë × mahtlactli?\n\nNo.\n\nSuppose \"on\" is a multiplicative operator.\n\nIn (1): (A on B) × A = C\n\nBut (4): mäcuïlli + öme = chicöme → addition\n\nSo different cases.\n\nBack to (14): cen-tzontli × (some term) = yànparo tarumba = 2 × H(H+2)\n\nAnd from (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nBut we have no value for tambaroy or asàr.\n\nLet’s try to find a value for H that makes the whole thing work.\n\nFrom (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n→ Likely a sum or compound\n\nBut we don’t have value.\n\nAnother idea: from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe may find that \"ndamno\" represents a number.\n\nIn (14), \"cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\" = yànparo tarumba\n\nBut yànparo = 2\n\nSo the left side is representing 2 × tarumba\n\nAnd from (15), cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose that \"on\" in compound terms means \"multiplied by\" or \"times\".\n\nBut in (14), it’s cen-tzontli-on-... = (something)\n\nThus, cen-tzontli × X = 2 × tarumba\n\nBut tarumba = H(H+2)\n\nSo cen-tzontli × X = 2H(H+2)\n\nAnd from (15): cen-tzontli = H(H+2) + tambaroy + (H+2) + (tambaroy – a)\n\n= H² + 2H + tambaroy + H + 2 + tambaroy – a \n= H² + 3H + 2 + 2 tambaroy – a\n\nLet S = S = cen-tzontli\n\nThen S × X = 2H(H+2)\n\nWe need to find integer H that makes this work with consistent values.\n\nBut we don’t know X.\n\nAnother idea: maybe the \"on\" structure in Nahuatl represents a fixed number construction.\n\nLook at (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ a on b + c", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10545.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "unit_audit", + "sample_index": 1, + "output": "We are given a set of equations in Nahuatl and Arammba, and asked to derive the Arammba forms of the numbers 43 and 569.\n\nWe must reason through the patterns in the equations to decode how numbers are formed in Arammba, using known arithmetic and structural patterns.\n\n---\n\nFirst, observe that the equations resemble arithmetic operations (addition, multiplication), and include compound constructions like suffixes or infixes. We must identify the base units and operations.\n\n---\n\nStep 1: Analyze Nahuatl equations for number patterns.\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nThis suggests that multiplication of a unit (mahtlactli) by itself produces a compound phrase.\n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n→ (C × O) = O \nThis looks like multiplication results in a simpler form — possibly identity operation or substitution.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ Addition of two compound terms gives a compound.\n\nEquation (4): \nmäcuïlli + öme = chicöme \n→ Addition pattern: two terms form a compound.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (X × Y) = compound \nEquation (6): \nmäcuïlli × ëyi = caxtölli \n→ (A × B) = C \n\nNote that in (4), addition of mäcuïlli and öme gives chicöme, so a + b = c.\n\nIn (6), mäcuïlli × ëyi = caxtölli — suggesting that multiplication of specific units yields another unit.\n\nAlso, (1) shows multiplication of mahtlactli × mahtlactli → result with pöhualli and mahtlactli.\n\nIn (2): cem-pöhualli × öme → öm-pöhualli — this seems to suggest that \"cem-pöhualli\" is “1” and “öme” is “2” or something, and multiplication gives a simpler result.\n\nBut let’s look at the compound forms.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nThis shows that a complex compound equals a result.\n\nEquation (15): \ncen-tzontli = tarumba tambaroy fete asàr \n\nEquation (16): \ncen-xiquipilli = weremeke tarumba nimbo yànparo \n\nSo \"cen-tzontli\" is a unit that expands into a sum of elements: tarumba, tambaroy, fete, asàr.\n\nSimilarly, cen-xiquipilli expands into weremeke, tarumba, nimbo, yànparo.\n\nNow, in Arammba, we see:\n\nEquation (7): ngámbi + ngámbi = ngámbi × yànparo \n→ (a + a) = (a × b) \nSo addition of equal items equals multiplication.\n\nEquation (8): ngámbi + asàr = tambaroy \n→ a + b = c \nAddition pattern.\n\nEquation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (A + B) = C \nInteresting: two compounds add to a simpler form. \"tàxwo\" may be a modifier (like a marker of \"by\" or \"to\").\n\nEquation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (X × Y) = Z \nY is \"yenówe tàxwo\", and the product is \"fete yenówe tàxwo\"\n\nEquation (11): nimbo × fete = tarumba \n→ Multiplication yields tarumba\n\nEquation (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ Addition of two units gives a product.\n\nNote that in (11): nimbo × fete = tarumba \nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nAlso in (9): (yànparo tàxwo + fete asàr tàxwo) = yànparo fete → seems like cancellation or simplification.\n\nBut key insight: in (11), nimbo × fete = tarumba \nSo possibly: \n- fete = 1 \n- nimbo = 2 \n→ 2 × 1 = 2, so tarumba = 2\n\nBut in (15): cen-tzontli = tarumba tambaroy fete asàr \nSo cen-tzontli expands to tarumba, tambaroy, fete, asàr\n\nIn Arammba, also (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nLet’s suppose that “yenówe” is a number, and “×” is multiplication.\n\nThen (yenówe × yenówe tàxwo) = fete yenówe tàxwo\n\nSuppose that “yenówe” = 2, then (2 × 2 tàxwo) = fete 2 tàxwo — seems like output is \"fete + 2 tàxwo\"\n\nBut (12): nimbo + yànparo tàxwo = yenówe tàxwo \nSo if nimbo = 2, then 2 + yànparo tàxwo = 2 tàxwo → implies yànparo tàxwo = 0? Odd.\n\nAlternatively, podría be that “×” or “+” corresponds to multiplication or addition, and “tàxwo” is a suffix marking a number.\n\nTry again:\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ If we suppose that (x × x) = fete x → then x = ? \nFor example, if x = 1 → 1 × 1 = fete 1 → false \nx = 2 → 2 × 2 = fete 2 → maybe plausible\n\nSo perhaps “yenówe” = 2, and “fete” = 1?\n\nThen 2 × 2 = fete 2 → so product is fete + 2\n\nSimilarly, (11): nimbo × fete = tarumba \nSo 2 × 1 = 2 → tarumba = 2\n\nSo tarumba = 2\n\nNow equation (15): cen-tzontli = tarumba tambaroy fete asàr \n→ 2 + tambaroy + 1 + asàr → so total = 3?\n\nBut if cen-tzontli = 3, then we can infer that the components sum to 3.\n\nNow equation (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n→ weremeke + 2 + 2 + yànparo → so total = 4?\n\nBut if “cen” is a unit for “10” or a base, and “tzontli” = 3, “xiquipilli” = 4?\n\nIn Nahuatl, the number system is vigesimal (base 20). \nIn general, Nahuatl uses compound forms: \n- 1 = cem \n- 2 = öme \n- 3 = cem-pöhualli? \nWait, we see in (2): cem-pöhualli × öme = öm-pöhualli \nThat is, (1 × 2) = 2 → so cem-pöhualli = 1? \nSo cem → 1 \nöme → 2 \nThus multiplication is consistent.\n\nIn (4): mäcuïlli + öme = chicöme \nSo mäcuïlli + 2 = chicöme \nIn (6): mäcuïlli × ëyi = caxtölli \nNot clearly linked.\n\nBut important: in (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nSuppose: \n- cem = 1 \n- öme = 2 \n- mahtlactli = 20? (common in Nahuatl) \n- cem-pöhualli → 1 × 2 = 2? or a unit?\n\nBut \"cen\" may be a base like 20.\n\nIn (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme \nBreak it into: \n- \"cen-tzontli\" → probably 3 or 13 or 23 \n- then \"on-cem-pöhualli\" → on 1 \n- \"om-mahtlactli\" → 20 \n- \"om-öme\" → 2 \n\nSo if \"on\" means \"plus\", then this is: \ncen-tzontli + 1 + 20 + 2\n\nAnd equals yànparo tarumba.\n\nFrom earlier, tarumba = 2 → so right-hand side is 2.\n\nSo left-hand side: (some value) + 1 + 20 + 2 = 2 → impossible, unless \"on\" is not addition.\n\nAlternatively, \"on\" is a structural particle.\n\nBut look at equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nThis is likely a number.\n\nWe are to convert 43 and 569 to Arammba.\n\nInstead, let's try to reconstruct the Arammba number system from the equations.\n\nFrom (11): nimbo × fete = tarumba \n→ We suspect: \n- fete = 1 \n- nimbo = 2 \n→ 2 × 1 = 2 \nSo tarumba = 2\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ 2 + yànparo tàxwo = yenówe tàxwo \n\nLet us suppose that “yànparo tàxwo” is a number, and the equation implies: \n2 + A = 2 × A → then 2 + A = 2A → A = 2 \nSo yànparo tàxwo = 2 \nThen 2 + 2 = 2×2 → 4 = 4 → true.\n\nSo we have:\n- yànparo tàxwo = 2 \n- nimbo = 2 \n- fete = 1 \n- tarumba = 2\n\nNow equation (8): ngámbi + asàr = tambaroy \n→ So asàr = ? \nngámbi = ? \nsuppose ngámbi = 1 → 1 + asàr = tambaroy\n\nEquation (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 1 + 1 = 1 × 2 → 2 = 2 → true.\n\nSo ngámbi = 1 \nasàr = ? \n1 + asàr = tambaroy → tambaroy = 1 + asàr\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr \n= (2) + (tambaroy) + (1) + (asàr) \n= 2 + (1 + asàr) + 1 + asàr = 4 + 2·asàr\n\nSo cen-tzontli = 4 + 2·asàr\n\nNow, if we can find what asàr is.\n\nBut we also have (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2) + (1 × asàr) = 2 fete → but “fete asàr tàxwo” likely means \"fete times asàr\" or \"fete with asàr\"\n\nBut in (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \nLeft: 2 + (fete × asàr) \nRight: 2 fete \nSo 2 + (1 × asàr) = 2 → implies asàr = 0 → not likely.\n\nSo “fete asàr tàxwo” may not be multiplication.\n\nPerhaps “fete asàr” is a compound meaning (fete) + (asàr) = some value.\n\nBut equation (9) says: \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \n\n→ Maybe adding (2) + (compound) → gives (2 fete)\n\nThus: 2 + X = 2 → X = 0 → again, not plausible.\n\nPossibility: \"tàxwo\" is a suffix meaning \"to the power of\" or \"with base\", but perhaps it's an operation marker.\n\nAnother idea: perhaps \"×\" and \"+\" are arithmetic operations, and “on” and “om” are infixes.\n\nBack to equation (10): \nyenówe × yenówe tàxwo = fete yenówe tàxwo \nSuppose that 'yenówe' is a number.\n\nLet X = yenówe \nThen X × (X tàxwo) = fete (X tàxwo)\n\nSuppose that 'X tàxwo' is X * something.\n\nBut if we suppose that multiplication by a number results in a compound including fete.\n\nTry X = 1: \n1 × (1 tàxwo) = fete (1 tàxwo) → plausible \nSo 1 × 1 = fete 1 → implies 1 = fete 1\n\nBut that would mean fete = 1\n\nX = 2: 2 × 2 = fete 2 → so 2 × 2 = fete 2 → suggests product is fete × 2\n\nThis is consistent with fete = 1\n\nSo we conclude:\n- fete = 1 \n- yenówe = 2 \n- (x × x) = fete x → means x² = 1 × x → x = 1 or x = 0 → contradiction\n\nUnless \"fete x\" means (fete) × x = 1 × x = x\n\nSo x × x = x → x = 1 or 0 → contradiction with x = 2\n\nSo this cannot be.\n\nAlternative: perhaps “fete” is not 1, but a unit.\n\nIn equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIn equation (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nIf we assume that the numbers in the expansion correspond to values, and \"cen\" is base 20:\n\nIn Nahuatl, 20 is base, so:\n- 1 = cem\n- 2 = öme\n- 3 = cem-pöhualli\n- 4 = cem-pöhualli-on-öme \n- etc.\n\nBut in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe suspect that \"cen-tzontli\" might be a compound number.\n\nIn many Nahuatl systems, \"tzontli\" = 20, or 3.\n\nBut \"cen\" may be 20.\n\nSo cen-tzontli = 20 + tzontli → if tzontli = 3, then 23\n\nThen on cem-pöhualli (1×2=2), om-mahtlactli (20), om-öme (2)\n\nBut that would be 23 + 2 + 20 + 2 = 47 → not matching right-hand side of 2.\n\nSo unlikely.\n\nPerhaps \"on\" means \"times\" or multiplication.\n\n(1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nIf \"on\" means \"times\", then (A × B) × A = C\n\nBut it's (A-on-B) × A = C\n\nSo (A-on-B) = A × B → and (A × B) × A = A² × B\n\nIn (1): A = mahtlactli, B = cë \nProduct (mahtlactli × cë) × mahtlactli = mahtlactli² × cë\n\nBut RHS is mäcuïl-pöhualli-om-mahtlactli — may represent 20×20 = 400?\n\nNot clear.\n\nBack to Arammba equations.\n\nWe have:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × ngámbi = ngámbi × yànparo → 2 = yànparo → so yànparo = 2\n\n(8) ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ 2 + (fete × asàr) = 2 fete → if \"fete asàr\" is multiplication, then 2 + fete×asàr = 2 fete\n\nSuppose fete = 1 → 2 + 1×asàr = 2×1 → 2 + asàr = 2 → asàr = 0 — impossible.\n\nSuppose \"fete asàr\" is a unit, and \"fete asàr tàxwo\" means \"fete", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10349.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "unit_audit", + "sample_index": 2, + "output": "First, analyze the patterns in both Nahuatl and Arammba to find arithmetic operations and how numbers are expressed.\n\nIn Nahuatl, equations involve operations like multiplication (×), addition (+), and composition with suffixes or prefixes. The key is to identify how numbers are formed through operations.\n\nLook at the equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nAlso:\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo \n\nNow, note that equations (1) and (2) resemble multiplication. For example, (1) might mean (a × b), and (2) suggests cem-pöhualli × öme = öm-pöhualli — note that öm-pöhualli may be a result, possibly related to symmetry or identity.\n\nBut more importantly, look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nWe consider: “yë-tzontli-on-...” may represent a compound number, where “on” links parts. This may be a number composed of components, possibly like a multiplication or size.\n\nBut (13) appears to be a specific value: 43? or 569?\n\nLet’s also look at (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n\nAnd (15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nThe pattern suggests that:\n\n- cen-tzontli might be a base number (like 1)\n- cen-xiquipilli may be 2 (or a base increment)\n- tarumba, yànparo, fete, etc., are units\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr \nSo “cen-tzontli” = “tarumba tambaroy fete asàr” → could mean 1 = tarumba + tambaroy + fete + asàr? \nBut (8): ngámbi + asàr = tambaroy → suggests addition \n(11): nimbo × fete = tarumba → multiplication\n\nWait — (11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nSo multiplication and addition are defined operationally.\n\nLook at (7): ngámbi + ngámbi = ngámbi × yànparo \nThis is unusual: sum of two ngámbi equals product of one ngámbi and yànparo. \nSo: ngámbi + ngámbi = ngámbi × yànparo → 2A = A × B → B = 2 → so yànparo = 2\n\nThis is critical.\n\nThus, yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \nSo, A + B = C → addition\n\nFrom (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n\"tàxwo\" seems like a suffix indicating a modification or quantity. \nSo: (yànparo) tàxwo + (fete) asàr tàxwo = (yànparo) fete \nThis resembles: (2) × something + (fete) × something → yields (2) fete?\n\nBut only if \"tàxwo\" is a multiplier or unit.\n\nWait: (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo: A × (A tàxwo) = (fete) (A tàxwo)\n\nThis suggests a number pattern where multiplying a number by a modified version gives a composite expression involving \"fete\".\n\nBut (10) suggests A × (A tàxwo) = fete × A tàxwo → so A × (A tàxwo) = fete × (A tàxwo)\n\nCancel (A tàxwo) → A = fete\n\nThus, yenówe = fete\n\nSo fete = yenówe\n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSince fete = yenówe → yenówe × (yenówe tàxwo) = yenówe × (yenówe tàxwo) → identity check → valid.\n\nSo fete = yenówe\n\nNow from (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba \nSo in terms of value, nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo \nWe know yànparo = 2 → yànparo tàxwo = 2 tàxwo \nyenówe tàxwo = fete tàxwo (since fete = yenówe)\n\nSo: nimbo + 2 tàxwo = fete tàxwo \nBut fete tàxwo = fete × tàxwo?\n\nWait — perhaps \"tàxwo\" indicates multiplication. Let’s suppose that \"X tàxwo\" = X × something.\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nSo: (2) tàxwo + (fete) asàr tàxwo = 2 fete \nThis suggests: 2 × something + fete × something = 2 × fete?\n\nBut doesn’t resolve.\n\nAlternatively, \"tàxwo\" might be a denominator or quantifier.\n\nBut earlier: (7) ngámbi + ngámbi = ngámbi × yànparo \n→ 2A = A × Y → Y = 2 \nSo yànparo = 2\n\nNow (8): ngámbi + asàr = tambaroy → addition\n\nThus, multiple values are defined via operations.\n\nNow (11): nimbo × fete = tarumba \n(12): nimbo + 2 tàxwo = fete tàxwo → if \"tāxwo\" means ×, then nimbo + 2 = fete × (something)\n\nBut observe (10): yenówe × (yenówe tàxwo) = fete (yenówe tàxwo) \n→ A × (A' ) = fete × (A' ) → implies A = fete → again fete = yenówe\n\nSo fete = yenówe\n\nThus: (11): nimbo × fete = tarumba → nimbo × fete = tarumba \n(12): nimbo + 2 tàxwo = fete tàxwo → nimbo + 2 = fete × (what?) \n\nIt’s unclear.\n\nBut from (15): cen-tzontli = tarumba tambaroy fete asàr \nSo 1 = tarumba + tambaroy + fete + asàr\n\nWait — no, it's listed as \"tarumba tambaroy fete asàr\" → could be a sum?\n\nBut from (8): ngámbi + asàr = tambaroy → so tambaroy = ngámbi + asàr\n\nSo: 1 = tarumba + (ngámbi + asàr) + fete + asàr → too many variables.\n\nBut unless these are units with value 1, etc.\n\nAlternative: maybe the expressions represent values in an arithmetic system.\n\nTry to identify how numbers are composed.\n\nBack to (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nFrom earlier: \n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli\n\nNotice that in (5): (A om ëyi) × ëyi = X on Caxtölli on nähui \nAnd (6): mäcuïlli × ëyi = caxtölli\n\nAlso (4): mäcuïlli + öme = chicöme\n\nBut (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nVery complex.\n\nBut look at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may represent a number. Could “ndamno” be 43?\n\nSimilarly, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nNow, suppose that “cen-tzontli” represents 1 \nThen (15): 1 = tarumba + tambaroy + fete + asàr — sum? \n(16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo\n\nBut what value is cen-xiquipilli?\n\nPossibly 2?\n\nIf so, 2 = weremeke + tarumba + nimbo + yànparo → sum?\n\nBut we need to find values for 43 and 569.\n\nGo back to pattern in Nahuatl.\n\nFrom (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"on\" may mean \"on\" in composite number, like \"10 times\" or \"times 10\", or \"positional.\"\n\nBut (1) may mean: (A on cë) × A = B → implies (A × 10) × A = B → A² × 10\n\nBut right side is mäcuïl-pöhualli-om-mahtlactli → may contain \"pöhualli\" which appears in (2)\n\nAnother idea: “pöhualli” is a base unit, like 20\n\nIn Nahuatl, 20 is a base. 20 is “pöhualli”.\n\nIn (2): cem-pöhualli × öme = öm-pöhualli → does this mean (13 × 20) × x = 13 × 20? Only if x=1.\n\nWait, if “cem” is 13, “öme” is 1 → then 13×20 ×1 = 13×20 → valid? But right is “öm-pöhualli” — öm is 13? or 14?\n\n“cem” and “öme” may be digits.\n\nIn Nahuatl, “cem” = 13, “öme” = 1 → so (13×20) × 1 = 13×20 → holds if multiplication is identity?\n\nBut (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli-om-ëyi → like “(A om y)” → may mean A × y?\n\nIf ëyi = 1 → then A × 1 = 13×20 on caxtölli on nähui\n\nBut that doesn’t help.\n\nAlternatively, the structure suggests that compound terms represent products or sums with positional value.\n\nBut for Arammba, we must deduce how the numbers 43 and 569 are formed.\n\nWe have:\n\n- yànparo = 2\n- fete = yenówe\n\nFrom (11): nimbo × fete = tarumba \nFrom (12): nimbo + yànparo tàxwo = fete tàxwo\n\nAssume \"tāxwo\" is multiplication → so yànparo tàxwo = 2 × ?\n\nBut in (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nSo: (2 × A) + (fete × B) = 2 × fete\n\nThis would require: 2A + fete B = 2fete → can only hold if A and B are small.\n\nSuppose A = 1, B = 1 → 2 + fete = 2fete → fete = 2 → then 2 + 2 = 4 → 2×fete = 4 → works.\n\nSo if fete = 2, then: 2 × 1 + 2 × 1 = 2 × 2 → 4 = 4 → valid.\n\nSo fete = 2\n\nThen from (11): nimbo × fete = tarumba → nimbo × 2 = tarumba → tarumba = 2 × nimbo\n\nFrom (12): nimbo + 2 tàxwo = fete tàxwo \nBut fete tàxwo = 2 tàxwo → and 2 tàxwo = 2 × something? \nSuppose \"tāxwo\" is multiplication → then 2 tàxwo = 2 × 1 = 2 → then: nimbo + 2 = 2 → nimbo = 0 → not sensible.\n\nAlternatively, \"tāxwo\" might be an indicator of a count.\n\nBut in (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nWith fete = yenówe = 2 → 2 × (2 tàxwo) = 2 × (2 tàxwo) → identity — true.\n\nSo no constraint.\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr \nIf cen-tzontli = 1, and values are additive, then:\n\n1 = tarumba + tambaroy + fete + asàr\n\nWith fete = 2 → so 1 = tarumba + tambaroy + 2 + asàr → impossible.\n\nContradiction.\n\nSo \"tarumba tambaroy fete asàr\" is not an addition.\n\nPerhaps it is a list of components that sum to the value of “cen-tzontli”.\n\nBut if fete = 2, and 1 = something including 2 → impossible.\n\nSo fete cannot be 2.\n\nThen where did we go wrong?\n\nGo back to (10): yenówe × (yenówe tàxwo) = fete (yenówe tàxwo)\n\nThis implies: A × (A tàxwo) = fete × (A tàxwo)\n\nIf A tàxwo ≠ 0, we can divide both sides → A = fete\n\nSo fete = yenówe — this is solid.\n\nNow in (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nLet’s write that as:\n\n(yànparo) tàxwo + (fete) asàr tàxwo = (yànparo) fete\n\nSuppose that \"X tàxwo\" means X × 1 → or X × a base?\n\nBut (7): ngámbi + ngámbi = ngámbi × yànparo → 2A = A × Y → Y = 2 → yànparo = 2\n\nSo yànparo = 2\n\nNow (9): 2 tàxwo + fete asàr tàxwo = 2 fete\n\nTry to assign values.\n\nSuppose that \"tāxwo\" means multiplication by 1 → then 2 ×1 + fete × asàr ×1 = 2 × fete\n\nBut \"asàr\" is a unit.\n\nFrom (8): ngámbi + asàr = tambaroy → so asàr is a number.\n\nAssume that \"tāxwo\" means \"× 1\" or is a unit.\n\nThen (9): 2 ×1 + fete × asàr ×1 = 2 × fete → 2 + fete × asàr = 2 fete\n\n→ fete × asàr = 2 fete - 2 = 2(fete - 1)\n\nSo asàr = 2 (fete - 1) / fete\n\nMust be rational.\n\nIf fete = 2 → asàr = 2(1)/2 = 1\n\nThen asàr = 1\n\nFrom (8): ngámbi + asàr = tambaroy → ngámbi + 1 = tambaroy\n\nFrom (7): ngámbi + ngámbi = ngámbi × 2 → true for any ngámbi, so no constraint.\n\nNow (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf cen-tzontli =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10131.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "unit_audit", + "sample_index": 3, + "output": "Begin by analyzing the given equations in Nahuatl and Arammba to infer linguistic patterns, particularly focusing on number expressions.\n\nWe are to write 43 and 569 in Arammba. First, inspect the equations and identify how numbers are formed.\n\nIn Nahuatl, the equations include:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nEquation (4): mäcuïlli + öme = chicöme → suggests a sum of two units results in a third. \nEquation (6): mäcuïlli × ëyi = caxtölli → multiplication. \nEquation (5): (mahtlactli-om-ëyi) × ëyi → yields a complex term. \n\nCompare to (7): ngámbi + ngámbi = ngámbi × yànparo \nThis suggests addition of a number (ngámbi) equals a product. But also, multiplicative structure is present.\n\nLook at (8): ngámbi + asàr = tambaroy → addition produces a compound value. \n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → shows that \"tàxwo\" is a marker of addition or duplication. \n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nHere, multiplying a term by its \"tàxwo\" version gives a compound. Note: \"tàxwo\" appears to mean \"doubled\" or \"twice.\"\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n\nFrom (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nThis suggests: (a) × (a tàxwo) = (fete a tàxwo) \nSo: a × (2a) = 2a × something? But result is \"fete a tàxwo\"\n\nBut: (12): nimbo + yànparo tàxwo = yenówe tàxwo \nLet us suppose \"yànparo tàxwo\" means \"two yànparo\". So nimbo + 2(yànparo) = yenówe tàxwo → possibly \"yenówe\" is a number, \"tàxwo\" is \"double\" or \"times two\".\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nThis implies: (2y) + (2f) = y f → suggests multiplication is involved.\n\nMore precise: (9) yànparo tàxwo = 2y, fete asàr tàxwo = 2f, and result is \"y f\" → which might mean \"y times f\" or \"product of y and f\".\n\nThus, addition of doubled terms equals product.\n\nThis mirrors equation (4): mäcuïlli + öme = chicöme → sum → product? But not exactly.\n\nWait: (4) mäcuïlli + öme = chicöme \nBut from (6): mäcuïlli × ëyi = caxtölli → this is multiplication.\n\nIn (1), mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"×\" and \"on\" suggest compound naming with a structure.\n\nBut financial numbers might be built via multiplication and addition.\n\nNow examine the target equations:\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n\nNow, 13, 14, 15, 16 are compound expressions equaling results.\n\nLook at (15): cen-tzontli = tarumba tambaroy fete asàr \n\"cen-tzontli\" is a unit. Right-hand side: tarumba, tambaroy, fete, asàr — which are terms from earlier equations.\n\nFrom (8): ngámbi + asàr = tambaroy → tambaroy = ngámbi + asàr \nFrom (11): nimbo × fete = tarumba → tarumba = nimbo × fete \nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo → suggests a sum to a product.\n\nAlso, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nLet’s try to interpret \"yenówe\" as \"1\", and \"yànparo\" as another number.\n\nBut observe (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ 2y + 2f = y × f \nSo: 2(y + f) = y × f → rearranged: y × f - 2y - 2f = 0 → (y - 2)(f - 2) = 4 \nThus, (y - 2)(f - 2) = 4 \nPossible integer solutions: \n(y-2, f-2) = (1,4) → (3,6) \n(2,2) → (4,4) \n(4,1) → (6,3) \n(1,4) → (3,6) \nSo possible pairs: (3,6), (4,4), (6,3) — multiple.\n\nBut in Nahuatl, (15): cen-tzontli = tarumba tambaroy fete asàr \n\"cen-tzontli\" may be a name for a number, possibly 100 or 1000. We can suspect that \"tarumba\" = nimbo × fete, and \"tambaroy\" = ngámbi + asàr.\n\nSo cen-tzontli = (nimbo × fete) + (ngámbi + asàr) — a sum of two expressions.\n\nNow look at (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \nThis is \"cen-xiquipilli\" = weremeke (some term) + tarumba + nimbo + yànparo\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n→ Left side: a complex term involving \"cen-tzontli\", which may be a numeral, attached to other units.\n\nBut perhaps \"cen-tzontli\" is 100, \"cen-xiquipilli\" is 1000 or \"cenzontli\" is based on 100.\n\nWe have equations connecting terms to outputs.\n\nBut we need to find values of 43 and 569 in Arammba.\n\nLook at (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSuppose that \"yenówe\" is the number 1. \nThen: 1 × 2(1) = 2 → 2 = fete × 2 → so fete = 1? But fete × 2 = 2 → yes.\n\nSo fete = 1.\n\nThen from (11): nimbo × fete = tarumba → nimbo × 1 = tarumba → tarumba = nimbo\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \nnimbo + 2(yànparo) = 2(yenówe) \nBut if yenówe = 1, then 2(yenówe) = 2 \nSo: nimbo + 2y = 2 → so nimbo = 2 - 2y \nBut nimbo must be positive → so y must be less than 1 → not possible.\n\nContradiction. So \"yenówe\" is not 1.\n\nTry other possibility: from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nLet a = yenówe \nThen: a × (a × 2) = (fete) × (a × 2) \n→ 2a² = 2a × fete \nDivide both sides by 2a (a ≠ 0): a = fete \nSo fete = a = yenówe\n\nTherefore: fete = yenówe\n\nNow from (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2(yànparo) = 2(yenówe) \nBut fete = yenówe → so: \nnimbo + 2y = 2f \nBut f = y (since fete = yenówe) \nSo: nimbo + 2y = 2y → nimbo = 0 → impossible.\n\nContradiction.\n\nTherefore, our interpretation of \"tàxwo\" as \"double\" must be revisited.\n\nAlternative: maybe \"tàxwo\" is \"plus\" or \"and\", not \"double\".\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nSo perhaps: [yànparo + fete asàr] = yànparo × fete\n\nSo this suggests: y + f = y × f → then (y-1)(f-1) = 1 → y=2, f=2\n\nSo y = 2, f = 2\n\nThus: yànparo = 2, fete = 2\n\nThen from (12): nimbo + yànparo tàxwo = yenówe tàxwo \nNow if \"tàxwo\" is just a connector or additive marker, perhaps \"yànparo tàxwo\" means \"yànparo + yànparo\" = 4 \nSimilarly, \"yenówe tàxwo\" = yenówe + yenówe = 2×yenówe\n\nSo (12): nimbo + 4 = 2×yenówe \nBut from earlier, (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ yenówe × (2 yenówe) = 2 yenówe \n→ 2 yenówe² = 2 yenówe → yenówe² = yenówe → yenówe(yenówe -1) = 0 → yenówe = 0 or 1 \nBut 0 invalid, so yenówe = 1\n\nThen from (12): nimbo + 4 = 2×1 = 2 → nimbo = -2 → invalid\n\nContradiction again.\n\nAlternative: \"tàxwo\" means \"times two\" but in (9), yànparo tàxwo means 2y, fete asàr tàxwo means 2f, and result is y f → y × f.\n\nSo equation: 2y + 2f = y f → yf - 2y - 2f = 0 → (y-2)(f-2) = 4 \nAs earlier.\n\nSolutions: (y,f) = (3,6), (4,4), (6,3)\n\nTry (y,f) = (4,4) → yànparo = 4, fete = 4\n\nThen from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ a × 2a = 4 × 2a → 2a² = 8a → 2a² - 8a = 0 → 2a(a - 4) = 0 → a = 0 or 4 → a = 4\n\nSo yenówe = 4\n\nThen from (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2×4 = 2×4 → nimbo + 8 = 8 → nimbo = 0 → invalid\n\nNext: (y,f) = (3,6)\n\nThen yànparo = 3, fete = 6\n\n(10): a × 2a = 6 × 2a → 2a² = 12a → a² = 6a → a(a-6)=0 → a=6\n\nSo yenówe = 6\n\n(12): nimbo + 2×3 = 2×6 → nimbo + 6 = 12 → nimbo = 6\n\nFrom (11): nimbo × fete = tarumba → 6 × 6 = 36 → tarumba = 36\n\nFrom (8): ngámbi + asàr = tambaroy\n\nWe don’t have value for these yet.\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis seems to be a compound expression.\n\nBut if \"tarumba tambaroy fete asàr\" means sum or product of these values?\n\nPossibly, the expression is a sum.\n\nBut tarumba = 36, fete = 6, asàr = ?\n\nWe need more.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nBut difficult.\n\nBut perhaps the key is in the basic numbers.\n\nIn Nahuatl, multiplication and addition are tagged with different markers.\n\nLook at (6): mäcuïlli × ëyi = caxtölli → suggests caxtölli = mäcuïlli × ëyi\n\n(4): mäcuïlli + öme = chicöme\n\nWe are to find 43 and 569 in Arammba.\n\nPerhaps the system is based on base-10 or factors.\n\nWe saw in Arammba that in (9): 2y + 2f = y f → (y-2)(f-2)=4\n\nWith (y,f) = (3,6), (4,4), (6,3)\n\nTry (4,4): y=4, f=4 → from (10): a=4 → yenówe=4, then (12): nimbo + 8 = 8 → nimbo=0 → invalid\n\n(3,6): valid, nimbo=6\n\n(6,3): y=6, f=3 → yànparo=6, fete=3\n\n(10): a × 2a = 3 × 2a → 2a² = 6a → a² = 3a → a(a-3)=0 → a=3\n\nyenówe=3\n\n(12): nimbo + 2×6 = 2×3 → nimbo + 12 = 6 → nimbo = -6 → invalid\n\nSo only valid solution is (y,f)=(3,6), with yànparo=3, fete=6, yenówe=6, nimbo=6\n\nNow, from (11): nimbo × fete = tarumba → 6 × 6 = 36 → tarumba = 36\n\nFrom (8): ngámbi + asàr = tambaroy\n\nWe do not have values.\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nAssuming \"weremeke\" is a fixed term, and the rest are numbers.\n\nPerhaps \"cen\" is a base number.\n\nIn many languages, \"cen\" may mean 100.\n\nIn Nahuatl, \"cantli\" or \"cenditl\" may be 100.\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nIf cen-tzontli is a number, and it equals sum of those terms (in value), then:\n\nTarget: cen-tzontli = 36 (tarumba) + tambaroy + 6 (fete) + asàr\n\nBut tambaroy = ngámbi + asàr, so:\n\ncen-tzontli = 36 + (ngámbi + asàr) + 6 + asàr = 42 + ngámbi + 2asàr\n\nWe have no value.\n\nBut in (16): cen-xiquipilli = weremeke + tarumba + nimbo + yànparo\n\nIf xiquipilli is a large number, perhaps 1000, and cen = 100, so cen-xiquipilli = 1000\n\nSo 1000 = weremeke + 36 + 6 + 3 = weremeke + 45 → weremeke = 955\n\nNot helpful.\n\nBack to number construction.\n\nNow, in (7): ngámbi + ngámbi = ngámbi × yànparo\n\nSo 2n = n × y → 2n = n y → if n≠0, then 2 = y\n\nSo yànparo = 2\n\nContradicts earlier value of 3 or 6.\n\nMajor conflict.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2n = n × y → 2 = y\n\nSo yànparo = 2\n\nBut in (9): 2y + 2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9644.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 0, + "output": "First, analyze the given sentences to extract patterns in Kunuz Nubian grammar, especially with regard to verb structure, particles, and the meaning of affixes.\n\nKey observations from the examples:\n\n1. \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → We bought the camels for the neighbours. \n - \"kanarriːcciːg\" = bought (past tense of \"buy\")\n - \"kamiːg\" = the camels\n - \"jaːnticcirsu\" = for the neighbours\n\n2. \"tirt kadeːg allesu\" → The owner repaired the dress. \n - \"tirt\" = repaired \n - \"kadeːg\" = the dress \n - \"allesu\" = the owner (subject)\n\n3. \"jahali waliːg darbadki biticcirra\" → The young men will give the chicken to the dogs. \n - \"jahali\" = young men \n - \"waliːg\" = will (future marker) \n - \"darbadki\" = the chicken \n - \"biticcirra\" = to the dogs\n\n4. \"man jahalgi kadeːcciːg maːgtirsu\" → He stole the dresses for the young man. \n - \"man\" = he \n - \"jahalgi\" = stole (past) \n - \"kadeːcciːg\" = the dresses \n - \"maːgtirsu\" = for the young man\n\n5. \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces. \n - \"ay\" = I \n - \"beyyeːcciːg\" = buying (present continuous) \n - \"ajaːnirri\" = the necklaces\n\n6. \"wal aygi baːbiːg eldeːnsu\" → The dog found the doors for me. \n - \"wal\" = the dog \n - \"aygi\" = found \n - \"baːbiːg\" = the doors \n - \"eldeːnsu\" = for me\n\n7. \"magas ikki waliːg ticcirsu\" → The thief gave you (pl.) the dogs. \n - \"magas\" = the thief \n - \"ikki\" = you (pl.) \n - \"waliːg\" = will (future) \n - \"ticcirsu\" = gave\n\n8. \"iːdi magaski kamiːg tirsa\" → The men gave the camels to the thief. \n - \"iːdi\" = the men \n - \"magaski\" = the camels \n - \"tirsa\" = gave to the thief\n\n9. \"ay hanuːg bijomri\" → I will strike the donkey. \n - \"ay\" = I \n - \"hanuːg\" = will (future) \n - \"bijomri\" = strike the donkey\n\n10. \"sarkaːyi aygi beyyeːcciːg adeːnda\" → The cowards are giving me the necklaces. \n - \"sarkaːyi\" = the cowards \n - \"aygi\" = are giving (present) \n - \"beyyeːcciːg\" = the necklaces \n - \"adeːnda\" = to me\n\nPattern extraction:\n\n- The verb stem often appears with a suffix for tense or aspect:\n - \"kanarriːcciːg\" = bought (past) → \"kanarriːg\" + \"iːcciːg\" = past of \"buy\"\n - \"beyyeːcciːg\" = buying / am buying → present\n - \"tirt\" = repaired → past\n - \"waliːg\" = will → future marker\n - \"aygi\" = is giving → present (stative or ongoing)\n\n- Objects are marked by a direct object noun with \"ki\" or \"g\" or \"i\" or \"ri\" suffixes:\n - \"kamiːg\" = the camels\n - \"kadeːg\" = the dress\n - \"darbadki\" = the chicken\n - \"kadeːcciːg\" = the dresses\n - \"ajomirra\" → could be \"the donkey\"\n\n- Prepositional/recipient objects:\n - \"jaːnticcirsu\" = for the neighbours\n - \"maːgtirsu\" = for the young man\n - \"eldeːnsu\" = for me\n - \"adeːnda\" = to me\n - \"biticcirra\" = to the dogs\n\n- Subject markers:\n - \"ar\" = we\n - \"tirt\" = the owner\n - \"jahali\" = young men\n - \"man\" = he\n - \"wal\" = the dog\n - \"iːdi\" = the men\n - \"ay\" = I\n - \"sarkaːyi\" = the cowards\n\nNow, analyze each new sentence:\n\n11. magasi argi ajomirra. \n - \"magasi\" = the thief (from \"magas\" + i) \n - \"argi\" = will (future) \n - \"ajomirra\" = the donkey? \n → \"The thief will strike the donkey.\"\n\n12. ay kanarriːg baːbki alletirsi. \n - \"ay\" = I \n - \"kanarriːg\" = bought (past stem) \n - \"baːbki\" = the doors \n - \"alletirsi\" = for me → \"I bought the doors for me.\"\n\n13. hanu tirtiːg elirsu. \n - \"hanu\" = will (future) \n - \"tirtiːg\" = repaired (past of \"tirt\") \n - \"elirsu\" = the doors? \n → \"I will repair the doors.\"\n\n14. tirti argi kamgi deːccirsa. \n - \"tirti\" = repaired (past) \n - \"argi\" = will (future) \n - \"kamgi\" = the camels \n - \"deːccirsa\" = to the thief \n → \"He repaired the camels to the thief\" — but syntactically, \"tirti\" is subject? \n Wait: \"tirti\" appears as verb root, so \"tirti\" = repaired, \"argi\" = will — but order is \"tirti argi\" — likely \"will repair\" \n Possible: \"The owner will repair the camels for the thief.\" \n But \"deːccirsa\" = to the thief? \n So → \"The owner will repair the camels to the thief.\" \n But in earlier examples, \"to\" is often in a recipient form. \n From (8): \"iːdi magaski kamiːg tirsa\" → men gave camels to thief → \"tirsa\" = to the thief.\n\n So \"deːccirsa\" = to the thief → recipient.\n\n Who is the subject? \"tirti\" is the verb. No subject given. \n But in (2): \"tirt kadeːg allesu\" → owner repaired dress → \"tirt\" = verb, subject implied.\n\n Maybe \"tirti\" is a verb phrase with \"tirt\" as root, \"i\" as marker? \n But structure: \"tirti argi kamgi deːccirsa\" \n → \"tirti\" = repaired (past), \"argi\" = will — how can a past verb be followed by will?\n\n Wait — is \"tirti\" used as a future verb? No, \"tirt\" is past, \"argi\" is future.\n\n Possible misreading: perhaps \"tirti\" is not past but present? \n But in (2): \"tirt\" = repaired (past), not present.\n\n Alternative: \"tirti\" = will repair? \n But \"argi\" is future — if \"tirti\" alone is future, it's redundant.\n\n Other possibility: \"tirti\" is the verb, \"argi\" is a marker for future form? \n But \"argi\" appears in \"argi ajomirra\" → future.\n\n Case: in (14): \"tirti argi kamgi deːccirsa\" \n → likely \"will repair the camels to the thief\" \n But who is the subject? Not given.\n\n In (2): \"tirt kadeːg allesu\" → owner repaired dress → subject is \"tirt\" if \"tirt\" is subject.\n\n But here, no subject — perhaps implied actor? \n But the structure is similar to (8): \"iːdi magaski kamiːg tirsa\" → men gave camels to thief → \"iːdi\" = subject.\n\n Here, no subject. \"tirti\" is verb. \n Is it possible \"tirti\" is a noun? No — \"tirt\" is verb.\n\n Perhaps it's a mixed construction: \"tirti\" = will repair → lost future marker?\n\n Look back at (3): \"jahali waliːg darbadki biticcirra\" → young men will give chicken to dogs \n → \"waliːg\" = future marker.\n\n In (9): \"ay hanuːg bijomri\" → I will strike → \"hanuːg\" = will.\n\n In (14): \"tirti argi\" — \"argi\" is likely the future marker. So \"tirti\" is base verb? \n But in (2), \"tirt\" = repair → past.\n\n So perhaps \"tirti\" = repair, and with \"argi\" = future, so \"will repair\"? \n But no subject.\n\n This seems like a mistake in parsing.\n\n Alternatively: maybe \"tirti\" is a verb stem, and \"argi\" modifies tense — future.\n\n → \"tirti\" is \"repair\", with future tense \"argi\" → \"will repair\"\n\n Object: \"kamgi\" = the camels \n Recipient: \"deːccirsa\" = to the thief\n\n → \"will repair the camels to the thief.\"\n\n But ownership? Likely a transfer.\n\n But no subject — perhaps unmarked subject (default subject).\n\n Compare with (10): \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me → subject is \"sarkaːyi\"\n\n So here, no subject, so likely the subject is missing or general.\n\n Still, the verb \"repair\" is used with recipient.\n\n Final: \"will repair the camels to the thief.\"\n\n15. ay darbadki bijaːndi. \n - \"ay\" = I \n - \"darbadki\" = the chicken \n - \"bijaːndi\" = strike? \n → \"I will strike the chicken.\"\n\nBut in (9): \"ay hanuːg bijomri\" = I will strike the donkey. \n\"bijomri\" = strike the donkey\n\nSo \"bijaːndi\" = strike the chicken\n\nTherefore: \"I will strike the chicken.\"\n\nNow, formalize:\n\n11. magasi argi ajomirra → \"The thief will strike the donkey.\"\n\n12. ay kanarriːg baːbki alletirsi → \"I bought the doors for me.\"\n\n13. hanu tirtiːg elirsu → \"I will repair the doors.\"\n\n14. tirti argi kamgi deːccirsa → \"will repair the camels to the thief.\"\n\n15. ay darbadki bijaːndi → \"I will strike the chicken.\"\n\nNow, check consistency:\n\n- \"argi\" appears in 11 and 14 — both with future meaning → \"will\"\n- \"hanu\" = will → in 13 → \"I will repair\"\n- \"tirti\" = repair → base verb\n- \"deːccirsa\" = to the thief → from (8) \"tirsa\" = to the thief\n- \"ajomirra\" = donkey (from (9) \"bijomri\" = strike donkey → \"ajomirra\" = donkey)\n- \"bijaːndi\" = strike chicken → from (9) \"bijomri\" = strike donkey → pattern: \"bij\" + noun → strike + noun\n- \"baːbki\" = the doors → like \"kamiːg\" = camels\n- \"elirsu\" = doors? In (6) \"eldeːnsu\" = for me; in (8) \"tirsa\" = to thief; so \"elirsu\" likely = doors?\n- In (13): \"hanu tirtiːg elirsu\" → will repair doors\n\nConsistency check with known forms:\n\n- \"tirt\" = repair → \"tirti\" = repair (past or base form with new stress)\n- \"kanarriːg\" = bought → in 12: \"I bought doors for me\"\n\nAll patterns match.\n\nFinal translations:\n\n11. The thief will strike the donkey. \n12. I bought the doors for me. \n13. I will repair the doors. \n14. Will repair the camels to the thief. → better: \"The owner will repair the camels to the thief\" — but no subject. \nWait — in (14), the subject is missing. \nBut in (2): \"tirt kadeːg allesu\" → tirt = owner → subject is attached.\n\nHere, no subject. Is \"tirti\" used as subject?\n\nCompare to (8): \"iːdi magaski kamiːg tirsa\" → iːdi = subject.\n\nIn (14): no subject.\n\nCould \"tirti\" be subject? Unlikely — \"tirti\" is verb.\n\nPerhaps it's a standalone verb phrase.\n\nBut in (5): \"ay beyyeːcciːg\" — \"ay\" is subject.\n\nSo in (14), no subject — default or missing.\n\nBut in (10): \"sarkaːyi aygi beyyeːcciːg\" — subject present.\n\nSo perhaps in (14), it's implied.\n\nStill, the grammar likely allows for the verb to stand independently.\n\nBut in context, likely \"Someone will repair the camels to the thief.\"\n\nHowever, no subject. But \"tirti\" is a verb, not a noun.\n\nTherefore, the subject is missing.\n\nBut in the original sentences, subject is usually present.\n\nPossibility: typo or misalignment.\n\nAlternative: \"tirti\" = the repair? Not derived.\n\nStick to pattern: verb + future marker + object + recipient.\n\nIn (14): tirti (verb) + argi (future) → will repair \nobject: kamgi = the camels \nrecipient: deːccirsa = to the thief\n\nSo translation: \"will repair the camels to the thief\"\n\nTo match style, like (7): \"magas ikki waliːg ticcirsu\" → thief gave you the dogs\n\nSo similar: \"will repair the camels to the thief\"\n\nNo subject needed — it's a standalone action.\n\nSimilarly, in (1): \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought\n\nSo action is complete.\n\nThus, final translations:\n\n11. The thief will strike the donkey. \n12. I bought the doors for me. \n13. I will repair the doors. \n14. Will repair the camels to the thief. \n15. I will strike the chicken.\n\nBut (14) lacks subject — is \"tirti\" the subject? No — it's the verb.\n\nCould it be that \"tirti\" is a noun? Only in (2): \"tirt\" is verb.\n\nNo.\n\nThus, likely the sentence is missing subject — but perhaps in context, it's \"he\" or \"they\".\n\nBut not specified.\n\nStill, based on pattern, we infer the verb and objects.\n\nThus, accept as: \"will repair the camels to the thief\"\n\nNow, table:\n\n| unit id | requested meaning/value | derived candidate | evidence |\n|--------|--------------------------|-------------------|--------|\n| 11 | magasi argi ajomirra | The thief will strike the donkey | magasi = thief; argi = will; ajomirra = donkey (from bijomri = strike donkey) |\n| 12 | ay kanarriːg baːbki alletirsi | I bought the doors for me | ay = I; kanarriːg = bought; baːbki = doors; alletirsi = for me (from eldeːnsu = for me) |\n| 13 | hanu tirtiːg elirsu | I will repair the doors | hanu = will; tirtiːg = repair; elirsu = doors (from eldeːnsu = for me; elirsu likely doors) |\n| 14 | tirti argi kamgi deːccirsa | will repair the camels to the thief | tirti = repair; argi = will; kamgi = camels; deːccirsa = to the thief (from tirsa = to thief) |\n| 15 | ay darbadki bijaːndi | I will strike the chicken | ay = I; darbadki = chicken; bijaːndi = strike (from bijomri = strike donkey) |\n\nAll derived with evidence.\n\nFinal answers:\n\n\\boxed{a.1: The thief will strike the donkey; a.2: I bought the doors for me; a.3: I will repair the doors; a.4: will repair the camels to the thief; a.5: I will strike the chicken}", + "generated_tokens": 3993, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: The thief will strike the donkey; a.2: I bought the doors for me; a.3: I will repair the doors; a.4: will repair the camels to the thief; a.5: I will strike the chicken", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 11616.0, + "ioling_final_answer_chars": 173.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 1, + "output": "First, analyze the given sentences to identify patterns in Kunuz Nubian syntax, especially in verb structure, semantics, and object/actor relations.\n\nLook at verb morphology and core semantic roles:\n\n- Sentence 1: *ar kanarriːcciːg kamiːg jaːnticcirsu* → \"We bought the camels for the neighbours.\" \n → \"kanarriːcciːg\" = bought, verb; \"kamiːg\" = camels (object); \"jaːnticcirsu\" = for the neighbours (beneficiary). \n → Verb root: *kanarri* + *-ciːg* (past, bought), object *kamiːg*, benefactive suffix *-cirsu*.\n\n- Sentence 2: *tirt kadeːg allesu* → \"The owner repaired the dress.\" \n → *tirt* = repaired; *kadeːg* = dress (object); *allessu* = (the) dress? Wait—sentence says \"the dress\", so object is *kadeːg*; verb *tirt* = repair. \n → *tirt* = repair; *kadeːg* = object; no beneficiary.\n\n- Sentence 3: *jahali waliːg darbadki biticcirra* → \"The young men will give the chicken to the dogs.\" \n → *jahali* = young men (subject); *waliːg* = will; *darbadki* = give (verb); *biticcirra* = the chicken (object); *to the dogs*? Not directly stated. \n → *darbadki* = give; object *biticcirra*; likely *biticcirra* = chicken; meaning: \"give the chicken\" → subject gives object.\n\n- Sentence 4: *man jahalgi kadeːcciːg maːgtirsu* → \"He stole the dresses for the young man.\" \n → *man* = he; *jahalgi* = stole; *kadeːcciːg* = the dresses (object); *maːgtirsu* = for the young man. \n → Verb *jahalgi* = stole; object *kadeːcciːg*; beneficiary *maːgtirsu*.\n\n- Sentence 5: *ay beyyeːcciːg ajaːnirri* → \"I am buying the necklaces.\" \n → *ay* = I; *beyyeːcciːg* = buying; *ajaːnirri* = the necklaces. \n → Present continuous; *beyyeː* = buy; + *-ciːg*; object *ajaːnirri*.\n\n- Sentence 6: *wal aygi baːbiːg eldeːnsu* → \"The dog found the doors for me.\" \n → *wal* = dog; *aygi* = found; *eldeːnsu* = doors (object); \"for me\" = *for me*, likely encoded in suffix or prepositional phrase. \n → *aygi* = found; object *eldeːnsu*; beneficiary *me*.\n\n- Sentence 7: *magas ikki waliːg ticcirsu* → \"The thief gave you (pl.) the dogs.\" \n → *magas* = thief; *ikki* = you (pl.); *ticcirsu* = gave the dogs. \n → *ticcirsu* = give; object *dogs*; recipient *ikki* (you).\n\n- Sentence 8: *iːdi magaski kamiːg tirsa* → \"The men gave the camels to the thief.\" \n → *iːdi* = men; *magaski* = to the thief (beneficiary); *kamiːg* = camels (object); *tirsa* = gave. \n → *tirsa* = gave; object *kamiːg*; beneficiary *magaski*.\n\n- Sentence 9: *ay hanuːg bijomri* → \"I will strike the donkey.\" \n → *ay* = I; *hanuːg* = will; *bijomri* = strike (the donkey). \n → *hanuːg* = will; *bijomri* = strike; object = donkey.\n\n- Sentence 10: *sarkaːyi aygi beyyeːcciːg adeːnda* → \"The cowards are giving me the necklaces.\" \n → *sarkaːyi* = cowards (subject); *aygi* = are giving; *beyyeːcciːg* = buying? No — *aygi* = give; *beyyeːcciːg* = necklaces; *adeːnda* = to me. \n → *adeːnda* = to me → beneficiary.\n\nNow observe patterns:\n\n- Verb roots: \n \"buy\" = *beyyeː* → *beyyeːcciːg*, *beyyeːcciːg* \n \"give\" = *darbadki*, *ticcirsu*, *tirsa*, *aygi* \n \"buy\" also appears with *aygi* — possibly variant?\n\nWait: sentence 10: \"giving\" → *aygi* = give → so *aygi* is \"give\", used in multiple forms.\n\nAlso, *tirsa* = gave; *ticcirsu* = give; *tirsa* in 8 → \"gave\", so likely past.\n\n- Object markers: \n After verbs, object noun appears directly (e.g., *kamiːg*, *kadeːg*, *biticcirra*, *kadeːcciːg*, *eldeːnsu*, *kamiːg*, *bijomri*). \n - Object noun always follows the verb.\n\n- Beneficiary: \n Phrases like *for the neighbours*, *for the young man*, *to me*, *to you*, *to the thief* \n → Often appear as suffixes or as prepositional phrases *-cirsu*, *-tirsu*, *-adeːnda*, *-maːgtirsu*\n\nNow examine inflectional suffixes:\n\nGeneral pattern: \n[Subject] [verb] [object] [suffix] → beneficiary or direction\n\nSpecifically:\n\n- *-cirsu* = for/about/for someone (beneficiary) \n- *-tirsu* = to someone (recipient) \n- *-maːgtirsu* = for the young man \n- *-adeːnda* = to me \n- *-elirsu* = to you? (In 13)\n\nNow, examine target sentences:\n\n11. *magasi argi ajomirra* \n→ *magasi* → likely derived from *magas* (thief) + suffix *-i*? \nPossibly \"thief\" → *magasi* = thief (used in 7 as *magas*; may be with -i for subject?) \n*argi* → verb? \n*ajomirra* → object?\n\nLook at (7): *magas ikki waliːg ticcirsu* → \"The thief gave you the dogs.\" \nSo *magas* = thief (subject); *ticcirsu* = gave; *ikki* = you (recipient); *dogs* = object.\n\nSo *ticcirsu* = give. Could *argi* be a variant of *ticcirsu*?\n\nBut *argi* is not *ticcirsu*.\n\nAlternatively, observe that in (2): *tirt* = repair \n(6): *aygi* = found \n(7): *ticcirsu* = gave \n(8): *tirsa* = gave — past tense \n(3): *darbadki* = gave \n(4): *jahalgi* = stole \n\nSo different verbs for different actions.\n\nNow: *argi* — not in list. But *ajomirra* = “strike”?\n\nLook at (9): *ay hanuːg bijomri* = \"I will strike the donkey.\" \n→ *bijomri* = strike.\n\nThus, *bijomri* = strike.\n\nSo *argi* may be a verb meaning “hit” or “strike”?\n\nCompare: \n(9): *hanuːg bijomri* → will strike → *bijomri* = strike.\n\nSo likely *argi* = strike, or *hit*?\n\nBut *argi* vs *bijomri* — different.\n\nCould *argi* = \"to strike\" or \"to hit\"?\n\nBut no example matches.\n\nAlternatively, is there a pattern of who is doing what?\n\nNote that in (1): *ar kanarriːcciːg kamiːg jaːnticcirsu* → \"We bought the camels for the neighbours\" \n→ *jaːnticcirsu* = for the neighbours → beneficiary.\n\nSimilarly, (4): *man jahalgi kadeːcciːg maːgtirsu* → \"He stole the dresses for the young man\" → *maːgtirsu* = for the young man.\n\n(6): *wal aygi baːbiːg eldeːnsu* → \"The dog found the doors for me\" → *eldeːnsu* = doors; implicit \"for me\"?\n\nNot clearly marked.\n\n(10): *sarkaːyi aygi beyyeːcciːg adeːnda* → \"The cowards are giving me the necklaces\" → *adeːnda* = to me.\n\nIn (8): *iːdi magaski kamiːg tirsa* → \"The men gave the camels to the thief\" → *magaski* = to the thief.\n\nThus, beneficiary/suffix: \n- *-cirsu* = for someone \n- *-tirsu* = to someone \n- *-maːgtirsu* = for the young man \n- *-adeːnda* = to me \n- *-elirsu* = ? → in (13) we have *hanu tirtiːg elirsu*\n\nSo likely *elirsu* = to you?\n\n(13): *hanu tirtiːg elirsu* → \"I will find you\" or \"I will strike you\"?\n\n*hanu* = will? → like *hanuːg* in (9) \n*hanu* = will/going to \n*hanuːg* in (9): “I will strike” \nSo *hanu* = will\n\nThen *tirtiːg* = verb? \n*tiːrt* = repair → *tirtiːg*? \nBut “repair” doesn’t make sense with “you”.\n\nWait — *tirt* in (2): \"repairs\" \n(6): \"found\" \n(7): \"gave\" \nNo such as “repair” with *elirsu*.\n\nBut *tirtiːg* → possibly a past tense of *tirt*?\n\nBut in (8) we have *tirsa* — past of *tirt*?\n\nPossibly: \n- *tirt* = repair \n- *tirsa* = gave (past) \n- *tirtiːg* = will repair? → but *hanu* = will, so *hanu tirtiːg* → \"will repair\"?\n\nBut then *elirsu* = to you?\n\nSo (13): \"I will repair you\"? That's odd — doesn't make sense.\n\nAlternative: *tirt* = find? \n(6): *wal aygi baːbiːg eldeːnsu* → \"The dog found the doors for me\" → *aygi* = found.\n\nSo *aygi* = found.\n\nIs *tirt* = found?\n\nIn (13): *hanu tirtiːg elirsu* → \"I will find you\" → more plausible.\n\nYes. \"I will find you\" makes sense.\n\nSo *tirtiːg* = \"will find\" (tirt = find; iːg = present/past? or inflected)\n\nBut *tirt* = find (in (6))\n\nSo likely *tirt* = find.\n\nThen *tirtiːg* = will find.\n\nThus, (13): \"I will find you.\"\n\nSimilarly, in (14): *tirti argi kamgi deːccirsa*\n\n→ *tirti* = will find? — but *tirti* → maybe \"will\" + *tirt*?\n\nBut *tirti* = will find?\n\nThen *argi* = verb; *kamgi* = object; *deːccirsa* = to whom?\n\n*deːccirsa* → could be *-cirsu* = for → but *deːccirsa*?\n\nNote that in (8): *magaski* = to the thief — so *-ski* = to the X?\n\nIn (10): *adeːnda* = to me → *-adeːnda*\n\nIn (13): *elirsu* → to you?\n\nSo *elirsu* = to you\n\nThen *deːccirsa* → if it's a form like *-cirsu*, maybe *-cirsu* or *-tirsu*?\n\nBut *deːccirsa* → could be *-cirsu* with *deː* preposition?\n\nAlternatively, observe that in (4): *kadeːcciːg maːgtirsu* → for the young man → *maːgtirsu*\n\nIn (6): *eldeːnsu* — doors; but not with suffix\n\nIn (10): *adeːnda* → to me\n\nSo possible recipient suffixes: \n- *-cirsu* = for \n- *-tirsu* = to \n- *-maːgtirsu* = for the young man \n- *-adeːnda* = to me \n- *-elirsu* = to you?\n\nYes — pattern supports *elirsu* = to you.\n\nNow, in (14): *tirti argi kamgi deːccirsa* \n→ *tirti* = will find? \n→ *argi* = verb? \n→ *kamgi* = object → dogs? \n→ *deːccirsa* = to whom?\n\nBut if *deːccirsa* = to you → then \"will find the dogs for you\"?\n\nBut *deːccirsa* — note that in (1): *jaːnticcirsu* = for the neighbours → *-cirsu* \nSo *deːccirsa* — *deː* + *-ccirsa*?\n\nPossibly *-cirsu* variant?\n\nBut *deː* may be preposition “to”?\n\nIn (10): *adeːnda* = to me → *adeː* + *nda*\n\nSo *adeːnda* = to me → so *adeː-* = to\n\nSimilarly, *elirsu* = to you → *elir-*?\n\nIn (13): *elirsu* → to you\n\nThus, *deːccirsa* → *deː* + *-cirsu* → to + (someone) → \"to the X\"?\n\nBut what is *ccirsa*?\n\nAlternatively, is there a verb *argi*?\n\nFrom (9): *bijomri* = strike\n\nIs *argi* = strike?\n\nUnlikely — different.\n\nPerhaps *argi* = hit?\n\nBut no other match.\n\nWait — in (3): *jahali waliːg darbadki biticcirra* → \"The young men will give the chicken to the dogs.\"\n\n→ *waliːg* = will → so *waliːg* = will\n\nIn (12): *ay kanarriːg baːbki alletirsi*\n\n→ *ay* = I \n→ *kanarriːg* = buy \n→ *baːbki* = object? \n→ *alletirsi* = suffix?\n\n*alletirsi* — like *-cirsu* or *-tirsu*?\n\nIn (1): *jaːnticcirsu* = for the neighbours → *cirsu* = for \nIn (4): *maːgtirsu* = for young man \nIn (6): *eldeːnsu* → no suffix \nIn (10): *adeːnda* = to me\n\nSo *alletirsi* → *al*? *letirsi*?\n\nCould be *-tirsu* for \"to\"?\n\nBut *alletirsu* — not matching.\n\nNote: (1): *kanarriːcciːg jaːnticcirsu* → buy + for \n→ *jaːnticcirsu* = for the neighbours\n\nSo suffix *-cirsu* = for\n\nBut *baːbki* → what is it?\n\nIn (4): *kadeːcciːg maːgtirsu* → for the young man\n\nSo *maːgtirsu* = for young man\n\nSo *baːbki* = probably \"the dresses\" or \"the clothes\"? \nBut in (4): *kadeːcciːg* = dresses\n\nCompare: (5): *ay beyyeːcciːg ajaːnirri* → \"I am buying the necklaces\"\n\nSo *beyyeːcciːg* = buy; *ajaːnirri* = necklaces\n\nThus, *kanaːriːg* or *kanarriːg* = buy\n\nSo in (12): *ay kanarriːg baːbki alletirsi* → I buy the [something] for [someone]\n\n*baːbki* = object? → likely \"the dresses\"?\n\n*alletirsi* = ? — suffix?\n\nPossibly *-tirsu* = to → \"to me\" or \"to you\"?\n\nBut in (6): *aygi baːbiːg eldeːnsu* → \"The dog found the doors for me\" → *eldeːnsu* = doors; no object suffix?\n\nNo — only object appears after verb.\n\nSo object is *baːbki*, then suffix.\n\n*alletirsi* → *al* + *letirsi*?\n\nIf *cirsu* = for, *tirsu* = to, then perhaps *al* is vowel infix?\n\nBut in (4):", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10549.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 2, + "output": "First, analyze the given sentences to identify grammatical patterns and meaning mappings in Kunuz Nubian.\n\nLook at the verb structure and agent/theme/recipient roles.\n\nSentence 1: \nar kanarriːcciːg kamiːg jaːnticcirsu. \nWe bought the camels for the neighbours. \n→ \"kanarriːcciːg\" = bought (a purchase, action of acquiring) \n\"kanarriːcciːg\" + \"kamiːg\" (the camels) + \"jaːnticcirsu\" (for the neighbours) \nStructure: [Subject] [verb] [object] [for-recipient]\n\nSentence 2: \ntirt kadeːg allesu. \nThe owner repaired the dress. \n→ \"tirt\" = repaired (past tense of repair) \n\"kadeːg\" = the dress \n\"allesu\" = the owner \n→ \"tirt\" + [object] + [agent] → repair [object] by [agent] \n→ Typically, in such languages, verb is transitive with object and agent as a complement.\n\nSentence 3: \njahali waliːg darbadki biticcirra. \nThe young men will give the chicken to the dogs. \n→ \"jahali\" = young men (subject) \n\"waliːg\" = will (future) \n\"darbadki\" = give \n\"biticcirra\" = chicken \n→ \"give [object] to [recipient]\" \nStructure: subject + future + verb + object + to + recipient\n\nSentence 4: \nman jahalgi kadeːcciːg maːgtirsu. \nHe stole the dresses for the young man. \n→ \"man\" = he \n\"jahalgi\" = stole (past) \n\"kadeːcciːg\" = the dresses \n\"maːgtirsu\" = for the young man \n→ \"steal [object] for [recipient]\" → likely same as \"buy for [recipient]\" → action with purpose or recipient\n\nSentence 5: \nay beyyeːcciːg ajaːnirri. \nI am buying the necklaces. \n→ \"ay\" = I \n\"beyyeːcciːg\" = buying (action) \n\"ajaːnirri\" = the necklaces \n→ \"I am buying [object]\" → present progressive, no recipient\n\nSentence 6: \nwal aygi baːbiːg eldeːnsu. \nThe dog found the doors for me. \n→ \"wal\" = dog \n\"aygi\" = found (past) \n\"baːbiːg\" = the doors \n\"eldeːnsu\" = for me \n→ \"found [object] for [recipient]\" → again, \"for\" introduces recipient\n\nSentence 7: \nmagas ikki waliːg ticcirsu. \nThe thief gave you (pl.) the dogs. \n→ \"magas\" = thief (subject) \n\"ikki\" = you (plural) \n\"ticcirsu\" = gave \n→ \"gave [object] to [recipient]\" \nStructure: [subject] [verb] [object] [to-recipient]\n\nSentence 8: \niːdi magaski kamiːg tirsa. \nThe men gave the camels to the thief. \n→ \"iːdi\" = men (subject) \n\"magaski\" = to the thief \n\"tirsa\" = gave \n→ \"gave [object] to [recipient]\" \n\"magaski\" = to the thief → indicates recipient\n\nSentence 9: \nay hanuːg bijomri. \nI will strike the donkey. \n→ \"ay\" = I \n\"hanuːg\" = will \n\"bijomri\" = strike (action) \n→ \"I will strike [object]\" → action on a single object, no recipient\n\nSentence 10: \nsarkaːyi aygi beyyeːcciːg adeːnda. \nThe cowards are giving me the necklaces. \n→ \"sarkaːyi\" = cowards (subject) \n\"aygi\" = are giving (present) \n\"beyyeːcciːg\" = necklaces \n\"adeːnda\" = to me \n→ \"are giving [object] to [recipient]\" — \"to me\"\n\nKey pattern: \n- Verbs often have a core meaning (buy, repair, give, steal, strike) \n- Objects are marked after the verb (kamiːg → camels, kadeːg → dress, etc.) \n- Recipient/receiver is introduced with a \"for\" or \"to\" marker \n- \"tirsa\" = give, \"kana...\" = buy, \"tirt\" = repair, \"hanuːg\" = strike, \"bijaːndi\" = give? \n- \"argi\" appears in 11 and 14; \"baji\" → 15; \"baːbki\" → 12; \"tirtiːg\" → 13\n\nLook at verb stems:\n\n- kana- → buy → 1, 5, 12 \n- tirt- → repair → 2 \n- darbad- → give → 3, 15 \n- kanarri- → buy → 1 \n- baːb- → find? → 6 → \"baːbiːg\" = doors → \"baːbki\" in 12? \n- hanu- → strike → 9 \n- maga- → thief? → 7,8 \n- jahal- → young men → 3,4 \n- sarkaːy- → cowards → 10 \n- argi → in 11, 14 → possibly \"give\"? \n- deːccir → camels? → 14 → \"kamgi deːccirsa\" → \"gave camels to...\"? \n- bijaːndi → in 15 → \"will give?\"\n\nCheck 11: magasi argi ajomirra \n- \"magasi\" = ? → similar to \"magas\" (theft) → possible agent \n- \"argi\" → verb stem? → not matched \nBut note: \"magas\" → thief → \"magasi\" → possessive form or agent? \n\"argi\" → possibly \"give\"? \n\"ajomirra\" → possibly \"the donkey\"? (like \"bijomri\" = strike donkey)\n\nSentence 9: ay hanuːg bijomri → I will strike the donkey \nSo \"bijomri\" = strike donkey\n\n\"ajomirra\" = likely \"the donkey\" (the object)\n\nSo \"magasi argi ajomirra\" → magic agent + verb \"argi\" + object = donkey \nIs \"argi\" a verb? Possibly \"strike\"? Or \"give\"?\n\nBut sentence 9: \"hanuːg bijomri\" = will strike \nIf \"argi\" = strike, then \"magasi argi ajomirra\" → the thief strikes the donkey?\n\nThat fits.\n\nBut in sentence 9: \"hanuːg bijomri\" = I will strike the donkey → present/future, \"hanu\" = will \nIn 11: \"magasi\" → thief? → \"argi\" = ? → not \"hanu\"\n\nLook at verb \"tirsa\" = give → in 7,8 \n\"tirtiːg\" = in 13 → likely verb form? \n\"tirtiːg\" → \"tirt\" + \"iːg\"? → future or passive?\n\nSentence 13: hanu tirtiːg elirsu \n\"hanu\" = will → \"tirtiːg\" = ? → \"tirt\" = repair → \"tirtiːg\" might be \"will repair\" \n\"elirsu\" = the doors? (elir → door; -su = the)\n\nCompare to sentence 6: wal aygi baːbiːg eldeːnsu → dog found the doors for me → \"eldeːnsu\" = for me\n\nSo \"elirsu\" → doors?\n\nThus, \"hanu tirtiːg elirsu\" → I will repair the doors.\n\nYes — \"tirt\" = repair, \"hanu\" = will → \"will repair the doors\".\n\nSentence 14: tirti argi kamgi deːccirsa \n\"tirti\" = ? → possibly future form of \"tirt\" \n\"argi\" = ? \n\"kamgi\" = dogs? (from \"kamiːg\" = camels → \"kamgi\" = dogs?) \n\"deːccirsa\" = ? → \"deːccir\" → from \"kamgi deːccirsa\" — but \"kamgi\" could be dog?\n\nWait: sentence 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs \n\"ticcirsu\" = gave → different verb?\n\nCompare verbs:\n\n- \"tirsa\" = gave \n- \"tirt\" = repaired \n- \"kanarriːcciːg\" = bought \n- \"bijaːndi\" = give? (sentence 15) \n- \"argi\" = possibly give?\n\nSentence 3: \"darbadki biticcirra\" → give the chicken to the dogs \n\"darbadki\" = give \nVerb: \"darbad-\" → give? \nSentence 15: ay darbadki bijaːndi → I will give the [something] to [someone]?\n\n\"bijaːndi\" → to whom? → likely \"to the dogs\"? \n\"bijaːndi\" → possibly \"to the young men\"? or \"to the donkey\"? \n\nWait, \"bijaːndi\" → is it like \"bijomri\" = strike donkey?\n\nPossibly, \"bij\" is root for \"hit\", \"strike\"? \n\"bijomri\" = strike donkey → \"bijaːndi\" = strike a person? or give?\n\nBut sentence 15: ay darbadki bijaːndi → I will give the [chicken? or something] to the dogs?\n\nWait: sentence 3: jahali waliːg darbadki biticcirra → young men will give the chicken to the dogs → \"darbadki\" = give\n\nSo \"darbadki\" = give \nThen \"bijaːndi\" = could be \"to the dogs\"? or \"to me\"? Not clear.\n\nBut \"bijaːndi\" → in 15: ay darbadki bijaːndi → I will give [object] to [place/person]? → likely \"to the dogs\"\n\nBut \"bijaːndi\" → could be \"the dogs\" (nominative)? \n\"bijaːndi\" → sounds like \"bijomri\" but with \"aːndi\" → may be \"dogs\" (same as \"waliːg\" = young men → people)\n\nBut in 9: \"bijomri\" = striketh donkey → \"bijomri\" = strike donkey → object = donkey \nSo \"bijaːndi\" = possibly \"to the dogs\" → if object is repeated?\n\nBut in 15: ay darbadki bijaːndi → I will give the chicken to the dogs.\n\nYes — likely.\n\nSo \"bijaːndi\" = the dogs → recipient.\n\nBack to 14: tirti argi kamgi deːccirsa \n\"tirti\" → future? of \"tirt\" = repair? \n\"argi\" → verb → possible \"give\"? \n\"kamgi\" → dogs? \n\"deːccirsa\" → ? \n\n\"deːccir\" — is this similar to \"kamgi\"? \nIn sentence 1: \"kamiːg\" = camels → \"kamgi\" → possibly dogs \n\"deːccir\" → could be door? or camel? \nNo obvious match.\n\nBut also, in sentence 8: iːdi magaski kamiːg tirsa → men gave the camels to the thief \n→ \"tirsa\" = give \nStructure: subject + to-recipient + object\n\nNow, 14: tirti argi kamgi deːccirsa \nCould \"tirti\" be \"give\"? But \"tirt\" is repair.\n\nAlternative: when \"tirt\" is paired with \"argi\", could \"argi\" be an object?\n\nBut \"kamgi\" and \"deːccirsa\" — likely object and recipient?\n\nBut \"argi\" is a verb.\n\nMore likely: \"argi\" is a verb root meaning \"give\" or \"give to\".\n\nIn sentence 3: \"darbadki\" = give \nSo why use \"argi\"?\n\nCheck other instances: \nSentence 4: man jahalgi kadeːcciːg maːgtirsu → he stole the dresses for the young man → \"kadeːcciːg\" = dresses → object, \"maːgtirsu\" = for young man → recipient\n\nSentence 10: sarkaːyi aygi beyyeːcciːg adeːnda → cowards are giving me the necklaces → \"adeːnda\" = to me → recipient\n\nIn 14: tirti argi kamgi deːccirsa → subject missing? \nPossibly \"I\" or \"he\"?\n\nNot clear.\n\nBut compare with sentence 7: magas ikki waliːg ticcirsu → thief gave you the dogs → verb = ticcirsu? Not matching.\n\nWait — is there a verb \"argi\" for \"give\"?\n\nSentence 13: hanu tirtiːg elirsu → will repair doors → tirtiːg = will repair\n\nSo \"tirti\" → future of repair?\n\n\"tirti\" = will repair?\n\nThen \"argi\" = ? \nUnless \"argi\" is not a verb.\n\nBut in 11: magasi argi ajomirra → thief + argi + donkey → likely verb → so \"argi\" is a verb.\n\nBut in 9: hanuːg bijomri → will strike donkey → verb \"bijomri\"\n\n\"argi\" → similar pattern? \n\n\"argi\" → could be \"strike\"? → then \"magasi argi ajomirra\" → the thief strikes the donkey\n\nThat would be consistent.\n\nSentence 14: tirti argi kamgi deːccirsa \n\"tirti\" = will repair? \n\"argi\" = strike? → strikes the dogs? \n\"kamgi\" = dogs? → object \n\"deːccirsa\" = ? → could be a possessive or complement?\n\n\"deːccirsa\" — possibly \"to the doors\"? or \"to the camels\"?\n\nNo.\n\nAnother idea: the verb \"argi\" is \"give\", and \"tirti\" is not a verb.\n\nBut \"tirt\" is repair — so \"tirti\" is likely \"will repair\".\n\nThen \"argi\" must be a different verb.\n\nBut only \"darbadki\" and \"kana\" are used for \"give\".\n\nIn 15: ay darbadki bijaːndi → I will give the chicken to the dogs → use of \"darbadki\" = give\n\nSo likely \"argi\" is not \"give\".\n\nPerhaps \"argi\" is a variant of \"strike\" (like \"bijomri\")\n\n\"argi\" → \"argi\" → similar to \"bij\"? → both start with \"bi\" or \"ar\"?\n\n\"ar\" → buy → \"kanarriːcciːg\" \n\"ar\" → in 11: \"magasi argi\" → \"argi\" not with \"ar\" → no.\n\nIn 11: \"magasi argi ajomirra\" → could be \"the thief strikes the donkey\"\n\nThat matches sentence 9 pattern: \"ay hanuːg bijomri\" = I will strike the donkey\n\nSo \"argi\" = strike? → then \"magasi argi ajomirra\" = the thief strikes the donkey\n\nYes.\n\nNow 12: ay kanarriːg baːbki alletirsi \n\"ay\" = I \n\"kanarriːg\" = buy (from \"kanarriːcciːg\" → buy) \n\"baːbki\" = ? → in sentence 6: \"baːbiːg\" = the doors → so \"baːbki\" = the doors? \n\"alletirsi\" = ? → likely \"for the dog\"? or \"for me\"?\n\n\"allegirsi\" → \"allegir\" = for? \"al-\" prefix? \nIn sentence 6: eldeːnsu = for me \nSo \"alletirsi\" = for the dog?\n\n\"tirt\" → repair → \"al\" prefix → \"al-\" = for → \"alletirsi\" = for the dog?\n\nYes — likely.\n\nSo \"ay kanarriːg baːbki alletirsi\" = I will buy the doors for the dog.\n\nNote: \"kanarriːg\" = buy (present), \"baːbki\" = doors, \"alletirsi\" = for the dog.\n\nMatches pattern: [subject] [verb] [object] [for-recipient]\n\n13: hanu tirtiːg elirsu → I will repair the doors → as established\n\n14: tirti argi kamgi deːccirsa \nPossible: \"tirti\" = will repair \n\"argi\" = strike (verb) \n\"kamgi\" = dogs (object) \n\"deːccirsa\" = ? → could be \"to the camels\"? or \"to the thief\"? \n\nBut no counterpart.\n\n\"deːccirsa\" — compare with \"kamiːg\" → camels \n\"deːccir\" → possibly \"camels\"? → could be a noun?\n\nBut in sentence 1: \"kamiːg\" = camels\n\n\"deːccir\" → perhaps same root? Unlikely.\n\nAnother possibility: \"argi\" = give \n\"tirti\" = will give? — but \"tirt\" is repair, not give.\n\nUnless it's a different verb.\n\nSentence 3: \"darbadki\" = give → used for giving\n\nSentence 10: \"beyyeːcciːg\" = buy\n\nSo \"argi\" — not clearly a give verb.\n\nBut in absence of a better fit, and given that \"argi\" is used with an object like \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11178.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 3, + "output": "Start by analyzing the given examples to extract the syntactic and semantic structure of Kunuz Nubian.\n\nObserve the verb patterns and their semantic roles.\n\nSentence 1: \nar kanarriːcciːg kamiːg jaːnticcirsu. \nWe bought the camels for the neighbours. \n→ \"kanarriːcciːg\" = bought (past) \n→ \"kamiːg\" = the camels (object) \n→ \"jaːnticcirsu\" = for the neighbours (beneficiary/location)\n\nSentence 2: \ntirt kadeːg allesu. \nThe owner repaired the dress. \n→ \"tirt\" = repaired \n→ \"kadeːg\" = the dress (object) \n→ \"allesu\" = (the) dress? But this seems redundant. Wait — “allesu” could be the repair result? But it’s “the dress” again. Actually, “allesu” might be a locative. Alternatively, perhaps “allesu” is a result or direction. \nBut: “tirt” = repair → verb \nObject: kadeːg → the dress \nResult: allesu? But that’s the same noun. So perhaps \"allesu\" is a locative or topicalizer? Not fitting. \nPossibly a typo or misreading. In contrast, Sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" — he stole the dresses for the young man. \n“kadeːcciːg” → the dresses \n“maːgtirsu” → for the young man → beneficiary\n\nSimilarly, Sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces. \n→ \"beyyeːcciːg\" = buying \n→ \"ajaːnirri\" = the necklaces\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → The dog found the doors for me. \n\"wal\" → the dog \n\"aygi\" → found \n\"baːbiːg\" → the doors (object) \n\"eldeːnsu\" → for me → beneficiary\n\nSentence 7: \"magas ikki waliːg ticcirsu\" → The thief gave you (pl.) the dogs. \n\"magas\" → thief \n\"ikki\" → you (pl) \n\"ticcirsu\" → gave \n\"walig\" → the dogs (object)\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → The men gave the camels to the thief. \n\"iːdi\" → men \n\"magaski\" → to the thief (direction) \n\"kamiːg\" → the camels (object) \n\"tirsa\" → gave\n\nSentence 9: \"ay hanuːg bijomri\" → I will strike the donkey. \n\"hanuːg\" → strike \n\"bijomri\" → the donkey\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → The cowards are giving me the necklaces. \n\"sarkaːyi\" → the cowards \n\"aygi\" → are giving \n\"beyyeːcciːg\" → the necklaces (object) \n\"adeːnda\" → to me (beneficiary)\n\nSo pattern: \n\"VERB + OBJ + FOR X\" → \"subject verb object for X\" \n\"VERB + OBJ + TO X\" → \"subject verb object to X\"\n\nBut meanings differ based on semantics. \nSpecifically: \n- “kanarriːcciːg” = buy \n- “tirt” = repair \n- “jahalgi” = will give \n- “kadeːcciːg” = steal \n- “beyyeːcciːg” = buy \n- “baːbiːg” = find \n- “ticcirsu” = give \n- “hanuːg” = strike \n- “magaski” = to the thief (direction or beneficiary)\n\nNow check affixes that mark direction/beneficiary.\n\nIn sentence 8: “iːdi magaski kamiːg tirsa” → “to the thief” \n“magaski” = to the thief → similar to “magaski” in “magas” = thief\n\nIn sentence 10: “adeːnda” = to me → added to the verb\n\nIn sentence 4: “for the young man” → “maːgtirsu”\n\nIn sentence 6: “eldeːnsu” → for me\n\nSo: \n“X + for Y” → beneficiary \n“X + to Y” → recipient or direction\n\nBut in Kunuz Nubian, the beneficiary is marked with a postposed particle.\n\nNow look at the target sentences.\n\n11. magasi argi ajomirra \n“magasi” → likely a form of “magas” (the thief) → possibly “the thief”? \n“argi” → a verb? \n“ajomirra” → likely “strike” (similar to “hanuːg bijomri”) \n“hanuːg bijomri” → I will strike the donkey \n→ “hanuːg” = strike \n→ “bijomri” = the donkey\n\nSo “argi” → possibly verb? \nIs there a verb “argi”?\n\nCompare to:\n\n- “hanuːg bijomri” → strike the donkey \n- “magasi argi ajomirra” → ?\n\nPossibility: “argi” = “will give” or “will strike”?\n\nBut “argi” is not clearly a verb in the list. However, sentence 3: “jahali waliːg darbadki biticcirra” → young men will give the chicken to the dogs. \n“jahali” → young men \n“waliːg” → will \n“darbadki” → give \n“biticcirra” → the chicken to the dogs\n\nSo “waliːg” = will \n“darbadki” = give\n\nBut in 11: “magasi argi ajomirra” → subject “magasi” (thief?), verb “argi”, object “ajomirra” (donkey?)\n\nSo possibly “argi” is a form of “will give” or “will strike”?\n\nBut “hanuːg” is for strike.\n\nAnother possibility: the verb “argi” is “strike” → “argi” = strike, as in “hanuːg bijomri” has “hanuːg” = strike.\n\nBut “magasi” is the thief.\n\nSo: “the thief strikes the donkey”?\n\nYes — plausible.\n\nBut is there a pattern?\n\nLook at 12: ay kanarriːg baːbki alletirsi \n“ay” = I \n“kanarriːg” = buy (like sentence 1) \n“baːbki” = the doors (like “baːbiːg” in sentence 6) \n“alletirsi” → what is this?\n\nIn sentence 6: “wal aygi baːbiːg eldeːnsu” → the dog found the doors for me → “eldeːnsu” = for me\n\nSo “alletirsi” → possibly “for the rooms” or “to the rooms”? Or a noun?\n\nBut “alletirsi” → could be “the rooms” or “the doors” — “alletirsi” might be a form of “allesu” or “allegu”?\n\nIn sentence 2: “tirt kadeːg allesu” → “allesu” → the dress? But “allesu” may be a result or direction.\n\nWait — “tirt” = repair → “allesu” → the dress? Repeated.\n\nBut in sentence 8: “magaski kamiːg tirsa” → to the thief → “magaski”\n\nIn sentence 12: “alletirsi” → could be similar to “eldeːnsu” → for me?\n\nSo “alletirsi” → for me?\n\n“ay kanarriːg baːbki alletirsi” → I buy the doors for me?\n\nThat makes sense — buying the doors for oneself?\n\nBut “for me” → “alletirsi”? → likely a beneficiary particle.\n\nSimilarly, sentence 10: “adeːnda” → for me\n\nSo “alletirsi” = for me?\n\nBut “alletirsi” → could be “for myself”?\n\nCheck 13: hanu tirtiːg elirsu \n“hanu” = strike (from “hanuːg bijomri”) \n“tirtiːg” = repair (from “tirt kadeːg allesu”) \n“elirsu” = ?\n\nIn sentence 3: “biticcirra” = to the dogs \nSo “elirsu” → likely to the thief? or to the dog?\n\nBut “tirtiːg” = repair \nSo “hanu tirtiːg elirsu” → strike repair → doesn’t make sense.\n\nWait — “hanu” = strike \n“tirtiːg” = repair? But is “tirtiːg” a verb?\n\n“tirt” = repair → “tirtiːg” could be a form? Like “tirt” is base, “tirtiːg” = repair (past form?) \nBut in sentence 8: “tirsa” = gave\n\nSo verb forms: \n- “kanarriːg” = past of “kanarri” → buy \n- “kadeːg” = the dress \n- “tirt” = repair \n- “tirsa” = gave (past) \n- “hanuːg” = strike (present or future)\n\nSo “tirtiːg” → possibly past of “tirt” → repair \nSo “hanu tirtiːg elirsu” → I strike the repair? → nonsense.\n\nWait — perhaps misreading. \n“hanu tirtiːg” — could “tirtiːg” be a noun?\n\nAlternatively, in sentence 8: “iːdi magaski kamiːg tirsa” — “tirsa” = gave\n\nSo “tirt” = repair, “tirsa” = gave\n\nSo “tirtiːg” is likely past form of “tirt”? So “tirtiːg” = repaired\n\nBut then “hanu tirtiːg elirsu” = I strike repaired elirsu? → no.\n\nAlternatively, could “tirtiːg” be “to the thief”?\n\nIn sentence 8: “magaski” = to the thief\n\nSo “tirtiːg” → is it a verb? Or a particle?\n\nLook at 14: tirti argi kamgi deːccirsa \n“tirti” → repair (me?) \n“argi” → verb? \n“kamgi” → the camels \n“deːccirsa” → to whom?\n\nSentence 8: “kamiːg” = the camels\n\nSo “deːccirsa” → possibly “to me” or “to the thief”?\n\nCompare with sentence 6: “eldeːnsu” → for me\n\nSentence 10: “adeːnda” → for me\n\nSo likely, “deːccirsa” = for me?\n\nSimilarly, “alletirsi” in 12 → for me?\n\nIn 13: “elirsu” → what?\n\nPossible patterns:\n\nVerbs:\n- kanarriːg → buy\n- tirt → repair\n- jahalgi → will give\n- kadeːcciːg → steal\n- beyyeːcciːg → buy\n- baːbiːg → find\n- ticcirsu → give\n- hanuːg → strike\n\nBut we don’t have “argi” in the verbs. \nBut in 11: “magasi argi ajomirra” — “argi” must be a verb.\n\nCheck sentence 3: “waliːg darbadki” → “waliːg” = will, “darbadki” = give\n\nNo “argi” verb.\n\nBut “hanuːg bijomri” → strike\n\nIs “argi” a form of “strike”?\n\nPossibly “argi” = strike? But “hanuːg” is already used for strike.\n\nWait — perhaps the verb “argi” is “strike” — and “magasi” is the subject.\n\nSo 11: the thief strikes the donkey.\n\nSimilarly, 12: ay kanarriːg baːbki alletirsi → I buy the doors for me.\n\n13: hanu tirtiːg elirsu → strike (tirtiːg)? No — tirtiːg is not a verb that means strike.\n\nCould “tirtiːg” be “to the thief”?\n\nLike “magaski” = to the thief?\n\nBut “tirtiːg” — what?\n\nConsider that “tirt” = repair, so “tirtiːg” = repaired (noun)\n\nThen “hanu tirtiːg” = strike the repaired thing? → not natural.\n\nAlternative: “hanu” = strike, “tirtiːg” = to the thief? But no “tirt” particle.\n\nI notice a pattern in beneficiary construction.\n\nIn:\n- 1: kanarriːcciːg kamiːg jaːnticcirsu → for the neighbours\n- 2: tirt kadeːg allesu → no benefit marked\n- 4: kadeːcciːg maːgtirsu → for the young man\n- 6: wal aygi baːbiːg eldeːnsu → for me\n- 8: iːdi magaski kamiːg tirsa → to the thief\n- 10: sarkaːyi aygi beyyeːcciːg adeːnda → to me\n\nSo particles marking beneficiary:\n- jaːnticcirsu → for neighbours\n- maːgtirsu → for young man\n- eldeːnsu → for me\n- magaski → to thief\n- adeːnda → to me\n\nSo markers:\n- for X → possible “jaːnticcirsu” (for neighbours), “maːgtirsu” (for young man)\n- to Y → “eldeːnsu” (for me), “adeːnda” (to me), “magaski” (to thief)\n\nSo the marker varies.\n\nNow in 11: magasi argi ajomirra \n“magasi” → the thief (like “magas”) \n“argi” → verb? Could be “strike” → like “hanuːg” \n“ajomirra” → the donkey → like “bijomri” in “hanuːg bijomri”\n\nSo perhaps “argi” is the verb “strike” — missing the “hanu”?\n\nBut “magasi argi ajomirra” → the thief strikes the donkey.\n\nSimilarly, 12: ay kanarriːg baːbki alletirsi \n“ay” = I \n“kanarriːg” = buy \n“baːbki” = the doors (object) \n“alletirsi” → likely for me → like “eldeːnsu” → “for me”\n\nSo I buy the doors for me.\n\n13: hanu tirtiːg elirsu \n“hanu” = strike \n“tirtiːg” → tirtiːg → what?\n\nCould “tirtiːg” be “repair” (past) → “tirt” → repaired? \nThen “hanu tirtiːg” = I strike (the repaired object)? → not natural.\n\nAlternative: “tirtiːg” = to the thief? But “tirt” = repair, not “to thief”.\n\nBut in sentence 8: “magaski kamiːg tirsa” → to the thief gave the camels.\n\nSo “magaski” = to thief → direction\n\nIn 13: “elirsu” → could be “to the thief”?\n\nIf so, then “hanu tirtiːg elirsu” → strike to the thief?\n\nBut “tirtiːg” — is it a verb? Not clear.\n\nBut “tirt” is repair, not strike.\n\nUnless “tirtiːg” is incorrectly parsed.\n\nWait — look at 14: tirti argi kamgi deːccirsa \n“tirti” → repair (verb) \n“argi” → verb? \n“kamgi” → the camels \n“deːccirsa” → to whom?\n\nIn 10: “adeːnda” → for me\n\nIn 12: “alletirsi” → for me\n\nSo “deːccirsa” → for me?\n\nSo “tirti” = repair \n“argi” = verb? (again)\n\nSo repair the camels for me?\n\nBut “argi” again.\n\nNow 15: ay darbadki bijaːndi \n“ay” = I \n“darbadki” = give (like “darbadki biticcirra” in sentence 3) \n“bijaːndi” = the chicken? → “biticcirra” was “the chicken”\n\n“biticcirra” → the chicken \nSo “bijaːndi” → “the chicken”?\n\nYes — “bijaːndi” = the chicken\n\nSo “I give the chicken” — but no beneficiary.\n\nSo “ay darbadki bijaːndi” → I give the chicken.\n\nNow back to 13: hanu tirtiːg elirsu \nIf “tirtiːg” is a noun meaning “the repair”, then “I strike the repair” — not meaningful.\n\nAlternative: misreading — is “tirtiːg” a particle?\n\nLike in sentence 8: “magaski” → to thief\n\nIn sentence 2: “allesu” → the dress\n\nBut “elirsu” — not found.\n\nBut “elirsu” may be “to me” → like “eldeːnsu”\n\nIn sentence 6: “eldeːnsu” = for me\n\nSo “elirsu” → for me?\n\nIf so, and “hanu” = strike, then “I strike for me” → doesn’t make sense.\n\nUnless “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10950.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "Start by analyzing the given sentences to identify patterns in Kunuz Nubian syntax, especially regarding:\n\n- Agent (who does the action)\n- Patient (what is acted upon)\n- Recipient (to whom)\n- Purpose/for-someone\n- Tense/mood (present, future, past, volitional)\n\nWe observe that many constructions follow a pattern: \n[Agent] [verb] [patient] [for/for-us/to/for-someone]\n\nLook at examples:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu. \n → \"We bought the camels for the neighbours.\" \n So: [we] [bought] [camels] [for the neighbours] \n Structure: Subject (we) + verb (bought) + object (camels) + for-recipient\n\n5. ay beyyeːcciːg ajaːnirri. \n → \"I am buying the necklaces.\" \n \"ay\" = I; \"beyyeːcciːg\" = buying; \"ajaːnirri\" = necklaces. \n So: [I] [buying] [necklaces]\n\n10. sarkaːyi aygi beyyeːcciːg adeːnda. \n → \"The cowards are giving me the necklaces.\" \n \"sarkaːyi\" = cowards; \"aygi\" = are giving; \"beyyeːcciːg\" = necklaces; \"adeːnda\" = to me. \n Structure: [Subject] [verb] [object] [for/to] [recipient]\n\nNow focus on verb forms and object/recipient markers.\n\nFrom (3): jahali waliːg darbadki biticcirra \n→ \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men; \"waliːg\" = will; \"darbadki\" = give; \"biticcirra\" = chicken; \"to the dogs\" implied or marked?\n\nBut no explicit \"to\" in original—so \"to the dogs\" may follow the verb and object.\n\nFrom (7): magas ikki waliːg ticcirsu. \n→ \"The thief gave you (pl.) the dogs.\" \n\"magas\" = thief; \"ikki\" = gave; \"waliːg\" = you (pl.); \"ticcirsu\" = dogs. \nSo verb \"ikki\" = gave; patient \"ticcirsu\" = dogs; recipient \"waliːg\" = you (pl.)\n\nFrom (8): iːdi magaski kamiːg tirsa. \n→ \"The men gave the camels to the thief.\" \n\"iːdi\" = men; \"magaski\" = gave; \"kamiːg\" = camels; \"tirsa\" = to the thief.\n\nSo pattern: [Subject] [verb] [object] [to] [recipient]\n\nIn (2): tirt kadeːg allesu. \n→ \"The owner repaired the dress.\" \nNo \"for\", no recipient. Only action on object.\n\nFrom (4): man jahalgi kadeːcciːg maːgtirsu. \n→ \"He stole the dresses for the young man.\" \n\"man\" = he; \"jahalgi\" = stole; \"kadeːcciːg\" = dresses; \"maːgtirsu\" = for the young man.\n\nSo \"for\" comes after patient, indicates recipient.\n\nFrom (6): wal aygi baːbiːg eldeːnsu. \n→ \"The dog found the doors for me.\" \n\"wal\" = dog; \"aygi\" = found; \"baːbiːg\" = doors; \"eldeːnsu\" = for me.\n\nThus, \"for\" is used to mark a recipient.\n\nSo general pattern:\n\n[Subject] [verb] [patient] [for/for-someone] → recipient\n\nVerb choice depends on action.\n\nNow go to the translation tasks:\n\n16. The neighbours are giving the necklace to the owner.\n\n- Subject: the neighbours → \"jaːnticcirsu\" or from example 1: \"kanarriːcciːg kamiːg\" → \"kanarriːcciːg\" = bought (past), but \"giving\" exists in (3) and (8).\n\nFrom (3): jahali waliːg darbadki biticcirra → \"young men will give chicken to dogs\"\n\nFrom (8): iːdi magaski kamiːg tirsa → \"men gave camels to thief\"\n\nSo \"give\" = darbadki or magaski?\n\nBut in (3): \"darbadki\" = give; \"biticcirra\" = chicken; \"to dogs\" → missing for?\n\nIn (8): \"magaski\" = gave; object \"kamiːg\" = camels; recipient \"tirsa\" = to the thief.\n\nSo \"tirsa\" = to the thief.\n\nThus, \"to\" is often marked with a specific morpheme or word.\n\nIn (10): sarkaːyi aygi beyyeːcciːg adeːnda → \"cowards are giving me the necklaces\" → \"adeːnda\" = to me.\n\nSo \"adeːnda\" = to me.\n\n\"eldeːnsu\" = for me (in 6) — likely \"for\" vs \"to\"?\n\n(6): wal aygi baːbiːg eldeːnsu → dog found doors for me.\n\nSo \"eldeːnsu\" = for me.\n\nIn (4): man jahalgi kadeːcciːg maːgtirsu → stole... for the young man → \"maːgtirsu\"\n\nSo \"maːgtirsu\" = for the young man.\n\nIn (10): \"adeːnda\" = to me.\n\nSo possibly:\n\n- \"for\" → used in a recipient addition after patient\n- \"to\" → marked with a specific word\n\nBut in (6): \"eldeːnsu\" = for me\n\n(4): \"maːgtirsu\" = for the young man\n\nSo \"maːgtirsu\" = for [someone]\n\n\"adeːnda\" = to me → possibly different from \"for\"\n\nBut many use \"for\" in both cases.\n\nIn (10): “are giving me the necklaces” → \"adeːnda\" = to me → likely \"to\" is a different marker.\n\nBut in (6): dog found doors for me → “eldeːnsu” = for me.\n\nSo perhaps:\n\n- \"for\" = to someone (recipient of an action)\n- \"to\" = not used; instead, \"for\" is used, and the object is marked that way.\n\nIn (16): \"giving the necklace to the owner\" → so recipient = the owner\n\nSo we need a form like [neighbours] + [give] + [necklace] + [for] + [owner]\n\nFrom example (1): \"bought the camels for the neighbours\" → \"kanarriːcciːg kamiːg jaːnticcirsu\" \n\"jaːnticcirsu\" = neighbours\n\nSo \"kamiːg\" + \"jaːnticcirsu\" → \"bought... for the neighbours\"\n\nSo for recipient, it is \"kamiːg jaːnticcirsu\" → thus \"for the neighbours\"\n\nSimilarly, in (3): \"give the chicken to the dogs\" → \"jahali waliːg darbadki biticcirra\" → no \"for\", just object then to dogs?\n\nBut no \"to\" word. So perhaps \"to the dogs\" is not marked explicitly.\n\nFrom (8): \"gave the camels to the thief\" → \"iːdi magaski kamiːg tirsa\"\n\n\"tirsa\" = to the thief.\n\nIn (6): \"found doors for me\" → \"eldeːnsu\" = for me\n\nSo two forms?\n\nBut in (10): \"giving me the necklaces\" → \"adeːnda\" → \"to me\"\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me?\n\nBut both are \"me\" — possibly different grammatical markers.\n\nPossibility: \"for\" = with a specific suffix or word; \"to\" = marked with a preposition-like form.\n\nIn (16): \"to the owner\" → which form?\n\nLook at example (1): \"bought for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = neighbours (specific noun phrase)\n\nSo must have a noun phrase for recipient.\n\nIn (16): recipient = owner → from original: \"the owner\" → likely \"tirt\" or \"tirtsu\" or \"tirtsu\"?\n\nFrom (2): \"tirt kadeːg allesu\" → \"the owner repaired the dress\" → \"tirt\" = the owner\n\nSo \"tirt\" = owner\n\nSo \"for the owner\" → \"for tirt\"?\n\nIn (1): \"bought the camels for the neighbours\" → \"kamiːg jaːnticcirsu\"\n\nSo for recipient: add \"kamiːg\" + recipient noun phrase\n\n\"kamiːg\" = for?\n\nYes — appears in (1): \"kamiːg jaːnticcirsu\" = for the neighbours\n\nSo \"kamiːg\" = for\n\nThen (4): \"stole the dresses for the young man\" → \"man jahalgi kadeːcciːg maːgtirsu\" → \"maːgtirsu\" = for young man\n\nSo \"maːgtirsu\" = for (young man)\n\n\"eldeːnsu\" = for me → in (6)\n\nSo \"kamiːg\" is used as \"for\", but only when the recipient is a noun phrase? Or not?\n\nBut \"eldeːnsu\" = for me → \"me\" is a pronoun.\n\nSo seems \"kamiːg\" + [noun phrase] = for [noun phrase]\n\n\"kamiːg\" is a particle used with object for recipient.\n\nSo \"for X\" = [kamiːg] + [X]\n\nBut in (10): sarkaːyi aygi beyyeːcciːg adeːnda → for me? → \"adeːnda\" = to me?\n\nContradiction.\n\nUnless \"adeːnda\" is to me, \"eldeːnsu\" is for me.\n\nSo \"for\" and \"to\" are distinct.\n\nBut in (2): tirt kadeːg allesu — no for or to\n\nIn (3): jahali waliːg darbadki biticcirra — give chicken to dogs? No \"to\" form.\n\nBut no explicit \"to\" in the sentence.\n\nSo perhaps in some forms, \"to\" is implied or not marked.\n\nBut in (8): iːdi magaski kamiːg tirsa → gave camels to thief → \"tirsa\" = to thief.\n\n\"tirsa\" = to thief\n\nIn (6): wal aygi baːbiːg eldeːnsu → found doors for me → \"eldeːnsu\" = for me\n\nSo two different forms for recipient:\n\n- \"for\" = marker like \"kamiːg\" + [noun phrase], e.g., \"kamiːg jaːnticcirsu\"\n- \"to\" = marked with \"tirsa\" for others, like \"tirsa\" = to thief\n\nBut in (10): \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\nThus:\n\n- \"to me\" → \"adeːnda\"\n- \"to thief\" → \"tirsa\"\n- \"for neighbours\" → \"kamiːg jaːnticcirsu\"\n\nSo is \"kamiːg\" always \"for\"?\n\nIn (4): man jahalgi kadeːcciːg maːgtirsu → for young man → \"maːgtirsu\"\n\nSo \"maːgtirsu\" = for young man\n\nThus, \"kamiːg\" is used with plural or specific noun phrases?\n\nNo — (4) \"maːgtirsu\" = for young man, which is a noun phrase.\n\nSo perhaps \"kamiːg\" is only used in a certain context?\n\nBut in (1): \"bought for neighbours\" → \"kamiːg jaːnticcirsu\"\n\nIn (4): \"stole for young man\" → \"maːgtirsu\"\n\nSo both use \"for\" with [noun phrase]\n\n(6): \"found for me\" → \"eldeːnsu\" → for me\n\nSo maybe \"kamiːg\" is used with direct object for recipient?\n\nBut in (3): \"give chicken to dogs\" → \"waliːg darbadki biticcirra\" → no \"kamiːg\", just \"biticcirra\" → implies \"to dogs\"\n\nSo \"to dogs\" is expressed directly?\n\nBut no \"kamiːg\"\n\nSo perhaps:\n\n- When recipient is a person or group → \"for\" marked with a specific particle\n- When recipient is a thing → \"to\" might be used?\n\nBut in (3): \"to dogs\" → dogs is thing → \"biticcirra\" is chicken, \"to dogs\" → used without particle?\n\nNo — in (3), \"give chicken to dogs\" → \"darbadki biticcirra\" — no explicit \"to\", just the object?\n\nIn (8): \"gave camels to thief\" → \"magaski kamiːg tirsa\" — has \"tirsa\" = to thief\n\nSo why no \"to\" in (3)?\n\nPossibly a non-contrastive pattern.\n\nBut (3): \"will give the chicken to the dogs\" → missing \"to\"? Or is it implied?\n\nActually, the sentence is: \"jahali waliːg darbadki biticcirra.\" \nNo \"to dogs\" explicit.\n\nBut in Chinese or similar languages, \"give A to B\" is expressed with \"to B\".\n\nSo likely in Kunuz Nubian, \"to\" is expressed with a particle or word.\n\nBut in (8): \"gave camels to thief\" → has \"tirsa\"\n\nIn (3): \"give chicken to dogs\" — missing \"to\"?\n\nBut it's written as \"biticcirra\" — only object.\n\nSo perhaps in (3) it's just stated, no \"to\" marker.\n\nBut in (8): \"tirsa\" = to the thief\n\nSo \"tirsa\" = to [someone]\n\n\"maːgtirsu\" = for [someone]\n\nSo \"for\" and \"to\" are distinct.\n\nBack to (16): \"The neighbours are giving the necklace to the owner.\"\n\nSo:\n\n- Subject: the neighbours → \"jaːnticcirsu\" (from (1))\n- Verb: \"are giving\" → from (8): \"iːdi magaski\" = gave (past), but (3): \"waliːg darbadki\" = will give\n- \"waliːg\" = will, so future\n- So \"are giving\" = present continuous or \"are\" = present progressive?\nIn (3): \"will give\" → \"waliːg darbadki\"\n\nSo \"waliːg\" = future\n\nBut (16) says \"are giving\" — present tense\n\nIn (5): \"I am buying\" → \"ay beyyeːcciːg\" — \"beyyeːcciːg\" = buying, no \"am\" marker\n\nIn (6): \"The dog found the doors for me.\" → \"aygi\" = found\n\n\"aygi\" = found (present)\n\nSo verbs can be present.\n\nBut no \"am\" in the verb.\n\nIn (5): \"ay beyyeːcciːg\" = I am buying → so \"ay\" + verb\n\nSo present tense: \"subject + verb\" without auxiliary.\n\nFor \"are giving\": likely \"iːdi\" or \"waliːg\" or \"tirt\"?\n\nIn (8): \"iːdi magaski\" = men gave → past\n\nIn (3): \"waliːg darbadki\" = will give → future\n\nSo no present future \"are giving\"\n\nBut (10): sarkaːyi aygi beyyeːcciːg adeːnda → \"are giving\" — \"aygi\" = are giving?\n\n\"aygi\" appears in (6): \"wal aygi baːbiːg eldeːnsu\" → \"found\"\n\n\"aygi\" = found\n\n(10): \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving\"?\n\n\"aygi\" = present tense, for \"are giving\"\n\nSo verb for \"are giving\" is \"aygi\"\n\nSo in (16): [neighbours] + [aygi] + [necklace] + [to owner]\n\nRecipient = owner → \"tirt\"\n\nSo to owner → \"tirsa\" (from (8)) or \"for\" ?\n\nIn (8): gave camels to the thief → \"tirsa\"\n\nIn (10): \"giving me\" → \"adeːnda\" → to me\n\nSo \"tirsa\" = to [someone]\n\nSo \"to the owner\" = \"tirsa tirt\"?\n\nBut \"tirt\" = owner → so \"tirsa tirt\"\n\nBut in (8): \"iːdi magaski kamiːg tirsa\" → gave camels to thief → \"tirsa\" = to thief\n\nSo \"tirsa\" = to [person/noun]\n\nSo in (16): \"neighbours aygi beyyeːcciːg tirt tirsa?\"\n\nBut \"beyyeːcciːg\" = necklace\n\nSo \"jaːnticcirsu aygi beyyeːcciːg tirt tirsa\"\n\nBut is \"beyyeːcciːg\" the necklace? Yes — from (5): \"beyyeːcciːg\" = necklaces\n\nSo yes.\n\nBut is the verb \"aygi\" used for \"are giving\"?\n\nIn (6): wal aygi baːbiːg eldeːnsu → dog found doors for me\n\n\"aygi\" = found\n\nIn (10): sarkaːyi aygi beyyeːcciːg adeːnda → cowards are giving me the necklaces → \"aygi\" = are giving\n\nSo yes.\n\nThus (16): \"jaːnticcirsu aygi beyyeːcciːg tirt tirsa\"\n\nBut in (1): \"bought for neighbours\" → \"kanarriːcciːg kamiːg jaːnticcirsu\" — \"kamiːg\" = for\n\nBut here we", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11415.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "First, analyze the given examples to identify patterns in Kunuz Nubian constructions.\n\nKey patterns from the examples:\n\n1. \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → We bought the camels for the neighbours. \n Structure: [Subject] [verb] [object] [for] [recipient] \n \"kanarriːcciːg\" = bought; \"kamiːg\" = the camels; \"jaːnticcirsu\" = for the neighbours.\n\n2. \"tirt kadeːg allesu\" → The owner repaired the dress. \n \"tirt\" = owner; \"kadeːg\" = repaired; \"allesi\" = dress.\n\n3. \"jahali waliːg darbadki biticcirra\" → The young men will give the chicken to the dogs. \n \"jahali\" = young men; \"waliːg\" = will; \"darbadki\" = give; \"biticcirra\" = chicken; \"to the dogs\" is implied.\n\n4. \"man jahalgi kadeːcciːg maːgtirsu\" → He stole the dresses for the young man. \n \"man\" = he; \"jahalgi\" = stole; \"kadeːcciːg\" = the dresses; \"maːgtirsu\" = for the young man.\n\n5. \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces. \n \"ay\" = I; \"beyyeːcciːg\" = buying; \"ajaːnirri\" = necklaces.\n\n6. \"wal aygi baːbiːg eldeːnsu\" → The dog found the doors for me. \n \"wal\" = dog; \"aygi\" = found; \"eldeːnsu\" = doors; \"for me\" implied in structure.\n\n7. \"magas ikki waliːg ticcirsu\" → The thief gave you (pl.) the dogs. \n \"magas\" = thief; \"ikki\" = gave; \"waliːg\" = you (pl.); \"ticcirsu\" = dogs.\n\n8. \"iːdi magaski kamiːg tirsa\" → The men gave the camels to the thief. \n \"iːdi\" = men; \"magaski\" = gave; \"kamiːg\" = camels; \"tirsa\" = to the thief.\n\n9. \"ay hanuːg bijomri\" → I will strike the donkey. \n \"ay\" = I; \"hanuːg\" = will strike; \"bijomri\" = donkey.\n\n10. \"sarkaːyi aygi beyyeːcciːg adeːnda\" → The cowards are giving me the necklaces. \n \"sarkaːyi\" = cowards; \"aygi\" = are giving; \"beyyeːcciːg\" = necklaces; \"adeːnda\" = to me.\n\nSummary of patterns:\n\n- Present tense: [Subject] [verb] [object] [for] [recipient] — common for \"X gives Y to Z\"\n- Future: \"waliːg\" (will) or \"aygi\" (are giving) used with future verbs\n- Stative/overall state: \"ay\" (I), \"iːdi\" (men), \"wal\" (dog), \"man\" (he), \"sarkaːyi\" (cowards)\n- \"for\" is marked with a prepositional phrase — e.g., \"jaːnticcirsu\" = for the neighbours; \"maːgtirsu\" = for the young man; \"adeːnda\" = to me\n- \"buy\" = beyyeːcciːg; \"steal\" = jahalgi kadeːcciːg; \"give\" = darbadki / magaski / aygi; \"repair\" = kadeːg; \"strike\" = hanuːg\n- Note: \"for\" or \"to\" is typically expressed by a postpositional phrase (e.g., \"jaːnticcirsu\", \"maːgtirsu\", \"adeːnda\")\n- \"will\" = waliːg; \"are giving\" = aygi (in 10), so future is marked directly on verb\n\nNow, derive each requested translation:\n\n16. The neighbours are giving the necklace to the owner. \n- Subject: \"kamiːg\" (neighbours) — from example 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\"\n- Verb: \"aygi\" = are giving (as in 10: sarkaːyi aygi beyyeːcciːg adeːnda)\n- Object: \"beyyeːcciːg\" = the necklace (from 5)\n- To: \"tirsa\" = to the owner (from 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\")\n→ \"kamiːg aygi beyyeːcciːg tirsa\"\n\n17. The young man bought the dog for us. \n- Subject: \"jahali\" = young man (example 3: jahali waliːg darbadki biticcirra)\n- Verb: \"kanarriːcciːg\" = bought (example 1)\n- Object: \"dog\" — what is \"dog\"? In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors\"\n→ \"dog\" is \"wal\" (example 6)\n- For: \"us\" = \"for us\" → what in English? From 4: \"for the young man\", \"maːgtirsu\"\n→ \"for us\" → \"adeːnda\"? In 10: \"adeːnda\" = to me → we need \"for us\"\nBut 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"to me\"\nSo \"for\" = \"maːgtirsu\" (for the young man), but what for \"us\"?\nIn 4: \"kadeːcciːg maːgtirsu\" = for the young man\nIn 6: \"wal aygi baːbiːg eldeːnsu\" = found the doors for me\n→ \"for us\" is likely \"maːgtirsu\" → but for a group?\nHowever, no example has \"for us\" directly. The example with \"me\" is \"adeːnda\"\nWe need \"for us\" → perhaps \"aːn\" or \"waliːg\"? But not found.\n\nWait — in 3: \"jahali waliːg darbadki biticcirra\" → \"will give\" → \"waliːg\" as future auxiliary\nIn 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole for the young man\"\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → \"found for me\"\nSo for \"us\" → must be equivalent of \"for you (pl.)\"\nBut no explicit example for \"us\". Only \"me\" and \"young man\" appear.\n\nBut in 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\"\n→ \"waliːg\" = you (pl.), \"ticcirsu\" = dogs\nSo \"waliːg\" is used as \"you (pl.)\" in object.\n\nBut we need \"for us\" — is \"for us\" the same as \"to us\"? In 10, \"adeːnda\" = to me\nSo possibly \"adeːnda\" for \"me\", and \"maːgtirsu\" for \"the young man\"\nWhat about \"for us\"? Is there an equivalent?\n\nLook at 1: \"for the neighbours\" → \"jaːnticcirsu\"\nSo \"jaːnticcirsu\" = for the neighbours\n\nSimilarly, \"for the young man\" = \"maːgtirsu\"\n\nSo for \"us\" → likely \"kamiːg\"? But \"kamiːg\" is neighbours.\n\nNo example has \"for us\". But \"kamiːg\" = neighbours, one group.\n\nBut 17: \"the young man bought the dog for us\"\n→ subject: \"jahali\"\n→ verb: \"kanarriːcciːg\"\n→ object: \"wal\"\n→ for: \"us\" → what is \"us\"?\n\nWe don’t have \"us\" directly, but \"waliːg\" is used for \"you (pl.)\" — so could \"waliːg\" be used for \"us\"?\n\nBut \"waliːg\" is an auxiliary verb in \"will give\", not a \"for\" phrase.\n\nAlternative: could \"for us\" be \"maːgtirsu\"? But that means \"for the young man\"\n\nNo clear case.\n\nWait — maybe \"for us\" is not a separate noun. Perhaps it's expressed via \"to us\" with \"adeːnda\"?\n\nBut \"adeːnda\" = to me.\n\nNo example has \"to us\".\n\nBut in 3: \"to the dogs\" = \"biticcirra\"\n\nIn 8: \"to the thief\" = \"tirsa\"\n\nSo object is specified with noun.\n\nThus, \"for us\" likely requires a preposition phrase.\n\nIn 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nIn 4: \"for the young man\" → \"maːgtirsu\"\n\nSo for \"us\", perhaps we use \"kamiːg\"? But \"kamiːg\" is neighbours.\n\nAlternatively, is there a word for \"us\"?\n\nNo direct example.\n\nBut look at 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving necklaces to me\n\n\"adeːnda\" = to me\n\nSo could \"adeːnda\" be extended to \"to us\"?\n\nBut not supported.\n\nAnother idea: in 17, \"for us\" might be \"maːgtirsu\" (we assume \"we\")?\n\nBut that doesn't fit.\n\nWait — perhaps \"for\" is marked with a different suffix.\n\nIn 1: \"for the neighbours\" = \"jaːnticcirsu\" \nIn 4: \"for the young man\" = \"maːgtirsu\"\n\nSo \"for X\" = [X] + suffix?\n\n\"jaːnticcirsu\" — is \"jaːnti\" + \"cirsu\"? \n\"maːgtirsu\" — \"maːgti\" + \"rsu\"?\n\n\"tirsa\" — \"tir\" + \"sa\"?\n\nNote that \"kamiːg\" = the camels? No — in example 1: \"kamiːg\" = camels\n\nIn 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → bought camels for neighbours → \"kamiːg\" = camels, \"jaːnticcirsu\" = for neighbours\n\nSo \"kamiːg\" is object, \"jaːnticcirsu\" is \"for neighbours\"\n\nSo object and for-recipient are separate.\n\nIn every case: [subject] [verb] [object] [for] [recipient]\n\nSo structure is: S V O P\n\nSo in 17: \n- S = \"jahali\" → young man \n- V = \"kanarriːcciːg\" → bought \n- O = \"wal\" → dog \n- P = \"for us\" → what?\n\nWe need a word for \"us\"\n\nIn the given data, only \"me\", \"you (pl.)\", \"neighbour\", \"young man\", \"thief\", \"dog\", \"cowards\" appear.\n\nBut \"us\" is not represented. However, in 7: \"magas ikki waliːg ticcirsu\" → thief gave you (pl.) dogs → \"waliːg\" = you (pl.)\n\nSo \"waliːg\" likely means \"you (pl.)\" or \"us\" in a verb phrase.\n\nBut it's used as auxiliary: \"waliːg\" = will\n\nSo not used as prepositional subject.\n\nCould \"waliːg\" be used as \"for us\"?\n\nUnlikely.\n\nAlternative: in 10, \"adeːnda\" = to me\n\n\"to us\" would be \"adeːnda\" but with plural? Not clear.\n\nBut no example supports.\n\nWait — perhaps \"for us\" is not a direct translation, but in form, similar to \"for the neighbour\" → \"jaːnticcirsu\"\n\n\"Jaːnticcirsu\" = for the neighbours → so \"neighbours\" is in a verbal construction.\n\nCould \"we\" be represented by \"kamiːg\"? But \"kamiːg\" = camels in 1.\n\nIn example 1: \"kamiːg\" = camels \nIn example 8: \"iːdi magaski kamiːg tirsa\" → men gave camels to thief → \"kamiːg\" = camels\n\nNo other use of \"kamiːg\" as a group.\n\nOnly in 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nNo \"for us\"\n\nBut unit 17 says \"for us\" → must use a group.\n\nPerhaps no direct word, and \"us\" is expressed as \"waliːg\" or \"me\"?\n\nNo.\n\nWait — perhaps \"us\" is \"kamiːg\" in some context? Unlikely.\n\nMaybe the pattern is to match object-recipient structure.\n\nBut only two groups: for, and to.\n\nLook: in 1: \"for neighbours\" \nin 4: \"for young man\" \nin 6: \"for me\" \nin 10: \"to me\"\n\nSo \"for\" uses specific prepositional phrases.\n\n\"us\" may be implied as \"we\" → but not in example.\n\nBut in 3: \"will give the chicken to the dogs\" → \"to the dogs\"\n\nSo \"to\" is used with noun.\n\nThus, \"for us\" may require \"for the young men\" or similar.\n\nBut we don't have \"us\".\n\nAnother idea: \"us\" may be encoded as \"kamiːg\" if \"kamiːg\" means \"we\" — but no.\n\nPerhaps \"waliːg\" in some sense means \"us\"?\n\nBut only appears in future tense.\n\nAfter careful review, no example has \"for us\".\n\nThus, by analogy: \n\"for the neighbours\" → \"jaːnticcirsu\" \n\"for the young man\" → \"maːgtirsu\" \n(for me) → \"adeːnda\"\n\nSo for \"us\" → perhaps \"waliːg\"?\n\nBut \"waliːg\" is auxiliary for future.\n\nAlternatively, is there a word meaning \"us\"?\n\nNone given.\n\nBut in example 16, \"the neighbours are giving the necklace to the owner\" → \"kamiːg aygi beyyeːcciːg tirsa\"\n\nSo for \"owner\" = \"tirsa\"\n\nSo in 17: similar structure: subject, verb, object, for us\n\n\"us\" → no direct match.\n\nBut in 10: \"for me\" = \"adeːnda\"\n\n\"for us\" might be \"adeːnda\" + plural? Unlikely.\n\nPerhaps in Kunuz Nubian, \"for us\" is expressed as \"waliːg\" in object?\n\nNo.\n\nWait — in 7: \"ikki waliːg ticcirsu\" → gave you (pl.) the dogs → \"waliːg\" = you (pl.)\n\nIn 3: \"jahali waliːg darbadki biticcirra\" → will give → with \"waliːg\" as auxiliary\n\nSo \"waliːg\" is not used as a prepositional phrase.\n\nTherefore, perhaps \"for us\" is not directly available.\n\nBut we must provide translation.\n\nPerhaps \"us\" is represented by \"kamiːg\" or \"waliːg\" as a noun?\n\nNo.\n\nWait — in 17: \"the young man bought the dog for us\"\n\n→ \"the dog\" = \"wal\"\n\n→ \"for us\" → must match structure of \"for the neighbours\", \"for the young man\"\n\n\"neighbours\" = \"jaːnticcirsu\"\n\n\"young man\" = \"maːgtirsu\"\n\n\"us\" = ? → perhaps \"kamiːg\" if \"kamiːg\" can mean \"we\"\n\nBut \"kamiːg\" = camels in 1.\n\nNo.\n\nIs there a word for \"us\"?\n\nNo.\n\nBut perhaps in this language, \"us\" is expressed via the verb \"aygi\" or something?\n\nNo.\n\nAlternative: perhaps \"for us\" is implied in the verb.\n\nBut no.\n\nAfter extensive search, the only plausible structure is that \"for us\" is expressed by the relevant noun phrase.\n\nBut no such phrase.\n\nWait — in example 9: \"ay hanuːg bijomri\" → I will strike the donkey → no \"for\"\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me the necklaces → \"to me\"\n\nSo \"to\" + pronoun.\n\nCould \"to us\" be formed with \"adeːnda\"?\n\nBut no plural.\n\nUnless \"adeːnda\" = to us — assumed.\n\nBut \"adeːnda\" = to me\n\nSo for \"us\", maybe it's \"adeːnda\" with plural marker? Not given.\n\nBut in the absence of data, use the pattern: \nin 1: \"for the neighbours\" → \"jaːnticcirsu\" \nin 4: \"for the young man\" → \"maːgtirsu\" \nin 10: \"to me\" → \"adeːnda\" \nSo \"for us\" could be \"adeːnda\" → to us?\n\nOnly if \"adeːnda\" is used for \"to us\"\n\nBut in 10 it's \"to me\"\n\nSo perhaps \"adeːnda\" is used for \"to [person]\"\n\nBut in 16, \"to the owner\" = \"tirsa\" — not \"adeːnda\"\n\n\"tirsa\" = to the thief\n\n\"maːgtirsu\" = for the young man\n\nSo separate: \"for\" and \"to\"\n\nTherefore, \"for\" is a separate prepositional phrase.\n\nIn 17, \"for us\" must be a new phrase.\n\nBut no such phrase found.\n\nThus, infer that \"us\" is expressed as \"waliːg\" — but \"w", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11239.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by analyzing the given examples to identify the semantic and syntactic structure of Kunuz Nubian.\n\nFirst, observe the verb patterns and arguments.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels (object) \n- \"jaːnticcirsu\" = for the neighbours (prepositional phrase, beneficiary)\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner (subject) \n- \"kadeːg\" = repaired (verb) \n- \"allegsu\" = the dress (object)\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men (subject) \n- \"waliːg\" = will (future) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = prepositional phrase marked by \"ki\" or \"to\"\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he (subject) \n- \"jahalgi\" = stole (verb) \n- \"kadeːcciːg\" = the dresses (object) \n- \"maːgtirsu\" = for the young man (beneficiary)\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I (subject) \n- \"beyyeːcciːg\" = buying (present) \n- \"ajaːnirri\" = the necklaces (object)\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = the dog (subject) \n- \"aygi\" = found (verb) \n- \"baːbiːg\" = the doors (object) \n- \"eldeːnsu\" = for me (beneficiary)\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = the thief (subject) \n- \"ikki\" = gave (verb) \n- \"waliːg\" = you (pl.) (indirect object) \n- \"ticcirsu\" = the dogs (direct object)\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = men (subject) \n- \"magaski\" = to the thief (prepositional phrase) \n- \"kamiːg\" = the camels (object) \n- \"tirsa\" = gave (verb)\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will (future) \n- \"bijomri\" = strike the donkey (verb + object)\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards (subject) \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces (object) \n- \"adeːnda\" = to me (beneficiary)\n\nNow, collect patterns:\n\n1. Subject + verb + object + (for X) \n - \"for\" is indicated by a prepositional phrase: \"kamiːg jaːnticcirsu\", \"maːgtirsu\", \"eldeːnsu\", \"adeːnda\", \"magaski\" \n - \"magaski\" = to the thief \n - \"jaːnticcirsu\" = for neighbours \n - \"maːgtirsu\" = for young man \n - \"eldeːnsu\" = for me \n - \"adeːnda\" = for me \n - \"tirsa\" = gave (may be verb, not prepositional) \n - \"kadeːg\" = repaired (no beneficiary)\n\n2. \"for\" construction is marked by specific postpositions: \n - jaːnticcirsu → for neighbours \n - maːgtirsu → for young man \n - eldeːnsu → for me \n - adeːnda → for me \n - magaski → to the thief (note: \"magaski\" seems to mean \"to the thief\", not \"for\")\n\nWait — in example 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \nSo \"magaski\" = to the thief (direction, recipient)\n\nBut in example 1: \"kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours\n\nSo two prepositions: \n- \"jaːnticcirsu\" = for \n- \"magaski\" = to (recipient)\n\nSimilarly, in 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → maːgtirsu = for the young man\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"giving me\" → adeːnda = for me\n\nSo:\n- for + entity → uses a specific form ending in -irsu or -nda, etc.\n- to + entity → magaski\n\nThus:\n- \"for\" = (in some cases) -jaːnticcirsu, -maːgtirsu, -adeːnda\n- \"to\" = -magaski (to the thief)\n\nBut in 10: \"adeːnda\" → for me \nIn 1: \"jaːnticcirsu\" → for neighbours\n\nSo \"to\" is marked with \"magaski\", \"for\" depends on the object.\n\nIn 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" \n\"darbadki\" = give, \"biticcirra\" = chicken, no \"for\" or \"to\" — but \"to the dogs\" is implied?\n\nWait: it says \"to the dogs\" — not in the given sentence. But the translation says \"give the chicken to the dogs\" — so the dogs are the recipient.\n\nBut in the sentence, the structure is: subject + verb + object + (to recipient)? \nNo: \"darbadki biticcirra\" → \"give the chicken\" — only object. \nThe \"to the dogs\" must be encoded in the verb or object.\n\nCompare to 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\" \nSo verb = \"ikki\" → gave \nThen \"waliːg\" = you (pl.) → indirect object (indirect recipient) \n\"ticcirsu\" = the dogs (direct object)\n\nSo structure:\nSubject + verb + indirect object + direct object → \"gave you the dogs\"\n\nBut in example 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" \nSo \"to the dogs\" is the recipient — but the sentence says \"give the chicken to the dogs\" — so direct object = chicken, indirect object = dogs?\n\nBut the verb is \"darbadki\" — give. \n\"biticcirra\" = chicken (object) \nNo mention of \"to the dogs\" in the structure.\n\nBut translation says \"to the dogs\" — so it must be encoded.\n\nSimilarly, example 10: \"giving me the necklaces\" = me is recipient.\n\nSo in example 10, the recipient is \"me\" → \"adeːnda\"\n\nIn example 1, \"for the neighbours\" → \"jaːnticcirsu\"\n\nIn example 4, \"for the young man\" → \"maːgtirsu\"\n\nSo:\n- For beneficiary (someone else) = ending in -irsu (e.g. jaːnticcirsu, maːgtirsu)\n- To recipient (object of act) = \"magaski\" (to the thief)\n\nBut in 3: \"give the chicken to the dogs\" → recipient = dogs → so should be \"magaski\" form?\n\nBut \"waliːg\" is \"you\", not \"dogs\".\n\nWait — in 3: \"jahali waliːg darbadki biticcirra\" → \"you\" is the recipient, \"chicken\" is the object.\n\nBut translation says \"give the chicken to the dogs\", not \"to you\".\n\nSo conflict.\n\nBut the translation says: \"The young men will give the chicken to the dogs.\"\n\nSo \"to the dogs\" → the dogs are the recipient.\n\nBut in the verb pattern, \"waliːg\" = \"you\", not \"dogs\".\n\nSo perhaps the structure is: \nSubject + verb + object + prepositional phrase (to X)\n\nIn example 3: \"waliːg\" = you? \nBut translation says \"to the dogs\", so it must be a mistake?\n\nWait — original: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\"\n\nBut \"waliːg\" in Kunuz Nubian — it appears in example 4: \"kahalgi\" = he stole (action), \"waliːg\" = young man.\n\nIn example 3: \"waliːg\" — likely \"the young men\" (subject), not \"you\" or \"to you\".\n\nThe sentence says \"give the chicken to the dogs\" — so the recipients are the dogs.\n\nSo where is \"to the dogs\"?\n\nPossibility: the preposition is encoded in the verb or object.\n\nIn example 3, \"darbadki\" may be intransitive?\n\nNo — component \"biticcirra\" = chicken (object), so verb takes object.\n\nLikely, \"to the dogs\" is encoded as a prepositional phrase.\n\nCompare 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"magaski\" = to the thief\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nSo:\n- \"for\" → used with certain noun phrases (beneficiary) → -irsu ending \n- \"to\" → used with recipient → -magaski?\n\nBut \"maːgtirsu\" = for the young man → \"for\", not \"to\"\n\nSo \"to\" is limited.\n\nAnother pattern: the verb with beneficiary is marked by specific suffixes.\n\nIn example 1: bought the camels for the neighbours → \"jaːnticcirsu\" \nIn example 4: stole the dresses for the young man → \"maːgtirsu\" \nIn example 10: giving me the necklaces → \"adeːnda\" → for me\n\nSo all are \"for\" constructions.\n\nThus, \"for\" is marked by a suffix like -irsu (e.g. jaːnticcirsu, maːgtirsu, adeːnda)\n\nBut \"magaski\" = to the thief → \"to\", not \"for\"\n\nSo:\n\n- For (beneficiary of action): suffix like -irsu (in -jaːnticcirsu, -maːgtirsu, -adeːnda) \n- To (recipient of object): suffix like -magaski\n\nIn example 3: \"give the chicken to the dogs\" → should be verb + object + to the dogs → so \"darbadki biticcirra magaski [dog expression]\"\n\nBut no such form appears.\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\" → \"waliːg\" = you (direct recipient), \"ticcirsu\" = the dogs (object)\n\nSo verb: \"ikki\" (gave) \nIndirect object: \"waliːg\" \nDirect object: \"ticcirsu\"\n\nSo structure: Subject + verb + indirect object + direct object\n\nIn example 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → so indirect object = dogs? Or is \"waliːg\" = \"the dogs\"?\n\nBut \"waliːg\" = young men in example 4.\n\nIn example 4: \"jahalgi\" = he stole (he is the subject), \"waliːg\" = young man (object)\n\nSo \"waliːg\" is a noun phrase — \"young man\"\n\nSo in example 3: \"jahali waliːg\" → \"the young men\" (subject), not \"to the young men\"\n\nTherefore, the prepositional phrase must be attached to the verb.\n\nThus, the verb form must include a prepositional marker.\n\nIn example 1: \"kanarriːcciːg kamiːg jaːnticcirsu\" → \"bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"adeːnda\" = for me\n\nSo the construction is: \nSubject + verb (with aspect) + object + for/beneficiary (postposition)\n\nBut for \"to\" (recipient), example 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" → \"magaski\" = to the thief\n\nSo two different postpositions:\n- -magaski → to the X \n- -jaːnticcirsu, -maːgtirsu, -adeːnda → for the X\n\nIn 8: \"magaski\" → to the thief \nIn 1: \"jaːnticcirsu\" → for the neighbours \nIn 4: \"maːgtirsu\" → for the young man \nIn 10: \"adeːnda\" → for me\n\nSo \"for\" = -irsu-type, \"to\" = -magaski\n\nNow, translate the required sentences.\n\n16. The neighbours are giving the necklace to the owner. \n→ Subject: \"the neighbours\" → from example 1, \"kamiːg\" = the camels; so \"kamiːg\" also used for \"the neighbours\"? \nBut in example 1: \"kamiːg\" = camels \nIn example 8: \"kamiːg\" = the camels \nNo \"the neighbours\" explicitly.\n\nBut in example 1: \"jaːnticcirsu\" = for the neighbours → so \"neighbours\" is a noun.\n\nLikely, \"neighbours\" = \"jaːnti\" or similar? \nBut no direct noun.\n\nFrom example 1: \"jaːnticcirsu\" — likely from \"jaːnti\" + -ccirsu\n\nSimilarly, \"owner\" = in example 2: \"tirt\" = the owner\n\nSo \"tirt\" = owner\n\nSo \"the neighbours\" → likely \"jaːnti\" or \"jaːntiːg\" \nFrom \"jaːnticcirsu\" → \"jaːnti\" + \"ccirsu\" → so \"jaːnti\" = neighbours?\n\nIn 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"neighbours\" appears as beneficiary\n\nSo \"jaːnticcirsu\" → for the neighbours\n\nThus, the noun for neighbours is \"jaːnti\"\n\nSimilarly, \"owner\" is \"tirt\"\n\n\"necklace\" = \"beyyeːcciːg\" — from example 5: \"beyyeːcciːg\" = the necklaces\n\nSo \"necklace\" = beyyeːcciːg\n\n\"give\" = verb: e.g. \"darbadki\", \"ikki\", \"tirsa\", \"aygi\"\n\nIn example 3: \"darbadki\" = give \nIn example 7: \"ikki\" = gave \nIn example 8: \"tirsa\" = gave \nIn example 10: \"aygi\" = are giving\n\nSo present continuous: \"aygi\" → are giving\n\nSo \"the neighbours are giving\" → \"jaːnti aygi beyyeːcciːg ???\"\n\nRecipient: \"to the owner\" → so \"to the tirt\" → use \"magaski\"\n\nSo \"jaːnti aygi beyyeːcciːg magaski tirt\"\n\nBut is \"jaːnti\" the noun? From \"jaːnticcirsu\", likely.\n\nIn 1, \"jaːnticcirsu\" = for the neighbours → so \"jaːnti\" = neighbours\n\nSimilarly, \"tirt\" = owner\n\nSo 16: \"jaːnti aygi beyyeːcciːg magaski tirt\"\n\n→ The neighbours are giving the necklace to the owner.\n\nNow 17. The young man bought the dog for us.\n\n\"young man\" = \"jahali\" (from example 3, 4)\n\n\"bought\" = \"kanarriːcciːg\" from example 1\n\n\"the dog\" = likely \"ticcirsu\" — from example 7: \"the dogs\"\n\nSo \"ticcirsu\" = the dog\n\n\"for us\" → \"us\" = \"we\"? In examples, \"we\" = \"ar\", \"me\" = \"eldeːnsu\", \"us\" = possibly \"aːjaː\"?\n\nIn example 6: \"for me\" = \"eldeːnsu\"\n\nIn example 10: \"giving me\" = \"adeːnda\"\n\nSo \"for us\" = for us → \"aːjaː\" or \"aːjaːnsu\"?\n\nIs there a form for \"us\"?\n\nIn example 3: \"waliːg\" = young men", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11774.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "First, identify the core grammatical patterns from the given examples.\n\nExamples:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu. \n→ \"We bought the camels for the neighbours.\" \nStructure: [Subject] [past tense verb] [object] [for [recipient]]\n\n2. tirt kadeːg allesu. \n→ \"The owner repaired the dress.\" \nStructure: [Subject] [verb] [object]\n\n3. jahali waliːg darbadki biticcirra. \n→ \"The young men will give the chicken to the dogs.\" \nStructure: [Subject] + [future] + [give] + [object] + [to [recipient]]\n\n4. man jahalgi kadeːcciːg maːgtirsu. \n→ \"He stole the dresses for the young man.\" \nStructure: [Subject] + [past] + [steal] + [object] + [for [recipient]]\n\n5. ay beyyeːcciːg ajaːnirri. \n→ \"I am buying the necklaces.\" \nStructure: [I] + [present progressive/ongoing] + [buy] + [object]\n\n6. wal aygi baːbiːg eldeːnsu. \n→ \"The dog found the doors for me.\" \nStructure: [Subject] + [found] + [object] + [for [recipient]]\n\n7. magas ikki waliːg ticcirsu. \n→ \"The thief gave you (pl.) the dogs.\" \nStructure: [Subject] + [give] + [to [recipient]] + [object]\n\n8. iːdi magaski kamiːg tirsa. \n→ \"The men gave the camels to the thief.\" \nStructure: [Subject] + [give] + [object] + [to [recipient]]\n\n9. ay hanuːg bijomri. \n→ \"I will strike the donkey.\" \nStructure: [I] + [future] + [strike] + [object]\n\n10. sarkaːyi aygi beyyeːcciːg adeːnda. \n→ \"The cowards are giving me the necklaces.\" \nStructure: [Subject] + [are giving] + [me] + [object]\n\nFrom these, we can infer:\n\n- The verb \"to give\" appears in multiple forms: \n - \"ticcirsu\" (give) \n - \"kadeːg\" (repair, but also used in \"repair the dress\") \n - \"kadeːcciːg\" (steal) \n - \"beyyeːcciːg\" (buy) \n - \"baːbiːg\" (find)\n\nBut the verb \"give\" is the key in multiple cases.\n\nIn sentences 3, 7, 8: \n- \"jahali waliːg darbadki biticcirra\" = \"The young men will give the chicken to the dogs\" \n- \"magas ikki waliːg ticcirsu\" = \"The thief gave you the dogs\" \n- \"iːdi magaski kamiːg tirsa\" = \"The men gave the camels to the thief\" \n→ All follow: [Subject] [verb] [object] [to [recipient]]\n\nAlso, the \"for\" construction appears in:\n- Example 1: \"We bought the camels for the neighbours\" → \"ar kanarriːcciːg kamiːg jaːnticcirsu\" \n→ \"kanarriːcciːg\" = bought, \"jaːnticcirsu\" = for the neighbours → \"for [recipient]\"\n\nSimilarly, 4: \"stole the dresses for the young man\"\n\n6: \"The dog found the doors for me\"\n\nSo \"for\" introduces a beneficiary or recipient, often with the structure: [verb] [object] [for [recipient]]\n\nUsing the pattern:\n\n16. The neighbours are giving the necklace to the owner. \n→ \"The neighbours\" = \"jaːnticcirsu\" (in example 1) → \"jaːnticcirsu\" is the group that receives? \nBut in example 10: \"The cowards are giving me the necklaces\" → \"sarkaːyi aygi beyyeːcciːg adeːnda\" \n\"adeːnda\" = \"me\" → \"giving me\" → \"to me\" → \"to [recipient]\"\n\nIn 8: \"The men gave the camels to the thief\" → \"iːdi magaski kamiːg tirsa\" → \"tirsa\" = to the thief\n\nSo \"to\" is used in \"give [object] to [recipient]\"\n\nIn example 6: \"found the doors for me\" → \"for\" is used for recipient\n\nSo two prepositions:\n- \"for\" = recipient (beneficiary)\n- \"to\" = recipient (in giving)\n\nBut in both cases, it's about transfer.\n\nIn example 8: \"to the thief\" → \"tirsa\" = to the thief \nIn example 10: \"giving me\" → \"adeːnda\" = me\n\nSo the preposition depends on whether it's \"to\" or \"for\".\n\nBut looking at 16: \"The neighbours are giving the necklace to the owner.\"\n\n→ \"are giving\" → from example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving\"\n\nSo \"aygi\" = present progressive / are giving\n\nSo: [Subject] + aygi + [verb base] + [object] + to [recipient]\n\n\"neighbour\" = jaːnticcirsu (from example 1: \"for the neighbours\") \nBut \"neighbours\" is the subject — in 1, “we bought the camels for the neighbours” → \"jaːnticcirsu\" is the recipient.\n\nSo \"the neighbours\" as subject → use a noun form.\n\nFrom example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \nSubject: \"ar\" (we), object: \"kamiːg\" (camels), recipient: \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = the neighbours (as a group)\n\nSimilarly, in 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"jaːnticcirsu\" \nVerb: \"aygi\" (are giving) \nObject: \"beyyeːcciːg\" (necklace) \nRecipient: \"owner\" → from example 2: \"The owner repaired the dress\" → \"tirt\" = owner\n\nSo “owner” = \"tirt\"\n\n\"to the owner\" → from example 8: \"to the thief\" → \"tirsa\"\n\nSo “tirsa” = to the thief → likely \"tirsa\" = to [person]\n\nSo: jaːnticcirsu aygi beyyeːcciːg tirt tirsa\n\n→ \"The neighbours are giving the necklace to the owner.\"\n\nCheck for consistency.\n\nNow 17: The young man bought the dog for us.\n\n\"bought\" → from example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → \"beyyeːcciːg\" = buying\n\nSo \"bought\" = \"beyyeːcciːg\" (past tense)\n\n\"the young man\" → from example 3: \"jahali waliːg\" = young men → \"jahali\" = young\n\nSo \"young man\" = \"jahali\" (singular)\n\n\"bought the dog\" → object = \"dog\" → what is \"dog\"? \nKunuz Nubian has \"wal\" = dog (example 6)\n\nSo “dog” = \"wal\"\n\n\"for us\" → \"for\" → from example 4: \"for the young man\" → \"for [character]\"\n\nSo \"for us\" → \"aygi\" or \"ajaygi\"? \nIn example 10: \"giving me\" = \"adeːnda\" = me → \"for me\" → \"for [me]\"\n\nBut in 4: \"stole the dresses for the young man\" → \"for\" → used after object\n\nSo \"bought the dog for us\" → [subject] [verb] [object] [for [recipient]]\n\n→ \"jahali beyyeːcciːg wal jaːnticcirsu\"\n\nBut wait — no \"jaːnticcirsu\" for \"us\"? \nIn example 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\n“us” is not directly present. But “we” is \"ar\" (example 1), \"us\" would be \"ajaygi\" or \"jaːnticcirsu\"?\n\nExample 10: \"the cowards are giving me the necklaces\" → \"adeːnda\" = me → likely \"me\" = \"adeːnda\"\n\nIn example 2: \"the owner\" = \"tirt\"\n\nSo \"us\" might be \"jaːnticcirsu\" or \"ajaygi\"? \nBut \"jaːnticcirsu\" = neighbours — possibly used for group.\n\nIn example 1: \"for the neighbours\" — so \"the neighbours\" = \"jaːnticcirsu\"\n\nIn example 3: \"the young men\" = \"jahali waliːg\"\n\nSo \"the young man\" = \"jahali\"\n\n\"bought\" → \"beyyeːcciːg\"\n\n\"for us\" → \"for\" + \"us\"\n\nBut what is \"us\"? Possibly \"ajaygi\", analogous to \"me\" = \"adeːnda\"\n\nNo direct example for \"us\", but \"me\" = \"adeːnda\" (example 10)\n\nSo \"us\" may be \"ajaygi\" → assumed from pattern.\n\nThus: jahali beyyeːcciːg wal ajaygi\n\nBut is \"bought\" with past tense?\n\nIn example 5: \"ay beyyeːcciːg\" = I am buying → present\n\nIn example 1: \"ar kanarriːcciːg\" = we bought → past\n\nSo \"bought\" = \"kanarriːcciːg\" (past) or \"beyyeːcciːg\" (present)\n\nExample 5: \"I am buying\" → present → \"beyyeːcciːg\"\n\nExample 1: \"we bought\" → past → \"kanarriːcciːg\"\n\nSo past tense of \"buy\" = \"kanarriːcciːg\"\n\nTherefore, \"bought\" = \"kanarriːcciːg\"\n\nSo: jahali kanarriːcciːg wal ajaygi\n\n→ The young man bought the dog for us.\n\n18. We will steal him.\n\n\"we\" = \"ar\"\n\n\"will\" = future — from example 3: \"will give\" → \"jahali waliːg darbadki\" → \"will give\"\n\nIn example 9: \"I will strike\" → \"ay hanuːg bijomri\" → \"hanuːg\" = will\n\nSo \"will\" = \"hanuːg\"\n\n\"steal\" → example 4: \"man jahalgi kadeːcciːg\" → \"stole\"\n\n\"stole\" = \"kadeːcciːg\" → past\n\nFuture of \"steal\" = \"kadeːcciːg\" with future marker?\n\nIn 9: \"will strike\" → \"hanuːg bijomri\"\n\nIn 3: \"will give\" → \"darbadki\" → future form\n\nSo \"will steal\" → \"kadeːcciːg\" with future marker?\n\nBut no direct form.\n\nAssume that \"will\" = \"hanuːg\" is a future auxiliary.\n\nSo \"will steal\" = \"hanuːg kadeːcciːg\"\n\n\"him\" → who is \"him\"? \nNo object in examples. \"the owner\", \"the dog\", \"me\"\n\n\"him\" → likely a pronoun.\n\nIn example 9: \"I will strike the donkey\" → \"bijomri\" = strike\n\nSo \"him\" → could be a pronoun like \"maːgtirsu\" or \"tirsa\"?\n\nNo clear pronoun.\n\nBut in English, \"him\" → could be \"him\" → object.\n\nIn Kunuz Nubian, object is marked after verb.\n\nIn 4: \"he stole the dresses for the young man\" → object = dresses\n\n\"for the young man\" = recipient\n\nNo object for \"him\"\n\nSo likely, \"him\" is an object: for example, \"maːgtirsu\" = him?\n\nNo example.\n\nBut in example 4: \"for the young man\" → \"maːgtirsu\" = young man\n\nSo \"maːgtirsu\" = young man\n\nSo \"him\" = ? Possibly \"maːgtirsu\" or \"tirt\" or \"wal\"?\n\nNo base.\n\nPossibly, \"him\" is the object, and must be a pronoun like \"ai\" or \"mä\" — not found.\n\nBut in example 9: \"I will strike the donkey\" → \"bijomri\" = strike — object is \"donkey\"\n\nSo object appears after verb.\n\nIn 18: \"we will steal him\" → so [subject] \"ar\" + \"will\" + \"steal\" + [object \"him\"]\n\nSo \"kadeːcciːg\" is the verb, future: \"hanuːg kadeːcciːg\"\n\nNow, who is \"him\"? In absence, likely a pronoun.\n\nIn example 4: \"for the young man\" → object is \"dresses\", then \"for young man\"\n\nNo object with \"him\" → so no example.\n\nBut since the word \"him\" is used in English, and no other pronoun, assume that \"him\" is a pronominal object.\n\nFrom context, in example 4, \"the young man\" → \"maːgtirsu\"\n\nSo \"him\" might be \"maːgtirsu\" or a variant.\n\nBut in example 10: \"giving me\" — \"adeːnda\" = me\n\nSo pronouns: \n- me = adeːnda \n- you = ? \n- us = ajaygi? \n- him = ? \n\nNot in examples.\n\nBut in example 4: \"stole the dresses for the young man\" — \"for maːgtirsu\"\n\n\"young man\" = maːgtirsu\n\nSo if \"him\" is a person, perhaps \"maːgtirsu\" = young man → but not \"him\"\n\nPerhaps \"him\" is a generic pronoun.\n\nBut in absence, since no alternative, and pattern is verb + object, we assume \"him\" = object, and use a form like \"it\" or \"him\".\n\nBut no example.\n\nLook at the verb \"kadeːcciːg\" — from \"stole\"\n\nIn example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\"\n\nSo structure: [subject] [past verb] [object] [for [recipient]]\n\nSo order: verb + object + for recipient\n\nSo for \"we will steal him\" → [subject] + [future verb] + [object]\n\n\"will steal\" → \"hanuːg kadeːcciːg\"\n\n\"him\" → ?\n\nBut in no example is a direct \"him\" used, only full noun phrases.\n\nSo \"him\" is likely the object, and we must use a pronoun.\n\nPossible that in Kunuz Nubian, \"him\" is not used — but it's in the translation.\n\nAlternatively, from example 8: \"gave you the dogs\" → \"waliːg ticcirsu\" → \"to you\"\n\nSo pronouns not directly given.\n\nBut in example 10: \"giving me\" → \"adeːnda\"\n\nSo pronouns: \n- me → adeːnda \n- us → ajaygi? \n- him → ??? \n\nNo mention.\n\nBut in example 4: \"for the young man\" → \"maːgtirsu\" = young man\n\nSo if \"him\" is a person, perhaps \"maːgtirsu\" is used — but not clearly.\n\nIn 19: \"The owners struck the thieves.\"\n\nSubject: \"owners\" — \"owner\" = \"tirt\" → \"owners\" = \"tirt\" plural? \n\"owners\" → \"tirt\" is owner, so plural \"tirtsu\" or \"tirtsu\"?\n\nIn example 2: \"the owner\" → \"tirt\"\n\nNo plural form.\n\nIn example 6: \"the dog\" → \"wal\"\n\nSo plural of dog? Not stated.\n\nBut in example 3: \"the young men\" → \"jahali waliːg\" → plural\n\nSo \"young men\" = \"jahali waliːg\"\n\n\"owners\" → could be \"tirt\" + plural? → \"tirtsu\"?\n\nIn example 8: \"the men\" → \"iːdi\" = men (plural)\n\nSo \"the men\" = \"iːdi\"\n\nSo \"the owners\" → \"iːdi tirt\"\n\n\"struck\" → from example 9: \"strike\" = \"hanuːg bijomri\"\n\nSo \"struck\" = past tense of strike → not present in examples.\n\nBut in example 9: \"I will strike\" → future\n\nNo past strike.\n\nBut \"struck\" may be past of \"bijomri\" → is \"bijomri\" past?\n\nIn 9: \"I will strike\" — future, so \"bijomri\" = base\n\nNo past form given.\n\nBut in example 4: \"stole\" = \"kadeːcciːg\" — past\n\nIn 2: \"repaired\" = \"kadeːg\" — past\n\nSo past action verbs: \n- stole → kadeːcciːg \n- repaired → kadeːg \n- struck → ? \n- give → ticcirsu\n\nSo \"struck\" = likely \"bijomri\" in past? But no example.\n\nExample 9: \"I will strike\" → \"hanuːg bijomri\" — future\n\nSo \"bijomri\" = strike, future with \"hanuːg\"\n\nSo past strike → not known.\n\nBut perhaps no future from \"will\" in past.\n\nBut sentence is \"The owners struck the thieves\" → past tense.\n\nSo verb must be past.\n\nBut not in examples.\n\nOnly example with strike is 9 — future.\n\nSo must infer.\n\nNo past form of strike.\n\nBut in item 18: \"we will steal him\" → future\n\n19: \"The owners", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11695.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 0, + "output": "Step-by-step analysis:\n\nWe are given English sentences and their Kilivila translations. Our task is to infer the underlying linguistic patterns to translate sentences 14–18 into English, with one of them having two plausible translations.\n\nWe begin by observing recurring structures and word patterns.\n\nFirst, identify key morphemes and their roles:\n\n- \"navila\" → how many (quantity question)\n- \"bikota\" → that (demonstrative)\n- \"lekota\" → this\n- \"legisi\" → that (demonstrative)\n- \"waga\" → sees, observes\n- \"minasina\" → these four fish (plural noun phrase)\n- \"makwena\" → stone\n- \"mtona\" → man\n- \"gwadi\" → child\n- \"tewa\" → will\n- \"vivila\" → clever\n- \"tau\" → one\n- \"nayu\" → two\n- \"bunukwa\" → pig\n- \"gudigasisi\" → wild pig? (likely derived from \"gudigasi\" + \"si\" = see/observe + pig)\n- \"ma\" → \"will\", \"did\", \"had\"\n- \"kweyu\" → will (future tense)\n- \"tevila\" → how many\n- \"bikamkwamsi\" → which men?\n- \"biyamatasi\" → old women\n- \"bigisesi\" → sees\n- \"gugwadi\" → those canoes\n\nNow, observe sentence patterns:\n\n1. \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = one; \"navasi yena\" = one man; \"minasina\" = these four fish; \"tetala tau\" = will catch\n\n2. \"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = man\n\n3. \"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive\n\n4. \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = saw; \"makesiwena\" = those canoes\n\n5. \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs\n\n6. \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two men\n\n7. \"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"minawena\" = will see; \"nakabitam\" = something\n\n8. \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived\n\n9. \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = saw; \"legisesi\" = that canoe; \"gweguyau\" = the chiefs\n\n10. \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = stone; \"gwadi\" = child; \"magudiwena\" = saw; \"gudimanabweta\" = this\n\n11. \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = those white men; \"mtosiwena\" = ate\n\n12. \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = pig; \"gagasisi\" = wild pig; \"guyau\" = chief; \"tokabitam\" = clever\n\n13. \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = clever; \"biyamatasi\" = women; \"tau\" = one; \"mtona\" = man\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n\"navila\" = how many \n\"vivila\" = clever \n\"biyamata\" = women (from \"biyamatasi\" → women; likely \"biyamata\" is a variant) \n\"tomwaya\" = will look after (from \"tauwau\" = look after, \"tomwaya\" = will look after?) \n\"mtona\" = man \n→ \"How many clever women will look after this man?\" \n→ Matches structure of 13: \"navila vivila biyamatasi tau mtona?\" → how many clever women will look after this man?\n\n→ So \"tomwaya\" likely = \"will look after\" \n→ \"biyamata\" = women (plural) \n→ So: \"How many clever women will look after this man?\"\n\n15. Bikamkwamsi kweyu vivila minasina. \n\"bikamkwamsi\" = which men? \n\"kweyu\" = will \n\"vivila\" = clever \n\"minasina\" = these fish \n→ \"Which clever men will catch these fish?\" \n→ But \"minasina\" in sentence 1: \"catch these four fish\" → \"tetala tau\" → so \"minasina\" = these fish. \n\"vivila\" = clever → \"clever men\" \n\"kweyu\" = will \n→ So: \"Which clever men will catch these fish?\"\n\n16. Amagudina gwadi lekota? \n\"amagudina\" = which stone? \n\"gwadi\" = child \n\"lekota\" = this \n→ \"Which child did this stone?\" — sounds odd. \nBut look: in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" — that child saw this stone \n\"makwena\" = stone; \"gwadi\" = child; \"gudimanabweta\" = this \nSo \"gwadi\" = child; \"makwena\" = stone → so \"gwadi lekota\" = this child? \n\"amagudina\" → which stone? \nBut \"amagudina\" = which (like \"amtona\") \nIn 5: \"amtona tau lekalimati\" → which man killed \nSo \"amagudina\" → which stone \n\"gwadi lekota\" → this child? \nIt would be \"Which stone did this child see?\" \nBut \"gwadi\" = child; \"lekota\" = this → \"this child\" \nSo: \"Which stone did this child see?\" \nYes — fits pattern: \"which X did Y\" = \"Amagudina X did Y\" \nBut \"amagudina\" = which X, \"gwadi lekota\" = this child → so \"which stone did this child see?\" \n\"See\" is implied by \"gudima\" / \"magudiwena\" etc. \n→ So translation: \"Which stone did this child see?\"\n\n17. Tevila tauwau bigisesi gugwadi gudigasisi? \n\"tevila\" = how many \n\"tauwau\" = two men \n\"bigisesi\" = sees \n\"gugwadi\" = those canoes \n\"gudigasisi\" = wild pig? \nWait — \"gugwadi\" = those canoes? \nBut \"bigisesi\" = sees \n\"gugwadi\" = those canoes → so \"bigisesi gugwadi\" = sees those canoes \n\"gudigasisi\" = wild pig? \nMismatch. \nWait: \"bigisesi gugwadi\" = sees those canoes — standard \nBut after that: \"gudigasisi\" → likely a separate noun \nDoes it mean \"those chief pigs\"? Unlikely.\n\nBut compare to sentence 12: \"lekalimati natala bunukwa nagasisi guyau tokabitam\" → killed one wild pig \n\"nagasisi\" → chief; \"guyau\" → chief; \"tokabitam\" → clever \n\"nagasisi guyau\" = chief? \n\"gudigasisi\" → likely a compound: \"gudigasi\" + \"si\" → pig + see → \"sees a pig\"? \nBut here: \"bigisesi gugwadi gudigasisi\" — sees those canoes, [something]? \n\nWait — in sentence 12: \"gudigasisi\" → \"wild pig\" \nSo \"gudigasisi\" = wild pig \n\nBut \"bigisesi\" = sees \n\"gugwadi\" = those canoes \nSo \"bigisesi gugwadi\" = sees those canoes \nThen \"gudigasisi\" = wild pig \nBut that doesn't fit.\n\nWait — could \"gugwadi\" be intended as \"those women\"? In 6: \"teyu tauwau nunumwaya\" → looked after two men \n\"tauwau\" = two men \n\"nunumwaya\" = women → \"looked after\" → \"teyu\" \n\nBut \"gugwadi\" is not a known noun for women.\n\nAnother possibility: \"bigisesi gugwadi\" → the one who sees those canoes \n\"gudigasisi\" → wild pig \nBut \"gugwadi\" is not a direction.\n\nWait — look at sentence 9: \"Amakena waga legisesi gweguyau?\" → \"Which canoe did the chiefs see?\" \n\"legisesi\" = that canoe \n\"gweguyau\" = the chiefs \nSo \"waga\" = saw \n→ \"waga\" = saw \nSo \"bigisesi\" = sees → same as \"waga\" \n\"bigisesi gugwadi\" → sees those canoes \n→ So \"which sees those canoes?\" \n\"tevila\" = how many \n\"tauwau\" = two men \nSo \"how many two men see those canoes?\" — ungrammatical.\n\nWait: \"tevila tauwau\" → how many two men → doesn't parse.\n\n\"tevila\" → how many \n\"tauwau\" → two men \n→ \"how many two men\" → grammatical? Only if \"tauwau\" acts as a noun phrase.\n\nBut in sentence 8: \"navila ka’ukwa lekotasi?\" → how many dogs arrived \n\"navila\" → how many; \"ka’ukwa\" → dogs\n\nSo \"tevila\" = how many \n\"tauwau\" = two men → would be \"how many two men\" — unusual.\n\nBut in sentence 6: \"teyu tauwau nunumwaya\" → looked after two men \n\"tauwau\" = two men\n\nSo \"tauwau\" = two men\n\n\"bigisesi gugwadi\" = sees those canoes\n\nSo \"tevila tauwau bigisesi gugwadi\" → how many two men see those canoes? \nUnlikely.\n\nBut perhaps \"tauwau\" is not \"two men\" but \"two\" as an adjective? \nNo — \"tauwau\" is a noun phrase for two men.\n\nWait — in sentence 17: \"tevila tauwau bigisesi gugwadi gudigasisi?\"\n\nCould it be: \"How many two men did see those canoes and wild pigs?\" — no, \"gudigasisi\" = wild pig\n\nBut plausible: \"How many of these two men saw those canoes and wild pigs?\" — but no plural for \"two men\", and \"gudigasisi\" = pig\n\nAlas, \"bigisesi gugwadi gudigasisi\" → sees those canoes and wild pigs?\n\nYes — possible.\n\nBut \"bigisesi\" → sees, \"gugwadi\" → those canoes, \"gudigasisi\" → wild pig → so \"sees those canoes and wild pigs\"?\n\nThat would require \"gugwadi\" and \"gudigasisi\" to be objects of \"see\".\n\nBut in sentence 4: \"legisi waga makesiwena namwaya minana\" → \"saw those canoes\" — so \"waga\" = saw → object is \"makesiwena\" = canoes; \"namwaya\" = those → same as \"gugwadi\"?\n\nYes — \"gugwadi\" = those canoes\n\nSo \"bigisesi gugwadi\" = sees those canoes\n\n\"bigisesi gudigasisi\" = sees wild pigs\n\nBut it's not connected by \"and\" — no conjunction.\n\nSo perhaps it's \"how many two men saw those canoes and wild pigs\"?\n\nBut gramatically odd.\n\nAlternative: \"gugwadi gudigasisi\" = those canoes and wild pigs?\n\nBut \"gugwadi\" is \"those canoes\", \"gudigasisi\" = wild pigs — so together: \"those canoes and wild pigs\"\n\nSo: \"How many two men saw those canoes and wild pigs?\"\n\nBut \"tauwau\" = two men — so \"how many two men\"?\n\nStill awkward.\n\nWait — is \"tauwau\" = \"two\" — perhaps it is \"two\" as a quantifier?\n\nBut earlier, \"tauwau\" = two men.\n\nBut notice sentence 13: \"Navila vivila biyamatasi tau mtona?\" → how many clever women will look after this man?\n\n\"tau\" = one\n\n\"tauwau\" = two men\n\nSo \"tauwau\" is a noun phrase (two men)\n\nSo \"tevila tauwau\" → how many two men? → grammatical only as \"how many of the two men?\"\n\nSo more likely: \"How many of the two men saw those canoes and wild pigs?\"\n\nBut the sentence structure is: \"tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n\"bigisesi gugwadi\" → sees those canoes → one object \n\"bigisesi gudigasisi\" → sees wild pigs — second object?\n\nPossibly, \"sees\" can take multiple objects.\n\nBut is that how it's being used?\n\nIn sentence 4: \"waga makesiwena namwaya minana\" → \"saw those canoes\" — one object\n\nNo compound object.\n\nBut in sentence 12: \"lekalimati natala bunukwa nagasisi guyau tokabitam\" — killed one wild pig (only one)\n\nNo multiple objects.\n\nSo perhaps \"gugwadi gudigasisi\" = those canoes and wild pigs — a compound noun?\n\nUnlikely.\n\nAlternatively, a parsing error.\n\nWait — is \"bigisesi\" only once?\n\nYes — one verb.\n\nSo likely: the structure is \"how many [X] did [Y] see [Z]?\"\n\nBut \"tevila\" = how many \nThen \"tauwau\" = two men — who? \nThen \"bigisesi\" = sees \nThen \"gugwadi\" = those canoes — object \nThen \"gudigasisi\" = wild pig — next object?\n\nThen: \"how many two men saw those canoes and wild pigs?\"\n\nBut missing subject.\n\n\"tevila tauwau\" → how many of the two men?\n\nSo: \"How many of the two men saw those canoes and wild pigs?\"\n\nBut \"bigisesi\" is the verb — it may be part of the verb phrase.\n\nAlternatively, \"gugwadi gudigasisi\" = \"those canoes and wild pigs\" — a compound object.\n\nYes — plausible.\n\nBut observe sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" — that beautiful child saw this stone\n\n\"magudiwena\" = saw \n\"gudimanabweta\" = this\n\nSo \"saw\" → verb\n\n\"bigisesi\" = sees — same verb\n\nSo \"bigisesi gugwadi gudigasisi\" = sees those canoes and wild pigs\n\n\"tevila tauwau\" → how many two men\n\nSo \"how many of the two men saw those canoes and wild pigs?\"\n\nYes — fits.\n\nBut is there a better alternative?\n\nAnother possibility: \"gugwadi\" = those women? But no such use.\n\nOr \"gugwadi\" = those people — but only for canoes.\n\nNo — only \"gugwadi\" appears with \"makesiwena\" = canoes.\n\nSo likely: compound object.\n\nSo translation: \"How many of the two men saw those canoes and wild pigs?\"\n\nBut is that natural?\n\nAlternatively, could \"tauwau\" be a quantifier for \"many\"?\n\nUnlikely — \"tauwau\" = two men\n\nSo only one plausible reading.\n\nProceed.\n\n18. Legisesi ketala waga vivila minasiwena. \n\"legisesi\" = that \n\"ketala\" = will (future) \n\"waga\" = saw \n\"vivila\" = clever \n\"minasiwena\" = something? → in sentence 7: \"minawena\" = will see something → in 7: \"vivila minawena nakabitam\" → will see something \n\"minasiwena\" = something? \nPossibly → \"something\" \nSo: \"That clever woman will see something.\" \nBut \"legisesi\" = that, \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11913.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 1, + "output": "Step 1: Analyze the English-Kilivila parallel to identify recurring patterns.\n\nLook at sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"Bibani\" = one; \"navasi\" = man; \"yena\" = these; \"minasina\" = fish; \"tetala\" = four; \"tau\" = will catch.\n\n\"navasi\" = man; \"minasina\" = fish; \"tetala\" = four; \"tau\" = catch.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n\"Lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n\"Bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n\"Legisi\" = this; \"waga\" = old; \"makesiwena\" = woman; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n\"Le matasi\" → old; \"teyu\" = women; \"tauwau\" = looked after; \"nunumwaya\" = two men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"Bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n\"Navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"Legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? Wait — \"gwadi magudiwena\" appears again — \"gwadi\" = child, \"magudiwena\" = will arrive? But context: \"saw this stone\" → so likely \"magudiwena\" is not \"will arrive\" here. Misreading?\n\nWait — \"gwadi magudiwena\" in sentence 10: subject is \"that beautiful child\", so \"gwadi\" = child; \"magudiwena\" = saw this? But in sentence 3, \"magudiwena\" = will arrive.\n\nBut in sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\".\n\nSo \"magudiwena\" here = saw. But in sentence 3, it's \"will arrive\".\n\nSo likely \"magudiwena\" = saw / will arrive — not a fixed meaning. But syntactically, must track.\n\nAlternative: perhaps agent is \"gwadi\" (child), \"magudiwena\" is a verb? But \"gwadi magudiwena\" = child saw?\n\nBut in sentence 3: \"Bikota gwadi magudiwena\" = that child will arrive → \"gwadi magudiwena\" = will arrive.\n\nSo the structure is: [determiner] + [noun] + [verb]?\n\nBut in sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" — breaks up: \"Legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? Duplicated?\n\nThat suggests \"gwadi\" = child, and \"magudiwena\" = saw?\n\nBut in sentence 3: \"gwadi magudiwena\" = will arrive.\n\nContradiction? Not necessarily. Likely \"magudiwena\" is a verb stem, and meaning depends on context.\n\nBut in 10, it follows \"saw this stone\", so \"magudiwena\" = saw.\n\nIn 3: \"will arrive\", so \"magudiwena\" = arrive.\n\nThus, the verb \"magudiwena\" is context-sensitive.\n\nBut still, the same verb form appears in different senses.\n\nSimilarly, in 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"le kalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"gagasisi\" = chief? → \"gagasisi guyau\" = chief?\n\n\"gagasisi guyau\" → guyau = chief?\n\nIn sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"Navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this man.\n\n\"tau\" = this man in both sentence 1 and 13.\n\nNow examine the requested sentences:\n\n14. Navila vivila biyamata tomwaya mtona? \n\"Navila\" = how many; \"vivila\" = women; \"biyamata\" = ?; \"tomwaya\" = ?; \"mtona\" = this man.\n\n\"vivila\" = woman (from sentence 7: \"vivila\" = woman)\n\n\"biyamata\" — in sentence 13: \"biyamatasi\" = will look after → so \"biyamatasi\" = will look after; \"biyamata\" might be same root with different form.\n\n\"biyamata\" → possibly \"will look after\" or \"look after\".\n\n\"tomwaya\" — in sentence 6: \"nunumwaya\" = two men → \"mwaya\" = man; \"nunum\" = two → \"nunumwaya\" = two men.\n\nSimilarly, \"tomwaya\" = this man? But \"tau\" already means this.\n\n\"tomwaya\" → perhaps \"man\"? But \"mtona\" = this man.\n\nPossibility: \"tomwaya\" = man? But then \"how many women will look after this man?\" → structure matches 13.\n\nBut 13 is: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\nSo 14: \"Navila vivila biyamata tomwaya mtona?\" → could be a variant.\n\nBut \"biyamata\" vs \"biyamatasi\": suffix -i → may indicate plurality or verb stem.\n\nIn 13: \"biyamatasi\" → \"will look after\" (third person plural or formal?)\n\nIn 14: \"biyamata\" — possibly same verb, but without -i → maybe not complete form.\n\nBut \"biyamata\" could be \"will look after\" in singular?\n\nBut \"vivila\" = women → plural.\n\nSo \"how many women will look after this man?\" → same as 13.\n\nThus 14 and 13 are nearly the same.\n\nBut 14 says \"tomwaya\" instead of \"tau\" → \"tomwaya\" = man?\n\nIn 13: \"tau mtona\" → \"this man\"\n\nIn 14: \"tomwaya mtona\" → redundant? But \"tomwaya\" = man, \"mtona\" = this?\n\nAmbiguity: is \"tomwaya\" = man or another word?\n\nIn sentence 6: \"nunumwaya\" = two men → so \"mwaya\" = man.\n\nSo \"tomwaya\" = man.\n\nSo \"how many women will look after this man?\" → same as 13, but with \"tomwaya\" instead of \"tau\"?\n\nBut \"tau\" is used for \"this\", and \"mwaya\" for \"man\", so possibly \"mtona\" = this man.\n\nSo 14: \"Navila vivila biyamata tomwaya mtona?\" = how many women will (look after) a man (this man)?\n\nWait — \"biyamata\" vs \"biyamatasi\"\n\nIn 13: \"biyamatasi\" = will look after — likely plural verb.\n\nIn 14: \"biyamata\" → possibly singular? But \"vivila\" = women (plural).\n\nSo \"will look after\" is likely plural.\n\nPossibly \"biyamata\" is a variant form, or typo.\n\nBut missing -i → perhaps \"biyamata\" means \"will look after\" without marking plurality? Unlikely.\n\nAlternatively, maybe \"biyamata tetala\" → like \"vivila minasina\" (fish) — but no.\n\nAnother possibility: \"tomwaya\" might be an error or alternative for \"tau\".\n\nBut let's compare others.\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n\"Bikamkwamsi\" → in 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\"\n\n\"lekamkwamsi\" = things → \"kamkwamsi\" = things.\n\nIn 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n\"Bikamkwamsi\" = that/these things? \"Bi\" = that?\n\n\"kweyu\" = two? \"kweyu\" → in 2: \"dimdim\" = white; in 5: \"nayu\" = two.\n\n\"kweyu\" = two?\n\n\"vivila\" = woman; \"minasina\" = fish?\n\nSo \"that two women will catch fish?\"\n\nBut \"vivila minasina\" = women fish → \"will catch\" = \"minasina\" verb?\n\nBut \"bikamkwamsi\" = that/these things?\n\nIf \"bikamkwamsi\" = that things → \"that two women will catch fish\"?\n\nUnlikely.\n\n\"bikamkwamsi\" = that person?\n\nIn 7: \"bigisi kwetala vivila minawena\" → \"that clever woman will see something\"\n\nSo \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see.\n\nSimilarly, \"bikamkwamsi\" → \"bi\" = that; \"kamkwamsi\" = things?\n\n\"vivila minasina\" = women fish → could be a noun phrase?\n\nBut \"kweyu\" = two?\n\nSo \"two women catch fish\"?\n\nBut \"bikamkwamsi\" = that/these things?\n\nThen: \"that thing, two women will catch fish\"?\n\nNo.\n\nPossibility: \"bikamkwamsi\" = \"that old\" or \"that, in terms of...\"?\n\nNo.\n\nAnother hypothesis: \"kamkwamsi\" = things; \"bikamkwamsi\" = these/those things.\n\n\"kweyu\" = two → \"two\" → possibly a quantity.\n\n\"vivila\" = woman → so \"two women\"?\n\n\"minasina\" = fish?\n\nBut what happens to \"kamkwamsi\"?\n\nPossibly \"kamkwamsi\" is a noun — \"things\".\n\nSo: \"These things, two women will catch fish\" — but \"bikamkwamsi\" = these things?\n\n\"bikamkwamsi kweyu vivila minasina\" — structure: [noun] [quantity] [subject] [verb]?\n\nBut missing verb.\n\n\"vivila minasina\" = women fish — but \"fish\" is object.\n\nSo likely: \"two women will catch these things\" → but \"minasina\" not \"things\".\n\nBut in sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" → so \"lekamkwamsi\" = things.\n\nSo \"kamkwamsi\" = things.\n\nThus \"bikamkwamsi\" = that/those things.\n\nThen \"kweyu\" = two → \"two\"\n\n\"vivila\" = women → \"women\"\n\n\"minasina\" = fish?\n\nSo \"that two women will catch fish\" — but \"fish\" = minasina.\n\nBut it's not grammatical.\n\nUnless the verb is missing.\n\nBut the sentence is \"Bikamkwamsi kweyu vivila minasina\" → likely \"that two women catch these fish\".\n\nBut no verb.\n\nIn all other verb forms, verbs are last.\n\nIn 1: \"navasi yena minasina tetala tau\" → so verb at end.\n\nIn 2: \"lekota dimdim mtona\" → verb at end.\n\nIn 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → verb at end: \"magudiwena\" = saw, \"gudimanabweta\" = this stone.\n\nSo likely: \"Bikamkwamsi kweyu vivila minasina\" → lacks verb.\n\nBut only way: \"kweyu vivila minasina\" = two women catch fish?\n\nThen \"bikamkwamsi\" = that/those things?\n\nSo \"that (things), two women catch fish\" — ungrammatical.\n\nAlternative: \"bikamkwamsi\" = that man? But \"bikamkwamsi\" → \"bi\" = that; \"kamkwamsi\" = not man.\n\nIn 5: \"amtona tau lekalimati nayu bunukwa\" → \"which man killed two pigs\"\n\nSo \"tau\" = man.\n\n\"nayu\" = two.\n\nSo \"kweyu\" = two.\n\n\"vivila\" = woman.\n\n\"minasina\" = fish.\n\nPossibility: \"which two women will catch fish\"?\n\nBut \"bikamkwamsi\" is not \"which\".\n\n\"bikamkwamsi\" = that things?\n\nSo \"that two women will catch fish\" — possible meaning.\n\nBut \"will\" not present.\n\nCheck sentence 18: Legisesi ketala waga vivila minasiwena.\n\n\"Legisesi\" = that; \"ketala\" = see; \"waga\" = old; \"vivila\" = woman; \"minasiwena\" = fish?\n\nIn 7: \"minawena\" = will see; in 10: \"gudimanabweta\" = stone → so \"minasiwena\" = fish?\n\nIn 1: \"minasina\" = fish → so likely \"minasiwena\" = fish.\n\nSo \"that old woman saw these fish\"?\n\nStructure: \"legisesi ketala waga vivila minasiwena\" → that old woman saw fish.\n\n\"vivila\" = woman; \"waga\" = old; \"ketala\" = saw.\n\nYes — matches sentence 4: \"legisi waga makesiwena namwaya minana\" → that old woman saw canoes.\n\nSo here: \"legisesi ketala waga vivila minasiwena\" → that old woman saw fish.\n\nBut \"waga vivila\" → \"old woman\"? \"waga\" = old, \"vivila\" = woman → old woman.\n\nYes.\n\nSo \"vivila\" = woman.\n\nNow 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n\"Te\" = how many? \"Tevila\" = how many?\n\n\"tauwau\" = looked after (in sentence 6: \"teyu tauwau\") → \"looked after\"\n\n\"bigisesi\" = that? (in sentence 7: \"bigisi\" = that)\n\n\"gugwadi\" = what? \"gugwadi\" → in 10: \"gwadi\" = child → so \"gugwadi\" = child?\n\n\"gudigasisi\" = ? → \"gudigasisi\" — in 12: \"gagasisi guyau\" = chief → so \"gagasisi\" = chief; \"gudigasisi\" = chief?\n\n\"gudigasisi\" → likely \"chief\"\n\nSo \"bigisesi\" = that; \"gugwadi\" = child; \"gudigasisi\" = chief?\n\n\"tauwau\" = looked after.\n\nSo \"how many times did that child look after the chief\"?\n\nBut \"tevila\" = how many? → \"how many times\"?\n\n\"tauwau\" = looked after → verb.\n\nSo \"how many times did that child look after the chief\"?\n\nYes.\n\nIn sentence 12: \"nagasisi guyau tokabitam\" → \"chief killed pig\" — so \"gagasisi guyau\" = chief.\n\nSo \"gudigasisi\" = chief.\n\n\"gugwadi\" = child.\n\n\"bigisesi\" = that.\n\nSo sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" = How many times did that child look after the chief?\n\nNow 16: Amagudina gwadi lekota?\n\n\"Amagudina\" = which? (like \"amtona\" = which)\n\n\"gwadi\" = child\n\n\"lekota\" = this\n\n\"amagudina\" = which?\n\n\"amagudina gwadi lekota\" = which child this?\n\n\"which child is this?\" — possible.\n\nBut in 2: \"lekota dimdim mtona\" = this white man arrived.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11560.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 2, + "output": "Start by analyzing the patterns in the given English-Kilivila pairs to deduce the structure and meaning of the word classes and syntactic constructions.\n\nLook at the verb structure and object placement.\n\nSentence 1: \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\"\n\n- \"navasi\" = man; \"tetala tau\" = will catch; \"minasina\" = these four fish.\n\nSentence 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\"\n\n- \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \"That child will arrive.\" → \"Bikota gwadi magudiwena.\"\n\n- \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\"\n\n- \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n- \"amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\"\n\n- \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\"\n\n- \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\n- \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n- \"amakena\" = which; \"waga\" = canoe; \"legisesi\" = the chiefs; \"gweguyau\" = saw.\n\nSentence 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n\n- \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = saw; \"magudiwena\" = this; \"gudimanabweta\" = stone.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n- \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n- \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"gagasisi\" = chief; \"tokabitam\" = clever.\n\nWait: \"nagasisi\" — likely \"gagasisi\" is chief, \"tokabitam\" is clever → seems like two adjectives.\n\n\"nagasisi guyau tokabitam\" → \"chief clever\" — this seems like a noun + adjectives.\n\nSentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\n- \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nNow, examine the patterns in the elements:\n\n- Determiners: \"le\" (this), \"bi\" (that), \"na\" (those), \"ka\" (how many), \"am\" (which), \"lekota\", \"bikota\", \"legisi\", \"navila\", etc.\n\n- Noun phrases: often determiner + adjective + noun.\n\n- Verbs: generally precede the object? Or are embedded in clauses.\n\nLook at the structure of the translation.\n\nObservation: The verb phrases often follow the pattern of subject + verb + object.\n\nBut in many cases, the verb has a construction involving \"vivila\", \"minasina\", \"makwena\", \"magudiwena\" — which seems to be used as an \"existential\" or \"event\" clause.\n\n- \"vivila\" = woman; \"minasina\" = fish; so \"vivila minasina\" = woman catches fish?\n\nBut in sentence 1: \"navasi yena minasina tetala tau\" → man will catch four fish.\n\nSo \"navasi yena\" = one man; \"minasina\" = these four fish; \"tetala tau\" = will catch.\n\nSo the objective appears to be embedded as a noun phrase with a structural complement.\n\nNow look at sentence 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n- \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man.\n\nSo \"how many women will look after this man?\" → matches sentence 13.\n\nIn 13: \"how many women will look after this man?\" → Navila vivila biyamatasi tau mtona\n\nSo here, \"biyamata\" vs \"biyamatasi\" — comma or similar? Probably a morphological variation.\n\n\"biyamata\" → \"biyamatasi\" — is this \"women\" or \"woman\"?\n\n\"vivila\" = woman (singular), \"vivila\" may be pluralized as \"vivilasi\" or \"vivila\"?\n\nBut in sentence 13: \"vivila biyamatasi\" — \"biyamatasi\" = look after → seems like a verb in perfect or future.\n\nIn 13: \"biyamatasi\" = will look after.\n\nIn 14: \"biyamata\" — same verb, possibly tense or form difference?\n\nWait: \"biyamata\" — could be \"will look after\" (same as \"biyamatasi\") — but \"biyamatasi\" seems to be for \"women\" (plural), while \"biyamata\" could be for \"one\" or \"a woman\"?\n\nBut \"navila\" means \"how many\" so it's asking for quantity.\n\nStructure: \"how many women will look after this man?\"\n\nSo 14 is almost identical in form to 13. The difference is in the verb form: biyamata vs biyamatasi.\n\nIn 13: \"vivila biyamatasi tau mtona\" → plural women (vivila) will look after this man.\n\nIn 14: \"vivila biyamata tomwaya mtona?\" → women will look after this man?\n\nBut \"biyamata\" — if \"biyamatasi\" is plural verb, then \"biyamata\" may be singular.\n\nBut \"navila\" asks for count, so it must be plural.\n\nSo possibly \"biyamata\" = \"will look after\" with specific object.\n\nAlternatively, \"biyamata\" might be a different verb.\n\nBut lack of examples.\n\nNow sentence 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n- \"bikamkwamsi\" — \"that\" + \"something\"? \"bika\" = that, \"mkuwamsi\" = things?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n- \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSo \"lekamkwamsi\" = things.\n\nThus \"bikamkwamsi\" = that thing(s)? → \"that things\"?\n\nGrammatically odd.\n\nBut in 14: \"vivila biyamata tomwaya mtona\" — might be a direct translation of \"how many women will look after this man?\"\n\nBut 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n→ \"that thing will catch these four fish?\"\n\nBut \"vivila minasina\" = woman catches fish?\n\nNo. In sentence 1: \"one man will catch these fish\" = \"navasi yena minasina tetala tau\"\n\n\"bikamkwamsi\" — likely \"that thing\" (thing = kweyu, thing = things).\n\n\"minasina\" = four fish.\n\nSo \"that thing\" will catch \"these four fish\"?\n\nMakes sense.\n\nSo in 15: \"that thing will catch these four fish?\"\n\nBut sentence 1: \"one man\" did it; here it's \"thing\" — could be an object.\n\nNow sentence 16: \"Amagudina gwadi lekota?\"\n\n- \"amagudina\" = which? (am- = which); \"gwadi\" = child; \"lekota\" = this?\n\n\"which child is this?\" → \"which child is this?\"\n\nBut \"lekota\" = this, likely refers to pronoun.\n\nSo \"which child is this?\"\n\nYes, likely.\n\nSentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n- \"tevila\" = how many; \"tauwau\" = two; \"bigisesi\" = chief; \"gugwadi\" = beautiful; \"gudigasisi\" = woman?\n\n\"gudigasisi\" = woman?\n\nLook at sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"gwadi\" = child; \"magudiwena\" = this; \"gudimanabweta\" = stone.\n\n\"magudiwena\" = this stone? → could be \"this\" as determiner.\n\nIn sentence 6: \"leyamatasi teyu tauwau nunumwaya\" → \"old women looked after two men.\"\n\n\"tauwau\" = two.\n\nSentence 12: \"lekalimati natala bunukwa nagasisi guyau tokabitam\" → \"killed one wild pig, the clever chief.\"\n\n\"gagasisi\" = chief; \"guyau\" = clever; \"tokabitam\" = woman? → \"clever woman\" → must be \"tokabitam\" = woman.\n\nSo \"tokabitam\" = woman, \"guyau\" = clever → \"clever woman\".\n\nSo \"gugwadi\" = beautiful → \"gugwadi\" = beautiful child?\n\n\"gudigasisi\" = woman?\n\nYes.\n\n\"bigisesi\" = chief?\n\n\"bigisi\" = that; \"kwetala\" = clever → \"bigisi\" = that clever woman.\n\nSo \"bigisesi\" = chief?\n\nBut \"bigisesi\" — likely the chief.\n\n\"bigisesi\" = the chief.\n\n\"gugwadi\" = beautiful.\n\n\"gudigasisi\" = woman?\n\nSo \"two beautiful women\" → \"tauwau bigisesi gugwadi gudigasisi\"?\n\n\"tauwau\" = two; \"bigisesi\" = (the) chief; \"gugwadi\" = beautiful; \"gudigasisi\" = woman?\n\nSo \"two beautiful women\"? But chief is male — \"bigisesi\" = chief → probably a man.\n\n\"bigisesi\" = chief → male.\n\n\"tewila tauwau\" = how many two?\n\nSo \"how many two chiefs beautiful women\"?\n\nUnbalanced.\n\nWait: \"tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n→ \"how many two chiefs beautiful women?\"\n\nNo.\n\nBut sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\nCould be: \"How many two chiefs saw beautiful women?\"\n\nBut in sentence 9: \"which canoe did the chiefs see?\" → \"amakena waga legisesi gweguyau\" → \"which canoe did the chiefs see?\"\n\n\"legisesi\" = chiefs → \"gweguyau\" = see.\n\nSo \"gweguyau\" = see.\n\nSo in 17: \"tevila tauwau bigisesi gugwadi gudigasisi\" → \"how many two chiefs beautiful women did see?\"\n\nNo — no verb.\n\nNo verb at all? That’s a problem.\n\n\"tevila\" = how many; \"tauwau\" = two; \"bigisesi\" = chief; \"gugwadi\" = beautiful; \"gudigasisi\" = woman.\n\nBut no verb — the sentence lacks a verb.\n\nSo what is the verb?\n\nPossibly missing — or a structure where \"see\" is not expressed?\n\nBut in 10: \"saw\" is \"gwadi\" → \"magudiwena\" = this, \"gwadi\" = saw.\n\nSo in 17: no verb.\n\nHence, likely a misreading.\n\nWait — looks like the verb is missing.\n\nBut sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\"\n\nSo \"gwadi\" = saw.\n\nIn sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\nIs \"gugwadi\" = saw? Or \"gugwadi\" = beautiful?\n\nYes — in sentence 10, \"dakuna makwena gwadi\" → \"beautiful child saw\".\n\nSo \"gwadi\" = saw.\n\nSo \"gugwadi\" = beautiful saw?\n\nNo — \"gugwadi\" = beautiful — \"gwadi\" = saw.\n\nSo in 17: \"gugwadi\" = beautiful → so \"bigisesi gugwadi\" = chief beautiful? — but \"gugwadi\" is adjective.\n\n\"bigisesi gugwadi gudigasisi\" = chief beautiful woman?\n\nSo \"how many two chief beautiful woman\"?\n\nStill no verb.\n\n\"tevila\" = how many; object = \"two chief beautiful woman\"?\n\nNo verb — incomplete.\n\nBut in all the other sentences, there is a verb.\n\nIn 17, it's missing.\n\nCould be a typo? Or misread.\n\nWait — look at the original:\n\n\"17. Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\nNo verb.\n\nBut in sentence 2: \"lekota dimdim mtona\" → \"this white man arrived\" — \"mtona\" = arrived.\n\nIn sentence 3: \"bikota gwadi magudiwena\" → \"that child will arrive\" — \"magudiwena\" = will arrive.\n\nIn sentence 10: \"gwadi\" = saw.\n\nSo \"gwadi\" is a verb in some cases.\n\nYes — in 10: \"gwadi\" = saw.\n\nIn 3: \"magudiwena\" → will arrive — so \"gwadi\" is not used with \"saw\", but with \"will arrive\"?\n\nNo — 3: \"gwadi magudiwena\" = that child will arrive — so \"magudiwena\" is verb.\n\nIn 10: \"makwena gwadi magudiwena\" → \"beautiful child saw this stone\" — \"gwadi\" = saw.\n\nSo \"gwadi\" is used as a separate verb.\n\nIn 17: \"bigisesi gugwadi gudigasisi\" — this must be \"the chief beautiful woman\"?\n\nBut no verb.\n\nSo likely the structure is: \"how many two chiefs beautiful women?\"\n\nBut that doesn't have a verb — so it can't be a full sentence.\n\nUnless \"tevila\" is not asking for quantity, but for something else.\n\nAlternatively, \"tevila\" might mean \"how long\" or something else.\n\nBut in 8: \"navila ka’ukwa lekotasi?\" = how many dogs arrived?\n\nSo \"navila\" = how many.\n\nIn 11: \"kwevila lekamkwamsi dimdim mtosiwena?\" = how many things did those men eat?\n\nSo \"kwevila\" = how many.\n\nIn 13: \"navila vivila biyamatasi tau mtona\" = how many women will look after this man?\n\nSo \"navila\" always = how many.\n\nSo 17: \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two chiefs beautiful woman?\"\n\nBut again — awkward.\n\nPossibility: \"gugwadi\" = saw.\n\nSo \"bigisesi gugwadi\" = chief saw?\n\nBut \"gugwadi\" = beautiful — not saw.\n\nIn 10: \"dakuna makwena gwadi magudiwena\" → \"beautiful child saw this stone\"\n\nSo \"gwadi\" = saw.\n\nSo in 17: \"bigisesi gugwadi gudigasisi\" → the chief beautiful woman?\n\nNo.\n\nUnless it's a typo — maybe it's \"bigisesi gugwadi gudigasisi\" should be \"bigisesi gweguyau\" = chief saw?\n\nBut \"gweguyau\" = saw — from sentence 9.\n\nIn sentence 9: \"gweguyau\" = saw.\n\nSo perhaps \"gugwadi\" should be \"gweguyau\"?\n\nBut it's written as \"gugwadi\".\n\nNot possible.\n\nAlternative: the verb is missing — so the sentence is malformed.\n\nBut the question says \"one of these sentences has two possible translations\" — so likely one is ambiguous.\n\nNow sentence 18: \"Legisesi ketala waga vivila minasiwena.\"\n\n\"legisesi\" = that; \"ketala\" = will see; \"waga\" = old; \"vivila\" = woman; \"minasiwena\" = something?\n\nIn sentence 7: \"bigisi kwet", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12077.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "unit_audit", + "sample_index": 3, + "output": "Start by analyzing the given English-Kilivila pairs to detect patterns in word order, morphological structure, and semantic roles.\n\nStep 1: Identify core syntactic and semantic components.\n\nFrom sentence 1:\n- \"One man will catch these four fish.\"\n- \"Bibani navasi yena minasina tetala tau.\"\n→ \"Bibani\" = one; \"navasi\" = man; \"yena\" = these; \"minasina\" = fish; \"tetala\" = will catch; \"tau\" = four.\n\nNote: \"tetala\" is likely \"will catch\", and \"tau\" (four) is in the number clause.\n\nSentence 2:\n- \"This white man arrived.\"\n- \"Lekota dimdim mtona.\"\n→ \"Lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3:\n- \"That child will arrive.\"\n- \"Bikota gwadi magudiwena.\"\n→ \"Bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4:\n- \"This old woman saw those canoes.\"\n- \"Legisi waga makesiwena namwaya minana.\"\n→ \"Legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5:\n- \"Which man killed two pigs?\"\n- \"Amtona tau lekalimati nayu bunukwa?\"\n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6:\n- \"The old women looked after two men.\"\n- \"Leyamatasi teyu tauwau nunumwaya.\"\n→ \"Leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7:\n- \"That clever woman will see something.\"\n- \"Bigisi kwetala vivila minawena nakabitam.\"\n→ \"Bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8:\n- \"How many dogs arrived?\"\n- \"Navila ka’ukwa lekotasi?\"\n→ \"Navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived?\n\nSentence 9:\n- \"Which canoe did the chiefs see?\"\n- \"Amakena waga legisesi gweguyau?\"\n→ \"Amakena\" = which; \"waga\" = canoe; \"legisesi\" = the chiefs; \"gweguyau\" = saw?\n\nSentence 10:\n- \"That beautiful child saw this stone.\"\n- \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n→ \"Legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child (repeated); \"magudiwena\" = saw; \"gudimanabweta\" = this stone.\n\nNote: \"makwena\" = child, \"gwadi\" = child → likely dual use of \"gwadi\" for \"child\".\n\nSentence 11:\n- \"How many things did those white men eat?\"\n- \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n→ \"Kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12:\n- \"The clever chief killed one wild pig.\"\n- \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n→ \"Lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"gagasisi\" = chief; \"guyau\" = clever; \"tokabitam\" = one.\n\nWait — \"guyau\" = clever, \"tokabitam\" = one? But \"toma\" or \"tau\" is number.\n\nCheck: sentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n→ \"nagasisi guyau\" = the clever chief; \"tokabitam\" = one? But \"natala\" = one.\n\nPossibly \"tokabitam\" = one wild pig? But earlier \"tau\" = four, \"nayu\" = two.\n\nRecheck: sentence 5 → \"nayu\" = two; sentence 12 → \"natala\" = one; \"tokabitam\" = one? But \"guyau\" = clever.\n\nActually, \"guyau\" = chief? But word order suggests: \"nagasisi guyau\" = the chief who is clever.\n\nSo \"guyau\" = clever (an adjective), like \"dimdim\" = white.\n\nSo adjective comes after noun in many cases.\n\nNow sentence 13:\n- \"How many women will look after this man?\"\n- \"Navila vivila biyamatasi tau mtona?\"\n→ \"Navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi\" = women who will look after.\n\nNow analyze the query:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"Navila\" = how many; \"vivila\" = women; \"biyamata\" = look after? (mata = to look after); \"tomwaya\" = this; \"mtona\" = man.\n\n→ \"How many women will look after this man?\"\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n\"Bikamkwamsi\" = that thing? Or \"something\"? \"kweyu\" = will? \"vivila\" = woman; \"minasina\" = fish?\n\n\"vivila minasina\" = woman and fish → but \"minasina\" means fish.\n\nLikely: \"Bikamkwamsi\" = that; \"kweyu\" = will; \"vivila\" = woman; \"minasina\" = fish → \"That woman will catch fish?\"\n\nBut in 1: \"one man will catch these four fish\" → \"navasi yena minasina tetala tau.\"\n\nSo \"tetala\" = catch, not \"minasina\" = fish.\n\nIn 15: \"kweyu\" = will, \"vivila\" = woman → \"will\" after subject.\n\nBut in 1: \"navasi yena minasina tetala tau\" — structure: subject, object, verb.\n\nNow 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n\"Bikamkwamsi\" = that; \"kweyu\" = will? But \"kweyu\" is not used in \"will\" in others — \"tetala\", \"magudiwena\", \"makwena\", \"mtosiwena\".\n\n\"tetala\" = catch; \"magudiwena\" = will arrive; \"mtosiwena\" = ate; \"waga\" = old.\n\nSo \"kweyu\" → possibly \"will\"?\n\nBut \"vivila minasina\" = woman and fish → so \"that woman will fish\"?\n\nUnlikely. \"minasina\" = fish; \"vivila\" = woman.\n\nBut is \"kweyu\" a verb?\n\nIn 1, \"tetala\" = catch.\n\nIn 3, \"magudiwena\" = will arrive.\n\nIn 11, \"mtosiwena\" = ate.\n\nSo do we have \"will\" when it's a modal?\n\nIn 3: \"gwadi magudiwena\" = child will arrive → \"magudiwena\" = will arrive.\n\nIn 13: \"biyamatasi tau mtona\" → will look after.\n\nSo modal verb is embedded in the verb form.\n\n\"Magudiwena\" = (will) arrive.\n\nSo \"kweyu\" is not a modal verb.\n\nCould \"kweyu\" = \"to be\" or something?\n\nBut no instance in examples.\n\nAlternative: \"kweyu\" = \"with\" or \"to\"?\n\nCheck sentence 10: \"gwadi magudiwena gudimanabweta\" → child saw stone → \"magudiwena\" = saw.\n\nSo \"magudiwena\" is a verb meaning \"saw\".\n\nIn 13: \"biyamatasi\" = will look after.\n\nSo \"vivila biyamatasi\" = woman will look after.\n\nSo \"kweyu\" may be a verb meaning \"to catch\" or \"to see\"?\n\nBut no example of \"kweyu\".\n\nIn sentence 1: \"tetala\" = catch.\n\nIn 12: \"nagasisi guyau tokabitam\" — \"guyau\" = clever, \"tokabitam\" = one.\n\nWait: \"minasina\" is fish; \"minasina\" appears in 1 and 1?\n\nIn 15: \"vivila minasina\" → woman and fish → possibly a noun phrase.\n\nBut subject is \"Bikamkwamsi\" → that.\n\n\"that woman {action} fish?\"\n\nCould it be \"that fishing woman\"?\n\nOr \"that woman who caught fish\"?\n\nBut \"kweyu\" is not a verb.\n\nPerhaps \"kweyu\" is a verb meaning \"to catch\" — like \"tetala\"?\n\nIn 1: \"tetala\" = catch.\n\nBut in 15: \"kweyu\" = catch?\n\nPossible.\n\nSo: \"Bikamkwamsi kweyu vivila minasina\" → \"that woman will catch fish\" → but \"vivila minasina\" = woman + fish? That doesn't make sense.\n\nUnless \"minasina\" is not fish.\n\nWait — \"minasina\" appears only in fish context.\n\n\"Minasina\" = fish.\n\nIn 1: fish; in 5: pigs are \"bunukwa\"; \"minasina\" = fish.\n\nSo \"vivila minasina\" = woman and fish → could be subject and object?\n\nBut \"kweyu\" = action?\n\nSo: \"that [something] will catch [woman and fish]\" — nonsense.\n\nReverse: \"kweyu\" as verb, so \"the woman will catch fish\" ⇨ but \"Bikamkwamsi\" is subject.\n\nSo \"that woman will catch fish\" → possible.\n\nBut \"vivila minasina\" = woman and fish → but \"vivila\" is woman, so \"minasina\" is object.\n\nThus: \"Bikamkwamsi kweyu vivila minasina\" = \"that woman will catch fish\"?\n\nBut \"vivila\" is woman — can't combine woman with fish.\n\nUnless \"minasina\" is a verb?\n\nBut in other cases, \"minasina\" = fish.\n\nSo likely not.\n\nAnother option: \"kweyu\" = \"with\" or \"together with\"?\n\nNo such verb in data.\n\nPerhaps it's a misread.\n\nWait: \"kweyu\" → compare to \"kwevila\" in sentence 11.\n\nSentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\"\n\n\"kwevila\" = how many → question word.\n\n\"kweyu\" → what is it?\n\nIn 15: \"Bikamkwamsi kweyu vivila minasina\" — \"that [something] will catch [woman and fish]?\"\n\nUnlikely.\n\nAlternatively: \"kweyu\" = \"will\" → perhaps unsupported.\n\nBut in 3: \"gwadi magudiwena\" = that child will arrive → modal verb is part of verb.\n\nIn 13: \"navila vivila biyamatasi tau mtona\" = how many women will look after this man?\n\nSo \"biyamatasi\" = will look after.\n\nSo \"biyamatasi\" = verb meaning \"will look after\".\n\nSo in 15: \"vivila minasina\" → likely a noun phrase: woman and fish → only if \"minasina\" is fish.\n\nSo \"that woman will fish\" is not possible.\n\nUnless \"kweyu\" is a verb meaning \"to fish\".\n\nBut no such verb.\n\nAnother idea: in 1, \"navasi yena minasina tetala tau\" → one man will catch these fish.\n\n\"minasina\" = fish.\n\nIn 15: \"vivila minasina\" → woman and fish → so \"that woman with fish\"?\n\nLike \"that woman who has fish\"?\n\nBut no such structure.\n\nBack to sentence pattern.\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\n→ \"biyamatasi\" = look after.\n\nSimilarly, in 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n\"biyamata\" = look after? (mata = to look after)\n\n\"tomwaya\" = this? (like \"tau\" = this)\n\n\"mtona\" = man.\n\nSo \"how many women will look after this man?\"\n\nThat matches 13.\n\n14 → same as 13 in structure → so likely same translation.\n\nBut now 15: \"Bikamkwamsi kweyu vivila minasina\"\n\nTry: \"kweyu\" = will → but \"will\" is embedded in verb.\n\nIn 3: \"gwadi magudiwena\" → will arrive.\n\nIn 13: \"biyamatasi\" → will look after.\n\nSo \"kweyu\" is not a modal.\n\nCould \"kweyu\" be \"to see\"?\n\nIn 4: \"makesiwena\" = saw.\n\nNo \"kweyu\".\n\nCould it be a verb meaning \"to catch\"?\n\nIn 1: \"tetala\" = catch.\n\nBut here, \"kweyu\" = catch?\n\nSo: \"that woman will catch fish\"?\n\nBut \"vivila minasina\" = woman + fish → then subject and object.\n\n\"that woman will catch fish\" → makes sense.\n\nBut is \"vivila\" the subject?\n\nYes — \"Bikamkwamsi\" is possessive? \"Bikamkwamsi\" = that.\n\n\"Bikamkwamsi kweyu vivila minasina\" → could be \"that [thing] will catch woman and fish\" — nonsense.\n\nUnless grammar is: subject is \"kweyu\" with object?\n\nBut \"Bikamkwamsi\" is first.\n\nSo likely \"that woman will catch fish\".\n\nSo \"vivila minasina\" = woman and fish → \"vivila\" is woman → so \"minasina\" = fish → object.\n\nSo \"that woman will catch fish\" — plausible.\n\nBut is \"vivila\" used for woman? Yes — in 7: \"vivila minawena\" = woman will see.\n\nIn 1: \"navasi\" = man, \"vivila\" = woman.\n\nSo yes.\n\nSo 15: \"That woman will catch fish.\"\n\nBut \"kweyu\" is not clearly defined as \"catch\".\n\nBut it is the only verb candidate.\n\nSo accept: \"That woman will catch fish.\"\n\nNow 16: \"Amagudina gwadi lekota?\"\n\n\"Amagudina\" = which? (like \"amtona\" = which)\n\n\"gwadi\" = child\n\n\"lekota\" = this\n\nSo: \"Which child is this?\"\n\nOr \"Which child is this one?\"\n\n\"Amagudina\" = which (question word)\n\n\"gwadi\" = child\n\n\"lekota\" = this → likely \"this one\"\n\nSo: \"Which child is this?\"\n\nNow 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n\"Tevila\" = how many?\n\n\"tauwau\" = two?\n\n\"bigisesi\" = chiefs?\n\n\"gugwadi\" = beautiful children?\n\n\"gudigasisi\" = something?\n\nIn sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → that beautiful child saw this stone.\n\n\"gakwena\" = beautiful, \"gwadi\" = child, \"magudiwena\" = saw.\n\n\"makwena\" = child.\n\nIn 17: \"gugwadi\" = beautiful child? \"gugwadi\" = plural of \"gwadi\"?\n\n\"bigisesi\" = chiefs → likely plural.\n\n\"gudigasisi\" → similar to \"guyau\" = clever, \"gudigasisi\" → could be \"something with chief\"?\n\n\"tauwau\" = two → number.\n\nSo \"how many two chiefs saw beautiful child\"?\n\nUnlikely.\n\n\"Tevila\" = how many?\n\nSo \"How many two chiefs saw beautiful child?\"\n\nGrammatically odd.\n\nPossibly: \"How many chiefs did the beautiful children see?\"\n\nBut \"gugwadi gudigasisi\" — \"gugwadi\" = beautiful child; \"gudigasisi\" = something? Or could \"gudigasisi\" = \"see\"?\n\nNo.\n\nIn 4: \"makesiwena\" = saw.\n\nIn 10: \"magudiwena\" = saw.\n\nSo \"gudigasisi\" not a verb.\n\nPossibly \"gudigasisi\" = the child?\n\nBut only \"gwadi\" = child.\n\nPerhaps \"gudigasisi\" = \"the child who is beautiful\"?\n\nBut \"gugwadi\" = beautiful child.\n\nSo \"bigisesi gugwadi gudigasisi\" = chiefs beautiful child?\n\nSeems like \"the chiefs saw the beautiful child\"?\n\nBut \"gudigasisi\" may be \"a child\"?\n\nNo.\n\nAnother possibility: \"Tevila\" = how many?\n\n\"tauwau\" = two — like \"nayu\" = two.\n\n\"bigisesi\" = chiefs\n\n\"gugwadi\" = beautiful child\n\n\"gudigasisi\" = something (like in 7: \"gudimanabweta\" = stone)\n\n\"gudigasisi\" may be a noun.\n\nBut no match.\n\nPerhaps \"gudigasisi\" = \"saw\"?\n\nBut no.\n\nCould \"gudigasisi\" be a verb?\n\nIn 10: \"gudimanabweta\" = stone.\n\n\"magudiwena", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11695.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 0, + "output": "Start by analyzing the given English-Kilivila pairs to detect patterns in syntax, word order, and question types (especially quantified questions, agent-patient relations, and possessive constructions).\n\nLook at the question types:\n\n1. Quantified questions (how many?) → often start with *Navila* (how many) in Kilivila.\n - Example 8: \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?*\n - Example 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?*\n - Pattern: *Navila* + noun + past tense verb + agent?\n\n2. Existential or which-type questions (which X?) → often start with *Am* (which) or *Am* + noun + verb.\n - Example 5: \"Which man killed two pigs?\" → *Amtona tau lekalimati nayu bunukwa?*\n - Example 9: \"Which canoe did the chiefs see?\" → *Amakena waga legisesi gweguyau?*\n - Pattern: *Am* + noun + (past tense) verb + agent?\n\n3. Future tense constructions → use *will* → often marked with *tau* or *mtona* (future marker).\n - Example 1: \"One man will catch these four fish\" → *navasi yena minasina tetala tau*\n - Example 6: \"The old women looked after two men\" → *Leyamatasi teyu tauwau nunumwaya*\n - Pattern: verb stem + *tau* or *teyu tauwau* for future.\n\n4. Agent + action + patient → structured as [agent] + [verb] + [object]\n - Example 4: \"This old woman saw those canoes\" → *Legisi waga makesiwena namwaya minana*\n - Note: *makesiwena* = saw, *namwaya minana* = those canoes\n\n5. Possessive or descriptive qualities → adjectives appear in front or before noun.\n - \"white man\" → *dimdim mtona* (white man)\n - \"clever woman\" → *gwisala* or *vivila* (clever, intelligent)\n - \"beautiful child\" → *dakuna* (beautiful)\n\nNow examine sentence-by-sentence and derive patterns for transformation.\n\n19. “How many canoes did those old women see?” \n- How many → *Navila* \n- canoes → *namwaya* \n- did → past tense verb → *makesiwena* (saw) \n- those old women → *legisi teyu waga* (those old women) \n- Query structure: *Navila [noun] [agent] makesiwena?* \n→ *Navila namwaya legisi teyu waga makesiwena?* \n→ But original 4 has \"Legisi waga makesiwena namwaya minana\" → agent + verb + object \nSo order is agent + verb + object. But question structure in 8 is \"Navila ka’ukwa lekotasi?\" → how many dogs arrived? \n→ Subject is after verb? \nBut 8: \"how many dogs arrived?\" → *Navila ka’ukwa lekotasi?* → *Navila* + noun + verb (arrived) \n→ But \"arrived\" is not marked with agent. \nSo perhaps in questions, the agent is not always present? \nIn 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* \n→ *Kwevila* = how many? \n→ *lekamkwamsi dimdim* = those white men \n→ *mtosiwena* = eat → past tense? \n→ So verb is after agent? \nThis suggests: *Kwevila* + agent + verb? \nBut 8 uses *Navila*, 11 uses *Kwevila*, which one is correct?\n\nCheck 8: \"How many dogs arrived?\" \n→ *Navila ka’ukwa lekotasi?* — \"Navila\" + \"dogs\" + \"arrived\" (lekotasi)? \n→ \"lekotasi\" = arrived? \nIn 2: \"This white man arrived\" → *Lekota dimdim mtona* → \"Lekota\" = arrived, \"dimdim mtona\" = white man \nSo \"lekota\" = arrived, verb \nSo 8: \"Navila ka’ukwa lekotasi?\" → how many dogs did [subject] arrive? → but \"arrived\" is not a verb with agent. \nActually, \"arrived\" is a stative verb — a consequence, not agentive. \nSo for questions with no agent (subject not specified), it may be \"Navila [object] [verb]\" — but verb must be in past tense with existential marker? \n\nCompare: \n11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* \n→ *Kwevila* = how many \n→ *lekamkwamsi dimdim* = those white men \n→ *mtosiwena* = eat \nSo structure: how many + [agent] + [verb]? \nBut no agent in 8: \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?* \n→ *Navila* + noun + verb \nSo different? \n\nBut in 11, agent appears before verb — *lekamkwamsi dimdim mtosiwena* \nIn 8, *navila ka'ukwa lekotasi* — noun + verb → no agent? \nSo what's the difference? \nIn 8, \"arrived\" is not agentive — it's intransitive → only subject \nIn 11, \"ate\" is transitive → requires agent and object \nSo when verb is transitive, agent is required? \n\nThus, rule: \n- For intransitive verbs (e.g. arrived), question uses *Navila [object] [verb]* \n- For transitive verbs (e.g. eat, kill, see), question uses *Kwevila [agent] [verb]*? \nBut 19: \"how many canoes did those old women see?\" → see is transitive → object is canoes \nSo see = transitive \n→ should use *Kwevila [agent] [verb]* \nAgent: those old women → *legisi teyu waga* \nVerb: *makesiwena* (saw) \nSo → *Kwevila legisi teyu waga makesiwena?* \nBut in sentence 4: \"This old woman saw those canoes\" → *Legisi waga makesiwena namwaya minana* \n→ Agent + verb + object \nSo order: agent + verb + object \nSo question: *Kwevila legisi teyu waga makesiwena?* → meaning: how many [canoes] did those old women see? \nYes — the quantifier comes first, then agent, then verb. \nThus, 19 → *Kwevila legisi teyu waga makesiwena?*\n\n20. \"These four white men will look after this clever child.\" \n- will → future marker → *tau* \n- These four → *yena* (these four) → from sentence 1: \"One man will catch these four fish\" → *navasi yena minasina tetala tau* \n→ \"yena\" = these four \n- white men → *dimdim mtona* \n- look after → verb → from 6: \"The old women looked after two men\" → *Leyamatasi teyu tauwau nunumwaya* \n→ \"tauwau\" = look after (future) \n→ \"nunumwaya\" = two men \nSo \"look after\" = *tauwau* \n- this clever child → \"gwadi vivila\" or \"gwadi magudiwena\"? \nIn 10: \"That beautiful child saw this stone\" → *Legisi dakuna makwena gwadi magudiwena gudimanabweta* \n→ \"gwadi magudiwena\" = that child \n→ \"dakuna\" = beautiful \nSo \"clever\" is *vivila* → appears in 7: \"That clever woman will see something\" → *Bigisi kwetala vivila minawena nakabitam* \nSo \"vivila\" = clever \nSo \"clever child\" = *gwadi vivila* (that clever child) \nNow subject: \"these four white men\" → *yena dimdim mtona* \nVerb: *tauwau* (will look after) \nObject: *gwadi vivila* \nSo full: *yena dimdim mtona tauwau gwadi vivila* \nBut is there any marker for \"this\"? \nIn 10: \"this stone\" → *gudimanabweta* → appears after \"gwadi magudiwena\" \nBut in 3: \"That child will arrive\" → *Bikota gwadi magudiwena* \n→ \"gwadi\" = that → relative or demonstrative \nSo \"this\" → likely *gwadi* as well? \nIn 10: \"saw this stone\" → *gudimanabweta* — \"this stone\" \nSo in 20: \"this clever child\" → likely *gwadi vivila* \nYes — matches previous uses. \nSo translation: *yena dimdim mtona tauwau gwadi vivila* \nNo need for \"will\" marker beyond *tauwau* — already included \nOrder: agent + verb + patient \nIn 6: \"The old women looked after two men\" → *Leyamatasi teyu tauwau nunumwaya* → agent + verb + object \nYes \nSo 20 → *yena dimdim mtona tauwau gwadi vivila*\n\n21. \"How many children will eat these pigs?\" \n- How many → *Navila* or *Kwevila*? \n- Verb: eat → transitive → *mtosiwena* → \"eat\" in 11: \"did those white men eat\" → *mtosiwena* \n- So for transitive verb, use *Kwevila* + agent + verb \nBut here, agent is \"children\" — not specified. \nBut the question is \"how many children will eat\" → agent is children, object is pigs \nSo structure: *Kwevila [agent] [verb] [object]* \nWith future → *tau* \nSo: *Kwevila minasina tau mtsosinaiyina?* \nWait — children = *minasina* \nIn 1: \"One man will catch these four fish\" → *navasi yena minasina tetala tau* \n→ \"minasina\" = man \nSo \"children\" → *minasina* \nPigs → \"bunukwa\" (pig) → from 5: \"which man killed two pigs?\" → *bunukwa* \nSo object: *bunukwa* \nNow, the question is: how many children → so quantifier comes first? \nBut from pattern: \n- 8: \"how many dogs arrived?\" → *Navila ka’ukwa lekotasi?* → Navila + object + verb (intransitive) \n- 11: \"how many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* → Kwevila + agent + verb \nIn 11, agent is *lekamkwamsi dimdim* → those white men \nSo here, agent = children → *minasina* \nSo: *Kwevila minasina tau mtsosinaiyina?* \nBut verb is \"eat\" → *mtosiwena* → but with future? \nIn 1: \"will catch\" → *tetala tau* \nIn 6: \"looked after\" → *tauwau* \nSo future marker is added to verb stem \nSo eat → *mtosiwena* → future → *mtosiwena tau*? \nBut in 1: *tetala tau* = will catch \nSo verb + tau → future \nSo \"will eat\" → *mtosiwena tau* \nSo full: *Kwevila minasina mtsosinaiyina tau?* → wait, grammar?\n\nWait — 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* \n→ *mtosiwena* is past tense? But it's a question — but in 2: \"This white man arrived\" → *Lekota dimdim mtona* → arrived \nSo \"did eat\" → past tense verb \nBut the question asks \"how many\" — meaning, how many child-eat-pigs — so we expect present or future? \n\"will eat\" → future \nSo future tense needed \nIn 1: \"will catch\" → *tetala tau* → verb + tau \nSo \"will eat\" → *mtosiwena tau* \nSo structure: *Kwevila minasina mtsosinaiyina tau?* — but \"these pigs\" → object \nSo: *Kwevila minasina mtsosinaiyina tau bunukwa?* \nBut object → \"these pigs\" → *bunukwa* \nIn example 5: \"which man killed two pigs?\" → *bunukwa* \nSo *bunukwa* = pigs \nSo object: *bunukwa* \nSo full: *Kwevila minasina mtsosinaiyina tau bunukwa?* \nBut order: agent + verb + object \nIn 11: \"how many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* — agent after *Kwevila*, verb after agent \nSo yes: *Kwevila minasina mtsosinaiyina tau bunukwa?* \nBut in 19, we used *Kwevila* with agent before verb — so consistent \nThus 21 → *Kwevila minasina mtsosinaiyina tau bunukwa?*\n\n22. \"Which woman caught those beautiful fish?\" \n- Which → *Am* \n- woman → *mtona* or *gwisala*? \n\"clever woman\" → *vivila* \n\"beautiful\" → *dakuna* \nSo \"beautiful fish\" → *dakuna minasina* (beautiful fish) \n\"caught\" → verb → from 1: \"one man will catch these four fish\" → *tetala* \nSo \"caught\" = *tetala* \n\"those beautiful fish\" → *dakuna minasina minasina* → but \"fish\" is *minasina* \nSo *dakuna minasina* = beautiful fish \n\"those\" → *minana* → from sentence 4: \"those canoes\" → *minana* \nSo \"those beautiful fish\" → *dakuna minasina minana* \nWhich woman → *Am* + woman → woman = *mtona*? \nIn 2: \"white man\" → *dimdim mtona* → *mtona* = man \nWomen → could be *mtona* for man, but what about woman? \nIn 12: \"The clever chief killed one wild pig\" → *lekalimati natala bunukwa nagasisi guyau tokabitam* \nNo woman. \nIn 13: \"How many women will look after this man?\" → *Navila vivila biyamatasi tau mtona?* \n→ *vivila* = women → so *vivila* = women \nYes — 13: \"how many women\" → *Navila vivila* \nSo \"women\" = *vivila* \nThus, \"which woman\" → *Am vivila* \nThen action: \"caught\" → *tetala* \nObject: *dakuna minasina minana* \nStructure: *Am vivila tetala dakuna minasina minana?* \nBased on 5: \"which man killed two pigs?\" → *Amtona tau lekalimati nayu bunukwa?* → Amtona (which man) + verb + object → *lekalimati* = killed \nSo yes — pattern: *Am [agent] [verb] [object]* \nSo 22 → *Am vivila tetala dakuna minasina minana?*\n\n23. \"Two wild dogs saw that old man.\" \n- Two → *yena* (two?) — but \"two\" not explicitly in data \n- \"wild dogs\" → \"wild\" = *guyau* → in 12: \"killed one wild pig\" → *guyau* \n\"dog\" → not directly, but \"dogs\" → likely *guyau* (wild) or *neti*? \nIn 12: \"wild pig\" → *guyau* → so \"wild\" = *guyau* \n\"dogs\" → not in data, but in 12: \"two wild dogs\" → not given — but 23: \"two wild dogs\" \n\"old man\" → \"old\" = *guyau* or *kayu*? \nIn 4: \"this old woman\" → *legisi* (old woman) — so \"old\" likely not marked \nBut in 2: \"white man\" — no old \nIn 13: \"how many women will look after this man?\" → \"this man\" \nIn 10: \"that beautiful child\" \nNo \"old man\" — but 23 says \"that old man\" → likely *guyau* for old? \nBut in 4: \"old woman\" → *legisi* \n\"old woman\" → *legisi* \n\"old man\" → *guyau*? or *legisi*? \n\"legisi\" likely means \"old\" → both old woman and old man? \nIn 4: \"this", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11850.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 1, + "output": "Start by analyzing the provided English-Kilivila pairs to detect patterns in word order, syntax, and the structure of questions.\n\nFirst, observe how quantifiers and questions are formed:\n\n- Questions starting with \"How many?\" → use structure like *Navila x lekotasi?* \n (e.g., 8. \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?*) \n → \"Navila\" = \"how many\" \n → \"lekotasi\" = \"arrived (something)\" \n → So \"how many X did Y see?\" = *Navila x lekotasi*? \n\nCheck 19: \"How many canoes did those old women see?\" \n→ Expected pattern: *Navila canoes lekotasi*? \n→ But in 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* \n→ \"Kwevila\" = \"how many\" (same as \"navila\"?)\n\nWait: 8 uses *Navila*, 11 uses *Kwevila*. So variation?\n\nCheck: \n8. \"How many dogs arrived?\" → *Navila ka’ukwa lekotasi?* → \"ka’ukwa\" = dogs, \"lekotasi\" = arrived \n11. \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?* → \"lekamkwamsi\" = \"those white men\", \"mtosiwena\" = \"ate\" \n→ \"Kwevila\" = \"how many\" → same phrasing?\n\nBut 8: Navila + noun + lekotasi \n11: Kwevila + noun + verb phrase (with subject) \n→ So perhaps \"navila\" and \"kwevila\" are both \"how many\", but used differently.\n\nBut 13: \"How many women will look after this man?\" → *Navila vivila biyamatasi tau mtona?* \n→ \"navila\" + \"vivila\" (women) + \"biyamatasi\" (look after) + \"tau mtona\" (this man) \n→ So \"how many X will do Y to Z?\" → *Navila X Y Z*\n\nAlso, 16 isn’t given, but in 13: \"Navila vivila biyamatasi tau mtona?\" \n→ So for \"how many X did Y see?\" → likely *Navila X lekotasi?* or *Navila X waga seesi?*\n\nBut 19: \"How many canoes did those old women see?\" \n→ \"old women\" = *legisi* (in 4: \"legisi waga makesiwena namwaya minana\" → legisi = old woman) \n→ \"see\" = *makesiwena* (in 4: \"saw those canoes\" → \"makesiwena\") \n→ So likely: *Navila canoes lekotasi*? — but lekotasi = arrived \n→ No: \"see\" is makesiwena, not lekotasi.\n\nSo \"see\" = makesiwena. \"arrived\" = lekotasi.\n\nSo in 4: \"legisi waga makesiwena namwaya minana\" → old women saw canoes.\n\nSo \"see\" = makesiwena.\n\nThus, \"how many canoes did those old women see?\" = *Navila namwaya legisi waga makesiwena?*\n\nBut word order in 13: *Navila vivila biyamatasi tau mtona* → how many women will look after this man?\n\nSo pattern: \n- For \"how many X did Y see?\" → *Navila X Y makesiwena?* \nBut in 13: \"how many women will look after\" → uses *bijamatasi* (look after)\n\nNow 19: \"How many canoes did those old women see?\" \n→ Morphemes: \"navila\" = how many, \"namwaya\" = canoes, \"legisi\" = old women, \"waga\" = those, \"makesiwena\" = saw\n\nBut in 4: \"legisi waga makesiwena namwaya minana\" → old women (legisi waga) saw canoes (namwaya)\n\nSo subject is \"legisi waga\", object \"namwaya\"\n\nSo in questions: \"how many X did Y see?\" → likely *Navila X Y waga makesiwena?*\n\nYes — because 13: \"Navila vivila biyamatasi tau mtona\" → how many women will look after this man → structure: Navila + X + verb + object?\n\nNo: in 13: \"Navila vivila biyamatasi tau mtona\" — \"vivila\" = women, \"biyamatasi\" = look after, \"tau mtona\" = this man\n\nSo verb + object? But in 19, \"makesiwena\" is the verb.\n\nSo in 4: \"legisi waga makesiwena namwaya\" → subject + waga + verb + object\n\nSo if we ask \"how many canoes did those old women see?\" → the object is \"canoes\", verb is \"see\", subject is \"those old women\"\n\nSo object comes after verb? So structure: *Navila namwaya legisi waga makesiwena?*\n\nBut that’s not typical. In all positive sentences, verb comes after subject? No:\n\n4: \"legisi waga makesiwena namwaya\" → subject (legisi waga) + verb (makesiwena) + object (namwaya)\n\nSo the question should follow that pattern: *Navila namwaya legisi waga makesiwena?* → \"how many canoes did those old women see?\"\n\nYes — matches known pattern.\n\nNow 20: \"These four white men will look after this clever child.\"\n\n\"these four\" = *navasi* (1: \"one man will catch these four fish\" → \"navasi\" = these four)\n\n\"white men\" = *dimdim mtona* (2: \"this white man\" = \"dimdim mtona\")\n\n\"will\" = future tense, often signaled by *will* in English, but in Kilivila, may be implied by structure\n\n\"look after\" = *biyamatasi* (13: \"look after two men\" → \"biyamatasi\")\n\n\"clever child\" = *gawetala*? → in 7: \"that clever woman\" → \"bigisi kwetala\" → \"kwetala\" = clever\n\n\"child\" = \"gwadi\" (in 3: \"that child\" → \"gwadi\")\n\nSo \"clever child\" = *gwadi kwetala*? → in 10: \"that beautiful child\" → \"dakuna gwadi\" → \"dakuna\" = beautiful\n\n\"beautiful\" = dakuna? So \"clever\" = kwetala?\n\nIn 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" → \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman\n\nSo \"clever\" = kwetala\n\nThus, \"clever child\" = *gwadi kwetala*\n\nSo 20: \"These four white men will look after this clever child.\" \n→ \"navasi\" = these four \n→ \"dimdim mtona\" = white men \n→ \"will\" = future marker, perhaps implied or marked by tense \n→ \"biyamatasi\" = look after \n→ \"this clever child\" = \"tau gwadi kwetala\" — \"tau\" = this, \"gwadi\" = child, \"kwetala\" = clever\n\nIn 13: \"Navila vivila biyamatasi tau mtona\" → \"how many women will look after this man?\"\n\nSo for future tense with \"will\", it’s natural — the structure is: [subject] [verb] [object] with future tense marked by \"will\" or implied.\n\nIn 20, subject: \"these four white men\" = \"navasi dimdim mtona\"\n\nVerb: \"will look after\" = \"biyamatasi\"\n\nObject: \"this clever child\" = \"tau gwadi kwetala\"\n\nSo full clause: *navasi dimdim mtona biyamatasi tau gwadi kwetala*\n\nBut in 13, the structure is \"Navila vivila biyamatasi tau mtona\" — so for questions, \"navila\" is first.\n\nIn 20, it’s declarative — no \"navila\"\n\nSo for declarative: [quantifier] [subject] [verb] [object]\n\nBut \"these four\" = navasi → used as adjective or quantifier?\n\nIn 1: \"one man will catch these four fish\" → \"navasi\" = these four → modifies \"fish\"\n\nIn 2: \"this white man\" → \"lekota dimdim mtona\" → \"lekota\" = this, \"dimdim\" = white\n\nSo \"navasi\" is not used for \"this\" — rather \"navasi\" means \"these four\"\n\n\"these four\" → navasi \n\"this\" → lekota\n\nSo in 20: \"These four white men\" → \"navasi dimdim mtona\"\n\n\"look after\" → \"biyamatasi\"\n\n\"this clever child\" → \"tau gwadi kwetala\"\n\nSo: *navasi dimdim mtona biyamatasi tau gwadi kwetala*\n\nNow 21: \"How many children will eat these pigs?\"\n\nPattern: \"how many X will do Y to Z?\"\n\nFrom 11: \"How many things did those white men eat?\" → *Kwevila lekamkwamsi dimdim mtosiwena?*\n\n\"Kwevila\" = how many → just like \"navila\"?\n\nBut in 13: \"Navila vivila biyamatasi tau mtona\" → navila\n\nSo both used? But in 11: it's \"kwevila\", in 13: \"navila\"\n\nPossibility: \"kwevila\" and \"navila\" are both \"how many\", but used differently by context?\n\nBut 11: \"how many things did those white men eat?\" → *kwevila lekamkwamsi dimdim mtosiwena?*\n\n\"lekamkwamsi\" = those white men \n\"mtosiwena\" = ate\n\nSo structure: *Kwevila [subject] [verb]?* → but no object? \nWait: \"eat\" → mtosiwena → object missing?\n\n\"these pigs\" — in original: \"these pigs\" → what is \"pigs\"?\n\nIn 21: \"these pigs\" → in similar example, 12: \"the clever chief killed one wild pig\" → \"nangasisi guyau tokabitam\" → \"guyau\" = wild pig\n\nSo \"pigs\" = ? → not directly given.\n\nBut 12: \"killed one wild pig\" → \"nangasisi guyau tokabitam\"\n\n\"nangasisi\" = killed \n\"guyau\" = wild pig \n\"tokabitam\" = one\n\nSo \"pigs\" may be implied as same as \"pig\" → use \"guyau\"?\n\nBut in 19, \"canoes\" → \"namwaya\"\n\nSo in 21: \"how many children will eat these pigs?\"\n\nChildren → \"gwadi\" → \"gwadi\" = child\n\n\"will eat\" → verb = \"mtosiwena\" (from 11: \"ate\")\n\n\"these pigs\" → \"navasi guyau\"? — but \"navasi\" = these four → not used with \"pigs\"\n\nIn 11: \"How many things did those white men eat?\" → *kwevila lekamkwamsi dimdim mtosiwena?* → subject (those white men), verb (ate)\n\nSo the object \"things\" is missing? No — in 11, it's not asked for object — the question is \"how many things did X eat?\" → so object is \"things\"\n\nSo structure: *kwevila [object] [subject] [verb]*? — but no\n\nIn 11: *kwevila lekamkwamsi dimdim mtosiwena?* → \"kwevila\" + \"lekamkwamsi\" (those white men) + \"mtosiwena\" (ate)\n\nSo verb after subject? But the object is not present in the sentence?\n\nThe question is about how many things were eaten — so \"how many\" refers to the things, not the people.\n\nThus, object of \"eat\" is missing — the verb is used without object.\n\nBut in other cases, object is in the clause.\n\nAlternatively, perhaps the structure is: *kwevila + X + [subject] + [verb]* — where X is the thing being eaten?\n\nIn 11: \"How many things did those white men eat?\" → the \"things\" are the subject of the quantifier.\n\nSo *kwevila* + *things* + *did X eat?*\n\nBut in translation: *kwevila lekamkwamsi dimdim mtosiwena?* → so \"kwevila\" + \"lekamkwamsi dimdim\" (those white men) + \"mtosiwena\" (ate)\n\nSo no object — the object is referred to implicitly.\n\nThus, for \"how many children will eat these pigs?\", the structure may be:\n\n*kwevila gwadi mtona navasi guyau?* → but \"mtona\" = man, \"guyau\" = pig — not matching\n\n\"children\" = \"gwadi\"\n\n\"will eat\" = \"mtosiwena\"\n\n\"these pigs\" = \"navasi guyau\" → but navasi is \"these four\"\n\nProblem: navasi = these four → not generic \"these\"\n\nSo \"these pigs\" = \"navasi guyau\" — ok\n\nBut the quantifier is \"how many children\" → so \"how many X\" = *kwevila gwadi?*\n\nSo likely: *kwevila gwadi mtona navasi guyau?*\n\nBut in 11, the structure is *kwevila lekamkwamsi dimdim mtosiwena?* — meaning: \"how many things did those white men eat?\"\n\nSo it’s: how many [object] did [subject] [verb]?\n\nSo for 21: how many children will eat these pigs? → object = children, subject = unknown, verb = eat? No — \"children will eat\" — so children are doing the eating.\n\nSo children = subject, verb = eat\n\nThus, the question is: how many children (subject) will eat (verb) these pigs (object)?\n\nSo structure: *kwevila gwadi mtona navasi guyau?* — meaning: how many children will eat these pigs?\n\nBut in the sentence, \"will\" is missing — but in the base, it’s present.\n\nIn 13: \"how many women will look after\" → \"navila vivila biyamatasi tau mtona\" — \"will\" is not marked explicitly\n\nIn 13, \"will\" is implied by context — so future is not marked with a word\n\nBut in 11, \"did\" is past — \"mtosiwena\" = ate\n\nIn 21, \"will\" — present future?\n\nIn 20, \"will look after\" — implicit\n\nSo likely, \"will\" is not marked — only verb form suggests tense.\n\nSo for 21: \"how many children will eat these pigs?\" → *kwevila gwadi mtona navasi guyau?*\n\nBut \"mtona\" = man — not \"eat\"\n\n\"eat\" = mtosiwena\n\n\"pigs\" = guyau (wild pig)\n\nSo verb: \"mtosiwena\"\n\nSo *kwevila gwadi mtona navasi guyau?* → could be interpreted as \"how many children (will) eat these pigs?\"\n\nYes.\n\nBut in 11, it's *kwevila lekamkwamsi dimdim mtosiwena?* → so \"how many things did those men eat?\"\n\nSo pattern: *kwevila [object] [subject] [verb]*?\n\nNo — object is \"things\", subject is \"those white men\", verb is \"ate\"\n\nSo object is first?\n\nIn 11: kwevila things (object) did men eat — so order: kwevila + object + subject + verb?\n\nBut in translation, \"lekamkwamsi dimdim mtosiwena\" → subject first?\n\n\"lekamkwamsi\" = those white men → subject\n\nSo order: kwevila + subject + verb\n\nNo object?\n\nSo the \"things\" is not in the sentence — the quantifier applies to the unknown thing being eaten.\n\nThus, \"how many things did X eat?\" → object is missing — assumed.\n\nSimilarly, \"how many children will eat these pigs?\" → the children are subject, \"pigs\" is object.\n\nSo to match structure: *kwevila gwadi mtona navasi guyau?* → no\n\nBut \"gwadi\" = child → subject\n\n\"navasi guyau\" = these pigs → object\n\nBut the verb \"mtosiwena\" must be somewhere.\n\nIn 11: verb is after subject: \"lekamkwamsi dimdim mtosiwena\" → subject then verb\n\nSo likely: *kwevila gwadi mtona navasi guyau?* → misspelled?\n\n\"kwevila gwadi navasi guyau mtona mtosiwena?\" — too many elements.\n\nBetter: structure is *kwevila [subject] [verb] [object]*?\n\nBut in 11: \"kwevila lekamkwamsi dimdim mtosiwena\" — subject then verb — no object\n\nIn 21: children will eat pigs → so subject = children, verb = eat, object = pigs\n\nSo likely: *kwevila gwadi mtosiwena navasi guyau?* → but \"mtosiwena\" = eat, not \"will eat\"\n\n\"will\" is not marked.\n\nSo it's future — just verb form.\n\nThus, *kwevila gwadi mtosiwena navasi guyau?*\n\nBut in 11: *kwevila lekamkwamsi dim", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12147.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 2, + "output": "First, analyze the given English-Kilivila sentences to identify patterns in word order, syntax, and question types.\n\nKey observations:\n\n1. Question types:\n- Questions starting with \"How many\" → use \"Navila\" (how many) + noun + past/future verb?\n- Questions starting with \"Which\" → use \"Am\" + noun + verb?\n- Statements use a subject + verb + object pattern.\n\n2. Use of particles:\n- \"Navila\" = how many\n- \"Am\" = which\n- \"Lekota\" = this\n- \"Bikota\" = that\n- \"Gwadi\" = child\n- \"Minasina\" = fish\n- \"Mtona\" = man\n- \"Makwena\" = white\n- \"Navasi\" = one\n- \"Tau\" = four\n- \"Waga\" = those\n- \"Tetala\" = these\n- \"Matesi\" = looked after\n- \"Makwena\" = white\n- \"Minana\" = canoes\n- \"Vivila\" = clever\n- \"Gudimanabweta\" = stone\n- \"Waga\" = those\n- \"Makwena\" = white\n- \"Tetala\" = these\n- \"Kwevila\" = how many\n- \"Lekamkwamsi\" = those white men\n- \"Tetala\" = these\n- \"Minasina\" = fish\n- \"Namwaya\" = canoes\n- \"Waga\" = those\n- \"Legisi\" = that\n- \"Dakuna\" = beautiful\n- \"Gwadi\" = child\n- \"Makwena\" = white\n\n3. Focus on question types:\n\nFor (19): \"How many canoes did those old women see?\"\n\n- \"How many\" → \"Navila\"\n- \"canoes\" → \"minana\"\n- \"those\" → \"waga\"\n- \"old women\" → \"legisi\" + \"biyamatasi\" (old women)\n- \"see\" → \"makesiwena\" (from sentence 4: \"saw those canoes\" → \"waga makesiwena namwaya minana\")\n\nSo: \n\"Navila minana waga legisi biyamatasi makesiwena\"\n\nCheck: “those old women” → “waga legisi biyamatasi” → in sentence 4: “Legisi waga makesiwena namwaya minana” → \"that old woman saw those canoes\" → \"legisi waga makesiwena\" → so “waga” is those, “legisi” is that → \"legisi waga\" = that old woman? But in 4, \"legisi\" is the subject, \"waga\" object.\n\nIn sentence 4: \"Legisi waga makesiwena namwaya minana\" → “that old woman saw those canoes”\n\nSo “legisi” = that old woman, “waga” = those canoes. So “waga” modifies object.\n\nBut in 19, we want “those old women” → “waga legisi biyamatasi” → “those old women” is correct.\n\nSee sentence 13: “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” → “Navila vivila biyamatasi” = how many women → \"vivila\" = woman, \"biyamatasi\" = women? But in 13, it is “vivila biyamatasi” → vivila is clever? No.\n\nIn 13: “How many women will look after this man?” → \"Navila vivila biyamatasi tau mtona?\"\n\n“vivila” → clever woman → not woman. So likely “vivila” is not woman.\n\nWait — in 13: “vivila biyamatasi” → likely “biyamatasi” = women, “vivila” = clever?\n\nAlternative: in 5: “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?” → “amtona” = which man? “tau” = two, “lekalimati” = man, “nayu” = killed, “bunukwa” = pigs.\n\nSo “tau” = two → number → quantity.\n\nIn 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” → “navila” = how many, “ka’ukwa” = dogs, “lekotasi” = arrived.\n\nSo pattern: “Navila [noun] [verb]?”\n\nBut in 19, we need “how many canoes did those old women see?”\n\n→ So “Navila minana waga lekisi biyamatasi makesiwena?”\n\nBut “lekisi” = that? What about “waga”?\n\nIn 4: “Legisi waga makesiwena namwaya minana” → “that old woman saw those canoes”\n\nSo “waga” = those → object marker.\n\nSo subject: “those old women” → “waga legisi biyamatasi” → but in 4, “legisi” is subject, “waga” is object.\n\nThus: “waga” modifies object, so object is “waga minana” → those canoes.\n\nBut we need subject: “those old women” → so must be “waga legisi biyamatasi” as subject?\n\nBut in 4, “legisi” is subject → “that old woman”\n\nSo is “legisi” a definite article or adjective?\n\nPossibly: “legisi” = that, “biyamatasi” = old women → so “legisi biyamatasi” = that old woman → so “waga” is not part of subject.\n\nThus, for “those old women” → “waga biyamatasi” → “those women” → but no “legisi”?\n\nSentence 3: “That child will arrive” → “Bikota gwadi magudiwena” → “bikota” = that, “gwadi” = child → “that child”\n\nSo “bikota” = that → article\n\nSentence 2: “This white man arrived” → “Lekota dimdim mtona” → “lekoa” = this, “dimdim” = white, “mtona” = man → “this white man”\n\nSo “leko” = this, “bikota” = that\n\nTherefore: “waga” = those (in fact, in 4, “waga” is object, “legisi” is subject)\n\nSo for “those old women” → “waga biyamatasi” → those women → “biyamatasi” = women?\n\nIn 13: “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” → “vivila biyamatasi” → “clever women”? So \"vivila\" = clever, \"biyamatasi\" = women?\n\nBut in sentence 13, it says “women” — but uses “vivila” which means clever?\n\nIn sentence 7: “That clever woman will see something” → “Bigisi kwetala vivila minawena nakabitam” → “bigisi” = that, “kwetala” = will see, “vivila” = clever woman\n\nSo “vivila” = clever woman → “vivila” includes “woman”\n\nThus, in 13: “Navila vivila biyamatasi tau mtona” — “how many clever women will look after this man?”\n\nBut the original says: “How many women will look after this man?” — so contradiction?\n\nWait: original: “How many women will look after this man?” → sentence 13\n\nBut translation: “Navila vivila biyamatasi tau mtona?”\n\nSo “vivila biyamatasi” → clever women?\n\nBut the question is about “women” not necessarily clever.\n\nSo perhaps “vivila” is not defining the category — or is a misreading?\n\nWait — sentence 13: “How many women will look after this man?” → translation: “Navila vivila biyamatasi tau mtona?”\n\nBut “vivila” = clever → so likely “vivila biyamatasi” is “clever women” — but the English doesn’t say clever.\n\nBut the translation says “vivila biyamatasi” → so maybe Kilivila uses “vivila” to mean \"woman\" in context?\n\nUnlikely.\n\nAlternative: “biyamatasi” = women, “vivila” = clever → but not in the base.\n\nIn sentence 6: “The old women looked after two men” → “Leyamatasi teyu tauwau nunumwaya” → “leyamatasi” = old women → so “biyamatasi” = women, “leyamatasi” = old women?\n\nIn 4: “Legisi waga makesiwena namwaya minana” → “that old woman”\n\nSo “legisi” = that, “biyamatasi” = woman? But “legisi biyamatasi” = that woman — but in 4 it’s “legisi” alone?\n\nSentence 4: “Legisi waga makesiwena namwaya minana” → no “biyamatasi”\n\nSentence 6: “Leyamatasi teyu tauwau nunumwaya” → “old women” → “leyamatasi”\n\nSo likely “biyamatasi” = women, “leyamatasi” = old women?\n\nSo in 13: “Navila vivila biyamatasi tau mtona?” → could be “how many clever women”, but the question says “how many women” — so contradiction?\n\nNo — maybe English doesn't imply cleverness. So perhaps “vivila” is not used for “woman”.\n\nBut in 7: “that clever woman” → “bigisi kwetala vivila minawena” → clearly “vivila” = clever woman → so “vivila” = clever woman → includes both quality and gender.\n\nIn 13: “how many women” — could be “biyamatasi” = women — but translation has “vivila biyamatasi” → which means “clever women”\n\nSo likely, in the translation, “vivila” is used only for clues, but in 13, it’s present — so maybe the Kilivila system uses “vivila” to mean “woman”, but with properties.\n\nAlternatively, maybe “vivila” is not gender-specific — it's a class.\n\nBut let’s focus on the pattern.\n\nBack to (19): “How many canoes did those old women see?”\n\n- “how many” → “navila”\n- “canoes” → “minana”\n- “those old women” → “waga biyamatasi” → “waga” = those, “biyamatasi” = old women? But in 4, “legisi” = that, “waga” = those canoes\n\nIn 4: “Legisi waga makesiwena namwaya minana” → “that old woman saw those canoes”\n\nSo subject: “legisi” = that old woman\n\nObject: “waga” = those canoes\n\nSo “waga” marks object → not subject.\n\nThus, “those old women” must be formed as “waga biyamatasi” → if “biyamatasi” = women, and “waga” = those\n\nIs there a phrase for “old” woman? In 4, “legisi” = that old woman → so “legisi” = that + old?\n\nSo “legisi” = that + old\n\nThus, “waga biyamatasi” = those women, not old\n\nThus, need “waga legisi biyamatasi” → those that old women?\n\nBut “legisi” is used only for “that”, not “old”\n\nIn 4: “legisi” = that old woman → likely “legisi” = that/old woman\n\nThus, likely “legisi” includes “that” and “old” → so “waga legisi” = those that old → not correct\n\nIn 6: “leyamatasi” = old women → “leyamatasi” → “le” = old? “yamatasi” = women?\n\nIn 4: “legisi” = that old woman → “legisi” = that + old woman?\n\nSo “biyamatasi” = woman, “leyamatasi” = old women\n\nIn 6: “leyamatasi” → “old women”\n\nSo “waga leymatasi” = those old women\n\nYes! So “waga leymatasi” = those old women\n\nIn 6: “Leyamatasi teyu tauwau nunumwaya” → “old women looked after two men”\n\nSo subject is “leyamatasi” → old women\n\nThus, “waga leymatasi” = those old women\n\n“see” → “makesiwena” (from 4)\n\nSo (19): “Navila minana waga leymatasi makesiwena”\n\nBut is “makesiwena” correct? In 4: “makesiwena” = saw\n\nYes.\n\nSo (19) = “Navila minana waga leymatasi makesiwena”\n\nNow (20): “These four white men will look after this clever child.”\n\n- “these four” → “tetala tau” → “tetala” = these, “tau” = four\n- “white men” → “dimdim mtona” → in 2: “leko dimdim mtona” — “leko” = this, “dimdim” = white, “mtona” = man\n- So “tetala tau dimdim mtona” → these four white men\n- “will look after” → in 6: “looked after” → “teyu tauwau” → “teyu” = look after, “tauwau” = after?\n- In 6: “Leyamatasi teyu tauwau nunumwaya” → “old women look after two men” → “teyu tauwau” = look after\n- So “teyu” = look after\n- “this clever child” → “this” = “leko”, “clever” = “vivila”, “child” = “gwadi”\n- So “leko vivila gwadi”\n\n“will” → future → in 7: “will see” → “kwetala”\n\nSo “kwetala” → will\n\nThus, (20): “Tetala tau dimdim mtona kwetala teyu leko vivila gwadi”\n\nBut order: in English, “these four white men will look after this clever child”\n\nIn Kilivila, likely subject then verb then object → so “tetala tau dimdim mtona kwetala teyu leko vivila gwadi”\n\nYes.\n\n(21): “How many children will eat these pigs?”\n\n- “how many” → “navila”\n- “children” → “gwadi”\n- “will eat” → “eat” → in 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?” → “kwevila” = how many, “lekamkwamsi” = those white men, “mtosiwena” = things eaten? “mtosiwena” = eat\n- So “mtosiwena” = eat\n- “these pigs” → “tetala bunukwa” → in 5: “Which man killed two pigs?” → “bunukwa” = pigs\n- “tetala” = these\n- So “tetala bunukwa”\n\nSo (21): “Navila gwadi kwetala mtsosiwena tetala bunukwa”\n\nBut is “mtosiwena” = eat? Yes — from 11.\n\n(22): “Which woman caught those beautiful fish?”\n\n- “which” → “am”\n- “woman” → “biyamatasi” or “leyamatasi” → likely “biyamatasi” or “woman”\n- In 1: “one man will catch these four fish” → “navasi navasi yena minasina tetala tau” → “navasi” = one, “yena” = man, “minasina” = fish\n- “caught” → “catch” → in 1: “will catch” → “navasi yena minasina tetala tau” — no verb? Wait\n\nActually: “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau.”\n\n“Bibani” = one? “navasi” = one? So “Bibani” = one?\n\nOr “navasi” = one?\n\nSentence 1: “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau.”\n\nSo “navasi” = man? “yena” = man — could be redundant.\n\nLikely “navasi” = one\n\n“will” → “bibani” → in sentence 1, “Bibani” likely = one\n\nBut in 13: “how many women” → “navila” = how many\n\nNot “bibani”\n\nIn sentence 5: “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?” → “amtona” = which man\n\nSo “am” structure: “am + [noun] + verb + object?”\n\nIn 9: “Which canoe did the chiefs see?” → “Amakena waga legisesi gweguyau?” → “amakena” = which canoe, “waga” = those, “legisesi” = chiefs, “gweguyau” = see\n\nSo “amakena” = which canoe, “waga legisesi” = those chiefs, “gweguyau” = see\n\nSo structure: “am + noun + [object phrase] + verb?”\n\nIn 9: “amakena waga legisesi gweguyau?” → “which canoe did the chiefs see?”\n\nSo order: am + noun + object phrase (waga legisesi) + verb (gweguyau)\n\nSo this seems: “am + noun + [object phrase] + verb?”\n\nBut “waga” is object marker.\n\nIn 22: “Which woman caught those beautiful fish?”\n\n→ “am + woman + object + verb?”\n\n“woman” → “biyamatasi” —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11675.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "unit_audit", + "sample_index": 3, + "output": "First, analyze the structure of the given English–Kilivila pairs to extract patterns.\n\nLook at questions involving quantifiers and noun phrases:\n\nSentence 1: \"One man will catch these four fish.\" \n→ \"Bibani navasi yena minasina tetala tau.\" \n\"navasi\" = man; \"yena\" = one; \"minasina\" = four; \"tetala\" = fish; \"tau\" = will catch.\n\nSentence 2: \"This white man arrived.\" \n→ \"Lekota dimdim mtona.\" \n\"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \"That child will arrive.\" \n→ \"Bikota gwadi magudiwena.\" \n\"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \"This old woman saw those canoes.\" \n→ \"Legisi waga makesiwena namwaya minana.\" \n\"legisi\" = old woman; \"waga\" = saw; \"makesiwena\" = canoes; \"minana\" = those.\n\nSentence 5: \"Which man killed two pigs?\" \n→ \"Amtona tau lekalimati nayu bunukwa?\" \n\"amtona\" = which man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \"The old women looked after two men.\" \n→ \"Leyamatasi teyu tauwau nunumwaya.\" \n\"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \"That clever woman will see something.\" \n→ \"Bigisi kwetala vivila minawena nakabitam.\" \n\"bigisi\" = clever woman; \"kwetala\" = will see; \"vivila\" = something.\n\nSentence 8: \"How many dogs arrived?\" \n→ \"Navila ka’ukwa lekotasi?\" \n\"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \"Which canoe did the chiefs see?\" \n→ \"Amakena waga legisesi gweguyau?\" \n\"amakena\" = which; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = canoe.\n\nSentence 10: \"That beautiful child saw this stone.\" \n→ \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"legisi\" = that; \"dakuna\" = beautiful; \"gwadi\" = child; \"waga\" = saw; \"gudimanabweta\" = stone.\n\nSentence 11: \"How many things did those white men eat?\" \n→ \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n\"kwevila\" = how many; \"lekamkwamsi\" = white men; \"mtosiwena\" = ate.\n\nSentence 12: \"The clever chief killed one wild pig.\" \n→ \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"gagasi\" = chief? \"guyau\" = wild? \"tokabitam\" = one? — likely \"guyau\" = wild, \"tokabitam\" = pig.\n\nSentence 13: \"How many women will look after this man?\" \n→ \"Navila vivila biyamatasi tau mtona?\" \n\"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nNow, pattern extraction:\n\n1. Quantifier of quantity: \n - \"How many\" → \"navila\" \n - \"One\" → \"yena\" \n - \"Two\" → \"nayu\" \n - \"These\" → \"yena\" or \"waga\" depending on context; \"makesiwena\" = those canoes\n\n2. Noun phrase structure: \n - Adjective + noun: e.g., \"white man\" = \"dimdim mtona\"; \"old woman\" = \"legisi waga\"; \"clever woman\" = \"bigisi\" \n - Possessive or object markers: e.g., \"these four fish\" → \"minasina tetala tau\"\n\n3. Verb structure: \n - Future tense: \"will catch\" = \"tau\" \n - Past tense: \"saw\" = \"waga\", \"arrived\" = \"mtona\"\n\n4. Questions: \n - \"How many X?\" → \"navila X?\" \n - \"Which X?\" → \"amtona X?\" \n - \"Did X do Y?\" → \"lek X Y?\"\n\nNow, apply to the requested translations:\n\n19. How many canoes did those old women see? \n→ \"navila\" = how many \n→ \"makesiwena\" = canoes \n→ \"legisi\" = old women \n→ \"waga\" = saw \n→ \"those\" is implicit in \"makesiwena\" or in \"waga\" context \nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"old woman saw those canoes\" \nSo \"legisi waga makesiwena\" = old woman saw canoes \nSo \"navila makesiwena\" = how many canoes \n\"did those old women see\" → \"legisi waga\" \nThus: \"navila makesiwena legisi waga?\"\n\nBut in sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"old woman saw those canoes\" \nHere \"namwaya\" = those; \"minana\" = those \nSo \"namwaya\" = those → likely \"waga\" is not used for \"those\" \nBut in sentence 10: \"gwadi magudiwena gudimanabweta\" → \"child saw stone\" \nNo \"those\" marker. \nSentence 8: \"navila ka’ukwa lekotasi?\" → \"how many dogs arrived?\" \nSo \"how many X?\" → \"navila X?\" \nSo \"how many canoes\" → \"navila makesiwena\" \n\"did those old women see\" → \"legisi waga\" \nSo: \"navila makesiwena legisi waga?\" \n\nBut it's a question, so \"how many canoes did those old women see?\" → \"navila makesiwena legisi waga?\" \nCheck sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → so \"waga\" = saw, \"legisesi\" = chiefs → so \"waga\" after noun? \nNo: \"amakena waga legisesi gweguyau?\" → structurally: \"which saw chiefs canoe?\" → so \"waga\" not before noun \nBetter: \"waga\" is the verb (saw), then \"legisesi gweguyau\" = the chiefs saw the canoe \nSo pattern: [subject] [waga] [object] \nBut for questions: [navila] [object] [subject] [waga]? \nSentence 8: \"Navila ka’ukwa lekotasi?\" → \"how many dogs arrived?\" → here \"lekotasi\" = arrived, not \"saw\" \nSo \"how many X did Y do?\" → \"navila X Y?\" \nBut in 8: \"navila ka’ukwa lekotasi?\" → \"how many dogs arrived?\" → not \"did dogs arrive?\" \nSo \"how many X?\" = \"navila X?\" \nAnd \"did Y see X?\" → \"Y waga X\" \nSo for 19: \"how many canoes did those old women see?\" \n→ \"navila makesiwena legisi waga?\" \nBut in sentence 4: \"legisi waga makesiwena\" → \"old woman saw canoes\" \nSo \"waga\" is the verb, and \"makesiwena\" is the object \nSo \"legisi waga makesiwena\" → old woman saw canoes \nThus, \"did those old women see\" → \"legisi waga makesiwena\" \nSo \"how many canoes\" → \"navila makesiwena\" \nSo question: \"navila makesiwena legisi waga?\" \nBut is \"legisi\" used with \"waga\"? \nIn sentence 4: \"legisi waga makesiwena\" — so word order: subject + verb + object \nSo \"navila makesiwena legisi waga?\" — would be \"how many canoes did old women saw?\" → wrong \n\"navila makesiwena + legisi waga\" — the waga is on the subject? \nWrong. \nBetter: in sentence 4: \"Legisi waga makesiwena namwaya minana\" — full structure \n\"legisi\" = subject; \"waga\" = verb; \"makesiwena\" = object \nSo: Subject + verb + object \nSo for \"how many canoes did those old women see?\" → \n\"navila makesiwena\" (how many canoes) → \"legisi waga\" = those old women saw → but \"legisi waga\" as subject? \nSo the structure is \"navila [object] [subject] [verb]\" → rare \nBut sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" \n\"amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu bunukwa\" = two pigs \nSo \"amtona [noun] [verb] [quantifier noun]\" \nSo pattern: \"which X did Y do?\" → \"amtona X verb Y\" or \"amtona verb X Y\"? \nNo — \"amtona tau lekalimati nayu bunukwa\" → which man killed two pigs → so \"amtona\" + \"tau\" (man) + \"lekalimati\" (killed) + \"nayu bunukwa\" (two pigs) \nSo \"amtona [noun] [verb] [quantifier-noun]\" \nSimilarly, sentence 9: \"Amakena waga legisesi gweguyau?\" → which canoe did the chiefs see? \n\"amakena\" = which; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = canoe \nSo \"amakena waga legisesi gweguyau?\" → which saw chiefs canoe? → incorrect \n\"amakena\" + \"waga\" + \"legisesi\" + \"gweguyau\" → which saw chiefs canoe? \nBut \"waga\" = saw; \"legisesi\" = chief; \"gweguyau\" = canoe \nSo likely: \"amakena [verb] [subject] [object]\" → \"which [verb] [subject] [object]\" \nBut \"amakena waga legisesi gweguyau\" = which saw chiefs canoe \nYes — meaning: which canoe did the chiefs see? \nSo structure is: [question marker] [verb] [subject] [object] \nIn sentence 5: \"amtona tau lekalimati nayu bunukwa\" → which man killed two pigs → \"amtona\" (which) + \"tau\" (man) + \"lekalimati\" (killed) + \"nayu bunukwa\" (pigs) \nSo \"amtona [noun] [verb] [quantifier-noun]\" \nBut in sentence 9: \"amakena waga legisesi gweguyau\" → \"which [verb] [subject] [object]\" \nSo inconsistent. \nBut in 5: \"amtona tau lekalimati nayu bunukwa\" — noun after \"amtona\", verb then \nIn 9: \"amakena waga\" — verb first? \nNo: \"amakena waga\" = which saw — so verb comes before subject and object? \nIn 5: \"amtona tau lekalimati\" — noun, verb, quantifier \nIn 9: \"amakena waga\" — verb, subject, object \nSo different structures. \n\nWait: in 9, it's \"which canoe did the chiefs see?\" → object first? \n\"amakena waga legisesi gweguyau\" — \"amakena\" = which; \"waga\" = saw; \"legisesi\" = chiefs; \"gweguyau\" = canoe \nSo likely: \"which [verb] [subject] [object]\" — but that would be \"which [saw] [chiefs] [canoe]\" → meaning \"which saw chiefs canoe?\" \nThat makes sense: \"which canoe\" → object? \nBut the word order is \"amakena waga legisesi gweguyau\" — which saw chiefs canoe \nSo if \"waga\" is the verb, \"legisesi\" is the subject, \"gweguyau\" is the object — so it's \"which saw chiefs canoe?\" \nThat is the correct question. \nSimilarly, in 20: \"These four white men will look after this clever child.\" \n→ \"These\" = \"yena\"? \"four\" = \"minasina\"? \"white men\" = \"dimdim mtona\"? \n\"will look after\" = \"tauwau\"? From sentence 6: \"leyamatasi teyu tauwau nunumwaya\" → \"old women looked after two men\" \n\"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men \nSo \"tauwau\" = looked after (but that must be a verb?) \n\"teyu\" = looked after — so verb = \"teyu\" \n\"will\" → \"tau\" \nIn sentence 1: \"navasi yena minasina tetala tau\" → one man will catch four fish → \"tau\" = will catch \nSo \"will\" = \"tau\" \nSo \"will look after\" = \"tau teyu\"? \nBut \"tauwau\" is used in \"tauwau nunumwaya\" — \"two men\" \nSo likely \"tauwau\" = two, not \"look after\" \n\"teyu\" = looked after \nSo \"will look after\" = \"tau teyu\" \n\"these four white men\" = \"yena minasina dimdim mtona\" \n\"this clever child\" = \"gwadi magudiwena bigisi\"? \n\"that clever woman\" = \"bigisi\" in sentence 7 \n\"child\" = \"gwadi\" \n\"clever\" = \"bigisi\" (only in woman) — so \"clever child\" = \"bigisi gwadi\"? \nPossibly \nSo full: \"yena minasina dimdim mtona tau teyu bigisi gwadi\" \nBut \"this\" = \"tau\"? In sentence 13: \"navila vivila biyamatasi tau mtona\" — \"how many women will look after this man?\" \n\"tau\" = this \nSo \"this\" = \"tau\" \nSo \"this clever child\" = \"tau bigisi gwadi\"? \nBut \"tau\" is \"this\", so \"tau bigisi gwadi\" = this clever child \nSo \"yena minasina dimdim mtona tau teyu tau bigisi gwadi\" \nBut redundant \"tau\" \nBetter: \"these four white men will look after this clever child\" \n→ \"yena minasina dimdim mtona tau teyu tau bigisi gwadi\"? \nBut \"tau\" used twice \nIn sentence 4: \"legisi waga makesiwena namwaya minana\" — \"those\" = \"namwaya minana\" \nSo \"these\" may not be \"yena\" \n\"yena\" = one \nSo \"four\" = \"minasina\" \n\"these\" = in context, may be \"yena\" or \"namwaya\" \nIn sentence 5: \"amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" \n\"tau\" = man \nNot \"these\" \nIn sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" \n\"this\" = \"tau\" — \"tau\" appears with \"stone\" — not directly \nBut in sentence 13: \"navila vivila biyamatasi tau mtona\" → \"how many women will look after this man?\" \n\"tau\" = this \nSo \"this\" = \"tau\" \nSimilarly, \"these\" might be \"yena\"? But \"yena\" = one \nSo \"these four\" = \"minasina\" with some marker? \nIn sentence 1: \"one man will catch these four fish\" → \"yena navasi minasina tetala tau\" \n\"yena\" = one; \"minasina\" = four; \"tetala\" = fish; \"tau\" = will catch \nSo \"these\" is not marked explicitly \nBut in sentence 4: \"those canoes\" = \"namwaya minana\" \nSo \"those\" = \"namwaya minana\" \n\"these\" = might be missing \nPerhaps \"these\" is \"yena\" with some context? \nBut \"yena\" means one \nSo more likely, in Kilivila, \"these\" is not marked as a separate word; quantity and determiner compose the phrase \nSo \"these four white men\" → \"minasina dimdim mtona\" \n\"will look after\" → \"tau teyu\" \n\"this clever child\" → \"tau bigisi gwadi\" \nSo full: \"yena minasina dimdim mtona tau teyu tau bigisi gwadi\"? \nBut \"yena\" = one — not four \n\"minasina\" = four — so \"these four\" = \"minasina\" \nSo \"minasina dimdim mtona\" = these four white men \n\"will look after\" = \"tau teyu\" \n\"this clever child\" = \"tau bigisi gwadi\" \nBut \"this\" appears twice — but in structure, likely \"tau\" for \"this\" is needed in object", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11750.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private answer audit. Before the final box, make a small scratch table with columns: unit id, requested meaning/value, derived candidate, and evidence. Check that every unit id appears exactly once in the final box, that answers are not swapped between units, and that no reasoning or alternative guesses are inside the box.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are asked to determine the theoretically possible translations of “word” and “to exhaust” into Rotuman, based only on the given word list and patterns.\n\nFirst, note that we cannot translate “word” or “to exhaust” directly from the list. So we must infer possible forms based on linguistic patterns in the data.\n\nStep 1: Analyze known compound words and non-transparent components.\n\nLook for compound forms and directional or nominal patterns.\n\nExample: \n- ‘a‘öf fau’ → year’s end \n → ‘fau’ = year; ‘a‘öf’ = end? Possibly. \n → ‘fau’ is a noun; ‘a‘öf’ is likely a preposition or suffix meaning “end”. \n\n- ‘huli’ = to turn over \n- ‘huni’ = lower end \n- ‘huag to‘a’ = courageous \n- ‘is susu’ = nipple \n- ‘ma.titi’ = coldness \n- ‘ma.tit mamasa’ = ice \n- ‘pala’ = pierce \n- ‘piri’ = to curl \n- ‘nu‘suar tiro’ = window \n- ‘nu‘sura’ = door \n\nObserve: Some nouns are derived from verbs with additions (e.g., ‘huni’ = lower end → possibly from ‘hun’ + ‘i’ or similar)\n\nLook for root + suffix patterns.\n\nConsider the word ‘pogi’ = night. Is there a pattern of ‘X + i’ or ‘X + o’ for abstract concepts?\n\nNow, consider a word that may be related to “to exhaust”:\n\nLook for verbs that suggest depletion or loss.\n\nIs there any verb meaning “to empty”? Or “to use up”?\n\nLook at: \n- ‘puruha.ki’ = to boil, to bubble up → suggests dynamic process, but not exhaustion \n- ‘pala’ = pierce → not clearly exhaustion \n- ‘hül ha.fu’ = to blow (of a hurricane) → one might blow out → might relate to “to exhaust”? \n→ “to blow out” = to extinguish, which could mean “to exhaust” (as in blow out a candle)\n\nIs there a verb meaning “to blow out”? Not directly listed.\n\nBut consider: ‘hül ha.fu’ = to blow (of a hurricane) — but “ha.fu” = rocky? Or is it a word for “blow”? \nWait: ‘ha.fu’ appears in ‘hül ha.fu’ = to blow (of a hurricane). \nSo → ‘ha.fu’ is not a standalone noun. \nBut look at: \n‘hün kia’ = base of the neck → kia may be a noun or classifier \n‘is’ = sharp-pointed \n‘is susu’ = nipple → ‘is’ as a root?\n\nAnother possibility: \n‘ma.titi’ = coldness; ‘ma.tit mamasa’ = ice → likely derived from ‘ma.tit’ + ‘mamasa’ \n‘mamasa’ = solid → so ice = coldness + solid → plausible\n\nNow: consider compound nouns.\n\n‘nu‘sura’ = door \n‘nu‘suar tiro’ = window \n→ ‘nu’suar’ shares prefix; ‘tiro’ = spectacles (via ‘maf tiro’) → so ‘tiro’ is a noun \n→ thus, ‘nu’suar tiro’ = window = window with spectacles? Unlikely. \nBetter: ‘nu‘suar’ may be a root, with ‘tiro’ modifying structure — but not clear. \n\nBack to “to exhaust” — think about verbs that mean “to use up” or “to deplete”.\n\nWhich verbs involve consumption or depletion?\n\nLook at: \n‘puri’ → not given \n‘pala’ = pierce — not directly about exhaustion \n‘pog’ = not present \nBut: ‘puri’ and ‘pug’ → not in list.\n\nWhat about ‘kia’? In ‘hün kia’ → “base of the neck” → kia may be a noun or part of noun phrase.\n\nAnother idea: in some languages, verbs related to “blow” or “empty” can mean “to exhaust”.\n\n‘hül ha.fu’ = to blow (of a hurricane) — could also imply “to blow out” — e.g., blow out a candle = to extinguish → to exhaust a source.\n\nThus, “to blow out” = to exhaust.\n\nSo, could ‘hül’ (to blow) + a suffix like ‘-out’ imply “to exhaust”?\n\nBut in Rotuman, is there a possible form based on the observed pattern?\n\nWe see compound verbs: \n‘fäeag ‘u‘u’ = to use sign language → two elements \n‘ha.fha.fu’ = rocky → two syllables with glottal stop \n\nAlso: ‘huag to‘a’ = courageous → noun derived from verb? \n\nCould there be a verb meaning “to use up”? \n\nNo such verb is directly listed.\n\nBut note: ‘is susu’ = nipple — a small bodily part \n‘is’ + ‘susu’ → root + noun \n\n‘pala’ = pierce — could “pierce” over time be used to mean “to deplete”? Unlikely.\n\nAlternative: look for a word that means “to fill up” — to be full → then “to exhaust” would be the opposite.\n\nWe do not have “to fill” or “full”.\n\nNow consider root + noun patterns.\n\nWe have: \n‘fau’ = year \n‘a‘öf’ = something (year’s end) \n→ could ‘a‘öf’ be a suffix meaning “end”?\n\nThen, a noun + ‘a‘öf’ = end of noun?\n\nIn ‘a‘öf fau’ = year’s end\n\nSo possible: ‘fau a‘öf’ might be parsed differently? But order is ‘a‘öf fau’ — so likely the adverb or preposition first?\n\nNow, consider a word for “word”. \n\nPossible patterns for abstract nouns: \n- ‘to‘a’ = hero \n- ‘rū huga’ = stomach-ache → “stomach” + “ache” \n- ‘ma.titi’ = coldness \n- ‘mamasa’ = solid \n- ‘pulu’ = glue \n\nNow, “word” — what abstract nouns are in the list?\n\nWe have:\n- coldness → ma.titi \n- sharp-pointed → is \n- base of neck → hün kia \n- fire? not here \n- glue? pulu \n- night? pogi \n\nNone clearly a linguistic unit like “word”.\n\nBut look: ‘fau’ = year → year is a discrete unit → so “word” could be a unit of linguistic expression → a “unit of language”?\n\nIs there any form that could be root + suffix?\n\nIn Rotuman, can we form a word like ‘word’ via a compound?\n\nWe see:\n- ‘nu‘sura’ = door \n- ‘nu‘suar tiro’ = window \n- ‘maf tiro’ = spectacles \n→ ‘tiro’ appears in both — suggests ‘tiro’ is a root meaning “spectacles” → then extended to window?\n\nBut window is not “spectacles”.\n\nAlternatively: ‘tiro’ in ‘nu‘suar tiro’ may modify window in a spatial sense?\n\nNo clear pattern.\n\nCould a word for “word” be derived from a root meaning “to speak”?\n\nWe have ‘ele’ = to be near \n‘ele’ = shallow → different meaning \n‘elo’? not given \n‘pala’ = pierce — could “pierce” be used to mean “to cut a word”? \n\n‘olo’ = to cut — to cut → could be used for cutting a word? \n\nSo “to cut” → “olo” \nIf you “cut” something, you may “cut out” a word? \n\nBut “to cut” doesn’t mean “to exhaust” — more about removal.\n\nBut “to exhaust” could be “to consume all” → equivalent to “to use up”.\n\nNo verb means “to use up” directly.\n\nBut: “to boil up” → puhra.ki → to bubble up — meaning to rise, not to deplete.\n\nAnother idea: in compound forms, is there a verb prefix?\n\nWe have:\n- ‘ha.fha.fu’ = rocky → not clear \n- ‘is’ = sharp-pointed → a root \n- ‘is susu’ = nipple → is + susu \n\nSo root + noun is common.\n\nFor “word” — could there be a word formed from a root meaning “to speak” + something?\n\nWe don’t have it.\n\nBut we have: ‘fäeag u‘u’ = to use sign language → “to use” sign language \n\n“to use” is a verb → so “to use” is the root?\n\nDoes “faeag” = to use?\n\nYes — ‘fäeag ‘u‘u’ = to use sign language → so the verb is ‘fäeag’\n\nSo ‘fäeag’ = to use\n\nSo “to use” is a verb in the language.\n\nNow, “to exhaust” = to use up → to use completely → could be “to use completely”?\n\nBut how to express “completely”?\n\nCould “to exhaust” be derived from ‘fäeag’ + something indicating fullness or completion?\n\nWe have no such word.\n\nBut look: is there a possibility that “to exhaust” is a compound of ‘to use’ + ‘end’?\n\nLike ‘to use to the end’?\n\nWe see ‘a‘öf’ = end — in ‘a‘öf fau’ = year’s end\n\nSo could ‘fäeag a‘öf’ = to use to the end → to exhaust?\n\nThis is promising.\n\nThus, “to exhaust” might be the compound verb: ‘fäeag a‘öf’\n\nThis would mean “to use to the end” → which is a standard meaning of “to exhaust”.\n\nSimilarly, “word” — what about “term”? “unit”?\n\nWe have: ‘to‘a’ = hero — no \nWe have ‘pala’ = pierce — not relevant \nBut consider: “to speak” is missing.\n\nAnother candidate: ‘huli’ = to turn over — could be used to mean “to restate”? Not directly.\n\nBut what about “to use” as “to speak”?\n\n‘fäeag’ = to use — could mean “to speak” as in “to use one’s voice”?\n\nIn many languages, ‘to use’ can cover ‘to speak’.\n\nSo if ‘fäeag’ = to use → could it cover ‘to speak’?\n\nThen “word” = “a unit of speech”?\n\nPossible forms using existing roots?\n\nWe have:\n- ‘puhra.ki’ = to boil → not helpful \n- ‘mamasa’ = solid \n- ‘ma.tit’ = coldness \n- ‘lala’ = deep\n\nNo clear noun for “word”.\n\nBut perhaps there is a root meaning “speak”?\n\nWe don’t have it.\n\nBut consider: in compound forms, “word” might be formed from a root meaning “speech”?\n\nNot in data.\n\nAnother idea: “word” might be a noun derived from a verb meaning “to speak”.\n\nBut no such verb is listed.\n\nSo, what can we infer from the data?\n\nWe have a verb ‘fäeag’ = to use.\n\nAnd a noun ‘fau’ = year.\n\nWe have ‘a‘öf’ = end.\n\nSo, we can form ‘fäeag a‘öf’ → to use to the end → to exhaust.\n\nThus, the theoretically possible translation of “to exhaust” is **fäeag a‘öf**\n\nNow for “word”?\n\nMissing.\n\nIs there a noun that could be considered a word?\n\nWe have:\n- ‘to‘a’ = hero \n- ‘pogi’ = night \n- ‘mamasa’ = solid \n- ‘lala’ = deep \n\nBut none clearly “word”.\n\nPossible that “word” could be derived from a root meaning “speech” — and we have no such root.\n\nBut could it be related to “to use”?\n\n‘fäeag’ = to use → but not a noun.\n\nIn compound nouns:\n\n- ‘huni’ = lower end \n- ‘hün kia’ = base of neck \n- ‘ma.tit mamasa’ = ice \n- ‘nu‘sura’ = door \n\nSo compound noun is formed from root + noun.\n\nCould “word” be formed from a root like ‘huli’ or ‘pala’?\n\nNo.\n\nBut note: ‘pogi’ = night — not helpful.\n\nWait — what about ‘fau’ = year → a unit of time \n‘a‘öf fau’ = year’s end — year’s end → the end of a year \n\nCould “a word” be a unit like a year? \nPossibly, but it doesn’t follow.\n\nAlternatively: is there a root meaning “thing” or “object”?\n\nNot in list.\n\nBut perhaps “word” is from a root like ‘is’ or ‘is susu’?\n\n‘is’ = sharp-pointed → not relevant.\n\nThus, there is no direct evidence for a word meaning “word”.\n\nBut the question asks: **what would the theoretically possible translations be?**\n\nSo, based on patterns, what forms are plausible?\n\nFor “to exhaust” → plausible form: ‘fäeag a‘öf’ → using the verb ‘fäeag’ (to use) + ‘a‘öf’ (end) → to use to the end → to exhaust.\n\nThis fits bilingual patterns.\n\nFor “word” — no such form is directly provided.\n\nBut could “word” be related to “to speak”?\n\nWe don’t have “to speak”.\n\nBut is there a word from which “word” might be derived?\n\nWe have: ‘pala’ = pierce — could “piercing” be used to cut a word? Not likely.\n\nAnother possibility: Rotuman may have a root for “speech” that isn’t listed.\n\nBut the only verb with broad applicability is ‘fäeag’ = to use.\n\nCould “word” be a noun built from the verb root?\n\nLike in English: “to speak” → “speech” → not present.\n\nNo such pattern.\n\nSo, is there a plausible noun?\n\nWe see compound nouns: \n- ‘huni’ = lower end \n- ‘ma.tit mamasa’ = ice \n- ‘nu‘sura’ = door \n\nAll are root + noun or root + noun.\n\nSo “word” might be **a word** in the sense of “a thing” or “something”?\n\nNo.\n\nBut notice: the list includes ‘is’ = sharp-pointed, which might be a root — and ‘is susu’ = nipple — so ‘is’ is a root.\n\nCould ‘is’ be used for a word?\n\nUnlikely.\n\nBut what is the most plausible theoretical form based on patterns?\n\nFor “word”, since no clear candidate, but if we assume that “word” is abstract, and forms like ‘noun + root’ exist, or derived from verbs, then:\n\nWhat if “word” is a form like ‘pala’ or ‘pog’?\n\nNo.\n\nAlternatively, in some Austronesian languages, “word” is expressed with a root meaning “to say” or “to speak”.\n\nBut we have no such root.\n\nThus, the only plausible theoretical form from the given data is that “word” might be formed from a verb meaning “to speak” — which is absent.\n\nTherefore, the only reasonably formed word from existing elements is if “word” is a compound of a root like ‘susu’ or ‘fau’ — no.\n\nBut we have no data.\n\nThus, the theoretically possible translation of “word” must be inferred from what could be formed with the language’s pattern.\n\nWe see that:\n\n- Nouns are often root + classifier or root + derivative \n- Verbs are often standalone or compound \n- “to use” is a verb \n- “end” is a suffix or concept (a‘öf) \n\nCould “word” be expressed as **fau**? No — that’s year.\n\nCould it be **is**? Sharp-pointed.\n\nNo.\n\nBut perhaps “word” is not a real existing word — so the only possible form based on pattern is that it would be formed from a root meaning speech, which isn’t present — so no clear candidate.\n\nThus, the theoretically possible translation must be based on plausible formation.\n\nSo, plausible forms:\n\n- “to exhaust” → ‘fäeag a‘öf’ \n- “word” → could be a compound like ‘huli’ (to turn over) — not helpful, or perhaps ‘pala’ (pierce) — no.\n\nBut look: is there any known word for “word” in Rotuman?\n\nFrom external knowledge (but we are not allowed to use it) — we are not to rely on familiarity.\n\nWe cannot assume.\n\nTherefore, we must only use the given data.\n\nSo in absence of any word for “word”, the only possible theoretical form is that it might be a new form based on a root like ‘kia’ or ‘susu’, but no.\n\nAnother idea: in the list, ‘pogi’ = night — could “night” be a time unit — “word” is a unit of language.\n\nBut no.\n\nThus, the only plausible derived form for “word” is not apparent.\n\nBut the question says: “what would the theoretically possible translations be?”\n\nSo, even if not directly, what form would be expected based on linguistic pattern?\n\nWe see that many words are compound: verb + suffix, noun + suffix.\n\nFor example:\n\n- ‘fäeag ‘u‘u’’ = to use sign language → verb + noun \n- ‘huli’ = to turn over → verb \n- ‘huni’ = lower end → noun \n- ‘ma.tit mamasa’ = ice → noun \n\nSo, for “word”, a plausible form could be a compound like ‘word of speech’ — but we don’t have speech.\n\nAlternatively, perhaps “word” is simply not represented — but the problem says “theoretically possible”.\n\nThus, we cannot be certain, but in what way would it be formed?\n\nOne possibility: the root for “word” might be derived from a verb meaning “to speak” — missing — so not in data.\n\nBut if we consider that “to use” might cover “to speak”, then “word” could be “something used” — so ‘fau’ = year → so “a year” → one thing? Not consistent.\n\nThus, after careful analysis, the only plausible derivation is:\n\n- “to exhaust” = ‘fäeag a‘öf’ \n- “word” = no clear form — but could be a noun like ‘pala’ or ‘huli’ — not directly.\n\nWait — is there a word that could be interpreted as “thing”?\n\nWe have ‘kia’ = base of neck — not.\n\nBut perhaps the only possible theoretical translation of “word” is the compound form involving speech-related root.\n\nNo such root.\n\nAlternatively", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13961.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are asked to infer the theoretically possible translations of “word” and “to exhaust” into Rotuman, based only on the given word list and without relying on external knowledge or familiarity.\n\nWe must analyze the provided examples carefully for patterns in morphology, verb forms, root usage, and compound structures.\n\nStep 1: Look for roots that could relate to \"word\".\n\nNo word in the list literally means \"word\". However, we see:\n- “pala” = pierce\n- “nu‘suar tiro” = window\n- “nu‘sura” = door\n- “maf tiro” = spectacles\n- “ka.lu” = bracelet; to encircle\n- “riamrima” = shiny\n- “poagpoga = palpala” = covered with holes\n- “huli” = to turn over\n- “huni” = lower end\n- “pogi” = night\n- “puru” — not listed, but “puhra.ki” = to boil, to bubble up\n- “mamasa” = solid\n- “ma.titi” = coldness\n- “ma.tit mamasa” = ice\n\nNo direct root for “word” appears.\n\nPossible candidates for “word”:\n- Word often relates to “to speak”, “to express”, “to convey”.\n- Is there a verb that involves expression or communication?\n\nWe have:\n- “fäeag ‘u‘u” = to use sign language → this involves communication, possibly a form of “word” or “expression”.\n- “hül ha.fu” = to blow (of a hurricane) → not relevant.\n- “huag ‘el‘ele” = impatient → impatience.\n- “huag to‘a” = courageous → courage.\n- “is ‘ā” = sharp-pointed → sharpness.\n- “is susu” = nipple → body part.\n- “lala” = deep\n- “maf tiro” = spectacles → visual tools.\n- “ka.lu” = to encircle → may imply boundary, or a circular form — not directly word.\n\nAnother candidate: “pala” = pierce — could “pale” be related? Not directly.\n\nNote: “to use sign language” is a form of communication. So \"fäeag ‘u‘u\" may be related to expression of meaning, possibly involving \"word\".\n\nBut no clear root for \"word\".\n\nAlternatively, interpret \"word\" as a linguistic entity. Words are units of meaning. Is there a word that shares a pattern with “sign language”?\n\n“fäeag ‘u‘u” = to use sign language → perhaps “word” is not a direct translation, but “meaning” or “expression”.\n\nBut we are to give a theoretically possible translation — not necessarily a direct one.\n\nIs there any form that might denote \"to speak\" or \"to express\"?\n\nNone directly.\n\nBut compound forms: “pogi” = night → not relevant.\n\n“poagpoga = palpala” = covered with holes — possibly a surface feature.\n\nNo clear morphology for “word”.\n\nConclusion: “word” may be derived from a verbal root involving communication, possibly from a verb like “to express” or “to speak”. In Rotuman, such a verb may be built from a root like “to speak” or “to convey”.\n\nLooking at “fäeag ‘u‘u” — “to use sign language” — this implies a reference to communication. The root “fäeag” may be a verb root meaning “to use” or “to employ”.\n\nCould “fäeag” be a possible root for “to express”?\n\nPossibly.\n\nSo “word” — the entity — may be related to a root that denotes a unit of meaning or expression.\n\nBut what compound might give a form for “word”?\n\nWe see no such thing.\n\nAnother idea: “to encircle” (ka.lu) — could “word” be circular in structure? Unlikely.\n\nNo form in the list indicates “to give a name”, “to utter”, or “to speak”.\n\nThus, the only possible theoretical translation for “word” must be a morphological construction involving a root associated with expression or communication.\n\nGiven the only related verb is “fäeag ‘u‘u” — “to use sign language” — the root “fäeag” may denote “to use”, which is a type of action involving language.\n\nBut “word” is a noun.\n\nNo noun meaning “word” exists.\n\nTherefore, the only theoretically possible translation for “word” would be a compound or a verb form that encodes expression — possibly built on a root like “fäeag” or a similar one.\n\nBut since no such word exists, we must conclude that “word” might be formed from a verb root meaning “to speak” or “to convey”.\n\nBut no such root is present.\n\nAlternatively, in Austronesian languages, “word” may be derived from a root related to “to speak” or “to name”.\n\nBut none is visible.\n\nNote: “ma.tit mamasa” = ice — coldness and solid — no link.\n\n“to exhaust” — meaning: to deplete, to use up.\n\nLook for verbs that mean “to use up”, “to deplete”, “to drain”.\n\nWe have:\n- “puhra.ki” = to boil, to bubble up — not exhaustion.\n- “pala” = pierce — could be a verb for penetrating a substance — related to \"to exhaust\" in physical sense?\n- “huli” = to turn over — not clear.\n- “huni” = lower end — small, possibly final part.\n- “hün kia” = base of the neck — body part.\n- “mamasa” = solid — not exhaustion.\n- “pogi” = night — not relevant.\n- “ka.lu” = to encircle — could be used in a metaphorical sense?\n\nNo verb directly means “to exhaust”.\n\nCould “to boil” be related to “to exhaust”?\n\nIn some languages, boiling implies depletion of energy. But no evidence.\n\nIs there a verb that means “to use up”?\n\nNo such form appears.\n\nPossible root: “to use” — we have “fäeag ‘u‘u” = to use sign language.\n\n“fäeag” — could be the root meaning “to use”.\n\nSo “to use” is possible.\n\nThus, “to exhaust” might be derived from “to use up” — i.e., to use completely.\n\nTherefore, “to exhaust” could be a form of “to use up” — a compound derived from “fäeag” + “up”.\n\nBut in Rotuman, how is “up” expressed?\n\nWe have:\n- “to‘a” = hero\n- “pala” = pierce\n- “ha.fha.fu” = rocky\n- “lala” = deep\n- “fau” = year\n- “a‘öf fau” = year’s end\n\nWe have “a‘öf” — which may mean “end of” — “a‘öf fau” = year’s end.\n\nSo “end” appears via “a‘öf”.\n\n“end” could be used in “to use up” = “to use the end”?\n\nUnlikely.\n\n“to exhaust” might be built from “to use” and “to lose” or “to deplete”.\n\nBut no such word exists.\n\nAlternatively, “to exhaust” might be “to break down”, “to wear out”.\n\nWe have “huag ‘el‘ele” = impatient — possibly related to waiting, not exhaustion.\n\n“hün kia” = base of the neck — not relevant.\n\n“pala” = pierce — could pierce something to exhaust it?\n\nPossible metaphor.\n\nBut no direct link.\n\nCould “to boil” (puhra.ki) imply heat, exhaustion?\n\nIn some meanings, boiling can imply depletion — as in “he is boiling over” — so emotional or physical exhaustion.\n\nThis might be metaphorical.\n\nBut is there a verb in the list that denotes “to deplete” or “to use up”?\n\nNo.\n\nTherefore, the only possible roots related to “to exhaust” are:\n- “to use” (from “fäeag ‘u‘u”)\n\nThus, “to exhaust” could be a form like “fäeag” (to use) + a suffix meaning “up” or “to the end”.\n\nBut we lack a word for “end”.\n\nWe have “a‘öf” = end → “a‘öf fau” = year’s end.\n\nSo “a‘öf” may mean “end”.\n\nThus, “to use up” might be “fäeag a‘öf” — “to use the end”.\n\nThat is plausible.\n\nHence, “to exhaust” = to use up = “fäeag a‘öf” (to use the end).\n\nIs this theoretically possible?\n\nYes — it is a construction that uses a known root (“fäeag” = to use) and a known particle (“a‘öf” = end).\n\nThis is a plausible morphological construction.\n\nSimilarly, for “word” — what could it be?\n\nWe see that communication is expressed by “fäeag ‘u‘u” — to use sign language.\n\n“Sign language” involves “signs” — which can be abstract units.\n\nIn some languages, “word” is expressed as “sign” or “unit of meaning”.\n\nCould “word” be related to “sign”?\n\nYes.\n\n“fäeag ‘u‘u” = to use sign language → the noun form of “sign” might be derived from “u‘u”?\n\n“u‘u” appears alone in “fäeag ‘u‘u”.\n\n“u‘u” is not in any other context.\n\nCould “u‘u” be a root meaning “sign” or “mark”?\n\nPossible.\n\nThen “word” (meaning a unit of language) might be “u‘u” or “a sign”.\n\nThus, a theoretically possible translation for “word” is “u‘u”.\n\nBut is there a reason to think “u‘u” means “word”?\n\nOnly indirectly — from “to use sign language” — so “sign” is the key.\n\nIn that context, “sign” is the unit.\n\nHence, “word” may be equivalent to “sign” → “u‘u”.\n\nThus, “u‘u” is the only known form related to communication units.\n\nTherefore, the theoretically possible translation of “word” is “u‘u”.\n\nSimilarly, “to exhaust” is built from “to use” and “end” → “fäeag a‘öf”.\n\nBut is “a‘öf” used with “to use”? We see “a‘öf fau” — year’s end — so “a‘öf” may be used in compound forms.\n\nThus, “fäeag a‘öf” = to use up (to exhaust).\n\nThis is a plausible theoretical form.\n\nNo other forms support a different root.\n\nThus, we conclude:\n\n- “word” → u‘u (as a unit of expression/sign)\n- “to exhaust” → fäeag a‘öf (to use up)\n\nThese are not direct translations, but theoretically possible given the linguistic patterns in the data.\n\nFinal answer:\n\n\\boxed{d.1: u‘u; d.2: fäeag a‘öf}", + "generated_tokens": 2415, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: u‘u; d.2: fäeag a‘öf", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 8330.0, + "ioling_final_answer_chars": 25.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "We are asked to find the theoretically possible translations of “word” and “to exhaust” into Rotuman, given only the provided word list and no direct examples of these terms.\n\nStep 1: Analyze known words and their forms for patterns in derivation or morphology.\n\nLook for roots or constructions that may be related to “word” or “to exhaust”.\n\nWe observe:\n- “pala” = pierce\n- “pogi” = night\n- “fau” = year\n- “a‘öf fau” = year’s end\n- “mamasa” = solid\n- “ma.tit mamasa” = ice\n- “lala” = deep\n- “huli” = to turn over\n- “huni” = lower end\n- “hün kia” = base of the neck\n- “nu‘suar tiro” = window\n- “nu‘sura” = door\n- “maf tiro” = spectacles\n- “pogil” is not listed, but “poagpoga = palpala” = covered with holes\n- “hül ha.fu” = to blow (of a hurricane)\n- “ka.lu” = bracelet; to encircle\n- “riamrima” = shiny\n\nNo direct word for “word” appears.\n\nBut consider: in many languages, “word” is derived from “to speak” or “to utter”. Is there a verb related to speaking?\n\nWe have “pala” = pierce, not speaking. “piri” = to curl. “huli” = to turn over. “to‘a” = hero — unrelated.\n\nNo clear verb for \"to speak\", so \"word\" likely cannot be derived directly.\n\nHowever, is there any root that could be extended?\n\nObserve that “nu‘suar tiro” = window; “nu‘sura” = door. So \"nu\" + suffix forms a noun: door/window. Could “word” be related to a similar construction?\n\nBut no root like “nu” for “word” appears.\n\nAlternatively, could \"word\" be a noun meaning “something small” or “an item”? Is there a common root for items?\n\nWe have “lala” = deep. “huni” = lower end. “hün kia” = base of the neck. “maf tiro” = spectacles.\n\nNo obvious construction for “word”.\n\nNow consider \"to exhaust\".\n\nWe have “puhra.ki” = to boil, to bubble up.\n\nIs there a verb meaning to consume, deplete, or use up?\n\nWe have “fäeag ‘u‘u” = to use sign language — “to use” is signaled here.\n\n“hün kia” = base of the neck — not relevant.\n\n“huli” = to turn over — not exhaustion.\n\nBut what about “to use”? “fäeag ‘u‘u” — “to use sign language”.\n\n“is susu” = nipple — a point of use?\n\nWhat about “to use up”?\n\nNote: “a‘öf fau” = year’s end — implies something ends.\n\n“moafmofa” = littered with rubbish — implies something is full or overflowing.\n\n“ka.lu” = to encircle. “pala” = pierce.\n\n“to‘a” = hero — not related.\n\nIs there a verb meaning “to consume” or “to use up”?\n\n“fäeag” = to use — already appears: “fäeag ‘u‘u” = to use sign language.\n\nSo “fäeag” may mean “to use”.\n\n\"To exhaust\" could be a form of \"to use up\" or \"to consume completely\".\n\nSo perhaps “to exhaust” would be a form of “to use up”, derived from “fäeag”.\n\nCould “fäeag” be extended via a suffix meaning “up” or “completely”?\n\nIn Rotuman, common derivational patterns include:\n\n- Possession: e.g., “ha.fha.fu” = rocky — could be derived from “ha.” + “fha” + “fu” — but not clear.\n- Compound nouns: e.g., “a‘öf fau” = year’s end — \"a‘öf\" (end) + \"fau\" (year)\n- Reduplication: “poagpoga” = covered with holes — reduplication?\n\n“poagpoga = palpala” — reduplication may indicate fullness.\n\nAlso, “moafmofa” — “littered with rubbish” — could imply something full.\n\n“puhra.ki” = to boil — boiling implies exhausting energy.\n\nBut still, no direct verb for “to exhaust”.\n\nCould “to exhaust” be formed from a root meaning “to use” + an aspect marker?\n\nGiven that “fäeag” means “to use”, and “to exhaust” is to use up completely, perhaps “to exhaust” could be expressed as “fäeag” with a suffix implying total consumption.\n\nAlternatively, in many Austronesian languages, a verb meaning 'to exhaust' might be built from a root meaning 'to consume' or 'to wear out'.\n\nBut no such verb exists directly.\n\nTherefore, based on the available vocabulary:\n\n- “word” has no direct parallel. Possible forms might emerge from compounds or derived nouns.\n\nBut we see verbs like “to use” (fäeag), “to pierce” (pala), “to blow” (hül), “to turn over” (huli).\n\nNo root for “word” appears. Similarly, no verb meaning “to exhaust” appears.\n\nSo, what would be *theoretically possible*?\n\nWe are to list the **theoretically possible** translations — not a certain one, but one that could arise from morphological patterns.\n\nCould “word” be a compound derived from abstract nouns?\n\nWe have:\n- “fau” = year\n- “pogi” = night\n- “is” = sharp-pointed\n- “lala” = deep\n- “huni” = lower end\n\nNo noun that resembles \"word\".\n\nCould “word” be a reflex of a verb meaning “to speak”? But we have no such verb.\n\nAlternatively, could “word” be expressed as a compound using a root like “pala” (to pierce) or “piri” (to curl)? Unlikely.\n\nBut consider: “nu‘suar tiro” = window — this is a compound: \"nu\" + \"suar\" + \"tiro\" (window). Could “word” be formed as a compound?\n\nBut no known root for “word”.\n\nSo, the only plausible theoretical form is a compound or derived form based on known roots.\n\nIs there any verb that could be extended?\n\nWe have “to use” = “fäeag”.\n\n“to use completely” → “to exhaust”.\n\nCould “fäeag” be used with a suffix meaning “up” or “out”?\n\nIn the list, “a‘öf fau” = year’s end → \"a‘öf\" (end) + \"fau\" (year). Time end.\n\n“moafmofa” = littered with rubbish → full of trash.\n\n“puhra.ki” = to boil — boiling to the point of overflow.\n\n“huli” = to turn over — could imply exhaustion in physical or metaphorical sense?\n\nBut still, no verb for “to exhaust”.\n\nStill, the root “fäeag” (to use) is the only verb involving consumption.\n\nSo, the most plausible theoretical translation for “to exhaust” would be a derived form of “fäeag” with a meaning of “to use up completely”.\n\nSimilarly, “word” has no direct equivalent. But are there any abstract nouns?\n\nWe have:\n- “ma.tit” = coldness\n- “mamasa” = solid\n- “riamrima” = shiny\n- “rū huga” = stomach-ache\n\nNo “word” — but “word” is a universal concept.\n\nPossible morphological patterns:\n- Compounding: e.g., \"tiro\" = spectacles, \"nu‘sura\" = door\n- Possession: \"hün kia\" = base of neck\n\nNo evidence for a root \"word\".\n\nTherefore, the only theoretical forms would be based on derivational patterns observed.\n\nFor “word”:\n- It could be a compound related to “to speak” — but no verb for speaking.\n- Or it could be a noun derived from a root like “pala” (to pierce), as words might be pierced or written?\n\nUnlikely.\n\nAlternatively, in some languages, “word” is formed from a root meaning “to be said”.\n\nNo such root.\n\nHence, “word” has no evidence from the data.\n\nBut we are told that we *cannot* translate with certainty — so the theoretically possible form must be one that could be built from roots or compounds in the language.\n\nThus, possible forms:\n\n- “word” → no direct word. But could it be formed from “pala” (to pierce) + something? Not supported.\n\n- “to exhaust” → could stem from “fäeag” (to use) with an aspect, like “to use up” → “fäeag” + “-kia” or “-ti”?\n\nBut no suffix appears.\n\nWe see “ha.fha.fu” = rocky — two repeated vowels.\n\n“poagpoga” = covered with holes — reduplication.\n\n“moafmofa” — reduplication of “mof”?\n\n“moafmofa” may be reduplicated.\n\nCould “to exhaust” be reduplicated? “paha paha” — not given.\n\nStill, no evidence.\n\nBut consider: “to boil” = “puhra.ki” — boiling is a form of exhaustion in some contexts.\n\nSo maybe “puhra.ki” is a possible candidate for “to exhaust” in metaphorical use.\n\nBut tempting.\n\nHowever, we must stick strictly to observed patterns.\n\nThe only verb related to consumption is “fäeag” = to use.\n\nTherefore, the only possible translation for “to exhaust” is a derived form of “fäeag”, possibly with an adverbial or aspectual suffix.\n\nBut no such suffix exists in the data.\n\nThus, “to exhaust” → theoretically possible form: “fäeag” with reduplication or addition of “ta” or “ki”, but none are listed.\n\nCould “to exhaust” be “huli” (to turn over)? Unlikely.\n\nConclusion:\n\n- “word” cannot be derived; its only possible theoretical form is a compound like “tiro” or “fau”, but no evidence. However, in Austronesian, some words are derived from \"to be\" or from language constructs. But none exist.\n\nBut consider: “pala” = pierce. Could “word” be a noun meaning “a thing that pierces”? Not likely.\n\nNo evidence.\n\nThus, based on available data, the only possible translation for “to exhaust” that can be inferred is a derivative of “fäeag” meaning \"to use up\".\n\nFor “word”, nothing is directly supported.\n\nSo, the theoretically possible translations are:\n\n- “word” → could be derived from a root like “pala” or “susu” (nipple), but nothing supports it. However, in some languages, “word” is related to “speak”, and if “pala” means “to pierce”, could “to pierce” be related to “a word being pierced”? Unlikely.\n\nAlternatively, is there any compound involving “tiro” or “nu”?\n\n“tiro” appears in “maf tiro” (spectacles), “nu‘suar tiro” (window), “nu‘sura” (door).\n\nCould “word” be “nu‘tiro” or “nu‘suar”?\n\nBut “nu‘suar” = window — no connection.\n\n“tiro” = spectacles — not a word.\n\nThus, no plausible word.\n\nBut consider: in some Austronesian languages, “word” is expressed via abstract nouns.\n\nNo example.\n\nTherefore, with the given data, the only possible theoretical root for “word” is a nominalization of a verb like “to speak” — but no such verb exists.\n\nThus, “word” has no theoretically possible form from observed data.\n\nBut the question says \"theoretically possible\" — meaning plausible under linguistic rules, not necessarily in the data.\n\nCould we form “word” as a compound from “fau” and “pala”? e.g., “fau pala” = year and pierce?\n\nNo.\n\nWe have no evidence.\n\nSimilarly, for “to exhaust”, only “fäeag” (to use) is relevant.\n\nSo, “to exhaust” = “fäeag” + something meaning “up” or “out”.\n\nIs there a suffix?\n\nWe see “ha.fha.fu” = rocky — has repeated vowel, long form.\n\n“moafmofa” = littered — reduplication.\n\n“poagpoga” = covered — reduplication.\n\nSo reduplication might signal fullness or intensity.\n\nThus, “to exhaust” could be formed as a reduplicated form of “fäeag”.\n\nHence: “fäeag fäeag” — meaning \"to use use\" → \"to use up\".\n\nCould be a plausible theoretical form.\n\nSimilarly, “word” — with nothing, no root.\n\nBut is there a word meaning “thing” or “object”?\n\n“tiro” = spectacles — object.\n\n“fau” = year — abstract.\n\n“huni” = lower end — bodily.\n\n“lala” = deep — abstract.\n\nNo “thing”.\n\nBut “pala” = pierce — action.\n\nNo noun for “word”.\n\nOne possibility: “is” = sharp-pointed — could a word be “is” (pointed)? Unlikely.\n\nSo, no plausible form.\n\nThus, the only theoretically possible translation for “to exhaust” is a reduplication of “fäeag”.\n\nFor “word” — nothing derived.\n\nBut the problem says \"theoretically possible\", so we must give a form that could exist in the language's morphological system.\n\nGiven that, and that “fäeag” means “to use”, and “to exhaust” is a kind of “to use up”, the derivational form “fäeag fäeag” is plausible.\n\nFor “word” — we have no root. But in Austronesian languages, words are often compound, and “word” might be expressed as a compound like “pala tiro” or “fau is”, but no support.\n\nAlternatively, could “word” be “pala” in some sense? No.\n\nWe have no evidence.\n\nBut the only noun that might fit is “tiro” — but it means spectacles.\n\nNo.\n\nThus, based only on the given data, no theoretical word for “word” can be derived.\n\nBut the question implies there may be a form based on patterns.\n\nWait: in the list, “pala” = pierce — and “pala” might be used in compounds.\n\n“ka.lu” = to encircle — could “word” be “ka.lu” — a word that circles? Unlikely.\n\nNo.\n\nThus, best conclusion:\n\n- “word” → theoretically possible form: none clearly derived; but if we must give one, perhaps “pala” (as a root for a word), but not supported.\n\nAlternatively, could “word” be “huli” (to turn over) — to flip a word?\n\nNo.\n\nWe must conclude based on evidence.\n\nFinal decision:\n\nFor “to exhaust” — derived from “fäeag” (to use), with reduplication indicating full consumption → “fäeag fäeag”\n\nFor “word” — no evidence. But is there a term like “kia” (base) or “susu” (nipple)? “is susu” = nipple — maybe a word is like a nipple? Not plausible.\n\nNo compound in the list means “word”.\n\nSo we have to say the theoretically possible form is “pala” or “tiro”? Not supported.\n\nBut perhaps in Rotuman, “word” is built from a verb like “to speak”, which is absent.\n\nThus, no theoretically possible form exists — but the question asks for it.\n\nTherefore, the only possible based on patterns is that “word” has no clear parallel, but “to exhaust” could be “fäeag fäeag”.\n\nAlternatively, “to exhaust” could be “puhra.ki” — roiling, boiling — which might metaphorically mean to exhaust.\n\nBut “puhra.ki” = to boil — not to exhaust.\n\nStill, in some contexts, boiling could imply exhaustion.\n\nBut not backed.\n\nOnly “fäeag” has a consumption meaning.\n\nThus, best inference:\n\n- “to exhaust” → “fäeag fäeag”\n\n- “word” → cannot be derived; but theoretically possible form based on word formation? No.\n\nBut we are to give a possible form.\n\nNotice that “lala” = deep — not a word.\n\n“riamrima” = shiny — not a word.\n\nNo.\n\nOne possibility: “word” might be expressed as “fau” — year — as in “the year” a word is given? Not literal.\n\nNo.\n\nAfter careful analysis, the only plausible derived form is for “to exhaust” as a reduplicated form of “fäeag”.\n\nFor “word”, the only possibility is absence — but since the problem says “theoretically possible”, and in morphological systems, new words can be formed from roots, perhaps using a root like “tiro” or “nu”.\n\nBut no support.\n\nGiven that, and the observation that many nouns are compound, perhaps “word” is formed from a root like “pala” or “huli”.\n\nBut no.\n\nFinal answer:\n\nd.1 / word: pala \nd.2 / to exhaust: fäeag fäeag\n\nBut “pala” = pierce — not a word.\n\nAnd “fäeag fäeag” is speculative.\n\nBut based on reasoning, “to exhaust” is most likely a reduplication of “fäeag”.\n\n“word” — no data.\n\nBut the problem says “using the material given” — so must come from it.\n\nIs there a noun that could be a word? “tiro” — spectacles — could be used as a word?\n\nPossibly.\n\nIn some contexts, “tiro” might mean “a thing”.\n\nBut in the list, “maf tiro” = spectacles — so “tiro” is a noun.\n\nCould “tiro” be used for “word”?\n\nUnlikely.\n\nPerhaps “nu‘sura” = door — not a word.\n\nNo.\n\nAfter full analysis, no word for “word” is present or derivable.\n\nThus, the theoretically possible form is not known, but for the sake of answering, given that “vä” or “tiro” are nouns, and “word” is a common noun, perhaps “tiro” is chosen.\n\nBut nothing supports it.\n\nAlternatively, consider “is” — sharp-pointed. Could a “point” or “pointed thing” be a word? “is” could be extended.\n\nBut “is susu” = nipple.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 14410.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are asked to find the theoretically possible translations for the English words \"word\" and \"to exhaust\" into Rotuman, given only the provided word list and no direct entries for these concepts.\n\nStep 1: Identify candidate roots or affixes that might relate to \"word\" or \"to exhaust\".\n\nLook for words involving \"word\" in a linguistic pattern.\n\nIn the list:\n- \"pala\" — pierce\n- \"nu‘suar tiro\" — window\n- \"nu‘sura\" — door\n- \"mamasa\" — solid\n- \"ma.titi\" — coldness\n- \"ma.tit mamasa\" — ice\n- \"poagpoga = palpala\" — covered with holes\n- \"pogi\" — night\n- \"hul\" — to turn over\n- \"huni\" — lower end\n- \"is\" — sharp-pointed\n- \"is susu\" — nipple\n- \"lala\" — deep\n- \"maf tiro\" — spectacles\n- \"hün kia\" — base of the neck\n- \"huli\" — to turn over\n- \"ka.lu\" — bracelet; to encircle\n- \"riamrima\" — shiny\n- \"rū huga\" — stomach-ache\n- \"to‘a\" — hero\n- \"a‘öf fau\" — year’s end\n- \"fäeag ‘u‘u\" — to use sign language\n- \"fau\" — year\n- \"ha.fha.fu\" — rocky\n- \"huag ‘el‘ele\" — impatient\n- \"huag to‘a\" — courageous\n- \"hül ha.fu\" — to blow (of a hurricane)\n\nObserve: nowhere is there a word directly for “word” or “to exhaust”.\n\nBut perhaps we can find a conceptual or morphological pattern.\n\nStep 2: Consider how compound or derived forms work.\n\nFor example:\n- \"nu‘suar tiro\" = window → \"tiro\" appears in \"maf tiro\" (spectacles), \"poagpoga = palpala\", possibly related to \"palo\" or \"tiro\" meaning \"to cover\" or \"object\"?\n\nBut note: \"pala\" = pierce; \"to pierce\" might be related to forming a \"word\" via interruption? Unlikely.\n\nAnother verb: \"to boil, to bubble up\" = \"puhra.ki\"\n\n\"To exhaust\" may involve a process of depletion — such as using up, draining, burning out.\n\nCheck verbs:\n- \"to cut\" = \"olo\"\n- \"to use sign language\" = \"fäeag ‘u‘u\"\n- \"to blow\" = \"hül ha.fu\"\n- \"to turn over\" = \"huli\"\n- \"to pierce\" = \"pala\"\n- \"to boil\" = \"puhra.ki\"\n- \"to encircle\" = \"ka.lu\"\n\n\"Exhaust\" is similar to \"to burn out\", \"to empty\", \"to deplete\".\n\n\"puhra.ki\" — to boil, to bubble up — involves energy, tremors, rising, possibly exhaustion if prolonged?\n\nBut that’s a stretch.\n\nAnother keyword: \"to be near\" = \"ele\"\n\n\"el‘ele\" — shallow\n\n\"el‘ele\" — shallow → could suggest depth, so \"deep\" is \"lala\", \"shallow\" is \"el‘ele\".\n\n\"word\" — in many languages, \"word\" is often linked to \"speech\", \"saying\", or \"sign\".\n\nWe have \"fäeag ‘u‘u\" — to use sign language.\n\n\"Sign language\" may be related to \"word\" via the concept of communication.\n\nSo perhaps a word for “word” is constructed from a verb meaning \"to speak\" or \"to signify\".\n\nBut no such form is given.\n\nIs there a common suffix or prefix?\n\nNotice affixes:\n- ha.fha.fu — rocky (involves repetition of consonants)\n- huag — person-related (impatient, courageous)\n- ‘el‘ele — shallow\n- is — sharp-pointed\n\nNo clear pattern for \"word\".\n\nNow, consider possibility of compound formation.\n\nFor instance, is there a root that can be used to generate \"to exhaust\"?\n\n\"puhra.ki\" — to boil (bubble up) — a process of energy release, may imply depletion.\n\n\"to boil\" can be taxed, and burning out is like boiling over — so \"to exhaust\" may be conceptually similar.\n\nThus, \"puhra.ki\" could be a cognate for \"to exhaust\" via extended metaphor.\n\nBut is this a stretch?\n\nAlternatively, \"to cut\" = \"olo\" — cutting could imply depleting, but \"cutting\" is not the same as \"to exhaust\".\n\n\"to lower\" = \"huni\" — lower end — not directly relevant.\n\n\"to turn over\" = \"huli\" — might be physical movement.\n\nWhat about the word \"nui\" or \"taro\"? Not in list.\n\nAnother idea: in Austronesian languages, many nouns are derived from verbs, and in particular, nouns may be formed by suffixation.\n\nFor \"word\": in many languages, \"word\" comes from \"speak\" → \"speech\" → \"word\".\n\nWe have \"fäeag ‘u‘u\" — to use sign language → \"to use\" + \"sign\" → \"sign language\" → could involve \"word\" as a medium.\n\n\"sign\" is not in the list, but \"fäeag\" means \"to use\", and \"‘u‘u\" might be a type of sign.\n\nCould \"‘u‘u\" be related to “word”?\n\n“to use sign language” → implies communication with signs → possibly a form of “word”.\n\nThus, “‘u‘u” might be a root meaning “word” or “sign”.\n\nThat is a plausible possibility.\n\nSimilarly, is there a word that suggests \"exhaust\"?\n\nAnother verb: “to blow” = “hül ha.fu” — a hurricane blows — blowing might exhaust something?\n\nBut not clearly.\n\n\"to boil\" — again, boiling can be a sign of energy flowing out — could be a metaphor for exhaustion.\n\n\"to boil\" might mean \"to become frantic\", or \"to be spent\".\n\nIn fact, in some languages, “to boil” is used metaphorically for \"to be exhausted\".\n\nThus, \"puhra.ki\" may be a candidate for \"to exhaust\", especially given the shared conceptual space.\n\nBut is there another option?\n\nCould “to turn over” imply exhaustion? Unlikely.\n\nWe must ask: what are the theoretically possible translations?\n\nThat means: which forms in the language could, in principle, express these meanings?\n\nFor “word”: \n- The only related form is “‘u‘u” in “fäeag ‘u‘u” — meaning “to use sign” — so “‘u‘u” may be a sign, or a word-like unit.\n\nThus, “‘u‘u” is the only candidate root in the list that may convey “word”.\n\nCould there be another root? For example, “pala” (to pierce) — could \"pierce\" a word? But that doesn’t mean \"word\".\n\n\"lala\" — deep — not meaningful.\n\nNo other word seems to relate directly to “word”.\n\nThus, the only plausible root for “word” is “‘u‘u”.\n\nSimilarly, for “to exhaust”:\n\nWe see \"puhra.ki\" — to boil, to bubble up — this is the only verb that involves a process of energy release or depletion.\n\n\"to blow\" — “hül ha.fu” — could be used in the sense of \"to blow out a fire\" → exhausting?\n\nBut “to blow” is more about force, not duration or elimination.\n\n\"to cut\" — \"olo\" — cutting might imply reduction, but not exhaustion.\n\n\"to turn over\" — \"huli\" — not relevant.\n\nOnly \"puhra.ki\" has the semantic field of consumption or overflow — which could metaphorically lead to exhaustion.\n\nHence, \"puhra.ki\" is the only plausible candidate for \"to exhaust\".\n\nThus, the theoretically possible translations are:\n\n- \"word\" → ‘u‘u \n- \"to exhaust\" → puhra.ki\n\nThese are not direct translations, but based on conceptual derivations from the given material, these are the only forms that could possibly encode the meaning, given the vocabulary.\n\nFinal answer:\n\n\\boxed{d.1: ‘u‘u; d.2: puhra.ki}", + "generated_tokens": 1827, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: ‘u‘u; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 6223.0, + "ioling_final_answer_chars": 24.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are given a set of Jaqaru words and their English translations. Our task is to translate three new Jaqaru words into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe must derive the meaning based on patterns in the given examples, avoiding assumptions based on familiarity.\n\n---\n\nFirst, examine the patterns in the provided data:\n\n1. aq”ipsa — the cave too \n aq”na — in the cave \n → “ipsa” is “too”, “na” is “in” \n → “in the cave too” = aq”na + ipsa → “in + cave + too” \n → “too” is an adverbial suffix, not a separate noun.\n\n2. qucxap”a — through the lake \n qucxst”psa — from our1+2 lake too \n → “qucx” = through/from, “st” = our1+2 (group), “psa” = lake \n → “from our1+2 lake too” → “qucxst”psa = from + our1+2 + lake + too \n → again, “too” is a suffix. “psa” is a noun.\n\n3. chushp”a — his corner \n chushuntxi — is it in the corner? \n → “chush” = corner, “untxi” = is it in? \n → “untxi” is a question form = “is it in?” \n → “untxi” = is it (in) → this structure repeats in “markstxi”: is it our1+2 town?\n\n4. marka — the town \n markp”t”a — from his town \n markstxi — is it our1+2 town? \n → “mark” = town \n → “p”t”a → “from his town” → “from + his + town” \n → “t”a” has “t” indicating possession (his), “a” ending \n → “markstxi” = is it our1+2 town?\n\n5. ishinhna — in my bed \n ishma — your bed \n p”ak”u — the pot \n p”ak”unhpsa — my pot too \n qaqat”a — from the cliff \n qaqat”a — from the cliff → “qaqat”a = from + the + cliff \n yapsanpsa — in our1+2 field too \n\n6. yapsanpsa — in our1+2 field too \n → “yapsa” = field, “n” = in, “psa” = too \n → “in + our1+2 + field + too”\n\nWe now see recurring patterns:\n\n- Existential questions: “untxi” = “is it...?” \n- Location: “in + noun” → e.g., ishinhna = in my bed \n- Possession: “p”t”a = from his town; “p”t”a” = from his town \n → “chushp”a = his corner → “p” = his \n → “markp”t”a = from his town → “p” = his \n- Quantifiers: “our1+2” appears in “qucxst”psa, “markstxi”, “yapsanpsa” \n- “Too” appears as a suffix: aq”ipsa, qucxst”psa, yapsanpsa → all end with “psa” \n- Structure: \n - noun (corner, lake, town, field) \n - “in” or “from” / “to” \n - “too” (suffix) \n\nNow analyze target words:\n\n1. utnhantxi \n → Compare to: ishinhna = in my bed, utamt”a = from your house, utnha = my house \n → “utn” likely = house \n → “utnha” = my house \n → “utnhantxi” → “in my house?” \n → “untxi” = is it in? \n → So: “utnhantxi” = is it in my house? \n → This mirrors “chushuntxi” = is it in the corner? \n → So “utnhantxi” → is it in my house?\n\n2. yapp”psa \n → Compare to: yapsanpsa = in our1+2 field too \n → “yapsa” = field → so “yaps” likely root \n → “yap” = field? \n → yapp”psa → perhaps “in the field too”? \n → But “yapsanpsa” = in our1+2 field too → has “n” = in, “psa” = too \n → yapp”psa → has “p” and “psa” → “p” may be possessive? \n → But no “n” → so possibly “the field too”? \n → What about “p” as in “his”? \n → But no owner specified → compare to p”ak”u = the pot, p”ak”unhpsa = my pot too → “unh” = my \n → So “unh” = my → “unhpsa” = my pot too \n → So suffix “psa” = too \n → “yapp”psa” → perhaps “in the field” → missing “n”? \n → But no “n” → so maybe “in” is omitted? \n → Can we reconstruct “yapsanpsa” = in our1+2 field too → so “n” = in, “psa” = too \n → “yapp”psa” → without “n” → could it be “in the field too” with “n” missing? \n → Unlikely. \n → Alternative: “yap” = field, “p” = possessive? \n → yapp”psa → “in the field (our) too”? \n → But no “n” \n → Wait — can we reverse the word? \n → Compare to: “yaputxi” = is it the field? → “yap” + “utxi” → “is it the field?” \n → So “utxi” = is it? \n → “yapp”psa” — has “pp” → possible typo? Or “p” = possessive? \n → Structure: “yap” + “p” + “psa” \n → “yap” + “psa” = field too → but “p” is medial? \n → Possible suffix: “p” = possessive, but no owner? \n → Or “p” = from? \n → Recall: qucxst”psa = from our1+2 lake too → “st” = our1+2 \n → But “yapp”psa” — “p” instead of “st”? \n → Is “p” a possessive form for “my”? \n → p”ak”u = the pot \n → p”ak”unhpsa = my pot too → “unh” = my \n → “unh” is possessive for “my” \n → Is there a possessive for “his” or “our”? \n → chushp”a = his corner → “p” = his \n → markp”t”a = from his town → “p” = his \n → So “p” = his \n → So “yapp”psa” → “his field too”? \n → But “yap” = field? \n → “yaputxi” = is it the field? → “yap” = field → “utxi” = is it? \n → So “yap” = field \n → So “yapp”psa” = his field too \n → Yes, consistent: \n - “p” = his \n - “psa” = too \n → “his field too” \n\n3. yapup”psa \n → yaputxi = is it the field? \n → yapup”psa → “yap” + “up” + “psa” \n → Compare to: \n - “yaputxi” = is it the field? \n - “p” used in “yapp”psa” as possessive → “yap” + “p” + “psa” → his field too \n → So “yapup”psa” → “yap” + “up” + “psa” \n → “up” — what does it mean? \n → Is “up” a positional word? \n → What is in the examples? \n → The forms with “in” and “from” exist: \n - “ishinhna” = in my bed \n - “utnha” = my house \n - “markstxi” = is it our1+2 town? \n → “in” appears as “n” in “ishinhna” → “is” + “hin” + “hna” → “in” = “n”? \n → ishinhna → likely “in” + “my” + “bed” \n → ishinhna → “in my bed” → “in” is prefix or embedded? \n → “yapup”psa” → “yap” + “up” + “psa” \n → if “up” = in? \n → But “in” is established as “n”, not “up” \n → Perhaps “up” is a different direction? \n → What about “from”? “qucx” = through/from \n → “qqa” = from the cliff → “qa” = cliff \n → “qucx” = direction \n → perhaps “up” is a direction — but no such stem \n → Alternative: possessive markers \n → In “yapp”psa” we had “p” = his \n → Could “up” be possessive? \n → “up” not a known possessive \n → Is there a form with “up”? \n → “up” appears in “yapup”psa” → perhaps “in” is missing? \n → Compare to “yaputxi” = is it the field? → has “utxi” = is it \n → “yapup”psa” has “psa” = too, but not “utxi” \n → So not a question \n → Perhaps “in the field too”? \n → But has “up” instead of “in” \n → What about “in” = “n”? \n → All examples with “in” have “n”: \n - ishinhna → in my bed \n - yapsanpsa → in our1+2 field too \n - markstxi → is it our1+2 town? \n → “n” appears as a marker for “in” \n → So “in” = “n” \n → “yapup”psa” → no “n” → so not “in” \n → unless “up” = in? No \n → Alternative: “up” = in? Unlikely \n → Is there a form like “yap” + “n” + “psa” → in the field too? \n → But the word is “yapup”psa” \n → “up” may be a typo or misread? \n → Compare to “yaputxi” = is it the field? \n → “yap” + “utxi” → “is it the field?” \n → So “utxi” = is it \n → “yap” = field \n → Therefore, “yap” is field \n → So “yapup”psa” → “yap” + “up” + “psa” \n → “up” → perhaps “my” or “our”? \n → “unh” = my → “unh” is “my” \n → “st” = our1+2 \n → “p” = his \n → So no “up” as a personal marker \n → But is there a form “up” meaning “my”? No \n → Could “up” = in? \n → Only if “n” is missing \n → But “yapup”psa” has “up” → could be a mistake? \n → Wait — is this a variant of “yapunhpsa”? \n → We have “p”ak”unhpsa = my pot too \n → “unh” = my \n → So “my” appears in structures \n → Could “up” be a spelling of “un”? \n → But “un” not directly in data \n → “yapup”psa” → might be “in the field too” with “n” missing \n → But “up” ≠ “n” \n → Alternatively, is “up” = “to”? \n → But no “to” in examples \n → The only consistent suffix is “psa” meaning “too” \n → Other word: “yaputxi” = is it the field? \n → So “yap” = field \n → So “yapup”psa” → “field + up + too” \n → But “up” unknown \n → Is there a word “in” embedded in “up”? \n → No \n → Another idea: could the “up” be part of a possessive? \n → No known structure with “up” \n → Re-examine: \n → What about taking “yapup”psa” as similar to “yaputxi”? \n → “yaputxi” = is it the field? \n → If we remove “utxi” and add “psa”, and replace “ut” with “up” → backward? \n → But “up” not in data \n → Must find pattern \n → All words with “in” have “n”: ishinhna, yapsanpsa \n → All words with “from” or “through” have “qucx” or “q” \n → All words with “is it” have “utxi” \n → So “yapup”psa” lacks “n” and lacks “utxi” → not a question \n → So likely not “is it” \n → So must be a locative or possessive \n → Could “up” = in? Not supported \n → Alternative: misreading — is it “yapunhpsa”? \n → But it's written as “yapup”psa” \n → The input says: “yapup”psa” \n → So must use as is \n → What if “up” is a possessive? \n → No known possessive “up” \n → But we do have: \n - “p” = his \n - “st” = our1+2 \n - “unh” = my \n → So no “up” \n → Perhaps “up” is a direction like “in” or “out”? \n → But no examples \n → Possible error — but the guidance says: do not rely on familiar words \n → Must derive from pattern \n → Look at “yapup”psa” vs “yaputxi” \n → Both have “yap” \n → “utxi” = is it \n → “psa” = too \n → “up” = ? \n → Could “up” be a typo for “n”? \n → But it’s not \n → Perhaps “up” stands for “in”? \n → But “n” is the marker \n → In “ishinhna” — “in my bed” — “n” at end \n → “ishinhna” → “in” at beginning or middle? \n → ishinhna → “in my bed” → suggests “is” + “hin” + “hna” \n → “hin” = my → “hna” = bed \n → so “in” is not explicit \n → In “yapsanpsa” — “in our1+2 field too” → “n” appears in “yapsanpsa” \n → So “n” = in \n → So any word with “n” = in \n → “yapup”psa” has “up” → not “n” \n → So not “in the field too” \n → Must be “his field too” or “our field too”? \n → “yapp”psa” = his field too → with “p” \n → “yapup”psa” → has “up” → not “p” \n → What if “up” is a different possessive? \n → No \n → Alternative: is “up” = possessive for “my”? \n → “unh” = my \n → “up” is not “unh” \n → But “up” and “unh” — could “up” be a misreading of “unh”? \n → Possibly a typo or soundalike? \n → But we must go by given spelling \n → Perhaps “yapup”psa” = “in the field too” with “n” missing \n → But no “n” \n → Unless “up” = “in” \n → But “in” is “n” \n → The only word with “n” is “ishinhna”, “yapsanpsa” \n → So no evidence “up” = in \n → Alternative: “up” = from? \n → “from” is “qucx” or “qa” \n → No \n → What about “to”? \n → Not in data \n → Is there a word with “to”? \n → No \n → Final possibility: “yapup”psa” is a typo of “yapunhpsa” \n → But not indicated \n → Must derive from structure \n → Now reconsider: in “yapp”psa” = his field too → “p” = his, “psa” = too \n → “yapup”psa” → has “up” → if “p” is changed to “up”, is “up”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10744.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Start by analyzing the given Jaqaru-English word pairs to identify patterns in structure, especially in relation to possessive markers, numerals, and locative constructions.\n\nFirst, observe how possessive markers are formed in the examples:\n\n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- utamt”a → from your house \n- utnha → my house \n- utnhp”sas → my house + something (we see \"p”ak”unhpsa\" = my pot too) \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nNote the pattern in possessive forms:\n\n- \"our1+2\" appears in multiple items: qucxst”psa, markstxi, yapsanpsa \n- The possessive construction seems to involve a numeral (1+2) attached to a noun and a specific suffix indicating direction or location.\n\nAlso note:\n- \"a\" is a common prefix in the word list (e.g., aq”ipsa, aq”na)\n- \"p”a\" appears in various forms: \"p”ak”u\" = the pot; \"p”ak”unhpsa\" = my pot too\n- “hpsa” appears in “p”ak”unhpsa” → “my pot too” → suggests \"hpsa\" may indicate “too” or \"also\"\n\nLook at “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → implies “unhpsa” = my + pot too \nSo “unhpsa” = my + too\n\nNow check for similar patterns in other examples:\n- utnha = my house \n- utamt”a = from your house \n- utnhantxi → similar structure? utnha + antxi → my house + antxi \nWhat is “antxi”? Compare with: \n- ishinhna = in my bed \n- ishma = your bed \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n\n“yaputxi” → is it the field? \n“yapsanpsa” → in our1+2 field too → so “sanpsa” = in our1+2 field \nThen “antxi” = in + something?\n\nSo if “utnhantxi” = my house + antxi → possible = in my house?\n\nBut “ishinhna” = in my bed → matches the pattern\n\nSo “in + [something]” → marked by “ntxi” or “antxi”?\n\n“ishinhna” → in my bed → “ishin” + “hna” \n“ishinhna” = in my bed \n“ishma” = your bed \n“p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unhpsa” = my + too\n\nSo where is “antxi”?\n\n“utnhantxi” → utnha + antxi → my house + antxi → in my house?\n\nIs there a parallel to “ishinhna” (in my bed)?\n\nYes — “ishinhna” = in my bed \nThus, “antxi” likely = in? \nSo utnhantxi = in my house\n\nThat makes sense.\n\nNow (2) yapp”psa \nBreak down: yap + p”psa \n“yap” appears in: yaputxi = is it the field? \nSo “yap” = field? \n“yaputxi” = is it the field? → so “yap” is field \n“yapsanpsa” = in our1+2 field too → so “yapsanpsa” = in our1+2 field → so “sanpsa” = in + our1+2 field \n\nSo “yap” = field \n“p”psa” → appears in “yapp”psa” — likely phonetic variant? \nCompare: “p”a” – could be “in” or “from”?\n\nBut “yap” = field — so yapp”psa = field + something?\n\nLook at possibilites: \np”a → appears in qucxap”a, qucxst”psa \nqucxap”a = through the lake \nqucxst”psa = from our1+2 lake too → so “st” may mean “from”?\n\nSimilarly, markp”t”a = from his town → p”t”a = his town? \nBut “marka” = the town → so “mark” + “p”t”a = from his town → so “p”t”a” = his town? \nSo “p”a” suffix with possession?\n\nBut “p”psa” — not present in known forms.\n\nWait: “yaputxi” = is it the field? \n“yapsanpsa” = in our1+2 field too \nSo “sanpsa” = in our1+2 field\n\nWhat if “p”psa” is “my” + field?\n\nWe have “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → so “unhpsa” = my + too?\n\n“unh” → my? “h” → ? “psa” → ?\n\nWhat about “utnha” = my house \n“ut” → my? \n“ut” appears in “utnha” and “utnha” = my house\n\nCould “un” = my? \n“unh” = my + h?\n\nBut “p”ak”unhpsa” → my pot too → so “p”ak”u” + “unhpsa” → the pot + my + too?\n\nBut “unhpsa” → my + too \nSo “unh” = my? \nAnd “psa” = too?\n\nThen “yapp”psa” → yap + p”psa” → field + my + too?\n\n= my field too?\n\nBut “yap” = field → “yapp”psa” = my field too?\n\nIs there a parallel?\n\nLook at “p”ak”unhpsa” = my pot too → uses “unhpsa” \n\nSimilarly, “q”ax”at”a” = from the cliff \n“yapsanpsa” = in our1+2 field too → “sanpsa” → in our1+2 field\n\nWhat about “q”ax”at”a” → “q”ax”a” + “t”a” → from the cliff?\n\nBut “markp”t”a” = from his town → “p”t”a” = his town?\n\nSo “p”a” suffix → possessive?\n\nBut in “yapp”psa”, is “p”psa” = my + field?\n\nPossible — if “unhpsa” = my + too → so “p”psa” = possible misalignment?\n\nWait — in “p”ak”unhpsa” = my pot too \n“unhpsa” = my + too\n\nSo “un” → my? \n“h” → possessive marker? \n“psa” → too?\n\nBut “p”psa” — same letters: p, p, s, a — but “p”psa” — if it's “p”psa” then it’s p-p-s-a\n\nBut “p”ak”unhpsa” → p”a k”u n h p s a → could be “p”a” + “k”u” + “unhpsa”\n\nSo “unhpsa” = my + too\n\nSo “p”psa” — only p and psa → p”psa” — could be a variant or mistake?\n\nWait: in “yapp”psa” — is it “ya p p s a”?\n\nStructure: yap + p”psa” — could be “field + my + too”?\n\nBut only if “p”psa” = my + too?\n\nCompare to “p”ak”unhpsa” → uses “unhpsa” for “my pot too”\n\nSo if “unhpsa” = my + too → then “p”psa” would be “p” + “psa” — possibly “p” + [my+too]?\n\nBut no “un” — so “p”psa” ≠ my + too\n\nAlternative: perhaps “p”psa” = in the field?\n\nBut “yaputxi” = is it the field?\n\n“yapsanpsa” = in our1+2 field too — so “sanpsa” = in + our1+2 field\n\nSo “san” → in? \n“p”psa” not in that.\n\nNow “yapup”psa” — (3)\n\nBreak down: “yap” + “up”psa”\n\n“yap” = field\n\n“up”psa” — could it be “my” + field?\n\n“yapup”psa” → field + my + ? \n\nBut in “p”ak”unhpsa” — “unhpsa” = my + too\n\nSo if “p”psa” is not “my + too”, then what?\n\nMaybe marker “p” = object? or direction?\n\nLook at direction markers:\n\n- qucxap”a” → through the lake \n- qucxst”psa” → from our1+2 lake too \n→ “st” appears in “from”?\n\n- markp”t”a” → from his town → “p”t”a” = his town → “p” + “t”a?” \n\n- utamt”a” → from your house → “t”a” = your house?\n\n“t”a” appears in “utamt”a” → “utam” + “t”a” → from your house?\n\nSo “t”a” = your house?\n\n“utnha” = my house\n\nSo “t”a” → from your house\n\nSimilarly, “markp”t”a” → from his town → so “p”t”a” = from his town → “p” + “t”a” = from his town\n\nSo a suffix “p” + “ta” = from + possessive noun?\n\nThen “qucxst”psa” → from our1+2 lake too → “st” + “psa” → from our1+2 lake too?\n\n“st” = from? \n“psa” = too?\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “san” = in? “psa” = too?\n\nSo “psa” = too? \nYes — appears in:\n- qucxst”psa” → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n- p”ak”unhpsa” → my pot too \n- markstxi → is it our1+2 town? — not “too” \n- markstxi → “is it our1+2 town?” → so “stxi” = is it?\n\nNow “p”psa” — “p”psa” — “p” + “psa” — could “p” be possessive?\n\nBut in “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → so “unhpsa” = my + too → so “un” = my?\n\nThen “p”psa” — could “p”psa” be “in the field”?\n\nBut “yapsanpsa” = in our1+2 field too → “sanpsa” = in + our1+2 field\n\nSo “san” = in?\n\nSo “p”psa” without “a” for in?\n\nNo — “p”psa” is different.\n\nWait — “yap” = field \n“yapup”psa” → field + up? \nCould “up” be “to” or “in”?\n\nCompare to “ishinhna” = in my bed → “ishin” = in? \n“ishma” = your bed → “ish” + “ma” = your bed?\n\nNo clear pattern.\n\nBack to (2) yapp”psa\n\nCould it be “field from my”? or “from my field”?\n\nWe have “utamt”a” = from your house\n\n“markp”t”a” = from his town\n\nSo “from + [noun]” = p + [noun]?\n\nThen “p”t”a” = from his town → yes\n\n“p”psa” → from my field? → “p” + “psa” = from my field?\n\nBut “psa” not known to mean “my”\n\nBut in “p”ak”unhpsa” = my pot too — “unhpsa” = my + too\n\nSo “unh” = my?\n\nThen “psa” = too\n\nSo “p”psa” — a different form?\n\nPossibly “p”psa” = in the field?\n\nBut “yapsanpsa” = in our1+2 field too → “san” = in?\n\nSo “an” = in?\n\n“san” = in?\n\nSo “yapsa” — “yapsa” = in field? possible\n\nBut “yapp”psa” — if “p” is not in, then “yap” = field, “p”psa” = something?\n\nAlternatively, “yapp”psa” = our field? or the field?\n\nBut no “our” here.\n\nAnother idea: “p”psa” could be “my” in some cases?\n\nBut only in “unhpsa” is “my” attached.\n\nWhat about the form “yapup”psa”?\n\n(3) yapup”psa”\n\n“yap” = field \n“up”psa” — could be “in the field”?\n\n“ishinhna” = in my bed → “ishin” → in?\n\nSo “in” is marked by “in”?\n\n“ishin” → in + my\n\n“ishma” → your bed\n\nSo “ishin” = in?\n\nThen “yap” → field → so “yap” + “in” → in the field?\n\nBut “yapsanpsa” = in our1+2 field too → “sanpsa” = in our1+2 field → so “san” = in?\n\nSo “san” = in?\n\nThus “yap” + “san” = in the field? — but here it is “yapup”psa”\n\n“up” not “san”\n\nUnless “up” = in?\n\nBut “san” appears in “yapsanpsa” → in our1+2 field → so “san” = in?\n\nSo “up” → not in?\n\nCould “up” be “my”?\n\nIn “p”ak”unhpsa” = my pot too → “unhpsa” = my + too\n\nSo “un” = my\n\n“p”psa” — could be “my” + field? if “p”psa” = my field?\n\nBut “p” not “un”\n\nMistake in parsing?\n\nThe form is “yapup”psa” — clearly two parts?\n\nyap + up”psa”?\n\n“up” is a prefix?\n\nWhat about “utnha” = my house \n“ut” = my?\n\n“p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too\n\nSo “ut” = my? \n“p”ak”unh” = my?\n\nSo “un” = my?\n\nThen “p” could be another marker?\n\nWait — “p” in “p”ak”u” = the pot\n\n“p” in “p”ak”unhpsa” = part of the root?\n\nPossibly “p” is root for pot\n\nSo “p” = pot\n\n“p” is not possessive.\n\nNow “yap” = field\n\n“up”psa” — perhaps “up” is a version of “in”?\n\nBut “yap” is field, so “in the field”?\n\nCompare to “ishinhna” = in my bed → in + my bed\n\n“ishma” = your bed → so bed is the thing\n\n“yaputxi” = is it the field? → the field\n\n“yapsanpsa” = in our1+2 field → in + our1+2 field\n\nSo “san” = in?\n\nThus “in” = “san”?\n\nSo “yap” + “san” = in the field\n\nBut our form is “yapup”psa”\n\n“up” is almost “in”?\n\nCould “up” be a variant of “san”?\n\nUnlikely — different sounds.\n\nAlternative: in (3) “yapup”psa” — could it be “our field”?\n\nWe have “our1+2” in lake, field, town.\n\n“qucxst”psa” = from our1+2 lake too \n“markstxi” = is it our1+2 town? \n“yapsanpsa” = in our1+2 field too\n\nSo “our1+2” appears in compounds with “st”, “t”, “san”\n\nBut not directly in “yap”\n\nSo “yapup”psa” — perhaps “in the field” or “our field” or “my field”?\n\nBut no evident numeral.\n\nNow reevaluate (2) yapp”psa\n\nIf “p”psa” = my field too?\n\nThen “yapp”psa” = field + my field too? — unclear.\n\nBut “p”ak”unhpsa” = my pot too → “unhpsa” = my + too\n\nSo if “p”psa” is not “my + too”, then it is not.\n\nCould “p”psa” be “from my field”?\n\nThen “from” = “p” + “something”?\n\nWe have “from” in “from his town” = “p”t”a”\n\nSo “p” + “ta” = from his town\n\nSimilarly, “p” + “psa” = from my field?\n\nYes — possible.\n\nSo “yapp”psa” = from my field?\n\nThen (1) utnhantxi = in my house \n(2) yapp", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10127.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Identify the core patterns in the given Jaqaru-English pairs.\n\nLook at the structure of the words, especially the presence of numerals like \"our1+2\" and the use of \"from\" or \"in\" constructions.\n\nExample 1: \n\"qucxap”a\" = \"through the lake\" \n\"qucxst”psa\" = \"from our1+2 lake too\" → \"from the lake (our1+2) too\" \n→ \"st”\" likely marks \"from\", and \"psa\" is \"lake\", \"our1+2\" is a collective pronoun.\n\n\"marka\" = \"the town\" \n\"markp”t”a\" = \"from his town\" → \"p”\" marks \"his\", \"t”a\" is \"town\" \n\"markstxi\" = \"is it our1+2 town?\" → \"stxi\" = \"is it?\" \n→ \"markstxi\" = \"is it our town?\"\n\n\"utamt”a\" = \"from your house\" → \"utam\" = house, \"t”a\" = from \n\"utnha\" = \"my house\" → \"utn\" = my, \"ha\" = house \n\"p”ak”u\" = \"the pot\" \n\"p”ak”unhpsa\" = \"my pot too\" → \"unhpsa\" = \"my pot too\" → likely \"unh\" = my, \"psa\" = pot too \n→ so \"psa\" appears in \"too\" constructions.\n\n\"qaqat”a\" = \"from the cliff\" \n\"yapsanpsa\" = \"in our1+2 field too\" → \"yap\" = field, \"san\" = our1+2, \"psa\" = too\n\nSo \"psa\" is consistently used in \"too\" constructions (e.g., \"too\", \"in addition\").\n\nAlso, \"stxi\" = \"is it?\" \n\"t”a\" = \"from\" or \"of\" \n\"p”\" = \"his\" \n\"unh\" = \"my\"\n\nOther patterns:\n\n- \"ishinhna\" = \"in my bed\" \n- \"ishma\" = \"your bed\" \n- \"p”ak”unhpsa\" = \"my pot too\"\n\nSo structure: \n[x] + [adjective or possessive] + [noun] \nor \n[adjective] + [noun] → \"in my bed\"\n\nLikely structure of \"utnhantxi\": \n\"utn\" → \"my\" → \"hantxi\"? \n\"utnha\" = \"my house\" \nSo \"utnhantxi\" = \"in my house?\" \n\nBut \"ishinhna\" = \"in my bed\" → \"ishin\" = bed? But \"ish\" might be bed, \"h\" = possessive, \"n\" = in? \nWait — \"ishinhna\" = in my bed → \"in\" + \"my\" + \"bed\" \n\"ish\" = bed? \"inh\" = my? \"n\" = in?\n\n\"ish\" + \"inh\" = \"my bed\"? But \"ish\" = bed, \"inh\" = my? But \"ishinhna\" = in + my + bed?\n\nWait — \"ishinhna\" = \"in my bed\" → \"ish\" = bed, \"inh\" = my, \"n\" = in? But \"inh\" is not \"my\" — \"utnha\" = \"my house\", \"utn\" = my → so \"utn\" = my.\n\nThus \"utn\" = my → in my house = \"utnhantxi\"? \n\n\"utnhantxi\" — \"utn\" = my, \"hantxi\" → \"antxi\" = in? \"hantxi\" = in?\n\n\"utnha\" = my house → \"ha\" = house \n\"utnhantxi\" — different ending: \"antxi\" → possibly \"in\"?\n\n\"ishinhna\" = in my bed → \"ishin\" = bed, \"h\" = my? But no \"h\" in \"utnhantxi\".\n\nWait — pattern: \n\"ishinhna\" = in my bed → possible: \"is\" + \"hin\" + \"hna\"? No.\n\nAlternative: all use \"stxi\" = \"is it?\"\n\n\"markstxi\" = is it our town? \n\"qucxst”psa\" = from our lake too \n\"yapsanpsa\" = in our field too \nSo \"psa\" = \"too\", \"stxi\" = \"is it\", \"san\" = \"our1+2\"\n\nThus:\n\n- \"qucxst”psa\" = from our1+2 lake too → \"from + our1+2 + lake + too\"\n- \"yapsanpsa\" = in our1+2 field too → \"in + our1+2 + field + too\"\n\nSo \"psa\" = \"too\" \n\"stxi\" = \"is it?\" \n\"san\" = \"our1+2\"\n\nSimilarly: \"p”ak”unhpsa\" = my pot too → \"my pot + too\" → \"unh\" = my, \"psa\" = too \n\"utnha\" = my house → \"utn\" = my, \"ha\" = house\n\nSo \"in\" or \"from\" appears in constructions:\n\n\"ishinhna\" = in my bed → likely \"in\" + \"my bed\" → \"ishin\" = bed, \"h\" = my? But \"utnha\" = my house → \"utn\" = my, so no \"h\" in \"my\".\n\nUnless possessive is marked by a suffix.\n\n\"p”ak”unhpsa\" = my pot too → \"unh\" = my? \"unh\" might stem from \"unh\" = my → as in \"utn\" = my? Not matching.\n\nWait — \"utnha\" = my house — \"utn\" = my, \"ha\" = house \n\"p”ak”u\" = the pot → \"p”ak”\" = pot \n\"p”ak”unhpsa\" = my pot too → so \"unh\" = my? Then \"unhpsa\" = my pot too → so \"unh\" = my\n\nBut \"utnha\" also has \"my\" — so \"utn\" = my? Is \"utn\" = \"my\" and \"unh\" = \"my\"? Possible parallel.\n\nBut also: \"markp”t”a\" = from his town → \"p”\" = his, \"t”a\" = from + town? Or \"p”t”a\" = from his town?\n\n\"markp”t”a\" = from his town → so \"p”\" = his, \"t”a\" = town, and \"from\" is implied by \"mark\" (the town) as in \"from the town\"?\n\nSimilarly, \"marka\" = the town → \"mark\" = the town \nSo \"markp”t”a\" = from his town → \"p”\" = his\n\n\"markstxi\" = is it our1+2 town? → \"stxi\" = is it, \"san\" = our1+2, \"mark\" = town\n\nTherefore, the structure of \"utnhantxi\":\n\n\"utn\" = my \n\"ha\" = house \n\"antxi\" = ? → \"antxi\" — in?\n\n\"ishinhna\" = in my bed → \"ishin\" = bed, \"h\" = my → \"inh\" = my? But \"utnha\" has \"utn\" = my.\n\nWait — \"utnhantxi\" — could this be \"in my house?\" \n\"antxi\" = \"in\"?\n\nIn \"ishinhna\" = in my bed → \"ishin\" = bed → \"inhna\" = in + my + bed? Or \"ishin\" + \"hna\"?\n\nBut \"hna\" → similar to \"ha\" — house → no.\n\nAlternatively: \"utnhantxi\" → \"utn\" + \"hantxi\"? \nCompare to \"ishinhna\" = \"ishin\" + \"hna\"?\n\n\"ishinhna\" = in my bed → \"ishin\" = bed, \"hna\" = in my? Or \"hna\" = in + my?\n\nBut \"ishinhna\" — syllables: i-shin-hna → could be \"in + my + bed\"?\n\n\"ish\" = in? \"inh\" = my? \"hna\" = bed?\n\nBut \"is\" appears in \"utnhantxi\"? No.\n\nAnother possibility: \"t”\" = from, \"stxi\" = is it, \"psa\" = too.\n\nBack to \"utnhantxi\":\n\n\"utnha\" = my house \n\"utnhantxi\" — adds \"antxi\"\n\n\"antxi\" — similar to \"stxi\" or \"hantxi\"?\n\n\"yaputxi\" = is it the field? → \"yap\" = field, \"utxi\" = is it?\n\n\"yapsanpsa\" = in our1+2 field too → \"yap\" = field, \"san\" = our1+2, \"psa\" = too\n\n\"yaputxi\" = is it the field? → \"utxi\" = is it?\n\nSo \"utxi\" = \"is it?\"\n\nTherefore, \"utnx\" → likely \"in my + ?\"\n\nNow look at \"utnhantxi\" = ? \nCompare to \"ishinhna\" = in my bed → could \"utnhantxi\" = in my house?\n\n\"utn\" = my → \"hantxi\" — hantxi → \"antxi\" = is it? No, \"utxi\" = is it.\n\n\"antxi\" — does not match \"utxi\"\n\nBut in \"yaputxi\" = is it the field → \"utxi\" = is it\n\nSo \"utxi\" = \"is it\"\n\nTherefore, \"utnhantxi\" — \"utn\" = my, \"hantxi\" → \"hantxi\" could be \"in my house\" → but \"hantxi\" has \"h\" and \"antxi\"\n\nWait — \"ishinhna\" = in my bed → if \"ish\" = bed, \"inh\" = my, \"n\" = in → then \"in + my + bed\"\n\n\"ishinhna\" → \"in\" + \"my\" (inh) + \"bed\" (ish)? Order: i-shin-hna\n\ni-shin-hna → is it possible that \"shin\" = bed, \"hna\" = in my?\n\nBut \"utnhantxi\" = u-t-n-h-a-n-t-x-i\n\nNow \"utn\" = my → \"utnha\" = my house → so \"utn\" = my\n\n\"ha\" = house\n\nSo \"utnha\" = my house\n\n\"utnhantxi\" — same root, with \"antxi\" → possibly \"in my house\"?\n\nIs there a \"in\" marker?\n\n\"yaputxi\" = is it the field → \"utxi\" = is it\n\n\"ishinhna\" = in my bed → \"inhna\" = in + my + bed?\n\n\"ishinhna\" → i-shin-hna\n\n\"ish\" + \"inh\" → \"in my\"?\n\n\"ish\" = bed? \"inh\" = my?\n\nThen \"inh\" = my\n\nSimilarly, \"utn\" = my → so \"utn\" is \"my\"\n\nThen \"utnha\" → my house\n\nNow \"utnhantxi\" → might be \"in my house\" → with \"antxi\" instead of \"inhna\"?\n\nBut \"antxi\" — if \"antxi\" = \"in\" + \"my\" + \"house\"?\n\n\"antxi\" — compared to \"inhna\" — \"inhna\" = in my bed?\n\nBut \"antxi\" — no direct match.\n\nWait — \"yaputxi\" = is it the field → \"utxi\" = is it\n\n\"yapsanpsa\" = in our1+2 field too → \"yap\" + \"san\" + \"psa\"\n\nNo \"utxi\"\n\n\"qucxap”a\" = through the lake → not \"in\"\n\nSo only \"in\" appears in \"ishinhna\" and \"yapsanpsa\"\n\n\"ishinhna\" = in my bed → \"inhna\" → \"in + my + bed\"\n\n\"yapsanpsa\" = in our1+2 field too → \"in + our + field + too\"\n\nSo \"in\" is marked by a structure that includes \"a\" or \"p\" or \"n\"?\n\n\"ishinhna\" → ends with \"hna\" → \"hna\" = in my bed?\n\nBut \"utnhantxi\" → ends with \"antxi\"\n\n\"antxi\" — a + n + t + x + i\n\n\"utxi\" = is it\n\nIf \"utxi\" = is it, then perhaps \"antxi\" = in + something?\n\nBut in \"yaputxi\" = is it field → \"utxi\" = is it\n\nSo \"utxi\" = \"is it\"\n\n\"antxi\" — perhaps \"ant\" = in? \"x\" = ? → unlikely.\n\nAlternative: \"utnhantxi\" = \"in my house\" → so suffix \"antxi\" may be a blend.\n\nBut no example has \"in\" + \"my\" + \"house\"\n\nWe have:\n\n- \"utnha\" = my house\n- \"ishinhna\" = in my bed\n- \"yapsanpsa\" = in our1+2 field too\n\nSo in those, \"in\" appears with possessive.\n\nSo in \"utnhantxi\", if it's \"in my house\", then it should have \"in\" + \"my\" + \"house\" → so \"in my house\"\n\nBut how to show?\n\nFrom \"ishinhna\" = in my bed → structure: possessive + noun → \"my bed\"\n\n\"bed\" = \"ishin\"? But \"ishin\" is not in the list.\n\n\"ish\" = bed? \"ish\" + \"inh\" → \"in my bed\"?\n\nIf \"inh\" = my, then \"ishin\" = bed → so \"ishinh\" = in my bed? But it's \"ishinhna\"\n\n\"ishinhna\" → i-shin-hna\n\nNo clear \"in\" marker.\n\nBut in \"yapsanpsa\" = in our1+2 field too → \"yap\" + \"san\" + \"psa\" → \"in our field too\"\n\nSo \"in\" is marked by \"yap\" + \"san\" → \"in our field\"?\n\nHere \"yap\" = field, so not.\n\n\"yapsanpsa\" = in our1+2 field too → the \"in\" is not tied to a word.\n\nPossibly all aspect markers are embedded.\n\nStructure of questions:\n\n- \"markstxi\" = is it our town?\n- \"yaputxi\" = is it the field?\n\nSo \"stxi\" = is it?\n\nSo if \"utnhantxi\" = is it my house?\n\n\"utn\" = my, \"hantxi\" = house?\n\nBut \"yaputxi\" = is it the field → \"yap\" = field, \"utxi\" = is it\n\nSimilarly, \"ishinhna\" = in my bed — not a question.\n\nBut \"utnhantxi\" — might be a question?\n\nIt ends with \"antxi\" — not \"utxi\"\n\n\"utxi\" is in \"yaputxi\" — is it the field?\n\n\"utnhantxi\" — similar structure?\n\nCompare: \"yaputxi\" = is it field → \"utxi\" = is it\n\n\"utnhantxi\" = ? → \"hantxi\"? \"hant\" = my? \"xi\" = is it?\n\n\"antxi\" — could be \"in my house\" — but \"in\" missing?\n\nWait — another word: \"qaaqat”a\" = from the cliff\n\n\"marka\" = the town\n\nNo \"in\" or \"from\" with \"my house\"\n\nBut \"p”ak”unhpsa\" = my pot too → \"unh\" = my, \"psa\" = too\n\nSo \"psa\" = too\n\n\"yapsanpsa\" = in our1+2 field too → \"psa\" = too\n\n\"qucxst”psa\" = from our1+2 lake too → \"psa\" = too\n\nSo \"psa\" = \"too\"\n\n\"stxi\" = \"is it\"\n\nSo if \"utnhantxi\" has \"antxi\", and we know \"utxi\" = \"is it\", then perhaps \"antxi\" = \"is it in\"?\n\nNo direct match.\n\nLook at \"utnhantxi\" — perhaps it is a variant of \"in my house\".\n\nBut no \"in\" marker.\n\nIn \"ishinhna\", \"in\" is part of \"inh\" → if \"inh\" = in my, then \"ish\" = bed.\n\nIn \"yapsanpsa\", no possessive in the middle.\n\nWait — in \"yapsanpsa\", \"san\" = our1+2, \"psa\" = too, \"yap\" = field → so \"in our1+2 field too\"\n\nSo \"in\" is separate.\n\nBut in \"utnhantxi\", no \"in\" or \"san\" or \"utxi\"\n\nWhat about the last word: \"yapup”psa\"?\n\n\"yapup”psa\" — \"yap\" = field, \"up”\" = ? \"psa\" = too\n\n\"yaputxi\" = is it the field? → \"utxi\" = is it\n\n\"yapup”psa\" = is it the field too?\n\n\"up”\" might be \"our1+2\"?\n\n\"qucxst”psa\" = from our1+2 lake too → \"st”psa\" = from our lake too\n\n\"yapsanpsa\" = in our1+2 field too → \"san\" = our1+2\n\n\"yapup”psa\" — \"up”\" might be \"our1+2\"\n\n\"up”\" = \"our1+2\" → similar to \"san\"?\n\n\"san\" = our1+2 → so \"up”\" might be an alternative for \"our1+2\"\n\n\"markstxi\" = is it our town? → \"our\" = our1+2\n\n\"qucxst”psa\" = from our1+2 lake too → \"our1+2\"\n\nSo \"san\" and \"up”\" both perhaps mean \"our1+2\"\n\nSo \"yapup”psa\" =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9917.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are given a set of Jaqaru words and their English translations. Our task is to translate three new words: \n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe must derive the pattern from the given examples.\n\n---\n\nFirst, identify recurring patterns.\n\nGiven examples:\n\n1. aq”ipsa → the cave too \n → \"the cave\" + \"too\" → possibly a determiner + an additive particle \n2. aq”na → in the cave \n → prepositional phrase: \"in the cave\" \n3. qucxap”a → through the lake \n4. qucxst”psa → from our1+2 lake too \n → \"from\" + \"our1+2\" + \"lake\" + \"too\" \n5. chushp”a → his corner \n6. chushuntxi → is it in the corner? \n → question form: \"is it in the corner?\" \n7. marka → the town \n8. markp”t”a → from his town \n9. markstxi → is it our1+2 town? \n10. ishinhna → in my bed \n11. ishma → your bed \n12. p”ak”u → the pot \n13. p”ak”unhpsa → my pot too \n14. utamt”a → from your house \n15. utnha → my house \n16. yaputxi → is it the field? \n17. yapsanpsa → in our1+2 field too \n\nNow look at the structure of the compound forms.\n\nNote: The particle “too” appears in:\n- aq”ipsa: “the cave too” \n- qucxst”psa: “from our1+2 lake too” \n- p”ak”unhpsa: “my pot too” \n- yapsanpsa: “in our1+2 field too”\n\nSo \"too\" is clearly a suffix, added to a phrase to indicate addition or a complementary meaning.\n\nSimilarly, questions are formed with \"is it\" + a prepositional phrase:\n- chushuntxi → is it in the corner? \n- ishinhna → in my bed → not a question \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field? \n\nSo this suggests:\n- \"is it\" + [noun phrase] → question form\n\nNow, let's examine the structure of the \"in\" and \"from\" phrases.\n\n\"aq”na\" = in the cave \n\"ishinhna\" = in my bed \n\"marka\" = the town \n\"markp”t”a\" = from his town \n\"utamt”a\" = from your house \n\"utnha\" = my house \n\"yapsanpsa\" = in our1+2 field too \n\nSo we see:\n- \"in\" + [something] → is used for location \n- \"from\" + [something] → for origin \n\nAlso: \n\"the cave\" appears in \"aq”ipsa\" (the cave too) and \"aq”na\" (in the cave) \n\"the pot\" → p”ak”u \n\"my pot\" → p”ak”unhpsa → so \"unhpsa\" likely means \"my\" \n\"my house\" → utnha \n\"from your house\" → utamt”a → \"tam\" may be \"your\" \n\"our1+2\" appears in:\n- qucxst”psa → from our1+2 lake too \n- markstxi → is it our1+2 town? \n- yapsanpsa → in our1+2 field too \n\nSo \"our1+2\" appears before a noun or noun phrase, and is used in spaces where the possessive is plural (one and two). \n\nNow look at the questions:\n\n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field? \n\nSo structure: \n\"is it\" + [possessive or determiner] + [noun] \n\nNow examine:\n- utnhantxi → likely another question, perhaps \"is it in my house?\" \nBecause utnha = my house \nAnd \"in\" is a common preposition \n\"antxi\" may be a form derived from \"in\" or \"in it\"? \n\nCompare:\n- ishinhna = in my bed \n- chushuntxi = is it in the corner? \n\nSo if we see \"in my house\", and the form is utnhantxi, it may be \"is it in my house?\" \n\nBut let’s check if \"antxi\" is a form of \"in\". \nWe have:\n- aq”na = in the cave \n- ishinhna = in my bed \n- marks txi → is it our1+2 town? \n- yaputxi → is it the field? \n\nNote: \"in\" appears only in two forms:\n- aq”na → in the cave \n- ishinhna → in my bed \n\nBut these both end with \"na\" and \"hna\"? Not clear.\n\nAlternatively, look at word endings:\n\n\"utnhantxi\" \n\"yapp”psa\" \n\"yapup”psa\" \n\nCompare to:\n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\n\"yaputxi\" → is it the field? \n\"yapsanpsa\" → in our1+2 field too \n\nBut \"yaputxi\" = “is it the field?” \nSo the form “yap” + “utxi” → is it the field \n\nNow “yap” is likely a root for “field” \n\"yap\" → field \n\"yaputxi\" → is it the field? \n\"yapsanpsa\" → in our1+2 field too → so “in + our1+2 + field too” \n\nSo the pattern for questions: \n“yap” + “[preposition]” + “[possessive]” + “[root]” \n\nBut \"yaputxi\" → is it the field? \nNo possessive or preposition. \n\nSo perhaps:\n\n- yap [root] + txi → is it [root]? \n- yapsanpsa → in our1+2 field too → preposition + possessive + root + too \n\nNow, u is similar to t? Possibly a directional marker.\n\nNow focus on:\n\n1. utnhantxi \n\nBreak down:\n\n- utnha = my house \n- utnhantxi → may be “is it in my house?” \n- Compare to: ishinhna = in my bed → in + my (ishin) + bed \n- chushuntxi = is it in the corner? → is it in + corner? \n\nSo pattern: is it + in + [something]? \n\nBut we see:\n- ishinhna = in my bed → so “in” + “my” + “bed” \n- chushuntxi = is it in the corner? → is it in + corner? \n\nSo if utnhantxi = “is it in my house?” \nThen “utnhantxi” = “is it in + my house” \nWe already have “utnha” = my house → so “in” must be a separate morpheme \n\nBut “utnha” ends with “ha”, not “na” → whereas “aq”na → in the cave → “na” \n\nSo difference? \n\nBut “ishinhna” = in my bed → “ishin” = my → “hna” → may be the “in” or part of it? \n\nNo. “ishinhna” = in my bed → perhaps “is” + “hin” + “hna” → but “is” is not present.\n\nWait — the question forms are clearly “is it” + [phrase].\n\nSo we conclude: \n- All question forms start with “is it” → is + it + [phrase] \n- “it” is part of the verb “to be” or is a pronoun.\n\nSo:\n\n1. utnhantxi → likely “is it in my house?” \n\nBecause:\n- utnha = my house \n- “in my house” = in + my house → “in” + utnha \n- But in the given, “in the cave” = aq”na \n- So “in” is a preposition → “na” is the ending for “in the cave”?\n\nWait: aq”na → in the cave \nSo “na” may be the ending of the phrase “in the cave”\n\nBut “ishinhna” → in my bed \nSo “hna” is the ending → “in my bed”\n\nSo “na” may correspond to “in the” \n“hna” to “in my”\n\nSo in “utnhantxi”: \n- utnha = my house \n- if “antxi” = in + (something)? \n- But “in” appears as “na” in “aq”na → in the cave \n\nBut in “ishinhna” → in + my bed → so the “hna” portion includes “in” and “my”?\n\nPerhaps the preposition “in” is built into the structure.\n\nTry this:\n\n- “utnhantxi” = is it in my house? \n→ matches the pattern of “chushuntxi” = is it in the corner? \n→ matches “markstxi” = is it our1+2 town?\n\nSo all question forms are: is it in (place)? or is it (place)?\n\nNow, that leaves:\n- yapp”psa \n- yapup”psa \n\nCompare to:\n- yaputxi = is it the field? \n→ so “yap” + “utxi” = is it the field?\n\nSimilarly:\n- yapsanpsa = in our1+2 field too → in + our1+2 + field + too\n\nSo “yap” is field root \n“utxi” = the field (used in “is it the field?”) \n“sanpsa” = in our1+2 field too\n\nSo the form “yap” + “p” + “s” + “a” → may be derived from “field”?\n\nNow “yapp”psa” → yap + p” + psa \n“yapup”psa” → yap + up” + psa \n\nCompare to “yaputxi” = yap + utxi → “utxi” \n\nNow, in “yaputxi” = is it the field? \nSo “utxi” appears in a question form.\n\nBut “yapp”psa” — might be “is it in the pot?” or “my pot”, etc.\n\n“p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → so “unhpsa” = my pot → “my” + pot \n\nSo “p”ak”u” = the pot \n“yapp”psa” → yap + p” + psa → might be “is it in the pot?” \n\nBecause “in” may be a morpheme.\n\nSimilarly, “yaputxi” = is it the field? \nSo “utxi” = the field \n\nSo “p”psa” = in the pot? \nBut “p”psa” → not found.\n\nWait: “yapp”psa” → might be “in the pot”?\n\nBut “p”ak”u” = the pot\n\nSo “in the pot” → is it in the pot?\n\nThat would be: is it + in + the pot?\n\nBut no such form.\n\nHowever, “yaputxi” = is it the field? → so “utxi” = the field\n\nThen “yapp”psa” → perhaps “is it in the pot?” — but “p” is not clearly in the root.\n\nBut “p”ak”u” = the pot \nSo “pot” is root “p”?\n\n“yap” = field \n“p” = pot? \n\nThen “yapp”psa” = is it in the pot?\n\nBut “yapp”psa” → “yap” + “p” + “psa” → instead of “utxi”\n\nBut “psa” appears in “aq”ipsa → the cave too — “ipsa” \nAlso in “p”ak”unhpsa” → my pot too → “unhpsa” \nIn “yapsanpsa” → in our1+2 field too → “sanpsa” \n\nSo “psa” appears in:\n- aq”ipsa → the cave too \n- yapsanpsa → in our1+2 field too \n- p”ak”unhpsa → my pot too \n\nSo “psa” = “too”?\n\nYes — aq”ipsa → the cave too → “ipsa” \np”ak”unhpsa → my pot too → “unhpsa” → “hpsa” = too? \nBut “unhpsa” = my pot too → “unh” = my? “psa” = too? \n\nSimilarly, “yapsanpsa” = in our1+2 field too → “sanpsa” → “san” = in our1+2? “psa” = too?\n\nSo “psa” = “too” (additive marker)\n\n“na” = “in” \n“utxi” = “the field” \n“sanpsa” = in our1+2 field too → “san” = in + our1+2? “psa” = too?\n\nBut in “yaputxi” = is it the field? — no “too” → just “the field”\n\nSo “psa” = “too”\n\nNow go to “yapp”psa” → yap + p” + psa → yap + p” + psa \nBut “psa” = too → so “yapp”psa” = [something] + too?\n\nAnd “yap” = field → “field”?\n\nThen “yapp”psa” = the field too?\n\nBut we already have “yapsanpsa” = in our1+2 field too → includes “in”\n\nBut “yapp”psa” has “p” instead of “u”\n\nSo “p” → pot? \n“u” → field?\n\nAha! \n\nWe have:\n- p”ak”u → the pot \n- yap → field \n\nSo “p” = pot? → “yap” = field → different root \n\nBut “yapp”psa” → yap + p” → maybe “in the pot”?\n\nBut no obvious “in” marker.\n\nWait: “yap” + “p” + “psa” → perhaps “in the pot too”? \n\nThat would match the additive form.\n\nBut “yapp”psa” → could mean “in the pot too”?\n\nSimilarly, “yapup”psa” → yap + up” → up”?\n\n“p” and “up” are different.\n\nBut we have “utamt”a = from your house \n“utnha” = my house \n“marka” = the town \n\nNo “up” form.\n\nBut “yaputxi” = is it the field? → so “utxi” = the field \n\nThen “yapup”psa” → yap + up” + psa → ? \n\nCould “up” be “in” or “from”?\n\nBut “ut” is in “utamt”a, “utnha” → “ut” + “am” (your) → “your”?\n\n“ut” might be a root.\n\nIn “utnha” → my house \n“utamt”a → from your house \n“ut” may be “house”?\n\nSo:\n- “ut” = house \n- “nha” = my house → utnha \n- “amt”a → from your house → “am” = your? \n\nSo “ut” = house root \n“yap” = field \n“p” = pot \n\nThen “yap” + “p” + “psa” = field + pot + too? → unclear\n\nBut “yapp”psa” → if “p” = pot, then “field + pot”? No.\n\nAlternatively, “yap” = field, and “p” is a preposition? \n\nNo.\n\nAnother idea: the base structure is:\n\n- [question] + [preposition] + [possessive/determiner] + [noun]\n\nBut in “yaputxi” → is it the field? → no possessive, no preposition — just “the field”\n\nSo “yap” = field \n“utxi” = the field → so “utxi” = the field?\n\nIn “yapsanpsa” → in our1+2 field too → “san” = in our1+2? “psa” = too\n\nSo “sanpsa” = in our1+2 field too\n\nSimilarly, “yap” + “p” + “psa” → ? \n\nWait — in “p”ak”unhpsa” → my pot too → “unh” = my? “hpsa” = too → “hpsa” = too? \n\nBut “psa” appears in “psa” as the additive marker.\n\nSo “psa” = too → additive marker\n\nIn “aq”ipsa” → the cave too → “ipsa” = cave too → so “psa” = too\n\nSo every word ending with “psa” has “too” added.\n\nThus:\n\n- yapp”psa” = ? + too → the field + pot? but no link\n\nBut “yap” + “p” + “psa” — could “p” be a possessive?\n\nWait: we have:\n- marka → the town \n- markp”t”a → from his town → so “p” = his? \n- markstxi → is it our1+2 town? → “st” = our? \n- chushp”a → his corner → “p” = his \n\nSo “p” = his \n“t” = his? → in markp”t”a = from his town → “p” or “t”?\n\nmarkp”t”a → from his town \nchushp”a → his corner \n\nSo “p” = his \n\nSimilarly, “markstxi” → is it our1+2 town? → “st” = our1+2 \n\n“utamt”a → from your house → “am” = your \n\nSo:\n- p → his \n- t", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10901.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Analyze the structure of the sentences to identify core syntactic patterns.\n\nAll sentences follow a similar basic structure: \n[Subject] [verb] [object] [modifier phase]\n\nThe verb typically is a copular or a causative-like structure, often involving \"making\" or \"is doing to\" (e.g., \"is making X tired\", \"is carrying\", \"is following\").\n\nKey elements:\n- The verb \"baNgul\" appears frequently as \"is following\" or \"is carrying\" (e.g., 4, 9, 13, 2, 10, 12).\n- \"baNgu\" appears in a similar position and is often interpreted as \"is making\" (e.g., 1, 5, 8).\n- \"gurugugu\" = tired, \"waymin\" = fat, \"baman\" = healthy, \"yabu\" = strong, \"malayigara\" = smoke, \"gurugu\" = booze, \"diban\" = fat, \"bimabanéal\" = strong man, etc.\n\nFurther pattern:\n- The modifier phrase (like \"that is always being blamed\", \"that is always following death adders\") is often formed with:\n - [NP] + [modifier] + [possibly an adverbial suffix]\n - The modifier frequently includes \"always\", expressed as \"yaóa\", \"NunéaymuNa\", \"Nunéañu\", \"Numa\", \"biñéiriñéu\", etc.\n\nFrom sentence (1):\n- \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\"\n→ \"Booze is making the man that is always being blamed tired.\"\n\n\"yaóa\" = always being blamed / always being criticized \n\"biNgunman\" = tired \n\"baNgu\" = making \n\"bayi\" = booze\n\nSimilarly, sentence (5):\n- \"balan malayigara baNgu garandu biNgunman\"\n→ \"The smoke is making the scorpion tired.\"\n\nSo \"baNgu\" = making → causative verb \n\"biNgunman\" = tired \n\"garandu\" = scorpion \n\"malayigara\" = smoke\n\nIn sentence (3):\n- \"balan waymin bambun baNgu éugaNgu éamiman\"\n→ \"Sugar is making the healthy mother-in-law fat.\"\n\n\"waymin\" = fat \n\"bambun\" = healthy mother-in-law \n\"baNgu\" = making → causative \n\"éugaNgu\" = sugar\n\n\"éamiman\" = fat → so number/aspect/quality is attached via modifier\n\nNow sentence (8):\n- \"bayi gubimbulu biNgun baNgu gurugugu éagunman\"\n→ \"Booze is making the tired doctor fall asleep\"\n\n\"gurugugu\" = tired → modifies \"doctor\" \n\"biNgun\" = tired → modifier \n\"baNgu\" = making \n\"éagunman\" = fall asleep\n\nSo, \"gurugugu\" appears in both \"making tired\" and \"tired doctor\".\n\nThus:\n- \"biNgun\" = tired \n- \"gurugugu\" = fat / tired? But in (1), \"gurugugu\" is \"tired\" → consistent \n- \"gurugugu\" appears as head for \"tired\" and as separate noun/adj?\n\nWait: in (1) → \"gurugugu biNgunman\" → makes tired \nIn (8) → \"biNgun baNgu gurugugu éagunman\" → the tired doctor is falling asleep\n\nSo \"biNgun\" = tired \n\"baNgu\" = causing to be\n\nSo causative verb: [X] baNgu [Y] is making Y [quality]\n\nSo structure: \n[Subject] [modifier] [verb] [object] [quality aspect]\n\nNow look at sentence 17:\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\n\"balan\" = subject (likely the sugar or something in the category of \"making\") \n\"ñalNga\" = ? \n\"baNgul\" = following or carrying \n\"NumaNgu\" = always being followed? (from sentence 16: \"The man that is always being followed is offending the strong father\") \n\"guniymuNagu\" = ? \n\"bambunman\" = fat?\n\nFrom sentence 13:\n13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n→ The mother-in-law that is always pushing stones is looking at the smoke.\n\n\"garan\" = following \n\"baNgun\" = making? or is it \"is looking at\"?\n\nAh! Important:\n\n- \"garan baNgun\" → \"the mother-in-law is following the one that is making (or being) something\"?\n\nWait, compare:\n\nIn (9): bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan \n→ \"The lizard is following the mother-in-law that is always pushing stones\"\n\n\"baNgun\" = not \"making\", but \"following\"?\n\nNo — sentence 9: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\"\n\n\"garan baNgun\" → lizard is following the mother-in-law (subject) \n\"waymindu\" → fat? \n\"dibanbilmbalNaymuNagu\" → that is always pushing stones \n\"buóan\" → looking?\n\nNo — the structure seems to be:\n[Subject] [verb] [object] [modifier] [quality]\n\nIn (13): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"The mother-in-law that is always pushing stones is looking at the smoke.\"\n\nBut \"garan\" = following? \nNo — \"bala garan\" = lizard is following → so \"garan\" is verb \n\"baNgul\" is in (4,9,10,12,13) — appears in different forms.\n\nLook at sentence 4: \n4. bala yila wura baNgul bargandu biNgundu guniñu \n→ \"The tired wallaby is searching for the little feather\"\n\n\"yila\" = tired \n\"wura\" = searching \n\"baNgul\" = for? or is a preposition?\n\n\"baNgul\" appears as \"is searching for\" in sentence 4 → so \"baNgul\" = searching for\n\nIn sentence 9: bala garan baNgun yabuNgu NaéilmuNagu dimbañu \n→ \"The lizard is following the smoke\"\n\nWait: the first example is (9): \n\"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\" → \"The lizard is following the smoke\"\n\n\"garan\" = following \n\"baNgun\" = ? — same as (13): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\"\n\nBut in (9): \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\"\n\n\"baNgun\" appears after \"garan\"\n\nSo is \"baNgun\" a different verb? Or a transitive?\n\nWait — in (4): \"bala yila wura baNgul bargandu\" → \"tired wallaby is searching for the little feather\"\n\n\"baNgul\" = searching for \n\"bargandu\" = little feather\n\nIn (13): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\"\n\n→ \"The mother-in-law that is always pushing stones is looking at the smoke\" — so \"garan\" = following? \"baNgun\" = is looking at?\n\nNo — \"bala garan\" = lizard is following → so first verb is \"garan\"\n\nThen \"baNgun\" — in (13) it's not followed immediately by object of the same kind.\n\nBut in sentence (9): \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\" \n\"yabuNgu NaéilmuNagu dimbañu\" = the smoke? \n\"yabu\" = strong \n\"NaéilmuNagu\" = father? \n\"dimbañu\" = ignored?\n\nWait — from sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = offending \n\"baNgul\" = to the strong father\n\nSo \"baNgul\" can be a preposition meaning \"to\", \"at\", \"towards\"\n\nIn (9): \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\" \n→ \"The lizard is following the smoke\" \nSo \"ga\" = follow \n\"baNgun\" = is following the smoke? Or \"is being followed by\"?\n\nWait — structure:\n\nPossibility:\n- \"garan\" = causative or transitive verb \n- \"baNgun\" = is making, or is doing to?\n\nBut more structural: in (9) → \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\"\n\nCompare to (13): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\"\n\nBoth have \"baNgul\" and \"baNgun\" — perhaps a typo?\n\nWait — likely typo in the problem: sentence 9 says: \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\"\n\nBut from the translation: \"The lizard is following the smoke.\"\n\nSo \"garan\" = following \n\"baNgun\" may be a mistake — likely should be \"baNgul\" or comma?\n\nWait — sentence 4: \"bala yila wura baNgul bargandu\" → \"searching for\"\n\nSo \"baNgul\" = searching for\n\nSentence 9: \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\" → \"the lizard is following the smoke\"\n\nSo \"garan\" = following \n\"baNgun\" = not needed? Why is it there?\n\nUnless each verb has a specific role:\n\n- \"baNgul\" = search for / follow / is finding \n- \"baNgun\" = is making / have power over?\n\nBut in (1): \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → \"booze is making the man that is always being blamed tired\"\n\n\"baNgu\" = making\n\nIn (9): \"bala garan baNgun yabuNgu NaéilmuNagu dimbañu\" → \"lizard is following the smoke\" — but \"baNgun\" is not explaining \"following\"\n\nSo perhaps \"garan\" is the verb — following — and \"baNgun\" is a suffix?\n\nWait: syllabic structure — many nouns are modified with -a, -u, -NaymuNa, -Nagu\n\nKey pattern:\n\nFrom (1): \"NunéaymuNa\" = man that is always being blamed \nFrom (16): \"Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father\"\n\n\"Numa\" = always being followed \n\"yaóaNgu\" = the strong father? \n\"banéalmuNagu\" = strong? \n\"munduman\" = offends?\n\nSo \"Numa\" = always being followed (like yaóa = always being blamed) \n\"Numa\" is used as a modifier: [N] that is always being [followed]\n\nSimilarly, \"yaóa\" = always being blamed\n\nIn (1): \"NunéaymuNa\" = man that is always being blamed\n\nIn (17): \"NumaNgu guniymuNagu bambunman\"\n\n\"NumaNgu\" = man that is always being followed \n\"guniymuNagu\" = ? \n\"bambunman\" = fat?\n\nSo \"NumaNgu\" likely modifies a noun.\n\nSimilarly, in (18): \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject (lizard or animal) \n\"diban\" = fat \n\"bilmbalmuNa\" = that is always pushing stones? \n\"baNgun\" = making? \n\"biñéiriñéu\" = the one that is looking? \n\"guniñu\" = little feather?\n\nBut sentence (13): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"the mother-in-law that is always pushing stones is looking at the smoke\"\n\n\"garan\" = looking at \n\"waymindu\" = fat \n\"dibanbilmbalNaymuNagu\" = that is always pushing stones \n\"buóan\" = looking → so \"garan\" may be \"looking\"\n\nPossibility:\n- \"garan\" = looking at / following \n- \"baNgun\" = is making / causing (like causative)\n\nWait — now go to sentence (15): \n15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan \n→ \"The quiet boy is looking at the tired lizard\"\n\n\"biñéiriñ\" = quiet \n\"biNgun\" = tired \n\"baNgul\" = at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = fall asleep? \n\"buóan\" = look?\n\nNo — translation says \"looking at the tired lizard\"\n\nSo \"baNgul\" = at \n\"biñéiriñ\" = boy \n\"biNgun\" = tired \n\"ñalNgaNgu\" = lizard \n\"buóan\" = looking? But verb is \"is looking\"\n\nSo \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\"\n\n\"biNgun\" = tired → modifies \"lizard\" \n\"baNgul\" = at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" → ?? \n\"buóan\" → look?\n\nBut \"mugurugu\" is not in the translation. Translation says \"quiet boy is looking at the tired lizard\"\n\nSo likely \"buóan\" = look \n\"mugurugu\" may be a noun?\n\nBut from (18): \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = that is always pushing stones \n\"baNgun\" = is making \n\"biñéiriñéu\" = the one that is looking \n\"guniñu\" = little feather\n\nSo \"baNgun\" = is making → causative verb \n\"biñéiriñéu\" = one that is looking (thus, the one being made to look?)\n\nBut the object is \"biñéiriñéu\" — the one who is looking\n\nSo structure: [Subject] [quality] [modifier] [baNgun] [object] [quality]\n\nThus, \"baNgun\" = is making (someone) [X]\n\nNow in 19: \n19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\n\"bayi\" = subject (death adder?) \n\"bargan\" = ? \n\"baNgul\" = at \n\"yaóaNgu\" = the one that is always being blamed? \n\"gubimbuluNunéanaymuNagu\" = ? \n\"banéan\" = the one that is being followed?\n\nWait — from sentence 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father\"\n\n\"Numa\" = always being followed \n\"yaóaNgu\" = the strong father (object?) \n\"banéalmuNagu\" = strong? \n\"munduman\" = offending\n\nSo \"yaóaNgu\" = the strong father \n\"Numa\" = always being followed\n\nIn 19: \"gubimbuluNunéanaymuNagu\" → likely \"the one that is always being followed\" — similar to \"Numa\" but with \"gubimbulu\" + \"NunéanaymuNagu\"\n\nSo \"gubimbulu\" = offended or something?\n\nIn (6): \"bala gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ \"The offended father is carrying the booze\"\n\n\"gurugu\" = offended \n\"baNgul\" = carrying \n\"NumaNgu\" = father? \n\"munduNgu\" = carrying? \n\"dimbañu\" = one?\n\nSo \"gurugu\" = offended → adjective \n\"NumaNgu\" = father\n\nSo in (19): \"gubimbuluNunéanaymuNagu\" — may be \"the one that is always being offended\" → similar to \"Numa\" in being followed\n\nBut \"gubimbulu\" = offense?\n\nIn (6): \"gurugu\" = offended\n\nSo \"gubimbulu\" = offended? Possibly.\n\nAnd \"NunéanaymuNagu\" = the one that is always being blamed? — like \"NunéaymuNa\"\n\nSo \"gubimbuluNunéanaymuNagu\" = the one that is always being offended\n\n\"banéan\" = the one that is being followed?\n\nIn (16): \"Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ man that is always being followed is offending the strong father \n→ \"Numa\" = always being followed \n\"banéalmuNagu\" = strong father → so \"banéal\" = strong, \"muNagu\" = something?\n\nWait — \"banéal\" = strong? or \"banéan\" = being followed?\n\n\"banéan\" = being followed? \nIn (16): \"Numa guli baNgul yaó", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11990.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are given 17 sentences in Dyirbal with English translations, and we are to translate three new ones (17, 18, 19) into English.\n\nWe proceed step-by-step by identifying recurring patterns in the given examples.\n\n---\n\n**Step 1: Identify structure of the sentences**\n\nMost sentences follow a pattern:\n\n[Subject] + [verb] + [object] + [modifier phrase]\n\nThe verb often carries information about state or action. The modifier phrases typically describe the object (or subject) with a descriptive nominal clause.\n\nKey observations from the examples:\n\n- The verb is often part of a verb-stem followed by a classifier or complement.\n- The structure of nominal modifiers often follows: [X] + [that is always + Y] → used to describe a noun.\n- The modifiers are often of the form: \"that is always being X\" or \"that is always X\".\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \nHere, \"NunéaymuNa\" = \"that is always being blamed\", \"biNgunman\" = \"tired\"\n\nExample 2: \n\"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\" \n\"bimabanéalNaymuNa\" = \"that is always following\" \n\"bimabanéal\" = \"following\", \"NaymuNa\" = \"that is always\"\n\nSimilarly:\n- \"Nunéañu\" = \"death adders\"\n- \"bimabanéalNaymuNa\" = \"that is always following [something]\"\n\n\"bimabanéal\" = \"following\", \"NaymuNa\" = \"that is always\" → \"that is always following\"\n\nSo the suffix \"-NaymuNa\" = \"that is always\" (appears in many modifiers)\n\nSimilarly, \"NunéaymuNa\" = \"that is always being blamed\" \n\"Nunéañu\" = \"death adders\" → \"the mother that is always following death adders\"\n\nAnother pattern:\n- \"NunéaymuNa\" → \"that is always being blamed\"\n- \"Nunéañu\" → \"that is always following death adders\" — wait: \"NaymuNa\" = \"that is always\" \nSo likely \"NaymuNa\" = \"that is always\"\n\nAlso, \"bimabanéalNaymuNa\" = \"that is always following\"\n\nSimilarly:\n- \"malayigara\" in example 5 → smoke\n- \"gurugugu\" in example 1 → booze\n- \"waymin\" in example 3 → sugar\n- \"diban\" → fat\n- \"duNan\" → big\n- \"diban\" → fat\n- \"biba\" → X is being ignored? \"NaéilmuNagu\" = being ignored?\n\nIn example 11: \n\"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" \n→ \"The mother that is always being ignored is carrying the sugar\" \n\"NaéilmuNagu\" = \"being ignored\" → indicator of passive or state\n\nSo:\n- \"NaymuNa\" = \"that is always\"\n- \"NaéilmuNagu\" = \"being ignored\" → passive state\n- \"Nunéañu\" = death adders (noun)\n- \"guliNgu\" = following → \"that is always following\"\n- \"biNgunman\" = tired\n- \"éamiman\" = fat\n- \"baNgul\" = carrying\n- \"caNna\" → \"that is always being X\"\n\nAlso, from example 13: \n\"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ \"The mother-in-law that is always pushing stones is looking at the smoke.\" \n\"waymindu\" = pushing, \"dibanbilmbalNaymuNagu\" = that is always pushing stones → \"diban\" = fat → \"fat stones\"? \nWait, \"diban\" = fat, but here “dibanbilmbalNaymuNagu” — likely “the one that is always pushing stones” → “bilmbal” = pushing? \n\"bilmbal\" → push? \"bilmba\" appears in \"bilmban\" in (12), which is \"big stone\" → so possibly \"bilmba\" = stone\n\nBut “dibanbilmbal” → fat + stone + pushing? This is messy.\n\nLet’s focus on the word-forms that appear in (17), (18), (19):\n\n---\n\n**Sentence 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman**\n\nBreak down:\n- \"balan\" → likely \"the strong man\" (from example 2: \"balan yabu...\" = strong man is blaming)\n- \"ñalNga\" → what is \"ñalNga\"? \nCompare to example 15: \n\"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\" \n\"biñéiriñ\" = quiet → so \"ñalNga\" might be a similar modifier? \n\"ñalNga\" appears alongside \"ÑalNgaNgu\" → in 15: \"ñalNgaNgu\" = \"the quiet boy\" → \"ñalNga\" = quiet?\n\nWait: \"bayi biñéiriñ\" = quiet boy → but \"biñéiriñ\" = quiet \nSo \"biñéiriñ\" = quiet → so \"ñalNga\" might be \"quiet\"?\n\nCheck if \"ñalNga\" appears in other forms: \nIn 17: \"ñalNga\" → likely a noun or adjective.\n\nBut: \"balan ñalNga\" → \"the strong man [who is]\"?\n\n\"baNgul\" = carrying / following (from example 2, 3, 11, etc.)\n\n\"NumaNgu\" = something with \"Numa\" → what is \"Numa\"?\n\nIn example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\" \n\"Numa\" = \"always being followed\" → \"Numa\" = \"that is always being followed\"?\n\nYes: \"Numa\" appears with \"guli\" = \"following\", so \"Numa guli\" = \"that is always being followed\"\n\nIn 17: \"NumaNgu\" → likely \"that is always being followed\"\n\n\"guniymuNagu\" → what is this?\n\nCompare with:\n- \"guniñu\" in example 4: \"the little feather\" → \"guniñu\"\n- \"guniymuNagu\" → likely derived from \"guniñu\" with \"NaymuNa\"?\n\n\"guniymuNagu\" → likely \"that is always being [something]? or that is always [something]?\"\n\n\"guni\" may be a root.\n\nFrom example 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" \n→ \"The tired wallaby is searching for the little feather\" → \"guniñu\" → little feather\n\nSimilarly, \"guni\" = feather?\n\nYes → so \"guniñu\" = little feather\n\nSo \"guniymuNagu\" → modified with \"NaymuNa\" → \"that is always being [feather]-something\"\n\nWait: \"guniymuNagu\" → \"guni\" + \"ymuNagu\"? Perhaps \"ymuNagu\" = being? But “ymuNagu” not found.\n\nAlternative: likely \"guniymuNagu\" = \"that is always being [feather related]\" — but “y” vs “n”?\n\nIn example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ \"The big grasshopper is searching for the bent spear\" → \"guniñu\" = bent spear? But “guni” seems not to mean “spear”\n\nWait, “bundiñéu” = bent, “éagiñéu” = spear? \n\"éagiñéu\" = spear → possible.\n\nSo “guniñu” = “bent spear”? No — \"guniñu\" appears again in \"baliyila\" in 4 → \"little feather\"\n\nSo likely \"guni\" = feather\n\nThus \"guniymuNagu\" → possibly \"that is always being [feathered]\" or \"that is always [feather]\"\n\nBut → \"guniymuNagu\" → likely the same structure as \"NaymuNa\" → \"that is always\"\n\nSo: \"guniymuNagu\" = \"that is always being feathered\"? Unlikely.\n\nWait — could \"guni\" be a noun meaning “feather”?\n\nThen “guniymuNagu” = “the one that is always feathered”?\n\nBut “yangum” or “yam” is used elsewhere?\n\nAlternatively, consider that “NaymuNa” = “that is always” → so any phrase ending in “NaymuNa” likely means “that is always X”.\n\nNow, 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nElements:\n- \"balan\" → strong man (from example 2)\n- \"ñalNga\" → ? \n - In example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at tired lizard\"\n - \"biñéiriñ\" = quiet\n - So \"ñalNga\" → possibly “quiet”? But \"ñalNga\" is not “quiet” — \"biñéiriñ\" is quiet.\n\nBut why is \"ñalNga\" in the subject?\n\n\"balan ñalNga\" = \"the strong man who is [something]\"?\n\nWe need to find a noun/quality for \"ñalNga\".\n\nLook for other uses of \"ñalNga\".\n\nOnly example 15: \"ñalNgaNgu\" → \"quiet boy\"\n\nSo \"ñalNga\" = quiet → \"quiet\"?\n\nYes — \"ñalNga\" = quiet\n\nThen \"balan ñalNga\" = \"the strong quiet man\"\n\nThen \"baNgul\" = carries / follows\n\n\"NumaNgu\" = \"that is always being followed\"\n\n\"guniymuNagu\" = ? — what could this be?\n\n\"guniymuNagu\" — likely “that is always being [feathered]”? But doesn't fit.\n\n\"guni\" → feather → so \"guniymuNagu\" → \"that is always being feathered\"? \nBut \"feathered\" doesn’t quite work.\n\nAlternatively, could \"guni\" be a root meaning \"to be\" or \"existence\"?\n\nNo — earlier \"guniñu\" = feather (specific).\n\nWait — perhaps “guniymuNagu” is a mistake in parsing.\n\nWait: \"guniymuNagu\" → \"guniy\" + \"muNagu\"?\n\n“muNagu” → could be \"being\" or \"state\"?\n\nIn example 1: \"gurugugu biNgunman\" → \"making the man tired\"\n\n\"biNgunman\" = tired\n\nSo \"NaymuNa\" = that is always\n\nIn 17: \"guniymuNagu\" — structure: \"guni\" + \"ymuNagu\"\n\nCompare with example 4: \"biNgundu guniñu\" → \"tired feather\"?\n\n\"biNgundu\" = tired, \"guniñu\" = feather\n\nSo \"biNgundu guniñu\" = \"tired feather\"\n\nSo \"guni\" = feather → so \"guniymuNagu\" = \"feather that is always being [something]?\"\n\nBut \"ymuNagu\" — is that a derived form?\n\nThen \"bambunman\" = fat\n\nIn example 3: \"éamiman\" = fat\n\nSo \"bambunman\" → fat\n\nThus:\n\nSentence 17: \"The strong quiet man is following the one that is always being followed, that is always feathered, who is fat?\"\n\nThat doesn't make sense.\n\nAlternatively, is \"guniymuNagu\" a modifier for “bambunman”?\n\nBut order is: NumaNgu guniymuNagu bambunman\n\nSo: [subject] carries [object that is always being followed, that is always feathered, and is fat]\n\nBut no clear connection.\n\nWait — could “guniymuNagu” be “that is always (feather-related)”?\n\nBut is there an alternative?\n\nAnother possibility: perhaps “guniymuNagu” is a misreading — but let’s consider that “guniy” = “feather”, and with “muNagu” = “being”?\n\nNo — no clear verb.\n\nBut in example 4: “bundinéu éagiñéu guniñu” → “bent spear, feather” — so “guniñu” = feather\n\nNo \"feathered\" usage.\n\nAlternatively, is “guniymuNagu” = “that is always [feather]”?\n\nBut then \"bambunman\" = fat\n\nSo object: the one that is always being followed, that is always feather, and is fat?\n\nBut why?\n\nWait — is there a verb that means “being followed” or “being feathered”?\n\nIn example 16: \"Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\nSo \"Numa\" + \"guli\" → “that is always being followed”\n\nSo \"Numa\" = always being followed → \"Numa\" used as adjective\n\nSimilarly, \"NumaNgu\" → might be the same → \"that is always being followed\"\n\nNow, \"guniymuNagu\" → structure: \"guni\" + \"ymuNagu\"\n\n\"ymuNagu\" → possibly \"being\" + \"something\"\n\nBut “yaóaNgu” → “being blamed” → “yaóaNgu” = being blamed\n\nSimilarly, “NaéilmuNagu” = being ignored\n\nSo “ymuNagu” → “being [something]”?\n\nYes — likely “being” suffix.\n\nSo “guniymuNagu” = “being feathered”?\n\nBut “feathered” is not a common trait.\n\nBut “guni” → feather → so “being feathered”?\n\nUnlikely in context.\n\nCould it be “that is always [feathered]” — as a state?\n\nStill odd.\n\nAnother possibility: “guni” is not “feather” — but root?\n\nWait — is there another reading?\n\nCould “guniymuNagu” be a noun meaning “feather” with “always”?\n\nThen “NumaNgu” = “always being followed”, “guniymuNagu” = “feather” or “feathered”?\n\nBut “bambunman” = fat\n\nSo phrase: \"that is always being followed, feather, and fat\"?\n\nStill odd.\n\nWait — perhaps the structure is:\n\n[Subject] is carrying [object] that is [X] and [Y]\n\nAnd X and Y are qualities.\n\nSo: The strong quiet man is carrying the one that is always being followed, that is always feathered, and is fat.\n\nBut no such thing in the examples.\n\nAlternative: perhaps \"guniymuNagu\" is \"that is always [being feathered]\" — but not used.\n\nWait — could it be that “guni” is used in other contexts?\n\nIn example 4: \"guniñu\" = \"little feather\"\n\nSo \"guni\" = feather\n\nSo “guni” is only a noun meaning feather.\n\nSo in \"guniymuNagu\", “guni” = feather, “ymuNagu” = “being” or “that is always being”?\n\nBut “ymuNagu” → not present.\n\nIs there a form like “yam” or “ya”?\n\nExample: \"yaóaNgu\" = being blamed — \"ya\" is root\n\n\"NaéilmuNagu\" = being ignored\n\nSo \"ymuNagu\" — \"y\" + \"muNagu\" — likely a variant of “being”\n\nSo perhaps \"guniymuNagu\" = \"being feathered\"\n\nBut then object = “the one that is always being followed, being feathered, and is fat”\n\nStill not meaningful.\n\nWait — perhaps the whole phrase \"NumaNgu guniymuNagu bambunman\" is a compound noun phrase modifying the object.\n\nBut not supported.\n\nAlternative idea: is there a verb missing?\n\nNo — structure is clear: [subject] [verb] [object with attributes]\n\nSo for 17: \nSubject: balan ñalNga = strong quiet man \nVerb: baNgul = carrying \nObject: NumaNgu guniymuNagu bambunman = the one that is always being followed, that is always being feathered, and is fat?\n\nBut no such object.\n\nUnless “guniymuNagu” is actually “that is always (feather-related)”, but that doesn't help.\n\nWait — what about example 14: \n\"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ \"The big grasshopper is searching for the bent spear, feather\"\n\nHere, \"bundiñéu éagiñéu guniñu\" = bent spear feather → perhaps \"feather\" is the last object?\n\nBut no.\n\nAnother possibility: “guniymuNagu” is a typo or misreading — but all are given.\n\nWait — could “guniymuNagu” be “that is always [followed]” — like “Numa”?\n\nBut “Numa” already has that.\n\nNo.\n\nPerhaps “guniymuNagu” = “that is always fat”?\n\nBut “bambunman” = fat → so “bambunman” is fat.\n\nSo why repeat", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12247.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze the core structure of Dyirbal sentences.\n\nAll sentences follow a basic pattern: \n[adjective/agent] [verb] [object/subject with modifier] [event/result].\n\nThe verb often appears in a form like \"baNgul\" (to follow), \"baNgu\" (to make), \"yabu\" (to blame), \"gurugugu\" (to make tired), etc.\n\nNote that:\n- \"baNgul\" commonly means \"to follow\" or \"to search for\" (e.g. 4, 9, 10, 18).\n- \"baNgu\" appears in constructs like \"baNgu gurugugu\" meaning \"is making tired\".\n- \"babi\", \"bayi\", \"balan\", \"bala\" are subject markers. \"bayi\" = thing/boozing entity; \"balan\" = strong man; \"bala\" = animal or individual; \"bala\" often appears with agentive role.\n\nStep 2: Identify function of each element.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n\"yaóa\" = booze; \"NunéaymuNa\" = is always being blamed; \"baNgu\" = makes; \"gurugugu\" = tired; \"biNgunman\" = the man.\n\nSo: baNgu = makes → \"is making\"\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ \"Smoke is making the scorpion tired\" \n\"malayigara\" = smoke; baNgu = makes; garandu = scorpion; biNgunman = tired.\n\nThus, baNgu → makes → resource → X → tired (or affected)\n\nExample 9: \n\"bala garan baNgul biñéiriñéu banéan\" \n→ \"The lizard is following the smoke\" \n\"garan\" = lizard; baNgul = following; biñéiriñéu = smoke; banéan = the thing.\n\n→ baNgul = follow → X → Y\n\nExample 10: \"balan duNan baNgul yiriñéilagu guniñu\" \n→ \"Dragonfly is searching for stinging tree\" \n→ duNan = dragonfly; baNgul = searching for; yiriñéilagu = stinging tree; guniñu = that.\n\n→ baNgul = search for → object.\n\nSo pattern: \n[S] [baNgul] [O] → S is following/searching for O \n[S] [baNgu] [O] → S is making O X (X = emotion/state)\n\nStep 3: Identify noun modifiers\n\n- \"NunéaymuNa\" = is always being blamed → relates to blame\n- \"yaóaNgu\" = always being followed → going to be followed\n- \"diban\" = fat\n- \"biñéiriñéu\" = smoke\n- \"numaNgu\" = always being followed\n- \"gugiña\" = always searching\n- \"bambun\" = fat\n- \"bambunman\" = fat (agent or patient)\n\nCompare with 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nBreak it down:\n- \"balan\" = strong man (subject)\n- \"ñalNga\" = appears to be a noun; look at similar forms\n- \"baNgul\" = following\n- \"NumaNgu\" = is always being followed\n- \"guniymuNagu\" = ? → appears like \"guni\" + \"ymuNa\" → similar to \"guli\" = following\n- \"bambunman\" = fat\n\nIn 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"quiet boy is looking at the tired lizard\" \n\"biñéiriñ\" = quiet; \"biNgun\" = tired; \"baNgul\" = looking at; \"ñalNgaNgu\" = lizard; \"mugurugu\" = tired\n\nSo \"ñalNga\" = lizard \n→ thus \"ñalNga\" = lizard\n\nSo in 17: \n\"balan ñalNga\" = the strong man is doing something to the lizard. \n\"baNgul\" = is following \n\"NumaNgu\" = is always being followed \n\"guniymuNagu\" → likely \"is always being followed\" (guni = follow) \nbut \"guniymuNagu\" → appears similar to \"NumaNgu\" — \"Numa\" = always being followed?\n\nBut \"Numa\" = \"always being followed\"? \nIn 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father\" \n\"Numa\" = always being followed → \"Numa\" → agent being followed\n\nSo \"Numa\" = \"always being followed\", so \"NumaNgu\" = \"is always being followed\"\n\nNow in 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nWe have:\n- balan = strong man\n- ñalNga = lizard\n- baNgul = following\n- NumaNgu = is always being followed\n- guniymuNagu = ? → guni = follow, ymuNagu = ? → must be a modifier\n- bambunman = fat\n\nCheck if \"guniymuNagu\" = \"is always being followed\"? \n\"Numa\" = always being followed → \"Numa\" = follows? — no.\n\nLook for other \"guni\" forms:\n\nIn 16: \"guli\" → \"is following\", \"guli\" = following\n\nIn 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"tired wallaby is searching for little feather\" → guniñu = little feather\n\nIn 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → \"death adder that is always searching for scorpions is following the possum\" \n\"midin\" = always searching for → \"midin\" = always searching for\n\n\"malayigaraguninaymuNagu\" = scorpion → a long form.\n\nSo \"gurugugu\" = tired; \"gubimbulu\" = tired? In 8: \"bayi gubimbulu biNgun baNgu gurugugu éagunman\" → \"boozing is making the tired doctor fall asleep\" → \"gubimbulu\" = tired\n\nAh — many adjectives:\n\n- gurugugu → tired\n- gubimbulu → tired\n- biNgun → tired\n- bambun → fat\n- diban → fat\n- numa → always being followed\n- yaóa → booze\n- yaabu → strong\n- malayigara → smoke\n\nSo adjectives:\n- \"tired\" = gurugugu, gubimbulu, biNgun\n- \"fat\" = bambun, diban\n- \"always being blamed\" = NunéaymuNa\n- \"always being followed\" = NumaNgu\n\nIn 17: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\" — similar structure?\n\n18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\nBreak down:\n- bala = animal/subject\n- diban = fat\n- bilmbalmuNa = ? → bilmba = big stone? bilmbal = big stone?\n- baNgun = is making\n- biñéiriñéu = lizard\n- guniñu = little feather?\n\nWait — in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law that always pushes stones is looking at smoke\" \n\"waymindu\" = always pushing; \"dibanbilmbalNaymuNagu\" = mother-in-law who always pushes stones\n\nSo \"dibanbilmbal\" → fat and pushing stones\n\nThus, in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject\n\"diban\" = fat\n\"bilmbalmuNa\" → likely \"one who is pushing big stones\" → \"bilmbal\" = stone; \"muNa\" = being\n→ \"bilmbalmuNa\" = is pushing stones\n\"baNgun\" = is making\n\"biñéiriñéu\" = lizard\n\"guniñu\" = little feather (from 4)\n\nBut in 13, \"dibanbilmbalNaymuNagu\" = mother-in-law who always pushes stones → so \"bilmbal\" = stone, \"diban\" = fat, \"NaymuNagu\" = always does\n\nSo in 18: \"bilmbalmuNa\" = is pushing stones\n\nSo full meaning: \"The fat person (who is pushing stones) is making the lizard look for little feather?\"\n\nBut \"is making\" → baNgun → \"is causing\"\n\nSo \"diban\" = fat → \"fat one who pushes stones\" → is making the lizard search for little feather?\n\nBut \"look for\" is not normal; before, \"baNgul\" is follow/search\n\nBut here baNgun = make → so \"is making [lizard] look for feather\"\n\nBut in English, \"is making [X] search for Y\" is a common construction.\n\nIn 11: \"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" → \"mother always ignored is making sugar carry the strong father\" → sugar makes strong father carry?\n\nWait — \"yabuNgu\" = strong father? \"NaéilmuNagu\" = is always carrying?\n\nSo baNgun = makes → subject makes object do X\n\nIn 11: \"makes\" → sugar makes strong father carry\n\nSo yes, baNgun = makes\n\nThus 18: \"The fat person who is pushing stones is making the lizard search for little feather\"\n\nBut \"bilmbalmuNa\" = is pushing stones → \"is pushing\" — could be present, implying habitual\n\n\"guniñu\" = little feather → from 4\n\nSo b.2: \"The fat person who is pushing stones is making the lizard search for the little feather.\"\n\nNow 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\n\"bayi\" = booze/agent\n\"bargan\" = ? \nLook at similar words:\n- in 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"man that is always being followed is offending the strong father\"\n- in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at the tired lizard\"\n\nSo \"bargan\" — not directly seen.\n\nBut in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law who is always pushing stones is looking at smoke\"\n\n\"garan\" = lizard\n\nIn 19: \"bargan\" — perhaps a noun?\n\nIn 15: \"ñalNga\" = lizard → so bargan may be similar?\n\nIn 13: \"garan\" = lizard → so \"bargan\" could be a variant?\n\nCompare: \n\"garan\" and \"bargan\" — differ by 'b' to 'ba'? Possibly a variant.\n\nCheck 19: \n\"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\n\"bayi\" = booze \n\"bargan\" = ? \n\"baNgul\" = following \n\"yaóaNgu\" = strong father (from 16: \"yaóaNgu\" = strong father) \n\"gubimbuluNunéanaymuNagu\" → gubimbulu = tired → \"tired\" + \"NunéanaymuNagu\" = that is always being blamed? \nNunéanaymuNagu = always being blamed\n\nSo \"gubimbuluNunéanaymuNagu\" = the tired one that is always being blamed \n\"banéan\" = the thing — what?\n\nIn 1: \"biNgunman\" = tired man \nIn 7: \"biNgun baNgu\" — tired doctor\n\n\"banéan\" = the possum? From 7: \"banéan\" at end → \"is following the possum\"\n\nSo \"banéan\" = the possum\n\nSo: \"booze is following the strong father who is tired and always being blamed, and is following the possum?\"\n\nBut it says: \"baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nSo: \"is following the strong father who is tired and always being blamed\" → and \"is following the possum\"?\n\nSeems redundant.\n\nBut structure: [S] baNgul [O1] [O2] → may be two objects?\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at the tired lizard\" → one object\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke → one object\n\nSo in 19: only one \"baNgul\"? \n\"baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\nPossibly: \"is following the strong father who is tired and always being blamed\" → and \"the possum\"?\n\nBut writing it as two nouns?\n\nBut no preposition.\n\nAll examples have one verb.\n\nIn 15: \"looking at\" → baNgul with \"at\" implied\n\nIn 9: \"is following smoke\"\n\nIn 19: \"is following the strong father who is tired and always being blamed\" and \"is following the possum\"?\n\nUnlikely.\n\nPossibly \"baNgul\" applies to both?\n\nBut ergative structure?\n\nLook at 1: \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ booze makes the man being blamed tired\n\nSo baNgu → makes\n\nBut in 19: baNgul → following → so the object is what is being followed.\n\nSo \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\n→ \"booze is following the strong father who is tired and always being blamed\" and the possum?\n\nBut way too many objects.\n\nPossibility: \"bargan\" = lizard? As in 13: \"garan\" = lizard → \"bargan\" may be a variant spelling.\n\nBut \"bargan\" ≠ \"garan\"\n\nIn 7: \"bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan\" → \"death adder that always searches for scorpions is following possum\"\n\nSo \"baNgul\" → following something\n\nIn 19: \"bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\"\n\n→ if bargan = lizard → \"lizard is following strong father who is tired and always being blamed\"\n\nThen banéan = possum?\n\nBut no \"following possum\" in the sentence.\n\nIn 7: \"death adder is following possum\" → so \"following\" + object\n\nSo if only one baNgul, then only one object.\n\nThus: \"booze is following the strong father who is tired and always being blamed\"\n\n\"banéan\" = the possum, but not followed?\n\nBut in 7: \"is following the possum\"\n\nSo perhaps the possum is the object of \"following\".\n\nSo \"bargan\" must be the subject.\n\n\"bayi\" cannot be subject of \"baNgul\" — in 1: \"bayi\" = booze, not doing following.\n\nIn 15: \"bayi\" = quiet boy, doing \"looking at\"\n\nIn 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → subject is \"quiet boy\", doing \"looking at\"\n\nIn 16: \"bayi Numa\" → agent\n\nSo \"bayi\" is agent.\n\nSo in 19: \"bayi bargan\" → \"booze\" and \"bargan\"? → two nouns?\n\nNo — likely \"bargan\" is a noun, and \"bayi\" is agent.\n\n\"bayi bargan\" = booze is referenced only if \"bayi\" is subject.\n\nBut in 15: \"bayi\" = subject (quiet boy)\n\nIn 1: \"bayi\" = subject (booze)\n\nIn 1: \"bayi yaóa\" = \"booze is making\"\n\nSo in 19: \"bayi bargan\" — perhaps \"booze\" is subject? Then \"bargan\" = object?\n\nBut \"baNgul\" → following, so if \"bayi\" is following, then \"bargan\" = object.\n\nBut \"bargan\" not in known list.\n\nEarlier: \"garan\" = lizard → so \"bargan\" could be a variant form.\n\nIn 13: \"bala garan\" = mother-in-law is following smoke.\n\nIn 19: \"bayi bargan\" → if \"bargan\" = lizard, then \"booze is following the lizard\"?\n\nThen \"baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan\" → but follows whom?\n\nNo — \"baNgul\" applies only once.\n\nStructure: \"S baNgul O\" → S is following O\n\nSo in 19:", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11752.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Analyze the grammatical structure and semantic roles in the given examples.\n\nLook at the first sentence:\n1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n→ \"Booze is making the man that is always being blamed tired.\"\n\nStructure: [subject] [verb] [modifier of the thing being affected] [effect].\n\n\"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = making → appears as a linking structure \n\"gurugugu\" = tired → effect\n\nSo: [X] is making [Y] [effect].\n\nPattern: [A] [verb] [B] [effect], where A is a thing causing an effect on B.\n\nIn sentence 2:\n2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"balan\" = strong man (subject) \n\"yabu\" = is blaming \n\"bimabanéalNaymuNa\" = mother that is always following \n\"baNgul\" = the (relative or inherent relation) \n\"yaóaNgu\" = that is always following \n\"guliNgu\" = death adders → object\n\nSo: [subject] is blaming [object] that is always [follows].\n\nBut \"baNgul\" seems to mark possession or relation to a nominal, and \"yabu\" is the verb.\n\nNote: In 1, \"baNgu\" appears with \"gurugugu\" (tired), likely as \"X is making Y tired\".\n\nIn 3: \n3. balan waymin bambun baNgu éugaNgu éamiman. \n→ \"Sugar is making the healthy mother-in-law fat.\"\n\n\"waymin\" = sugar \n\"bambun\" = the healthy mother-in-law \n\"baNgu\" = making \n\"éugaNgu\" = fat\n\nSo: [A] is making [B] [effect]\n\nIn 4: \n4. bala yila wura baNgul bargandu biNgundu guniñu. \n→ \"The tired wallaby is searching for the little feather.\"\n\n\"bala\" = tired wallaby → subject \n\"yila\" = is searching \n\"wura\" = for \n\"baNgul\" = the \n\"bargandu\" = little feather\n\nSo: [subject] is searching for [object]\n\nIn 5: \n5. balan malayigara baNgu garandu biNgunman. \n→ \"The smoke is making the scorpion tired.\"\n\n\"balan\" = smoke \n\"baNgu\" = is making \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired — same pattern as 1 and 3.\n\nIn 6: \n6. bala gurugu baNgul NumaNgu munduNgu dimbañu. \n→ \"The offended father is carrying the booze.\"\n\n\"bala\" = offended father \n\"gurugu\" = is carrying \n\"baNgul\" = the \n\"NumaNgu\" = booze\n\nSo: [subject] is carrying [object]\n\nIn 7: \n7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan. \n→ \"The death adder that is always searching for scorpions is following the possum.\"\n\n\"bayi\" = death adder \n\"midin\" = that is always searching for scorpions \n\"baNgun\" = is following \n\"banéan\" = possum\n\nSo: [X] that is [searching for Y] is following [Z]\n\nIn 8: \n8. bayi gubimbulu biNgun baNgu gurugugu éagunman. \n→ \"Booze is making the tired doctor fall asleep.\"\n\n\"bayi\" = booze \n\"gubimbulu\" = tired \n\"biNgun\" = is making \n\"baNgu\" = the \n\"gurugugu\" = fall asleep\n\nSo: [X] is making [Y] tired → [Y] is tired → effect\n\nIn 9: \n9. bala garan baNgul biñéiriñéu banéan. \n→ \"The lizard is following the smoke.\"\n\n\"bala\" = lizard \n\"garan\" = is following \n\"baNgul\" = the \n\"biñéiriñéu\" = smoke\n\nSo: [subject] is following [object]\n\nIn 10: \n10. balan duNan baNgul yiriñéilagu guniñu. \n→ \"The dragonfly is searching for the stinging tree.\"\n\n\"balan\" = dragonfly \n\"duNan\" = is searching for \n\"baNgul\" = the \n\"yiriñéilagu\" = stinging tree\n\nSo: [subject] is searching for [object]\n\nIn 11: \n11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu. \n→ \"The mother that is always being ignored is carrying the sugar.\"\n\n\"bala\" = mother \n\"éuga\" = that is always being ignored \n\"baNgun\" = is carrying \n\"yabuNgu\" = sugar\n\nSo: [subject] is carrying [object]\n\nIn 12: \n12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban. \n→ \"The fat doctor is pushing the big stone.\"\n\n\"bala\" = fat doctor \n\"diban\" = fat \n\"éagiñ\" = is pushing \n\"baNgul\" = the \n\"gubimbulugu\" = big stone\n\nSo: [subject] is pushing [object]\n\nIn 13: \n13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan. \n→ \"The mother-in-law that is always pushing stones is looking at the smoke.\"\n\n\"bala\" = mother-in-law \n\"garan\" = is looking at \n\"baNgun\" = the \n\"waymindu\" = that is always pushing \n\"dibanbilmbalNaymuNagu\" = stones \n\"buóan\" = smoke\n\nSo: [subject] is looking at [object]\n\nIn 14: \n14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu. \n→ \"The big grasshopper is searching for the bent spear.\"\n\n\"balan\" = big grasshopper \n\"baNgay\" = is searching for \n\"waóu\" = the bent spear? \n\"baNgun\" = the \n\"bundiñéu\" = bent spear \n\"éagiñéu\" = ? → seems to be part of noun, possibly \"bent\"\n\n\"waóu\" likely describes \"bundiñéu\", meaning \"bent spear\"\n\nSo: [subject] is searching for [object]\n\nIn 15: \n15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan. \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"bayi\" = quiet boy \n\"biñéiriñ\" = is looking at \n\"biNgun\" = is making \n\"baNgul\" = the \n\"ñalNgaNgu\" = tired \n\"mugurugu\" = lizard\n\nWait — structure seems off.\n\n\"biñéiriñ\" = is looking at \n\"baNgun\" = is making → perhaps a second verb?\n\nBut \"ñalNgaNgu\" = tired → so \"is making [X] tired\"?\n\nNo: \"the quiet boy is looking at the tired lizard.\"\n\nSo: [subject] is looking at [object that is tired]\n\nSo: [X] is looking at [Y], where Y is tired.\n\n\"biñéiriñ\" = looking at \n\"baNgul\" = the \n\"ñalNgaNgu\" → tired \n\"mugurugu\" → lizard\n\nSo: \"the quiet boy is looking at the tired lizard\"\n\nSo \"baNgul\" used with noun to mark possession or close reference.\n\nIn 16: \n16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman. \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"bayi\" = man \n\"Numa\" = that is always being followed \n\"guli\" = is offending \n\"baNgul\" = the \n\"yaóaNgu\" = strong father\n\nSo: [subject] is offending [object]\n\nNow examine the words used in the target:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\n\"balan\" = likely a noun (subject) \n\"ñalNga\" = quiet? (from 15: biñéiriñ → quiet boy) \n\"baNgul\" = the \n\"NumaNgu\" = that is always being followed? (from 16: Numa → always being followed) \n\"guniymuNagu\" = ? \n\"bambunman\" = fat? → from 3: \"bambun\" = healthy mother-in-law, but \"bambunman\" = fat? \nPossibly \"bambunman\" = fat\n\nFrom 3: \"bambun\" = healthy mother-in-law \nBut \"bambunman\" likely = fat (suffix \"-man\" for fat?)\n\nFrom 15: \"biñéiriñ\" = quiet → \"ñalNga\" = quiet?\n\nIn 15: \"biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"quiet boy is looking at tired lizard\"\n\n\"ñalNgaNgu\" = tired → \"ñalNga\" = quiet? No — \"ñalNgaNgu\" = tired\n\nSo \"ñalNga\" is not quiet.\n\nWait — in 15: the boy is \"quiet\" — \"biñéiriñ\" = is looking at → \"quiet boy\" → so the adjective \"quiet\" is separate.\n\nSo \"biñéiriñ\" = quiet? Or is it the action?\n\nPossibly \"biñéiriñ\" = quiet → but in the sentence it's a verb: \"is looking at\"\n\nSo likely, \"biñéiriñ\" = is looking at \nAnd \"ñalNga\" = quiet? But then \"ñalNgaNgu\" = quiet → but in 15 it's \"tired\"\n\n\"ñalNga\" appears as a noun in 17.\n\nIn 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\n\"balan\" = subject (likely a person or thing) \n\"ñalNga\" = noun (what?) \n\"baNgul\" = the \n\"NumaNgu\" = that is always being followed \n\"guniymuNagu\" = ? (like \"follows\" or \"searching\") \n\"bambunman\" = probably fat (from similar to \"bambun\" = healthy, \"bambunman\" = fat?)\n\nBut look at 11: \"bala éuga baNgun yabuNgu NaéilmuNagu dimbañu\" → mother that is always being ignored is carrying sugar.\n\n\"éuga\" = always being ignored → seems like a participle form\n\nIn 16: \"Numa\" = always being followed → \"Numa\" is a participle\n\nIn 17: \"NumaNgu\" = that is always being followed\n\nSo: [X] that is always being followed\n\n\"guniymuNagu\" → look for equivalent to \"searching\", \"looking\", \"following\"?\n\nIn 10: \"duNan\" = is searching for \nIn 13: \"waymindu\" = that is always pushing \nIn 14: \"baNgay\" = is searching for\n\n\"guniymuNagu\" — sounds like a participle or adjective meaning \"searching\" or \"looking\"?\n\nIn 15: \"biñéiriñ\" = looking at \nIn 13: \"garan\" = is looking at → \"garan\" in 13 and 9\n\n\"garan\" appears in:\n- 9: bala garan baNgul biñéiriñéu banéan → lizard is looking at smoke\n- 13: bala garan baNgun waymindu... → mother-in-law is looking at stone\n\nSo \"garan\" = is looking at\n\n\"biñéiriñéu\" = smoke → similar to \"biñéiriñéu\"\n\nIn 17: \"guniymuNagu\" — could it be a participle meaning \"is searching for\"?\n\nCompare with 10: \"duNan\" = is searching for → \"duNan\" \nIn 14: \"baNgay\" = is searching for\n\nIn 17: \"guniymuNagu\" → possibly \"is searching for\" or \"is looking for\"\n\n\"bambunman\" → from 3: \"bambun\" = healthy mother-in-law → \"bambun\" is a noun\n\n\"bambunman\" → likely means \"fat\" (as in 15: \"mugurugu\" = lizard, \"ñalNgaNgu\" = tired) → so \"man\" or \"fat\"?\n\nIn 3: \"bambun\" = healthy mother-in-law → \"bambun\" is the noun\n\nIn 17: \"bambunman\" → could be “a fat person”?\n\nBut in 3: \"bambun\" = healthy (which is opposite of fat)\n\nPerhaps \"bambunman\" = fat?\n\nIn 15: \"mugurugu\" = lizard → common noun\n\nIn 17: \"bambunman\" → likely describes the person → fat?\n\nSo reconstruct:\n\n\"balan\" = subject → likely a person \n\"ñalNga\" = quiet? or a noun?\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n\"ñalNgaNgu\" = tired → not quiet\n\nSo \"ñalNga\" is not quiet.\n\n\"ñalNga\" might be a noun like \"boy\" or \"child\"?\n\nIn 15: \"bayi\" = quiet boy\n\nSo \"ñalNga\" is not \"quiet\"\n\nPerhaps \"ñalNga\" is \"man\" or \"person\"?\n\nBut in 15, \"ñalNgaNgu\" = tired → so \"ñalNga\" likely modifies a noun\n\nSo in 17: \"balan ñalNga\" = the [X] that is [something]? Or \"X with attribute\"?\n\nWait — structure: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nPossibly: [X] [attribute] is [doing something to] [Y which has property Z]\n\nBut more likely: [subject] is [verb] [object with modification]\n\nIn 17, what is the verb?\n\n\"garan\" is \"is looking at\" \n\"yabu\" is \"is blaming\" \n\"duNan\" = is searching for \n\"gurugu\" = is carrying \n\"midin\" = is searching for scorpions \n\"éagiñ\" = is pushing\n\nIn 17: \"balan\" + \"ñalNga\" — both could be subject?\n\nPossibly \"balan\" is a noun (person), and \"ñalNga\" is a participial modifier or another noun.\n\nBut \"balan\" and \"ñalNga\" both look nominal.\n\nPerhaps \"balan\" is the subject, and \"ñalNga\" is an attribute like \"the quiet one\"?\n\nBut no \"quiet\" in the derivation.\n\nIn 15: \"biñéiriñ\" = looking at → verb\n\nBut in 17, no verb?\n\nWait — the sentence: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nPossibly: [X] is [doing something to Y]\n\nBut no verb?\n\nWait — no verb? That can't be.\n\nUnless \"baNgul\" is not a preposition.\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is looking at smoke\"\n\n\"baNgul\" is the article before \"biñéiriñéu\", which is the object.\n\nSo in 17: \"baNgul\" likely precedes a noun.\n\nSo likely: [A] [B] is [doing something to] [C that has property D]\n\nThe verb might be \"guniymuNagu\"?\n\n\"guniymuNagu\" — similar to \"guniymu\" in 10: \"guniñu\" = little, \"yiriñéilagu\" = stinging tree\n\n\"guni\" = little, \"ymu\" might be a suffix.\n\nBut in 14: \"bundiñéu\" = bent spear → \"bundi\" = bent\n\nIn 14: \"baNgay\" = is searching for → \"baNgay\" is verb\n\nBut in 17, what is the verb?\n\nPerhaps \"guniymuNagu\" = is searching for?\n\nCompare with 10: \"balan duNan baNgul yiriñéilagu guniñu\" → man is searching for stinging tree.\n\n\"duNan\" = searching for\n\nSo \"duNan\" is verb\n\n\"guniymuNagu\" → might be \"is searching for\"?\n\nIn 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\nPerhaps: [A] [is searching for] [B that has property C]\n\nBut what is the subject? \"balan\" or \"balan ñalNga\"?\n\n\"balan\" is often a subject (in 2, 5, 6) \n\"ñalNga\" is not a verb.\n\nAnother possibility: \"balan\" = man, \"ñalNga\" = the one who is [something]\n\nBut in 15: \"bayi biñéiriñ biNgun baNg", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11385.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Identify relevant verb forms from the given list.\n\nWe are to translate:\n1. \"I begin to eat it\"\n2. \"we1+2 lay it flat by hand\"\n3. \"he digs a hole\"\n4. \"he walks out\"\n\nStep 2: Find verb roots matching the meaning.\n\nFirst translation: \"I begin to eat it\"\n\nLook for verbs related to “begin” and “eat”.\n\n- \"kewǣpeqtaq\" = we1+2 begin → root \"kewǣp\" + \"eqtaq\" (perhaps \"begin\")\n- \"wǣpohnæw\" = he begins walking → \"wǣp\" = begin; \"ohnæw\" = walking\n- \"kewǣpānæhkæq\" = we1+2 begin to dig → \"kewǣp\" + \"ānæhkæq\" → implies \"begin to dig\"\n\nNote: \"begin\" is encoded in roots like \"kewǣp\", \"wǣp\".\n\n\"Eat\" or \"bite\" is related to \"kēska\" or \"keq\" forms.\n\nLook for “bite” or “gnaw”.\n\n- \"kekǣtohnæq\" = we1+2 walk out\n- \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it\n- \"kekēskahtæq\" = we1+2 bite it through\n\nSo “bite” is in \"ketāwahtæq\" and \"kekēskahtæq\"\n\nBut we need “I begin to eat it” — that is, initiate eating.\n\n\"to eat\" is likely “gnaw” or “bite”\n\nBut the verb in the list that means \"bite\" is \"ketāwahtæq\" (we1+2 bite, gnaw a hole in it)\n\nSo \"I begin to eat it\" = \"I begin to bite it\" → need \"begin\" + \"bite\"\n\n\"begin\" = \"kewǣp\" (in \"kewǣpeqtaq\", \"wǣpohnæw\")\n\nBut \"begin\" for \"I\" (singular) — the form \"kewǣp\" is used in \"we1+2\" (inclusive plural)\n\nWe need singular \"I\" + begin + eat.\n\nIs there a “begin” form for singular “I”?\n\nNo direct form, but \"kewǣp\" may be used with subject markers.\n\nIn Menominee, verbs are often inflected for subject.\n\nLook for a verb with \"begin\" + \"bite\" or \"eat\".\n\n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → so it means “bite”.\n\nBut we need to “begin to bite”.\n\nWe have \"begin\" in \"kewǣpeqtaq\" (we1+2 begin)\n\nSo perhaps we can take \"kewǣp\" + \"āwaht\" (from ketāwahtæq) → “begin to bite”\n\nBut is there a singular form?\n\nNo such form directly given.\n\nBut the grammar may allow \"kewǣp\" to be used with \"I\" subject with specific form.\n\nWait — check for \"eat\" directly.\n\nIs there a verb for “eat”?\n\n\"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths → implies eating.\n\nSo bringing in mouth = eating.\n\nBut \"kepītahtæq\" has \"come eating\" or \"bring in mouth\" — not “begin to eat”.\n\nBut \"kepītahtæq\" has “eating” as verb.\n\nCould “begin to eat” be “begin to bring in mouth”?\n\nThat seems stretched.\n\nAlternatively, “bite” is close to “eat” (especially gnawing).\n\n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it\n\nSo perhaps “I begin to bite it” is acceptable as “I begin to eat it”\n\nSo possibility: \"kewǣp\" + \"āwaht\" → but \"āwaht\" is in \"ketāwahtæq\"\n\nBut which form does \"kewǣp\" take for \"I\"?\n\nLook at other forms:\n\n\"kewǣpeqtaq\" = we1+2 begin → plural\n\n\"ne...\" forms for singular \"I\"\n\n\"nekāweqtam\" = I lie down\n\n\"nekāwāhpem\" = I fall over laughing\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"nepītohnæm\" = I walk here\n\nSo I verbs start with \"ne...\"\n\nFor \"begin\" — is there a form?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"kewǣp\" + \"ānæhkæq\" = begin to dig\n\nSo \"kewǣp\" is likely the stem for \"begin\"\n\nAnd \"kewǣp\" is used in plural (we1+2), so for singular, we might need \"ne\" or another prefix.\n\nBut no expression for \"begin to eat\" directly.\n\nBut \"begin to eat\" → start to eat.\n\nThe closest semantic match is \"begin to bite\".\n\nBut \"bite\" is expressed in \"ketāwahtæq\" (we1+2)\n\n\"begin to bite\" = kewǣp + ketāwaht?\n\nBut is there a \"begin\" form for \"I\"?\n\nNo form provided.\n\nBut note: \"kewǣp\" is the base for \"begin\", and it may be used with a stem.\n\nAlternatively, look at \"wǣpohnæw\" = he begins walking → \"wǣp\" = begin, \"ohnæw\" = walking\n\nSo \"wǣp\" = begin\n\nSo “he begins walking” = \"wǣpohnæw\"\n\nSo “I begin to eat” could be: \"wǣp\" + \"āwaht\" → but “āwaht” is part of “ketāwahtæq”\n\nIs “āwaht” the root of “bite”?\n\nNote: \"ketāwahtæq\" → \"ketāwaht\" + \"æq\"\n\nSimilarly, \"kekēskahtæq\" → \"kekēskaht\" → “bite through”\n\nSo “bite” root = “keta-waht”?\n\nBut \"wǣp\" + \"āwaht\" = \"wǣpāwaht\" — not directly in list.\n\nBut perhaps the verb “begin to eat” is “wǣpāwaht”?\n\nBut we need to see if “eat” or “bite” is the best fit.\n\nNo direct verb for “eat”.\n\n\"kepītahtæq\" = we1+2 come eating it → eating behavior\n\nSo perhaps not.\n\nThus, “I begin to eat it” most plausibly means “I begin to bite it”\n\nSo form: \"wǣpāwaht\" — begin to bite\n\nBut “wǣp” is used in “wǣpohnæw” for “he begins walking”\n\nSo “wǣp” can be used independently.\n\nAnd “āwaht” from “ketāwahtæq” → bite\n\nSo “wǣpāwaht” → he begins to bite? → but that's \"he\"\n\nWe need \"I\"\n\nSo need \"I\" subject.\n\nBut \"kewǣp\" is more common in we1+2.\n\nIs there a stem for \"I\"?\n\nWe have:\n- \"nekǣtahan\" = I pry it out by tool\n- \"nepītohnæm\" = I walk here\n- \"nekāweqtam\" = I lie down\n\nSo “I” verbs start with “ne”\n\nBut “begin” does not appear with “ne”\n\nFrom the list, \"kewǣpeqtaq\" — “we1+2 begin” — has “kewǣp”\n\nNo “ne” + “begin”\n\nSo no direct “I begin” form.\n\nBut perhaps the root “kewǣp” is used with subject prefix.\n\nBut “kewǣp” is clearly used in plural.\n\nAlternatively, is there an alternate root for “begin”?\n\n“wǣpohnæw” = he begins walking\n\nSo “wǣp” = begin\n\nSo use “wǣp” as the stem, and for “I” — perhaps “ne” + “wǣp”?\n\nLike “nekewǣp”?\n\nNot in list.\n\nBut no example shows “I begin” — so must infer pattern.\n\nBut every action has a subject.\n\nWe can use the stem “wǣp” + verb of eating.\n\nBut “eat” not directly available.\n\nBut “bite” is available.\n\n“begin to bite” → best fit.\n\nSo for “I begin to eat it” → “I begin to bite it”\n\nStem: “wǣp” + “āwaht” → “wǣpāwaht”\n\nBut must assign subject.\n\nIn Menominee, \"I\" may be marked by a prefix.\n\nBut no example shows “I begin” — so perhaps the “kewǣp” root is used universally, but adjusted.\n\nWait — is “begin” a separate root?\n\nIn “kewǣpānæhkæq” = begin to dig\n\n“kewǣpeqtaq” = begin\n\nSo “kewǣp” = begin\n\nSo for “I”, is there a form?\n\nNo.\n\nBut perhaps the “kewǣp” form is used with subject prefixes, though not provided.\n\nBut we must derive from given examples.\n\nFor “I”, singular, “begin” may be missing.\n\nBut perhaps “wǣp” is the root.\n\nAnother idea: “kepītahtæq” = we1+2 come eating it — so eating = in mouth\n\n“come eating” = bring in mouth\n\nSo \"begin to eat\" → perhaps \"begin to bring in mouth\"?\n\nSo \"kewǣp\" + \"epītaht\"?\n\nBut \"epītaht\" not in list.\n\n\"kepītahtæq\" = bring in mouth\n\nSo “begin to bring in mouth”?\n\nBut “bring in mouth” is a stretch for “eat”.\n\nBut “eat” is not directly named.\n\nSo proceed to next one.\n\nSecond: “we1+2 lay it flat by hand”\n\nWe want “we1+2” + “lay flat” + “by hand”\n\nLook for verbs with “lay flat”.\n\n“nepītohnæm” = I walk here — not relevant\n\n“pāhkeqtaw” = he opens up\n\n“pāhkaham” = he opens it by tool\n\n“tawǣsam” = he cuts a hole in it\n\n“pahkǣsam” = he cuts it off\n\n“nekǣtahan” = I pry it out by tool\n\n“pītenam” = he passes it here\n\n\"kepītahtæq\" = we1+2 come eating it — eating\n\nIs there a verb for “lay flat”?\n\nNo direct form.\n\n“lay flat by hand” — similar to “place” or “set down”.\n\n“by hand” may be implied by “hand”.\n\nLook for verb with “place”.\n\n“pāhkeqtaw” = he opens up — opening\n\n“pāhkaham” = opens it by tool\n\nNo.\n\n“kewǣpānæhkæq” = we1+2 begin to dig — digging\n\nBut “lay flat” is close to “put down”.\n\nNo root.\n\nAnother possibility: “lay” like “set”.\n\nBut not in list.\n\nWait — “we1+2 walk out” is in list — \"kekǣtohnæq\" = we1+2 walk out\n\nSo “walk out” = kekǣtohnæq\n\nBut we need “we1+2 lay it flat by hand”\n\nNo such verb.\n\nBut perhaps “place” is found in “kēskenam” = he breaks it through by hand — “break through by hand”\n\n“pītenam” = he passes it here — not.\n\nPerhaps “lay flat” is not directly translatable — but must find.\n\nWait — look at “pahkǣsam” = he cuts it off\n\n“tawǣsam” = he cuts a hole in it\n\n“pāhkaham” = opens it by tool\n\n“kekēskahtæq” = we1+2 bite it through\n\nIs there a verb for “place”?\n\nNone.\n\nAlternative: “lay flat” may be “put down” — perhaps \"kepītaht\" → bring in mouth, not relevant.\n\nAnother idea: “we1+2 come eating it” = \"kepītahtæq\"\n\nSo “come eating” = bringing in mouth — so “eat” is encoded in that verb.\n\nBut “lay flat” not.\n\nBut perhaps a verb for “place” is missing.\n\nWait — is “lay flat” related to “set?\n\n“kewǣpānæhkæq” = begin to dig — digging\n\nNo.\n\nPerhaps “by hand” is key.\n\n“by hand” is in “kēskenam” — “he breaks it through by hand”\n\n“nekǣtahan” — “I pry it out by tool”\n\n“pāhkaham” — “by tool”\n\nSo “by hand” may be implied by absence of tool.\n\nBut no verb for “lay flat”.\n\nWait — perhaps “lay” is in “walk here”?\n\n“nepītohnæm” = I walk here\n\n“pītenam” = he passes it here — pass through\n\n“walk here” = place it here?\n\nNo.\n\nBut “lay it flat” might be a specific action.\n\nPerhaps no direct form — but must derive.\n\nAnother possibility: “we1+2 lay it flat” may be a compound of “set” or “place”.\n\nBut not available.\n\nGo to third: “he digs a hole”\n\nLook for “dig a hole”\n\n“kewǣpānæhkæq” = we1+2 begin to dig → “begin to dig”\n\n“pahkǣsam” = he cuts it off — not\n\n“tawǣsam” = he cuts a hole in it — cuts a hole\n\n“wackōhnæw” = he walks roundabout\n\n“pāhkaham” = opens it by tool\n\nSo “cut a hole” = tawǣsam\n\nBut “dig a hole”?\n\nIn Menominee, “dig” might not be same as “cut” — but “cut a hole” may be equivalent.\n\n“dig a hole” → possibly “tawǣsam”\n\nBut “tawǣsam” = he cuts a hole in it — so “cuts a hole” — very close to “dig a hole”\n\nSo feasible.\n\nSo “he digs a hole” → “tawǣsam”\n\nFourth: “he walks out”\n\nWe have \"kekǣtohnæq\" = we1+2 walk out\n\nSo “he walks out” → not directly.\n\nBut is there a form for “he walks out”?\n\n\"kekǣtohnæq\" = we1+2 walk out\n\nSo for “he” — must infer.\n\nBut no singular “he walks out” form.\n\nBut “walk out” is a common action.\n\nNo “he walks out” in list.\n\nBut “he walks out” must be derived.\n\nGiven that “we1+2 walk out” is “kekǣtohnæq”, and no singular form, likely “he walks out” = same root with “he” subject.\n\nIn Menominee, “he” subject may be marked with a prefix.\n\nBut no such form in list.\n\nBut perhaps “kekǣtohnæq” is the only form, and for “he” it is adapted.\n\nBut in other cases: “he fells it by tool” = “kawāham”\n\n“he breaks it through by hand” = “kēskenam”\n\n“he cuts it off” = “pahkǣsam”\n\nSo each verb has a subject prefix.\n\nIn “kawāham” = he fells — “kaw” = fell\n\n“kēskenam” = he breaks — “kēs” = break\n\nSo similarly, “he walks out” should be from “kekǣtohnæq” but with “he” prefix.\n\nBut “kekǣtohnæq” already has “we1+2” — includes “we and you”\n\nFor “he” alone, we need a different form.\n\nBut is there such a form?\n\nNo.\n\nBut perhaps “kekǣtohnæq” is used for all, or he is implied.\n\nBut “he walks out” is not “we1+2 walk out” — different subject.\n\nIn this context, “he” is isolated.\n\nBut in the list, no “he walks out” — only “we1+2 walk out”\n\nSo likely the form is “kekǣtohnæq” with subject marking.\n\nBut which?\n\nPerhaps the root is “kekǣtoh” — “walk out”\n\nAnd for “he”, it might be “kekǣtoh” + suffix — but no.\n\nAlternatively, is there a form like “kekǣt”?\n\nWe have “ketǣnam” = he takes it out by hand → “takes it out”\n\n“ketāwahtæq” = we1+2 bite, gnaw a hole in it\n\nSo “takes it out” = ketǣnam\n\n“walks out” = different.\n\n“kekǣtohnæq” = we1+2 walk out\n\n“ketǣnam” = he takes it out by hand\n\nSo “walks out” is separate.\n\nSo “he walks out” likely needs a form.\n\nBut no such form exists — so must be “kekǣtohnæq” with proper subject.\n\nBut subject not specified.\n\nPerhaps the verb for “walk out” is the same base.\n\nBut must use only given forms.\n\nNow back to first: “I begin to eat it”\n\nThe only verb close is “bite” — “ketāwahtæq” — so “begin to bite”\n\nBut “begin” = kewǣp or wǣp\n\nFor “I”, may use “ne” + “wǣp”?\n\nNo.\n\nBut in Menominee, “I” may be marked by “ne-”\n\nSo “ne” + “begin”\n\nBut no form.\n\nNote: “nepītohnæm” = I walk here\n\n“ne” + “pītoh” → walk here\n\nSimilarly, “kawāham” = he fells — “kaw” = fell\n\nSo likely, “I begin” = “ne” + “wǣp”?\n\nBut no such form in list.\n\nBut “kewǣpeqtaq” = we1+2 begin — “kew” = begin, “ā” = infix?\n\n“kew” + “ā” → “kewǣp”\n\nSo “kew” may be root for", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11564.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We analyze each target translation using the provided verb forms and their English equivalents.\n\n1. \"I begin to eat it\" \nLooking for a verb meaning \"begin\" (from \"we1+2 begin\" → kewǣpeqtaq) and \"eat\" (involving \"come eating it\" → kepītahtæq, which is \"we1+2 come eating it; we1+2 bring it in our mouths\"). \nThe verb \"begin\" is kewǣpeqtaq → we1+2 begin. \nFor \"I begin to eat it\", we need the verb \"begin\" in first person singular, modified by \"to eat\". \nBut no direct verb for \"eat\" is given. However, \"kepītahtæq\" means \"we1+2 come eating it\", suggesting eating is involved in the action. \nBut \"begin to eat\" is not directly listed. However, \"begin\" is in kewǣpeqtaq, and \"begin to dig\" is kewǣpānæhkæq → we1+2 begin to dig. \nSo, “begin” is attached to an action. \nIs there a form for “begin” in first person? \nWe see \"kewǣpeqtaq\" (we1+2 begin), no singular \"I begin\". \nBut in Menominee, verbs often attach to the subject and action. \nIs “begin to eat” parallel to “begin to dig”? \n\"we1+2 begin to dig\" is kewǣpānæhkæq. \nSo, \"begin to eat\" would be a variant with \"eat\" as the action. \nBut we have no verb for \"eat\" directly. \nHowever, “come eating” is kepītahtæq. \nIs “begin to eat” a form of that? \nPossibly not. \nBut observe: \"kepītahtæq\" = \"we1+2 come eating it\" — involves eating. \nNo direct verb for \"begin to eat\". \nWait — is there a form like \"kewǣpeqtaq\" (we1+2 begin), and perhaps a first-person version? \nNo such form is given. \nBut perhaps we reconstruct based on pattern. \nWe observe that \"begin\" verbs often have the form kew- or kewǣ- + something. \n\"we1+2 begin\" → kewǣpeqtaq \n\"we1+2 begin to dig\" → kewǣpānæhkæq \nSo, the base is kewǣp-, and the suffix changes with the object. \nWe need “I begin to eat it”. \nSo, first person singular, \"begin\", followed by \"eat it\". \nBut there's no verb for \"eat\" in the list. \nHowever, \"kepītahtæq\" = \"we1+2 come eating it\" — implies an action of eating. \nBut \"come eating\" may not mean \"begin to eat\". \nIs there a form for \"begin\" in first person? \nThe only forms are in plural (we1+2) and third person (he). \nFor example: \n- kawāham → he fells it by tool \n- nepītohnæm → I walk here \n- pāhkeqtaw → he opens up \nSo, for \"I\", we have \"nepītohnæm\" = I walk here \n\"nekāweqtam\" = I lie down \nSo, first person with \"I\" verbs exists. \nNow, find a form meaning \"begin to eat\". \nNo exact match. \nBut note: \"kepītahtæq\" = we1+2 come eating it — “come eating” could imply starting to eat. \nBut “begin to eat” is not the same as “come eating”. \nAlternatively, could “begin to eat” be derived from “begin” and “eat” in the same structure? \nBut no verb for \"eat\". \nWait — perhaps \"eat\" is represented by a verb we have not seen. \nBut we do have “kepītahtæq” = \"we1+2 come eating it\" — so \"eating\" is part of the verb. \nIs there a verb that starts with \"kew\" and has \"eat\" as the complement? \nWe have \"kewǣpeqtaq\" = begin \n\"kewǣpānæhkæq\" = begin to dig \nSo, the pattern is: kewǣp- + [object suffix] \nSo, \"begin to eat\" would be kewǣp- + suffix for \"eat\" \nBut what is the suffix for \"eat\"? \nNo such verb appears. \nAlternatively, perhaps \"begin to eat\" is not expressed through a single verb, but must be inferred. \nBut no verb for \"eat\" is listed. \nSo, perhaps the closest is a form with \"begin\" and \"eat\", but we don't have a direct match. \nWait — another possibility: \"bite\" and \"gnaw\" are given. \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it \n\"ketǣnam\" = he takes it out by hand \nSo, \"bite\" is \"gnaw\", \"take out\" is \"ketǣnam\". \n\"eat\" is not directly there. \nBut \"come eating\" is \"kepītahtæq\", so eating is part of it. \nTherefore, “I begin to eat it” might be equivalent to “I come eating it”? \nBut “come eating” is \"we1+2\" — plural. \nAnd it's an iterative or ongoing action. \n\"begin to eat\" is not the same. \nPerhaps there is a missing word. \nBut let’s recheck all forms. \nWe have: \n- kewǣpeqtaq → we1+2 begin \n- nepītohnæm → I walk here \n- kēskenam → he breaks it through by hand \n- pahkǣsam → he cuts it off \n- kekǣtohnæq → we1+2 walk out \n- pītenam → he passes it here \n- kewǣpānæhkæq → we1+2 begin to dig \n- tawǣsam → he cuts a hole in it \n- nekǣtahan → I pry it out by tool \n- pāhkaham → he opens it by tool \n- kekēskahtæq → we1+2 bite it through \n- wackōhnæw → he walks roundabout \n- newāckesan → I cut around it \n- ketǣnam → he takes it out by hand \n- ketāwahtæq → we1+2 bite, gnaw a hole in it \n- wǣpohnæw → he begins walking \n- nekāweqtam → I lie down \n- pāhkeqtaw → he opens up \n- kepītahtæq → we1+2 come eating it; we1+2 bring it in our mouths \n- nekāwāhpem → I fall over laughing \n\nSo, the only verb with \"eat\" is in \"kepītahtæq\" — \"come eating it\". \n\"Come eating\" is not \"begin to eat\". \nHowever, \"begin to eat\" may be a translation of \"come eating\" in some contexts. \nBut \"come\" is different from \"begin\". \nAlternatively, is there a verb for \"begin\" in first person? \nWe don’t have one. \nThe only forms with \"begin\" are plural or third person. \nBut \"wǣpohnæw\" = he begins walking → he begins walking \nSo, \"he begins\" is possible. \nSo, \"I begin\" would be a derived form. \nBut no first-person \"begin\" is listed. \nSo, perhaps the verb for \"begin\" is \"kewǣpq-\", and for \"I\", we need to use a first-person stem, like \"nepī\" for \"I walk\". \nBut no such stem is available. \nWait — is \"begin to eat\" synonymous with \"come eating\"? \nIn context, \"we1+2 come eating it\" means we bring it into our mouths to eat. \nSo, eating is the action. \nPerhaps \"I begin to eat it\" is meant to be \"I come eating it\". \nBut \"come eating\" is not a tight synonym for \"begin to eat\". \nHowever, in absence of a better option, and since \"kepītahtæq\" is the only verb with \"eating\", and it's in first person plural, perhaps for singular \"I\", we use a similar form. \nBut we have no singular form. \nAlternatively, perhaps the verb \"begin\" is used with a modified object. \n\"begin to dig\" is kewǣpānæhkæq → with \"dig\" as object. \n\"begin to eat\" would be with \"eat\" as object. \nBut no \"eat\" verb exists. \nUnless \"to eat\" is part of \"come eating\". \nSo, perhaps \"I begin to eat it\" → \"I come eating it\", using the form kepītahtæq but in first person. \nBut kepītahtæq is \"we1+2 come eating it\". \nSo, for first person, could it be \"nekāpītahtæq\"? \nNo such word is listed. \nOr \"kewǣparæq\"? \nNo. \nAlternatively, perhaps \"begin to eat\" is expressed as \"begin\" + \"eat\", but the verb stem is missing. \nWait — perhaps \"eat\" is not expressed, and there is a verb for \"bite\" which is similar. \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — not exactly eating. \nSo, perhaps the intended verb is not available. \nBut let's move on and revisit. \n\n2. \"we1+2 lay it flat by hand\" \n\"lay flat\" — what does \"lay\" mean? \nWe have: \n\"walk here\" = nepītohnæm (I) \n\"walk out\" = kekǣtohnæq (we1+2) \n\"walk roundabout\" = wackōhnæw \n\"cut around it\" = newāckesan \n\"pry it out by tool\" = nekǣtahan \n\"open it by tool\" = pāhkaham \n\"open up\" = pāhkeqtaw \n\"break it through by hand\" = kēskenam \n\"cut it off\" = pahkǣsam \n\"cut a hole in it\" = tawǣsam \n\"bite it through\" = kekēskahtæq \n\"begin to dig\" = kewǣpānæhkæq \n\"begin to walk\" = wǣpohnæw \n\n\"lay it flat by hand\" — similar to \"break it through by hand\" — both involve \"by hand\" and physical action. \n\"break\" and \"lay\" are different. \n\"lay flat\" might be like \"open up\" or \"arrange\". \nBut \"pāhkeqtaw\" = he opens up — that could be opening, not laying flat. \n\"lay flat\" is more like spreading or placing. \nWe have \"walk here\", \"walk out\" — not applicable. \n\"cut\" is cutting — not laying. \n\"pry\" is pulling. \nIs there a verb for \"place\" or \"set down\"? \nNo clear match. \nBut \"lay it flat\" could be equivalent to \"place it flat\" — perhaps \"break it through\" is not similar. \nAlternatively, is \"lay flat\" like \"open\" or \"spread\"? \nNo. \nPerhaps \"by hand\" is a red flag. \nLook: \"kēskenam\" = he breaks it through by hand — object is thing being broken. \nSimilarly, \"pāhkaham\" = opens it by tool — so \"by tool\" is marked. \nWe have \"by hand\" in kēskenam. \nSo, perhaps a verb with \"by hand\" is needed. \nBut no verb for \"lay\" exists. \nHowever, \"lay it flat\" might be similar to \"set it down\". \nIs there a verb that means \"place\" or \"set\"? \nNo. \nWait — \"we1+2 lay it flat by hand\" — is there a verb meaning \"place flat\"? \nNot in list. \nBut perhaps \"break it through by hand\" includes laying or placing? \nUnlikely. \nSo, no clear match. \n\n3. \"he digs a hole\" \nWe have: \n\"kewǣpānæhkæq\" = we1+2 begin to dig \n\"he cuts a hole in it\" = tawǣsam \n\"he opens it by tool\" = pāhkaham \n\"he breaks it through by hand\" = kēskenam \n\"he cuts it off\" = pahkǣsam \nSo, \"digs a hole\" — likely equivalent to \"cuts a hole in it\" → tawǣsam \nBut \"digs a hole\" is an action of creating a hole. \n\"cut a hole in it\" is a similar action. \nSo, \"he digs a hole\" → tawǣsam? \nBut tawǣsam = \"he cuts a hole in it\" — very close. \nBut is \"cut\" the same as \"dig\"? \nIn context, yes — both are to create a hole. \nSo, \"he digs a hole\" → tawǣsam \n\n4. \"he walks out\" \nWe have: \"kekǣtohnæq\" = we1+2 walk out \nSo, \"he walks out\" must be in third person. \nBut we have no third person singular \"he walks out\". \nWe have \"wackōhnæw\" = he walks roundabout \n\"wǣpohnæw\" = he begins walking \n\"pītenam\" = he passes it here \n\"kekǣtohnæq\" = we1+2 walk out \nSo, \"he walks out\" — no direct form. \nBut only \"we1+2 walk out\" exists. \nIs there a third-person form? \nPossibly not. \nBut perhaps the verb stem is shared. \nFor example, \"walk\" verbs: \n- nepītohnæm → I walk here \n- pītenam → he passes it here (possibly related to walking) \n- kekǣtohnæq → we1+2 walk out \n- wackōhnæw → he walks roundabout \n\nSo, \"walk out\" is \"kekǣtohnæq\" in plural. \nFor \"he walks out\", we might need to infer. \nBut no third-person singular form with \"walk out\" is given. \nSo, perhaps it's missing. \nBut let's re-check all. \n\"he walks out\" — in Menominee, the verb might be formed with stem \"kekt-\" or \"kektāw-\". \nWe have \"kekǣtohnæq\" — \"we1+2 walk out\" \nSo, third person \"he walks out\" might be formed by changing the subject prefix. \nBut no such form is given. \nGiven the data, the only form for \"walk out\" is in plural. \nThus, for \"he walks out\", likely a form derived from kekǣtohnæq with subject marker for \"he\". \nBut no such word is listed. \nWait — \"pītenam\" = he passes it here — passing is different from walking out. \n\"Walks out\" means leave a place. \n\"kekt\" is in kekǣtohnæq. \nSo, possibly \"he walks out\" = kekǣtohnæq with subject \"he\"? \nBut not provided. \nSo, the only form is plural. \nThus, perhaps the answer is \"kekǣtohnæq\", even though it's plural. \nBut the target is \"he walks out\", not \"we1+2\". \nSo, we must find a third-person form. \n\nLooking back: \nWe have \"wackōhnæw\" = he walks roundabout \n\"wǣpohnæw\" = he begins walking \nSo, \"he walks\" appears in both. \nBut \"walk out\" is only in plural. \nNo third-person \"he walks out\". \nThus, likely there is a missing form. \n\nBut perhaps we can reconstruct using patterns. \nThe form \"kekǣtohnæq\" has: \n- keka- (walk) \n- -tohnæq (out) \nSo, for \"he walks out\", if we take the same stem and change the subject, it would be \"he\" version. \nBut there is no such form listed. \nThus, in absence, perhaps the only verb available is kekǣtohnæq, and it's used even if it's plural. \nBut that would be incorrect. \n\nNow, back to first: \"I begin to eat it\" \nWe have no verb. \nBut we have \"kepītahtæq\" = we1+2 come eating it — so \"come eating\" means eating. \nSo, \"begin to eat\" could be interpreted as \"start eating\". \nSo, perhaps the verb is kepītahtæq, but in first person. \nBut no first-person version. \nHowever, in Menominee, first person might be implied. \nBut no form is given. \n\nAnother possibility: \"bite\" and \"gnaw\" are given, and \"begin to bite\" is not there. \nBut \"begin to eat\" is not directly there. \n\nGiven the constraints, the closest match is that \"I begin to eat it\" is translated as \"I come eating it\" — using \"kepītahtæq\" with subject \"I\". \nBut that's plural. \nWait — is there a verb that means \"begin\" and \"eat\"? \nNo. \n\nPerhaps \"begin to eat\" is not a direct verb. \nBut given the data, the only verb with \"eating\" is kepītahtæq. \n\nSo, for \"I begin to eat it\", we must use the verb \"come eating\" in first person. \nBut no such form. \n\nAlternatively, perhaps \"begin to eat\" is formed from \"begin\" with \"eat\" — and \"eat\" is not a word, so it is derived from \"come eating\". \n\nBut let’s try to match each item:\n\n1. \"I begin to eat it\" \n→ likely based on \"we1+2 come eating it\" → “come eating” \nSo, in first person: \"I come eating it\" \nBut \"come eating\" is not \"begin to eat\". \nHowever, in some contexts, \"come\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12664.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "We are given a list of Menominee verb forms with English translations, and we are to translate four new sentences into Menominee.\n\nStep 1: Analyze each target sentence and find the closest match in the given examples.\n\nTarget 1: \"I begin to eat it\"\n\nLook for verbs involving \"begin\" and \"eat\". \n- \"kewǣpeqtaq\" = we1+2 begin → \"begin\" \n- \"kewǣpānæhkæq\" = we1+2 begin to dig → \"begin to dig\" \n- \"wǣpohnæw\" = he begins walking → \"begin walking\" \n\n\"Begin\" is clear, and \"eat\" is not directly present. But note: \"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\" → implies ingestion, so \"eat\". \n\nBut here we need \"I begin to eat it\" — subject is singular (I), and the action is beginning to eat. \n\nNo direct verb for \"begin to eat\". However, the root meaning of \"begin\" is common. Look for a verb that has \"begin\" and an eating/ingesting component. \n\n\"kepītahtæq\" is a verb for \"we1+2 come eating it\" — not \"begin to eat\". \n\nIs there a form with \"begin\" + \"eat\"? Not directly. But perhaps \"begin\" is part of a structure. \n\nWait: the only \"begin\" verb is \"kewǣpeqtaq\" (we1+2 begin). But \"begin to eat\" would be an extension. In some languages, verbs are compound or derived. \n\nBut look: \"kewǣpeqtaq\" is the base \"we begin\". No \"eat\" part. \n\nHowever, \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\" — related to eating. \n\nBut \"begin to eat\" is not directly available. \n\nAlternatively, could \"begin\" be used with a root meaning \"consume\"? We see no such verb. \n\nBut wait — is there a verb that combines \"begin\" + \"eat\"? Not explicit. \n\nMaybe the verb \"begin\" is used as a stem, and \"eat\" is implied via context? Not supported. \n\nAlternative: in Menominee, verbs may be built from stems. We see \"kewǣpeqtaq\" = we begin. But for \"I begin to eat\", we need a singular subject, and \"eat\". \n\nBut \"begin\" is not directly paired with \"eat\". \n\nWait — is there a verb that means \"begin to bite\"? \"kewǣpānæhkæq\" = begin to dig. \"kēskenam\" = he breaks it through by hand. \n\nNo verb with \"eat\" or \"bite\" and \"begin\". \n\nBut note: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — this is an eating-related action. \n\nAnd \"kepītahtæq\" = we come eating it. \n\nBut no verb for \"I begin to eat it\". \n\nPerhaps \"begin to eat\" is derived from a verb like \"begin\" + \"consume\" — but none provided. \n\nHowever, let's consider whether \"begin\" is marked by the root \"kewǣp\" and perhaps the verb for \"eat\" is embedded. \n\nBut the only verb with \"eat\" is \"kepītahtæq\" — which is for \"we come eating it\", not \"begin to eat\". \n\nNo clear match. \n\nBut perhaps \"begin to eat\" is best formed from \"begin\" + \"eat\", and if \"begin\" is \"kewǣpeqtaq\", but that is plural. \n\nWe need \"I\". So no singular \"begin\". \n\nWait — the form \"kepītahtæq\" has \"come eating it\", which may be equivalent to \"begin to eat\" in some contexts? But \"come\" is not \"begin\".\n\nNot convincing. \n\nWait — look at \"kewǣpeqtaq\" = we1+2 begin. \"kewǣpānæhkæq\" = we1+2 begin to dig. The structure \"begin to X\" seems to exist. So perhaps \"begin to eat\" would be \"kewǣp\" + eating root.\n\nBut no such eating root is given. \n\nAlternatively, is \"eat\" related to \"bite\"? Yes — \"bite\" is used. \n\nSo perhaps \"begin to bite\" is implied? But the target is \"begin to eat\". \n\nBut in the list: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → could be equivalent to \"eat\" in some contexts. \n\nSo perhaps \"begin to bite\" = \"begin to eat\"? \n\nBut we need singular \"I\". \n\nWe have \"ne\" for \"I\". So is there an \"I begin to bite\"? \n\nWe have: \n- \"nekāweqtam\" = I lie down \n- \"nekāwāhpem\" = I fall over laughing \n- \"nekǣtahan\" = I pry it out by tool \n\nNo \"I begin to bite\".\n\nBut look: is there a verb with \"begin\" and a stem that can be used for \"bite\"? \n\nWe have \"kewǣpānæhkæq\" = begin to dig → so the structure is \"kewǣp\" + root. \n\nIs there a stem for \"bite\"? In \"ketāwahtæq\" — the root stem may be \"tāwāh\" or something. \n\nBut we see no \"begin to bite\". \n\nStill, the closest is \"ketāwahtæq\" — but that's \"we1+2 bite\", not \"begin to eat\". \n\nWait — perhaps \"begin to eat\" is formed with \"kewǣp\" + \"eat\", but no such form. \n\nAlternatively, could \"begin\" be semantically used with \"consume\"? \n\nNo. \n\nAnother idea: perhaps \"begin to eat\" is not directly available, but based on pattern, the verb form for \"begin\" is \"kewǣp\", and \"eat\" is a derived form. But none of the data provides that. \n\nBut wait — is there a verb intended to be used as \"begin to eat\"? \n\nNo. So perhaps the target \"I begin to eat it\" is meant to be translated using a verb that combines \"begin\" and \"ingest\", but we lack a direct form. \n\nBut in the list, we do have: \n- \"kepītahtæq\" = we1+2 come eating it — close in meaning. \n- \"ketāwahtæq\" = we1+2 bite, gnaw — like eating. \n\nBut both are not \"begin to eat\". \n\nPerhaps in Menominee, \"begin to eat\" is expressed by a verb with \"begin\" and a root. \n\nBut no such form. \n\nBut note: the verb \"wǣpohnæw\" = he begins walking — so \"begin\" is a root. \n\nSimilarly, \"kewǣpeqtaq\" = we begin. \n\nSo \"begin\" is clearly marked with \"kewǣp\". \n\nNow, for \"eat\", do we have a stem? \n\nWe have \"kepītahtæq\" — \"we come eating it\" — might be derived from a stem meaning \"consume\". \n\nBut \"come eating\" is not \"begin to eat\". \n\nStill, perhaps \"begin to eat\" is not in the data, and we must infer. \n\nBut the problem is to translate using the given examples. \n\nWait — is there a verb that means \"I begin to eat\"? \n\nNo direct match. \n\nBut perhaps the closest is a root with \"begin\" and \"consume\", even if unlisted. \n\nBut no such form. \n\nAlternative: could \"begin\" be used with the verb for \"consume\", and the subject is \"I\"? \n\nBut we lack a form. \n\nWait — look: \"pītenam\" = he passes it here — not relevant. \n\n\"pāhkeqtaw\" = he opens up — not related. \n\nOnly possible inference: perhaps \"begin to eat\" is formed from \"kewǣp\" + \"eat\", but we don't have it. \n\nBut in the list, \"kepītahtæq\" has \"come eating\", which could be interpreted as starting to eat. \n\nBut \"come\" vs \"begin\" — different. \n\nSo perhaps the verb is not directly present. \n\nBut we may have to use a verb that is closest. \n\nWait — the target is \"I begin to eat it\". \n\nNo verb for that. \n\nBut perhaps \"eaten\" is implied by \"bite\"? \n\nNot clearly. \n\nAnother thought: \"begin to eat\" might be translated with a verb like \"kewǣp\" + stem, but no such stem in the data. \n\nSo perhaps there is no verb, but we must derive from pattern. \n\nLook at other targets to see if we can find a better path.\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for verbs with \"lay flat\" and \"by hand\".\n\nWe have:\n- \"kēskenam\" = he breaks it through by hand → \"break by hand\"\n- \"nekǣtahan\" = I pry it out by tool → \"pry by tool\"\n- \"pāhkaham\" = he opens it by tool → \"open by tool\"\n- \"pahkǣsam\" = he cuts it off → not \"lay flat\"\n- \"pītenam\" = he passes it here → not relevant\n\nNo verb for \"lay flat\". But \"lay flat\" could be \"place down\" or \"set flat\".\n\n\"kepītahtæq\" = we come eating it — not related.\n\n\"kekǣtohnæq\" = we1+2 walk out → walking.\n\nWait — is there a verb with \"place\" or \"lay\"?\n\nWe have \"pāhkeqtaw\" = he opens up — \"open\" not \"lay flat\".\n\nBut look: \"pāhkaham\" = he opens it by tool — \"open\", not \"lay flat\".\n\nNo direct match.\n\nBut “by hand” might be a clue — many verbs have \"by hand\" or \"by tool\".\n\nLook at \"kēskenam\" = he breaks it through by hand → has “by hand”\n\n\"ne\" + \"kǣtahan\" = I pry it out by tool → by tool.\n\nBut \"lay flat\" is not in the data.\n\nNo verb for \"lay flat\".\n\nTarget 3: \"he digs a hole\"\n\nWe have:\n- \"kewǣpānæhkæq\" = we1+2 begin to dig\n- \"tawǣsam\" = he cuts a hole in it\n- \"pāhkaham\" = he opens it by tool\n\n\"dig a hole\" — a hole is dug or cut.\n\n\"tawǣsam\" = he cuts a hole in it → very close to \"he digs a hole\".\n\nSo likely: \"tawǣsam\" = he cuts a hole in it → \"he digs a hole\".\n\nYes.\n\nTarget 4: \"he walks out\"\n\nWe have:\n- \"kekǣtohnæq\" = we1+2 walk out\n- \"wackōhnæw\" = he walks roundabout, by a detour\n- \"ketǣnam\" = he takes it out by hand\n- \"pāhkeqtaw\" = he opens up\n\n\"we1+2 walk out\" is directly given in \"kekǣtohnæq\".\n\nSo \"he walks out\" should be \"kekǣtohnæq\", but subject is \"we1+2\", not \"he\".\n\nWe need singular \"he\".\n\nIs there a form for \"he walks out\"? \n\nWe have \"kekǣtohnæq\" — plural \"we1+2 walk out\".\n\nIs there a singular form of this?\n\nIn the list: \n- \"wǣpohnæw\" = he begins walking \n- \"wackōhnæw\" = he walks roundabout \n- \"ketǣnam\" = he takes it out by hand \n\nNo \"he walks out\" with a distinct verb.\n\nBut \"kekǣtohnæq\" is the only verb for \"walk out\". It is used with \"we1+2\".\n\nCould it be that \"he walks out\" is a translation of \"kekǣtohnæq\" with subject changed?\n\nBut likely not — the verb may be fixed.\n\nBut the data gives no verb for \"he walks out\".\n\nHowever, \"we1+2 walk out\" is in the data, and \"he\" is the subject.\n\nDoes \"kekǣtohnæq\" have a singular form?\n\nUnlikely — no other form for \"he walk out\" is given.\n\nBut note: the verb \"wackōhnæw\" = he walks roundabout — different from \"walk out\".\n\nSo no direct match.\n\nTherefore, the only verb that means \"walk out\" is \"kekǣtohnæq\", which is for \"we1+2\".\n\nSo for \"he walks out\", perhaps it is not derivable from the data, but we must use the closest.\n\nBut in linguistic tasks like this, we use the closest form based on meaning.\n\nBack to target 1: \"I begin to eat it\"\n\nWe don't have a form. But \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — which may be close to \"eat\".\n\nAnd \"begin\" is a root.\n\nBut \"begin to bite\" is not in data.\n\n\"kepītahtæq\" = we1+2 come eating it — which is \"start eating\" or \"begin eating\"?\n\n\"come eating\" may imply starting to eat.\n\nAnd \"we\" — not \"I\".\n\nBut perhaps \"I begin to eat it\" is formed from \"kewǣp\" + \"eat\", and the verb is not listed, but we have stem.\n\nBut no.\n\nAnother idea: is there a verb with \"begin\" and \"eat\" in the list?\n\nNone.\n\nBut look at \"kewǣpeqtaq\" = we1+2 begin — no eating.\n\n\"kepītahtæq\" = we come eating — \"come\" might be a form of \"begin\" in some contexts?\n\nNot likely.\n\nPerhaps the verb for \"eat\" is not needed — \"begin to eat\" might be a compound.\n\nBut no form.\n\nWait — the only verb that involves both \"begin\" and \"eat\" is not given.\n\nBut we have \"kepītahtæq\" — \"come eating it\" — which includes \"eating\", and \"come\" may be interpreted as \"start\".\n\nBut it's still not \"begin to eat\".\n\nStill, no better option.\n\nFor target 2: \"we1+2 lay it flat by hand\"\n\nWe do have verbs with \"by hand\", e.g. \"kēskenam\" = he breaks it through by hand.\n\n\"lay flat\" is \"place down flat\".\n\n\"pahkǣsam\" = he cuts it off — not related.\n\n\"nekǣtahan\" = I pry it out by tool.\n\n\"pāhkaham\" = he opens by tool.\n\nNo verb for \"lay flat\".\n\nBut is there a verb that means \"place\" or \"set\"?\n\nNo.\n\nBut perhaps \"come eating\" is not relevant.\n\nWait — \"kepītahtæq\" = we come eating it — could be \"bring in\", not \"lay flat\".\n\nNo.\n\nSo no match.\n\nFor target 3: \"he digs a hole\" → \"tawǣsam\" = he cuts a hole in it → very close. So likely \"tawǣsam\".\n\nFor target 4: \"he walks out\" → the only verb with \"walk out\" is \"kekǣtohnæq\" (we1+2 walk out). But subject is plural.\n\nHowever, in many verb systems, there may be a singular form, but not given.\n\nBut the verb \"wackōhnæw\" is for \"he walks roundabout\", not \"out\".\n\nSo likely, no direct form.\n\nBut maybe \"kekǣtohnæq\" is used for \"he walks out\" in singular form.\n\nBut the data does not show a singular form.\n\nHowever, in the list, \"kewǣpeqtaq\" = we1+2 begin — so \"we\" = plural.\n\n\"kekǣtohnæq\" = we1+2 walk out — plural.\n\n\"ketǣnam\" = he takes it out by hand — \"takes it out\", not \"walks out\".\n\nSo different.\n\nCould \"walk out\" be a misread?\n\n\"walk out\" is not \"take out\".\n\nSo not equivalent.\n\nThus, only possible verb for \"walk out\" is \"kekǣtohnæq\", and it may be used in singular form.\n\nBut the structure is \"we1+2\", so likely not.\n\nPerhaps there is a missing form.\n\nBut based on available data, only one verb has \"walk out\": \"kekǣtohnæq\".\n\nBut it's plural.\n\nWe have no verb for \"he walks out\".\n\nSimilarly, for \"I begin to eat\", no verb.\n\nBut let's re-evaluate all.\n\nTarget 3: \"he digs a hole\" — \"tawǣsam\" = cuts a hole in it — so yes.\n\nTarget 4: \"he walks out\" — \"kekǣtohnæq\" is the only verb with \"walk out\", even if plural.\n\nIn such puzzles, if the only verb with the meaning is given, and the subject is specified, it may be used with subject particle.\n\nBut Menominee does not have a verb form for \"he walks out\" separately.\n\nSo likely, we must use the closest.\n\nBut for \"he walks out\", the only form with the root motion \"walk out\" is \"kekǣtohnæq\".\n\nSimilarly, for \"I begin to eat\", no form.\n\nBut look: \"kepītahtæq\" = we1+2 come eating it — which is \"come to eat\", meaning \"start to eat\".\n\n\"come to eat\" may be interpreted as \"begin to eat\".\n\nAnd it has \"we1+2\", not \"I\".\n\nSo for \"I\", we need singular.\n\nWe have no singular \"come eating\".\n\nWe have \"nekāweqtam\" = I lie down.\n\n\"nekāwāhpem\" = I fall over laughing.\n\nNo eating.\n\nSo no.\n\nBut perhaps \"begin to eat\" is formed from a stem like \"kewǣp\" + \"eat\", and \"eat\" is from \"kepītahtæq\".\n\nBut no.\n\nPerhaps the verb is \"kewǣp\" + \"tāwāh\", from \"ketāwahtæq\".\n\n\"ketāwahtæq\" = bite, gnaw — which is a form of eating.\n\nSo perhaps \"I begin", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12985.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Identify the pattern of verb forms in the given data.\n\nLook at verb forms with the structure: subject + verb + object, and detect semantic correspondences.\n\nExample: \n- \"kewǣpeqtaq\" = we1+2 begin → \"we begin\" \n- \"kewǣpānæhkæq\" = we1+2 begin to dig → \"we begin to dig\" \n- \"kekǣtohnæq\" = we1+2 walk out → \"we walk out\" \n- \"nepītohnæm\" = I walk here → \"I walk here\" \n- \"pahkǣsam\" = he cuts it off → \"he cuts it off\" \n- \"pītenam\" = he passes it here → \"he passes it here\" \n- \"pekēskahtæq\" = we1+2 bite it through → \"we bite it through\" \n- \"wackōhnæw\" = he walks roundabout → \"he walks roundabout\" \n- \"nekwāckesan\" = I cut around it → \"I cut around it\" \n- \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"we bite, gnaw\" \n\nObserve that verbs often have semantic prefixes or roots that reflect the manner (by hand, by tool), object (it), and mode (begin, cut, open, walk, etc.).\n\nStep 2: Analyze each item in the translation task.\n\n1. \"I begin to eat it\" \n - \"begin\" appears in \"kewǣpeqtaq\" (we begin), \"kewǣpānæhkæq\" (we begin to dig) \n - \"begin\" + \"to eat\" → need a verb for \"begin to eat\" \n - \"kepītahtæq\" is \"we1+2 come eating it; we1+2 bring it in our mouths\" → involves eating \n - But \"begin to eat\" is not directly covered \n - Look for a verb that means \"begin\" with a relevant object \n - \"kewǣpeqtaq\" = we begin — no object \n - \"kewǣpānæhkæq\" = we begin to dig → \"begin to do X\" \n - So likely: \"begin to eat\" would be \"begin to eat it\" — use root \"kewǣp\" (begin) + \"eat\" \n - \"kepītahtæq\" = we bring it in our mouths → eating action \n - But \"begin to eat\" → likely \"kewǣp\" + \"eat\" \n - No clear \"eat\" verb, but “eating” is close to “come eating it” \n - But \"kepītahtæq\" is \"we come eating it\" → implies continuous action \n - Is there a verb for \"begin to eat\" with \"it\"? \n - Possibility: \"kewǣp\" root + \"eat\" → but no direct form \n - Wait — look for a verb that means \"begin\" and then modify with the object \n - “kewǣpeqtaq” = we begin → object implied? \n - Compare: \"kewǣpānæhkæq\" = begin to dig → dig is a strong action \n - What if “begin” is attached to “eat”? \n - But we have “kekāwāhpem” = I fall over laughing → not relevant \n - No verb seems to directly say \"begin to eat\" \n\n → But notice: \"kepītahtæq\" = we come eating it — i.e., we start to eat it, bring it in \n → Possibly, “come eating” is equivalent to “begin to eat” \n → So \"I begin to eat it\" → \"I come eating it\"? \n → But subject is “I” — not “we” \n → \"nepītohnæm\" = I walk here → \"I walk here\" \n → So \"I walk here\" is “nepītohnæm” \n → Similar: \"I begin to eat it\" → likely uses \"kewǣp\" root with \"eat\"? \n\n → But no direct verb for \"eat\" — is there a way to build it?\n\n Alternate: is \"begin to eat it\" equivalent to \"come eating it\"? \n → \"kepītahtæq\" is \"we1+2 come eating it\" → fits \n → So “I” would be first-person singular \n → Use \"nek\" for “I” — \"nepītohnæm\" is I walk here → \"ne\" prefix for \"I\" \n → So \"ne\" + \"kewǣp\" + \"eat\"? \n\n But no \"eat\" form. \n\n Wait — perhaps the verb is derived from \"kepītahtæq\" — which already involves eating. \n Since \"come eating\" implies beginning to eat, perhaps the form is \"nekewǣpītahtæq\"? \n\n But no such form is listed. \n\n → Instead, is there a form for “begin” + “eat”?\n\n No clear form — so maybe “begin” is not attached directly.\n\n Another thought: “begin to eat” = “start eating” — action of starting eating \n\n → Compare: “kepītahtæq” = “we1+2 come eating it” → we start eating it \n → So a form with “I come eating it” would be “nekepītahtæq” \n → But is that a known pattern? \n\n Verified in list: \"kepītahtæq\" = we1+2 come eating it → yes \n So singular: “ne” + “kepītahtæq” → \"nekepītahtæq\"? \n But no such form given. \n\n Wait — \"ne\" is used in \"nekāweqtam\" = I lie down → so \"ne\" is used with verbs for singular \n \"nekāweqtam\" → \"I lie down\" \n → \"ne\" prefix = first person singular \n → \"kepītahtæq\" = we come eating it → with \"ke\" prefix, \"we1+2\" \n → So first person: \"nekepītahtæq\"? \n → But that would be \"I come eating it\" → yes \n → So likely, \"I begin to eat it\" = \"nekepītahtæq\" \n\n Conclusion: \"I begin to eat it\" = **nekepītahtæq**\n\n2. \"we1+2 lay it flat by hand\" \n - \"lay flat\" = \"place flat\" \n - \"by hand\" = \"by hand\" \n - Look for verbs that mean \"lay flat\" or \"place\" \n - \"pahkǣsam\" = he cuts it off → not close \n - \"pītenam\" = he passes it here → \"pass\" \n - \"pāhkaham\" = he opens it by tool → \"open by tool\" \n - \"pāhkeqtaw\" = he opens up → “open up” \n - \"nepītohnæm\" = I walk here \n - \"kekǣtohnæq\" = we walk out \n - Is there a verb for \"lay\" or \"place\"? \n - “by hand” → contrast with “by tool” \n - “by hand” is marked in several forms: \n - \"kawāham\" = he fells it by tool \n - \"nekāweqtam\" = I lie down (no tool) \n - \"nekǣtahan\" = I pry it out by tool → “pry” by tool \n - \"pāhkaham\" = open by tool \n - So “by hand” is implied when not marked with tool \n - Look for “lay flat” \n - Is there a verb for “level”, “place flat”? \n - No direct one \n - But note: “we walk out” is “kekǣtohnæq” — may be different \n - What about “lay”? \n - No clear form \n - Could it be “pāhkeqtaw” = open up? \n - “lay it flat” = place it flat → not open \n - Alternatively, “walk” verbs are present \n - Perhaps there is no direct verb, but need to derive from structure \n - Consider “nepītohnæm” = I walk here → “walk” \n - “pītenam” = he passes it here → “pass” \n - Is there a “place” verb? \n\n → Think: do any verbs mean “put down”, “level”? \n → Perhaps “lay” is derived from “put down”, and we have “lay” via positioning \n\n → But in Menominee, verbs are often built from roots with prefixes and suffixes \n\n → Look for a form with “lay” and “flat”? \n\n What if “lay flat” is like “set down”? \n → No such form \n → Perhaps “we lay flat” → use “we” + “lay” \n → But no verb \n\n Wait — compare to “cut” verbs: \n - “tawǣsam” = he cuts a hole in it → cuts \n - “pahkǣsam” = cuts it off \n - “nekǣtahan” = pry out by tool \n - “pāhkaham” = open by tool \n - “wackōhnæw” = walks roundabout \n - “nekwāckesan” = I cut around it \n - So “cut” is common, but not “lay” \n\n Another possibility: “pāhkeqtaw” = he opens up → could “open” mean “lay” in some way? \n → Not really \n\n → Perhaps missing verb \n → But must exist in list \n\n Check: \"kekēskahtæq\" = we1+2 bite it through \n → Not matching \n\n → Wait — \"kepītahtæq\" = we come eating it → eating \n → Perhaps no form, but maybe \"we lay it flat by hand\" = \"we place it flat\" \n\n → Look at “pītenam” = he passes it here → “pass” \n → “passes” — could “lay” be a variant? \n\n → No \n → Perhaps the verb is missing \n → But likely a verb exists with “lay” or “set” \n\n Wait — in the list: \n - “nepītohnæm” = I walk here \n - “kēskenam” = he breaks it through by hand → breaks \n - “pahkǣsam” = he cuts it off \n - “pītenam” = he passes it here \n - “pāhkeqtaw” = he opens up \n - “wackōhnæw” = walks around \n - “nekwāckesan” = I cut around it \n → All involve motion or altering the object \n\n No verb for placing flat \n\n → Alternative: is “lay” = “set” → not in list \n\n → But note: \"we lay it flat by hand\" — “by hand” → distinct from tool \n → So could be a form with “hand” suffix? \n\n → Look for forms with “hand” or “by hand” \n - \"kēskenam\" = he breaks it through by hand → “by hand” \n - \"nekǣtahan\" = I pry it out by tool → “by tool” \n - \"pāhkaham\" = opens by tool \n - So “by hand” occurs in \"kēskenam\" \n - So \"break it through by hand\" → root “kēsken” \n - Could “lay flat by hand” be derived from similar root? \n\n → Possibly, a root for “lay” exists \n → But no form listed with “lay” \n\n → Perhaps “lay flat” is “set down” → not in list \n\n → Wait — “pāhkeqtaw” = he opens up — could “lay it flat” be a misinterpretation? \n\n → Maybe “lay flat” = “place on surface” → not in list \n\n → Perhaps it is “we walk” with a different meaning? No \n\n → Another idea: perhaps “lay flat” is equivalent to “place it down” → no verb \n\n → Must be a missing form? Unlikely \n\n → Wait — is there any verb with “set” or “place”? \n\n → No \n\n → Perhaps the intended verb is **kewǣpānæhkæq**? But that's \"begin to dig\" \n\n → No \n\n → Try to find a root with “place” \n\n After review: no such form \n → But could \"pītenam\" = pass it here → pass it to a place → implies placement? \n → “pass it here” → “carry to here” — not “lay flat” \n\n → No match \n\n Alternate: Is \"we lay it flat by hand\" meant to be \"we place it flat\" with a verb like “put”? \n\n → Not found \n\n → Possible oversight: is there a verb for “put” in the list? \n\n → No \n\n → Given the pattern, perhaps the closest verb is one using the “by hand” prefix? \n → But no “place” verb \n\n → Go back to pattern: many verbs have “by hand” or “by tool” \n → So “by hand” = specific manner \n → So we need a verb meaning “lay flat” with “by hand” \n\n After thorough search — no verb found \n → But likely we missed it \n\n Wait — “nepītohnæm” = I walk here — “walk” \n “we walk” = “kekǣtohnæq” → we walk out \n “lay” is not walk \n\n → Search for “flat” or “place” in meaning \n → Only one verb might be close: “pāhkeqtaw” = opens up — opens, not lays \n\n → Perhaps the intended form is derived from a root not listed? \n\n → But all verbs are given, so likely one is a transformation \n\n → Wait — “we1+2 lay it flat by hand” → might be “we place it flat by hand” \n → But no such form \n\n → Perhaps “lay” = “set” → and in Menominee, such a verb exists but not listed? \n\n → Must conclude that a form exists based on pattern \n\n How about “pītenam” = he passes it here → but “here” is location \n “lay it flat” might be place at a location \n\n → But not matching \n\n → Final possibility: perhaps “lay it flat” is a typo or misrendering of “walk out” or “cut”? \n\n No — not matching \n\n → After extensive review — no verb for “lay flat” — thus, may be a missing form \n\n But in the problem, the verb list includes \"pāhkeqtaw\" = he opens up \n Could “open up” be used for “lay flat”? No \n\n → Alternative: is there a verb for “set down”? \n\n → Not visible \n\n → Given no match, perhaps it is **kewǣpānæhkæq**? No — “begin to dig” \n\n → Another idea: “we lay it flat” → “we put it down” → “we place it” \n → But no such verb \n\n → Perhaps the verb is “nepītohnæm” with “here” — but “walk here” \n\n → Unlikely \n\n → Wait — “kewǣpeqtaq” = we begin → could “begin” mean “start placing”? \n\n → No \n\n → Conclusion: unable to find verb for “lay it flat by hand” — but must go with known structure \n\n → Could the form be **ne** + **pītenam**? → “I pass it here” — not “lay flat” \n\n → Possibly, there is a verb not listed — but must derive from pattern \n\n → Perhaps “lay flat” is equivalent to “set aside” → not in list \n\n → Given the time, skip and come back \n\n3. \"he digs a hole\" \n - “dig” → “dig a hole” \n - Look for verb for “dig” \n - “kewǣpānæhkæq” = we1+2 begin to dig \n - So “begin to dig” = kewǣpānæhkæq \n - “dig” = ? \n - “dig a hole” = the act of digging \n - So the root is “dig” → “kewǣpānæhkæq” has “dig” \n - But “he digs” = first person? No — “he” \n - So “he digs a hole” → “he” must be prefix \n - “he” in examples: “kawāham” = he fells it by tool → “kawāham” \n - “kēskenam” = he breaks it through by hand \n - “pahkǣsam” = he cuts it off \n - “pītenam” = he passes it here \n - So “he” = “k” prefix \n - “he digs” = “k” + “dig” \n - “dig” verb root — in “kewǣpānæhkæq” = we1+2 begin to dig → “kewǣpānæhkæq” \n - Break it down: “kewǣp” = begin \n - “ānæhkæq” = dig \n - So “a” or “ā” root = “dig” \n - So “he digs” = “kānæhkæq”? \n - But no such form \n - “kawāham” = he fells it by tool → “kawa” = fell, “ham” = by tool \n - “k” is common for “he” \n - So “k” + “dig” root = ? \n - Is “dig” a root? \n - In “kewǣpānæhkæq” →", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12083.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on the earlier examples.\n\nFirst, we analyze the pattern of temporal adverbs and their translations.\n\n---\n\n**Step 1: Identify the week-day structure**\n\nFrom the examples:\n\n- Bvutfu: \"Yesterday was Bvumbon\" (1)\n- On Bvumbon, I came to the market (2)\n- On Bvusɔw, you will steal yam (2)\n- On Bvuŋka, he found the book (4)\n- The day after tomorrow is Bvutfu (5)\n- On Bvutfu, I will choose the car (5)\n- Today, he killed the woman (6)\n- You heard the thief a long time ago (7)\n- Tomorrow is Bvuŋkaden (8)\n- On Bvuŋkaden, the thief will find us (8)\n- Today, I chose the book (9)\n- The man is about to see him (10)\n- The day before yesterday was Bvuŋka (11)\n- I am about to help the man (12)\n- On Bvutfu, the woman saw the market (13)\n- Today, we will steal the car (14)\n- They saw me at the market just now (15)\n\nFrom this, we know:\n- The days are: Bvutfu, Bvumbon, Bvusɔw, Bvuŋka, Bvuŋkaden\n- Bvuŋkaden = \"tomorrow\" (as per sentence 8: \"Tomorrow is Bvuŋkaden\")\n\nThus, when a sentence is spoken on Bvuŋkaden, the speaker is referring to events *on Bvuŋkaden*, which is *tomorrow* relative to the day of speaking.\n\nWe are to translate sentences spoken *on Bvuŋkaden*, so all translations must be from the perspective of the speaker on Bvuŋkaden — i.e., events that happen on that day, or events relative to it.\n\n---\n\n**Step 2: Analyze temporal markers**\n\nWe identify temporal markers from the examples:\n\n- **ntfǔː** = \"the day after tomorrow\"\n- **ntfǔː nú** = \"the day after tomorrow is [day]\"\n - e.g., \"The day after tomorrow is Bvutfu\" (5)\n- **ntfǔː nú bvúmbòn** = \"Yesterday was Bvumbon\"\n- **cɔ̌ŋ nú** = \"a long time ago\"\n- **me nú** = \"I will\" or \"I am about to\"\n- **wvù** = \"he\"\n- **wɔ̀** = \"you (sg)\"\n- **kwɔ᷆ːn** = \"the woman\"\n- **bèsèn** = \"today\"\n- **fɔ̀ shě** = \"the day after tomorrow\"\n- **nyɛ́n** = \"the day before yesterday\"\n- **wvù tɔ̀ nɔ̂ː** = \"he found\"\n- **bèsèn nǔ** = \"today, we\" (or \"today, you\") → from (14: \"Today, we will steal the car\")\n- **fɔ̀wǎy** = \"the market\"\n- **kèŋkfǔ** = \"the yam\"\n- **ɛ̀bɛ̀n** = \"the woman\"\n- **bɔ́ŋ** = \"the book\"\n- **ní** = \"to\"\n- **bɔ̌ː** = \"the car\"\n- **bóy** = \"the woman\" in one case, but \"the woman\" is consistently kwɔ᷆ːn or \"the woman\"\n\nFrom sentence 11: \"The day before yesterday was Bvuŋka\" → \"nyɛ́n\" = \"the day before yesterday\"\n\nSo:\n- \"the day after tomorrow\" = **ntfǔː**\n- \"today\" = **bèsèn**\n- \"yesterday\" = **fɔ̀ shě** or \"cǐ\"? In (1) \"yesterday was Bvumbon\" → cǐ = yesterday\n - In (1): \"fɔgò cǐ nú bvúmbòn\" → \"Yesterday was Bvumbon\"\n - So \"cǐ\" = yesterday\n- \"the day before yesterday\" = \"nyɛ́n\" → (11)\n- \"tomorrow\" = **ntfǔː**? No — 8 says \"tomorrow is Bvuŋkaden\" → so \"ntfǔː\" is *day after tomorrow*.\n\nSo:\n- \"today\" = bèsèn\n- \"yesterday\" = cǐ\n- \"the day before yesterday\" = nyɛ́n\n- \"tomorrow\" = not directly spelled, but from (8): \"Tomorrow is Bvuŋkaden\"\n- \"the day after tomorrow\" = ntfǔː\n\nAlso, we see:\n- On Bvusɔw: \"you will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → future\n- On Bvuzhi: \"the woman will help me\" → future\n- On Bvutfu: \"I will choose the car\" → future\n- On Bvutfu: \"the woman saw the market\" → past\n- \"Today, we will steal the car\" → future\n- \"They saw me at the market just now\" → recent past\n\nNow let's look at each target sentence.\n\n---\n\n**16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.**\n\nBreak down:\n- \"bvúsɔ̀w\" = Bvusɔw (a day)\n- \"nǔ\" = \"you (sg)\"\n- \"fɔ̀ shě\" = \"the day after tomorrow\"\n- So: \"On Bvusɔw, the day after tomorrow\" — that doesn't make sense.\n\nWait — structure might be: \"On Bvusɔw, you will steal the yam\" → sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\nSo \"bvúsɔ̀w\" is the day → \"On Bvusɔw, you will steal the yam\"\n\nBut here: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCould it be: \"On Bvusɔw, you will steal the day after tomorrow\"? That is illogical.\n\nAlternative: perhaps \"fɔ̀ shě\" is not \"the day after tomorrow\" here.\n\nWait — in sentence (1): \"fɔgò cǐ nú bvúmbòn\" → \"Yesterday was Bvumbon\"\n\nSo \"cǐ\" = yesterday\n\nIn (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" = \"the day after tomorrow\"\n\nYes — confirmed.\n\nSo \"fɔ̀ shě\" = day after tomorrow\n\nSo sentence: \"On Bvusɔw, you will steal the day after tomorrow\" → nonsense.\n\nAlternative: is it parallel to sentence 2?\n\nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo pattern: \"On [day], [subject] will [verb] [object]\"\n\nHere: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nSo perhaps: \"On Bvusɔw, you will [something] the day after tomorrow\"?\n\nBut \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" → object?\n\nNo verb — missing?\n\nWait: perhaps \"fɔ̀ shě\" is the verb?\n\nNo — \"fɔ̀ shě\" is a temporal expression.\n\nPossibly misparsed.\n\nAlternative: is there a pattern with \"nǔ\" — subject?\n\n\"nǔ\" = \"you\"\n\nSo: \"On Bvusɔw, you will [something]\"\n\nWhat about \"fɔ̀ shě ntfǔː\" — perhaps a verb? But \"fɔ̀ shě\" = temporal.\n\nAnother possibility: is \"fɔ̀ shě\" a verb meaning \"to steal\"?\n\nNo — in (2), \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" — \"you will steal the yam\"\n\n\"yúː cɔ́ŋ\" = steal → verb\n\n\"fɔ̀ shě\" is not the object.\n\nWait — is \"fɔ̀ shě\" the object?\n\nIn (2): \"kèŋkfǔ\" = yam → object\n\nSo \"fɔ̀ shě\" is not an object.\n\nBut \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow\"\n\nSo the structure is: \"On Bvusɔw, you will ... the day after tomorrow\"?\n\nWhat verb? No verb.\n\nUnless \"fɔ̀ shě\" is a verb — but \"fɔ̀\" is \"to see\" in some contexts?\n\nLook at sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo \"fɔ̀\" = \"to see\"\n\n\"yɛ᷅n\" = \"the man\"\n\n\"me lé\" = \"me at\"\n\n\"fɔ̀wǎy\" = market\n\nSo \"fɔ̀\" = see\n\nIn sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\nSo \"cǐ\" = yesterday → \"the woman saw the market yesterday\"\n\n\"nɔ̂ː\" = saw? Possibly a verb\n\nIn (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo \"nɔ̂ː\" = \"saw\"\n\n\"nɔ̂ː\" is the verb \"to see\"\n\nNow in sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCould \"fɔ̀ shě\" be the verb? But \"fɔ̀ shě\" = \"the day after tomorrow\"\n\nBut \"fɔ̀\" = \"to see\"\n\nAnd \"shě\" is likely a form of \"after\" or \"later\"\n\nIs there a verb \"to see\" with \"shě\"?\n\nIn (13): \"cǐ nɔ̂ː yɛ᷅n wáy\" → \"yesterday saw the market\"\n\nSo \"nɔ̂ː\" = saw\n\nBut no \"shě\" verb.\n\n\"fɔ̀ shě\" = \"the day after tomorrow\"\n\nBut \"fɔ̀\" + \"shě\" may not be verb.\n\nPerhaps it's \"you will see [the day after tomorrow]\"?\n\nThat is odd.\n\nAlternative: could \"fɔ̀ shě\" be a typo or misreading?\n\nCheck the original:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\n\n\"nú\" may be missing? No — all examples have subject, verb, object or time.\n\nCompare to sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo syntax: [day] [subject] [verb] [object]\n\nIn (16): [day] [subject] [expression] ?\n\nNo verb?\n\nUnless \"fɔ̀ shě\" is the verb.\n\nBut \"fɔ̀\" = \"to see\"\n\n\"shě\" = \"after\" → as in \"after tomorrow\"?\n\nBut \"shě\" is not a standard word.\n\nBetter: in (11): \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\" — \"cí\" = day before yesterday\n\n\"cí\" is used as temporal reference.\n\nIn (1): \"fɔgò cǐ nú bvúmbòn\" → \"Yesterday was Bvumbon\"\n\nSo \"cǐ\" = yesterday\n\nSo likely temporal expressions:\n- cǐ = yesterday\n- nyɛ́n = day before yesterday\n- fɔ̀ shě = day after tomorrow\n- bèsèn = today\n- ntfǔː = day after tomorrow — same as fɔ̀ shě?\n\nWait — (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" = day after tomorrow\n\n\"ntfǔː\" = day after tomorrow\n\nSo yes — \"fɔ̀ shě\" and \"ntfǔː\" both mean \"the day after tomorrow\"?\n\nYes — that is redundant.\n\nBut in (5): \"fɔ̀ shě ntfǔː nú\" — so both used?\n\nPossibly a duplication.\n\nSo in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nIf \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\", then sentence is:\n\n\"On Bvusɔw, you will [something] the day after tomorrow\"?\n\nMissing verb.\n\nNo verb present.\n\nCould it be \"you will see\" the day after tomorrow?\n\nBut no \"see\" verb.\n\nIs there a verb \"to steal\" or \"to see\" here?\n\nBack to sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo verbs: yúː = to steal? (cɔ́ŋ = steal)\n\nIn (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\" → \"On Bvutfu, the woman saw the market\"\n\nSo \"nɔ̂ː\" = saw\n\nSo \"nɔ̂ː\" = verb \"to see\"\n\nIn (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo consistent.\n\nNow in (16): no verb.\n\nBut perhaps \"fɔ̀\" is the verb?\n\nYes — \"fɔ̀\" = to see\n\nAnd \"shě\" may be an adverb or a temporal modifier.\n\nBut \"fɔ̀ shě\" → \"see after\" or \"see the day after tomorrow\"?\n\nBut \"shě\" is not a time adverb — \"shě\" appears with \"fɔ̀\"?\n\nWait — in some languages, \"see after\" might be \"fɔ̀ shě\", but we have no example.\n\nAlternatively, perhaps \"fɔ̀ shě\" is meant to be \"the day after tomorrow\", and the verb is missing?\n\nStructure mismatch.\n\nAnother thought: is \"nǔ\" the verb?\n\nNo — \"nǔ\" is a subject.\n\nCommon structure:\n\n- [day] + [subject] + [verb] + [object/time]\n\nIn (1): fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" — \"cǐ\" = time, \"nú\" = was (copula)\n\nSo \"cǐ nú\" = \"yesterday was\"\n\nSo \"cǐ nú\" = \"was yesterday\"\n\nIn (5): fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" — \"fɔ̀ shě ntfǔː nú\" = \"the day after tomorrow is\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nAnd \"nú\" = is\n\nSo yes — \"fɔ̀ shě ntfǔː\" = temporal expression = \"the day after tomorrow\"\n\nSo sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n= \"On Bvusɔw, you [do something] the day after tomorrow\"?\n\nStill missing verb.\n\nWait — perhaps \"nǔ\" is not subject, but verb?\n\nNo — \"nǔ\" is clearly \"you\"\n\nWhat verbs are used?\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo subject \"you\", verb \"will steal\", object \"the yam\"\n\nIn (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\" → \"the woman saw the market yesterday\"\n\nSo subject \"woman\", verb \"saw\", object \"market\"\n\nIn (14): \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\n\"nǔ\" = we\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — subject is \"you\" (nǔ), day is Bvusɔw, then \"fɔ̀ shě ntfǔː\"\n\nPossibility: \"you will see the day after tomorrow\"?\n\nBut there is no \"see\" verb.\n\n\"nɔ̂ː\" = saw, as in (13)\n\nSo is \"fɔ̀\" = \"saw\"?\n\nNo — \"fɔ̀\" is \"to see\" in (15)\n\nIn (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"They saw me at the market\"\n\nSo \"nɔ̂ː\" = saw\n\n\"bɔ́\" = they\n\nSo verb is \"nɔ̂ː\"\n\n\"nɔ̂ː\" = saw\n\n\"fɔ̀\" is not used as verb in these examples.\n\nSo \"fɔ̀\" alone is not a verb.\n\nBut in sentence 16: \"fɔ̀ shě\" appears — perhaps \"fɔ̀\" is the verb \"to see\", and \"shě\" means \"after\"?\n\nBut \"shě\" is not \"after\" — \"cǐ\" = yesterday, \"nyɛ́n\" = day before yesterday.\n\n\"shě\" — in (11): \"kefwé cí nú bvûŋka\" — no\n\nPossibly", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10538.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are given a set of Nooni sentences with known translations and are asked to translate four sentences (16–19) spoken on **Bvuŋkaden**, a day in the Nooni week. To do this, we must infer the grammatical and temporal patterns from the examples.\n\n---\n\n### Step 1: Observe the structure of temporal references\n\nWe are given days and their relationships:\n\n- **Bvutfu**: appears in multiple examples\n- **Bvusɔw**: appears in examples 2, 4, 5, 6, 7\n- **Bvuzhi**: appears in example 3\n- **Bvuŋka**: appears in examples 4, 5, 6, 7, 8, 9, 12, 13, 14\n- **Bvuŋkaden**: appears in examples 8, 11\n\nWe are to translate sentences spoken on **Bvuŋkaden**, which is a day after **Bvuŋka**.\n\nFrom example 8:\n> 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n\nThis shows:\n- **Tomorrow** = **Bvuŋkaden**\n- So, **Bvuŋkaden** is the day after **Bvuŋka**\n\nSimilarly, from example 11:\n> 11. kefwé cí nú bvûŋka. The day before yesterday was Bvuŋka.\n\nSo:\n- Day before yesterday = Bvuŋka\n- Yesterday = Bvuŋkaden\n- Today = Bvuŋkaden + 1 day\n\nWait — contradiction?\n\nNo: if \"day before yesterday was Bvuŋka\", then:\n- Two days before today = Bvuŋka\n- So today = day after Bvuŋka → today = Bvuŋkaden\n\nSo **today is Bvuŋkaden** → confirmed.\n\nThus, in all sentences spoken **on Bvuŋkaden**, the reference is **today**.\n\n---\n\n### Step 2: Identify patterns in temporal markers\n\nLook at the temporal expressions used:\n\n- \"The day after tomorrow\" → (15) in example 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n- \"Tomorrow\" → in example 8: \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"Tomorrow is Bvuŋkaden\"\n- \"Today\" → in example 9: \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → \"Today, I chose the book\"\n- \"The day before yesterday\" → example 11 → \"The day before yesterday was Bvuŋka\"\n- \"Just now\" → example 15: \"They saw me at the market just now\"\n\nNote:\n- Temporal references are marked with verbs or pre-verbal expressions.\n\n---\n\n### Step 3: Analyze the structure of the sentences\n\nWe now analyze each target sentence.\n\n---\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\nBreak it down:\n- \"bvúsɔ̀w\" → likely \"on Bvusɔw\" (from example 2: \"On Bvusɔw, you(sg) will steal the yam\")\n- \"nǔ\" → likely \"you (sg)\"\n- \"fɔ̀ shě ntfǔː\" → \"the day after tomorrow is\"\n\nWait — but \"fɔ̀ shě ntfǔː\" appears in example 5: \"The day after tomorrow is Bvutfu\"\n\nBut here, it's used as a verb phrase meaning \"the day after tomorrow is [a day]\"\n\nSo: \"On Bvusɔw, the day after tomorrow is [something]\"\n\nBut \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" → but what is it equal to?\n\nInstead, maybe it's \"the day after tomorrow is Bvusɔw\"? But that would be strange.\n\nWait — the entire phrase is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nCould it mean: \"On Bvusɔw, you (sg) will have the day after tomorrow\" — no.\n\nMore likely: It is **\"On Bvusɔw, the day after tomorrow is [X]\"**, but what is X?\n\nWait — look for parallel language.\n\nIn example 5:\n> fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) have the day after tomorrow\"?\n\nThat doesn’t make sense.\n\nWait — perhaps it's misordered.\n\nAlternative: maybe \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is [day]\"\n\nBut where is the day?\n\nIt must be missing. But we can infer.\n\nWait — is this a descriptive phrase?\n\nAlternative interpretation: could \"fɔ̀ shě ntfǔː\" be \"is the day after tomorrow\"?\n\nNo, it's the opposite.\n\nActually: \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" → requires a complement.\n\nSo the structure is: [day] + [subject] + [fɔ̀ shě ntfǔː] → but \"fɔ̀ shě ntfǔː\" is not a verb of being.\n\nWait — perhaps the marker is \"fɔ̀ shě\" meaning \"the day after tomorrow\", and \"ntfǔː\" is the day name?\n\nIn example 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" → no, \"fɔ̀ shě\" = \"day after tomorrow\", \"ntfǔː\" = \"is\", \"bvútfu᷅\" = \"Bvutfu\"\n\nAh — no. \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" — missing the day.\n\nSo \"fɔ̀ shě ntfǔː\" is an expression meaning \"the day after tomorrow is\" — but it must be followed by a day.\n\nBut in this sentence, it's not — it's \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\nSo perhaps it is: \"On Bvusɔw, you (sg) will have [the day after tomorrow]\" — still not meaningful.\n\nWait — perhaps the structure is: \"On [day], [subject] [event]\"\n\nCompare to example 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you(sg) will steal the yam\"\n\nSo: \"On X, Y will [do something]\"\n\nSo the structure is: [on day] [subject] [verb] [object]\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" = \"you (sg)\"\n\n\"fɔ̀ shě ntfǔː\" — this may be a verb phrase.\n\nBut \"fɔ̀ shě\" = \"the day after tomorrow\"\n\nSo is this: \"On Bvusɔw, you (sg) [are the day after tomorrow]\" — a nonsense translation.\n\nWait — perhaps it's a typo or misreading.\n\nWait — what if \"fɔ̀ shě\" is not a temporal marker?\n\nBut in example 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" = \"day after tomorrow\", \"ntfǔː\" = \"is\"\n\nBut here, in 16: there is no \"nú\"\n\nCould \"fɔ̀ shě ntfǔː\" be a standalone phrase meaning \"the day after tomorrow\"?\n\nNo — it's not parallel.\n\nAlternative idea: maybe \"fɔ̀ shě\" means \"will be\" and \"ntfǔː\" is the day?\n\nNo — in example 5, \"fɔ̀ shě ntfǔː\" is not \"will be Bvutfu\" — the full phrase is \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nSo \"fɔ̀ shě ntfǔː\" alone is incomplete.\n\nSo in sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — likely typo or missing element.\n\nWait — perhaps it's \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you (sg) will have [the day after tomorrow]\" — no.\n\nAnother possibility: the word order is misread.\n\nCould \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" and the day is implied?\n\nBut in the sentence, the day is not mentioned.\n\nAlternatively, maybe it's a subject-verb-object with temporal marker.\n\nCompare example 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo it's a statement of time: [temporal expression] is [day]\n\nBut sentence 16 is not a statement of time — it has \"on Bvusɔw\" and \"you\"\n\nSo likely: \"On Bvusɔw, you (sg) will have (the day after tomorrow)\" — still not natural.\n\nWait — is “fɔ̀ shě” a verb?\n\nNo — it's clearly a time expression.\n\nWait — perhaps “fɔ̀ shě” = “the day after tomorrow” and “ntfǔː” = “is” — so “the day after tomorrow is” — but it's missing the day.\n\nUnless the day is Bvusɔw?\n\nBut Bvusɔw is the day of the event.\n\nSo: “On Bvusɔw, you (sg) are the day after tomorrow” — that makes no sense.\n\nWait — maybe it's a mistake in the problem? Unlikely.\n\nAlternative: maybe \"fɔ̀ shě\" means \"there will be\" or \"will be\"\n\nBut in example 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — the \"fɔ̀ shě\" is before \"ntfǔː\", and together they mean \"the day after tomorrow is\"\n\nSo likely \"fɔ̀ shě\" is a temporal classifier.\n\nBut in 16, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — perhaps it's missing a day.\n\nWait — could it be: \"On Bvusɔw, you (sg) will be [the day after tomorrow]\" — still wrong.\n\nUnless \"fɔ̀ shě\" means \"will have\" or \"will be in\" — not clear.\n\nWait — look at example 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"On Bvutfu, the woman saw the market just now\"\n\n\"just now\" is indicated by \"fɔ̀wǎy\"\n\nSimilarly, in example 15: \"They saw me at the market just now\" — \"fɔ̀wǎy\"\n\nSo temporal expressions are used with verbs.\n\nIn 16: \"fɔ̀ shě ntfǔː\" — not a verb.\n\nBack to structure.\n\nPossibility: sentence is **\"On Bvusɔw, you (sg) will [have] the day after tomorrow\"** — but what does that mean?\n\nNo — the only time marker used for a future event in the language is \"will\" or \"will steal\".\n\nIn example 2: \"you will steal the yam\"\n\nSo \"cɔ́ŋ\" = \"will steal\"\n\nBut here, \"fɔ̀ shě\" is not a verb.\n\nWait — what if \"fɔ̀ shě\" is an error and should be \"cɔ́ŋ\"?\n\nNo — that’s not supported.\n\nAnother idea: in example 5, \"the day after tomorrow is Bvutfu\" — so \"fɔ̀ shě ntfǔː\" is a phrase meaning \"the day after tomorrow is [X]\" — and here, perhaps it's \"on Bvusɔw, you will (the day after tomorrow is)\" — nonsense.\n\nPerhaps the sentence is misparsed.\n\nAnother possibility: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"You (sg) on Bvusɔw will have the day after tomorrow\" — but still.\n\nWait — look at sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\nThis has \"me nú\" → \"I will\" or \"I am about to\"\n\n\"ŋgéː\" → likely \"see\" (from example 12: \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\"; \"nfí\" = \"help\")\n\n\"nyɛ́n\" → \"the man\" (from example 10: \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" → \"The man is about to see him\" → \"yɛ́n\" = \"him\")\n\nSo \"nyɛ́n\" = \"the man\"\n\n\"kèŋkfǔ\" = \"the yam\" (from example 2: \"will steal the yam\")\n\n\"lé\" = \"just now\" (from example 15: \"saw me at the market just now\")\n\n\"ɛ̀bɛ̀n\" = \"the woman\"\n\nSo sentence 17: \"I will see the man just now the woman\" — doesn't make sense.\n\nWait — \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n→ \"I will see the man the yam just now the woman\"?\n\nNo.\n\nWait — perhaps it's \"I will see the man [who is] the woman\" — no.\n\n\"kèŋkfǔ\" = \"the yam\", so \"see the man the yam\" — not clear.\n\nBut \"lé\" = \"just now\", so \"just now\" is attached to the verb.\n\nSo likely: \"I will see the man the yam just now\" — still odd.\n\nAlternative: \"I will see the man, the yam just now\" — no.\n\nWait — perhaps \"kèŋkfǔ\" is a person? But no — in example 2, \"you will steal the yam\" → \"kèŋkfǔ\" = \"the yam\"\n\nSo \"kèŋkfǔ\" = \"the yam\"\n\nSo \"I will see the man the yam just now\" — bad.\n\nBut in example 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\"\n\nSo \"cɔ́ŋ\" = \"will steal\"\n\nIn 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n\"me nú\" = \"I will\"\n\n\"ŋgéː\" = \"see\" (likely)\n\n\"nyɛ́n\" = \"the man\"\n\n\"kèŋkfǔ\" = \"the yam\"\n\n\"lé\" = \"just now\"\n\n\"ɛ̀bɛ̀n\" = \"the woman\"\n\nSo the full phrase: \"I will see the man, the yam just now, the woman\" — doesn't make sense.\n\nBut \"lé\" is an adverb — so \"just now\"\n\nSo: \"I will see the man just now, the yam the woman\" — still no.\n\nWait — could \"kèŋkfǔ lé\" = \"the yam just now\"?\n\nAnd \"nyɛ́n\" = subject?\n\nNo.\n\nMaybe it's \"I will see the man, the yam just now the woman\" — still not clear.\n\nWait — another possibility: \"kèŋkfǔ\" = \"the thief\" or similar?\n\nIn example 7: \"you heard the thief a long time ago\" → \"cɔ̌ŋ\" = \"the thief\"\n\nSo in example 2: \"will steal the yam\" → \"kèŋkfǔ\" = \"the yam\"\n\nSo consistent.\n\nBack to 16.\n\nPerhaps \"fɔ̀ shě ntfǔː\" is a verb phrase meaning \"the day after tomorrow is\", and in context, \"on Bvusɔw, you will have the day after tomorrow\" → not standard.\n\nWait — what if the structure is: \"On Bvusɔw, you (sg) will be the day after tomorrow\" — but \"day after tomorrow\" is a day, not a person.\n\nNo.\n\nAlternative: perhaps \"fɔ̀ shě\" is a verb meaning \"to be\" and \"ntfǔː\" is a noun?\n\nBut \"fɔ̀ shě\" is clearly a temporal expression.\n\nAnother idea: in example 5, \"the day after tomorrow is Bvutfu\" — so \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\"\n\nSo if we take that, then in 16: \"On Bvusɔw, you (sg) will be the day after tomorrow\" — still not.\n\nUnless \"on Bvusɔw\" is the day, and \"fɔ̀ shě ntfǔː\" is an event on that day.\n\nBut no.\n\nPerhaps the sentence is \"On Bvusɔw, you (sg) will [have the day after tomorrow]\" — which is out of order.\n\nWait — what if \"fɔ̀ shě\" is \"will have\" and \"ntfǔː\" is \"the day after tomorrow\"?\n\nBut in example 5, it's \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nSo \"fɔ̀ shě ntfǔː\" is not a verb, but a time phrase.\n\nSo likely, the sentence is malformed.\n\nPerhaps it's a typo and should be \"bvúsɔ̀w nǔ cɔ́ŋ kèŋkfǔ\" — \"On Bvusɔw, you will steal the yam\"\n\nBut it has \"fɔ̀ shě ntfǔː\"\n\nNo.\n\nWait —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11338.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Identify the day of the week the sentences are spoken on. \nWe are given sentences spoken on different days: \n- Bvutfu (sentence 1) \n- Bvusɔw (sentences 4–7) \n- Bvukema (sentences 8–11) \n- Bvuŋka (sentences 12–15) \n\nWe are to translate sentences spoken on **Bvuŋkaden**, a new day. \nFrom the context, it appears Bvuŋkaden is a day derived from Bvuŋka, possibly \"tomorrow\" of Bvuŋka.\n\nStep 2: Find patterns for how days are expressed. \nFrom sentence 8: \n\"Tomorrow is Bvuŋkaden\" → indicates Bvuŋkaden = tomorrow of Bvuŋka.\n\nFrom sentence 11: \"The day before yesterday was Bvuŋka\" → Bvuŋka was two days before the current day. \nSo the current day (spoken on Bvuŋkade) is **tomorrow of Bvuŋka**.\n\nHence, the day order is: \nBvuŋka → Bvuŋkaden (tomorrow) → then next day is Bvutfu? \nBut look at sentence 5: \"The day after tomorrow is Bvutfu\" → spoken on Bvusɔw. \nSo: \n- On Bvusɔw: day after tomorrow = Bvutfu \nThat means: Bvusɔw → day after tomorrow = Bvutfu \nSo Bvutfu is two days after Bvusɔw.\n\nBut we need to map the days relative to each other.\n\nLet’s list days in chronological order using known references.\n\nFrom sentence 1: spoken on Bvutfu → \"Yesterday was Bvumbon\" \nSo day before Bvutfu = Bvumbon\n\nFrom sentence 5: spoken on Bvusɔw → \"The day after tomorrow is Bvutfu\" \nSo: Bvusɔw → +2 days = Bvutfu \nTherefore, Bvutfu is two days after Bvusɔw → Bvusɔw → Bvutfu (after +2)\n\nAlso, from sentence 11: spoken on Bvukema → \"The day before yesterday was Bvuŋka\" \nSo: Bvukema → -2 days = Bvuŋka → Bvukema is two days after Bvuŋka.\n\nNow from sentence 8: \"Tomorrow is Bvuŋkaden\" → spoken on Bvukema → so: Bvukema → +1 day = Bvuŋkaden\n\nSo: \n- Bvukema → +1 = Bvuŋkaden \n- Bvukema → -2 = Bvuŋka → so Bvuŋka is 2 days before Bvukema \n- Bvusɔw → +2 = Bvutfu \n- Bvutfu → -1 = Bvumbon\n\nLet’s build a full sequence:\n\nStart at Bvukema → \n- Bvukema \n- +1 → Bvuŋkaden \n- +2 → Bvutfu \n- +3 → Bvusɔw? Wait — contradiction.\n\nWait: Bvusɔw is earlier than Bvutfu? From sentence 5: on Bvusɔw, day after tomorrow is Bvutfu → so Bvusɔw → +2 = Bvutfu \n\nBut from above: Bvukema → +1 = Bvuŋkaden → +2 = Bvutfu? That would mean Bvutfu is 3 days after Bvukema.\n\nBut from Bvusɔw → +2 = Bvutfu → so Bvutfu is 2 days after Bvusɔw.\n\nSo Bvutfu = Bvusɔw + 2 \nBvutfu = Bvukema + 3 \n\nSo: Bvukema + 3 = Bvusɔw + 2 → Bvukema +1 = Bvusɔw \n\nSo: \n- Bvukema \n- +1 → Bvusɔw \n- +2 → Bvutfu \n- +3 → Bvumbon (from 1: \"Yesterday was Bvumbon\" on Bvutfu)\n\nSo in sequence: \nBvukema → Bvusɔw → Bvutfu → Bvumbon → then next?\n\nWait: \"Yesterday was Bvumbon\" on Bvutfu → so Bvumbon is one day before Bvutfu → Bvutfu = Bvumbon +1\n\nSo time order: \nBvukema \n→ Bvusɔw (after +1) \n→ Bvutfu (+2) \n→ Bvumbon (+3)? No — Bvutfu = Bvumbon +1 → so Bvumbon = Bvutfu -1 → so Bvumbs = Bvutfu -1 → so Bvutfu -1 = Bvumbon\n\nSo: \nBvukema \n→ Bvusɔw \n→ Bvutfu \n→ Bvumbon\n\nSo Bvukema → +1 = Bvusɔw → +1 = Bvutfu → +1 = Bvumbon → then next day?\n\nBut from sentence 8: \"Tomorrow is Bvuŋkaden\" → spoken on Bvukema → so Bvukema +1 = Bvuŋkaden\n\nWait — contradiction: \nIf Bvukema → +1 = Bvusɔw, then Bvukema +1 = Bvusɔw \nBut also Bvukema +1 = Bvuŋkaden → so Bvusɔw = Bvuŋkaden? \n\nThat’s not possible — unless days are cycled.\n\nPerhaps we misassigned.\n\nLook at sentence 8: “Tomorrow is Bvuŋkaden” — spoken on Bvukema → so Bvuŋkaden = Bvukema +1\n\nSentence 11: “The day before yesterday was Bvuŋka” — spoken on Bvukema → so Bvuŋka = Bvukema -2\n\nSo Bvukema → -2 = Bvuŋka \n→ +1 = Bvuŋkaden\n\nSo: \nBvukema \n→ -2 → Bvuŋka \n→ -1 → Bvuŋka-1 \n→ 0 → Bvukema \n→ +1 → Bvuŋkaden\n\nFrom sentence 5: on Bvusɔw, “The day after tomorrow is Bvutfu” → so Bvutfu = Bvusɔw +2\n\nFrom sentence 1: on Bvutfu, “Yesterday was Bvumbon” → so Bvumbon = Bvutfu -1\n\nSo chain: \nBvusɔw → +2 = Bvutfu → -1 = Bvumbon\n\nSo Bvumbon = Bvusɔw +1\n\nSo now: Bvusɔw → +1 = Bvumbon → +1 = Bvutfu → +2 = Bvutfu? Confusion.\n\nWait: \nBvusɔw +2 = Bvutfu → so Bvutfu = Bvusɔw +2 \nBvutfu -1 = Bvumbon → so Bvumbon = Bvusɔw +1\n\nTherefore: \n- Bvusɔw \n- +1 = Bvumbon \n- +2 = Bvutfu \n- +3 = next? \n\nNow from earlier: \n- Bvukema → -2 = Bvuŋka → so Bvukema = Bvuŋka +2 \n- Bvukema → +1 = Bvuŋkaden → so Bvuŋkaden = Bvukema +1 = Bvuŋka +3\n\nNow, we have full sequence:\n\nLet’s assign actual days:\n\nLet day 0 = Bvuŋka \nThen: \n- day 0: Bvuŋka \n- day 1: Bvukema (since Bvukema = Bvuŋka +2 → no) — wait error.\n\nFrom sentence 11: “The day before yesterday was Bvuŋka” → on Bvukema \nSo Bvukema is two days after Bvuŋka \nSo: \nBvuŋka → +2 = Bvukema\n\nThen: \nBvukema → +1 = Bvuŋkaden (from sentence 8)\n\nSo: \n- Bvuŋka \n- +2 → Bvukema \n- +3 → Bvuŋkaden\n\nFrom sentence 5: on Bvusɔw → “day after tomorrow is Bvutfu” → so Bvutfu = Bvusɔw +2\n\nFrom sentence 1: on Bvutfu → “Yesterday was Bvumbon” → so Bvumbon = Bvutfu -1 → Bvumbon = (Bvusɔw +2) -1 = Bvusɔw +1\n\nSo: \nBvusɔw \n→ +1 → Bvumbon \n→ +2 → Bvutfu\n\nSo now, place all days:\n\nBvuŋka \n+2 → Bvukema \n+3 → Bvuŋkaden \n+4 → ??? \n+5 → Bvusɔw? \nBut Bvusɔw → +2 = Bvutfu → so Bvutfu is after Bvusɔw\n\nWe need to see if all days fit in a cycle.\n\nBut perhaps the week is 7 days? Let’s assign numerical order.\n\nSet Bvuŋka = Day 0 \nThen: \n- Bvuŋka = 0 \n- Bvukema = 0 + 2 = 2 \n- Bvuŋkaden = 2 + 1 = 3 \n- Bvusɔw = ? → from Bvusɔw +2 = Bvutfu, and Bvutfu = Bvusɔw +2 \nAlso, from Bvutfu -1 = Bvumbon → Bvumbon = Bvusɔw +1\n\nWe don’t know Bvusɔw yet.\n\nBut from the days spoken on: \n- Bvutfu: sentence 1 \n- Bvusɔw: sentences 4–7 \n- Bvukema: 8–11 \n- Bvuŋka: 12–15 \n→ so these are all distinct days.\n\nNow, we need to find the day of the week for each sentence.\n\nWe know:\n\n- On Bvutfu: yesterday = Bvumbon → so Bvumbon = Bvutfu -1 \n- On Bvusɔw: day after tomorrow = Bvutfu → so Bvutfu = Bvusɔw +2 \n→ so Bvutfu = Bvusɔw +2 \n→ Bvumbon = (Bvusɔw +2) -1 = Bvusɔw +1\n\nSo: \n- Bvusɔw \n- +1 → Bvumbon \n- +2 → Bvutfu\n\nNow, from Bvukema: \n- day before yesterday = Bvuŋka → Bvuŋka = Bvukema -2 → Bvukema = Bvuŋka +2 \n- tomorrow = Bvuŋkaden → Bvuŋkaden = Bvukema +1\n\nSo Bvuŋkaden = (Bvuŋka +2) +1 = Bvuŋka +3\n\nSo now, time order: \nBvuŋka \n→ +2 = Bvukema \n→ +3 = Bvuŋkaden \n→ +? = Bvusɔw\n\nWe need to place Bvusɔw.\n\nWe also have sentence 13: “On Bvutfu, the woman saw the market” → spoken on Bvuŋka → so on Bvuŋka, someone talks about Bvutfu.\n\nFrom above, Bvutfu = Bvusɔw +2 → so Bvutfu is after Bvusɔw.\n\nSo Bvusɔw must be before Bvutfu.\n\nNow, relative positions:\n\nSet Bvuŋka = 0 \nThen:\n\n- Bvuŋka = 0 \n- Bvukema = 2 \n- Bvuŋkaden = 3 \n- Bvutfu = ? \n- Bvusɔw = ?\n\nFrom Bvutfu = Bvusɔw +2 \nAnd Bvutfu = ? \n\nWe have another: on Bvusɔw, sentence 4: “On Bvuŋka, he found the book” — spoken on Bvusɔw → so on Bvusɔw, refers to Bvuŋka.\n\nThat suggests that Bvuŋka is a day that occurred on Bvusɔw.\n\nBut that would mean Bvuŋka = Bvusɔw.\n\nBut we already have Bvuŋka = 0, Bvukema = 2 → if Bvusɔw = 0 → then Bvusɔw = Bvuŋka → consistent.\n\nSo try: Bvusɔw = 0\n\nBut Bvuŋka = 0 → so Bvusɔw = Bvuŋka → possible?\n\nThen Bvutfu = Bvusɔw +2 = 0 +2 = 2\n\nThen Bvutfu = 2\n\nBut Bvukema = 2 → conflict.\n\nSo Bvusɔw ≠ 0\n\nTry Bvusɔw = 1 \nThen Bvutfu = 1+2 = 3 \nBvumbon = 1+1 = 2\n\nNow days:\n\n- 0: Bvuŋka \n- 1: Bvusɔw \n- 2: Bvumbon \n- 3: Bvutfu \n- 3: Bvukema? No — Bvukema = 2 → so 2 = Bvukema → conflict with Bvumbon at 2\n\nTry Bvusɔw = 4 \nThen Bvutfu = 6 \nBvumbon = 5\n\nBvuŋka = 0 \nBvukema = 2 \nBvuŋkaden = 3 \nBvusɔw = 4 \nBvutfu = 6\n\nAll distinct. Possible.\n\nNow check if any contradiction.\n\nOn Bvusɔw (day 4): “On Bvuŋka, he found the book” → refers to a past day (Bvuŋka at day 0) → so Bvuŋka is in the past → fine.\n\nOn Bvukema (day 2): “Tomorrow is Bvuŋkaden” → day 3 → yes.\n\n“The day before yesterday was Bvuŋka” → day 0 → from day 2: day -2 → yes.\n\nOn Bvutfu (day 6): “Yesterday was Bvumbon” → Bvumbon = day 5 → yes.\n\nOn Bvuŋka (day 0): sentence 12: “I am about to help the man” → present.\n\nSentence 13: “On Bvutfu, the woman saw the market” → spoken on Bvuŋka (day 0) → refers to Bvutfu (day 6) → future → fine.\n\nSentence 14: “Today, we will steal the car” → present future → day 0.\n\nSentence 15: “They saw me at the market just now” → recent past → fine.\n\nNow, we are to translate sentences spoken on **Bvuŋkaden** → which is day 3.\n\nNow, sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → spoken on Bvuŋkaden\n\nWe need to translate.\n\nBreak down: \n\"bvúsɔ̀w\" → from earlier, Bvusɔw is day 4 → but spoken on day 3 → so this is a time reference.\n\n\"nǔ\" → \"you (sg)\" \n\"fɔ̀ shě ntfǔː\" → \"the day after tomorrow is Bvutfu\"? \n\nBut look at sentence 5: on Bvusɔw, “The day after tomorrow is Bvutfu” → which is “fɔ̀ shě ntfǔː”\n\nSo “fɔ̀ shě ntfǔː” means “the day after tomorrow is Bvutfu”\n\nBut here it is used in a different context.\n\nIn sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) will have the day after tomorrow is Bvutfu\"?\n\nNo — that doesn’t make sense.\n\nPerhaps it's: \"On Bvusɔw, you (sg) will have a day after tomorrow, which is Bvutfu\"?\n\nBut likely, \"fɔ̀ shě ntfǔː\" is a fixed expression meaning \"the day after tomorrow is Bvutfu\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) will have the day after tomorrow being Bvutfu\"?\n\nNo — more likely: the structure is similar to “On X, Y will have Z”\n\nBut from earlier, on Bvusɔw, “fɔ̀ shě ntfǔː” is used to mean “the day after tomorrow is Bvutfu”\n\nBut here, it is used as a future event on Bvusɔw.\n\nAnother possibility: “fɔ̀ shě ntfǔː” is a clause meaning “the day after tomorrow is Bvutfu”\n\nSo if it is attached to “bvúsɔ̀w nǔ”, it may mean “On Bvusɔw, you (sg) will have [the day after tomorrow being Bvutfu]” — which is redundant.\n\nWait — perhaps “fɔ̀ shě ntfǔː” is a relative clause or a temporal marker.\n\nBut in sentence 5: on Bvusɔw, “fɔ̀ shě ntfǔː” is standalone — meaning “the day after tomorrow is Bvutfu”\n\nSo the phrase “fɔ̀ shě ntfǔː” has a fixed meaning.\n\nNow in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nIs “nǔ” subject? “you”?\n\nCould it be “On Bvusɔw, you (sg) will have [the day after tomorrow being", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9828.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\nWe must first infer the linguistic pattern of day references, tense markers, and verb constructions from the provided examples.\n\n---\n\n**Step 1: Identify the day names and their calendar positions**\n\nFrom the examples:\n\n- Bvutfu: spoken on Bvutfu → \"Yesterday was Bvumbon\" (1), \"The day after tomorrow is Bvutfu\" (5)\n- Bvusɔw: spoken on Bvusɔw → \"On Bvusɔw, you will steal\" (2), \"Today, he killed\" (6), \"You heard the thief a long time ago\" (7)\n- Bvuzhi: spoken on Bvuzhi → \"On Bvuzhi, the woman will help me\" (3)\n- Bvuŋka: spoken on Bvuŋka → \"On Bvuŋka, he found the book\" (4), \"The day before yesterday was Bvuŋka\" (11), \"Today, we will steal\" (14)\n\nNote that day names are used with temporal markers such as:\n\n- \"On X, Y\" → indicates reference to day X\n- \"The day after tomorrow is X\" → future\n- \"The day before yesterday was X\" → past\n- \"Tomorrow is X\" → future\n- \"The day after tomorrow is X\" → future\n- \"Today\" → present\n\nFrom the data:\n\n- (1): \"Yesterday was Bvumbon\" → Yesterday → Bvumbon\n- (5): \"The day after tomorrow is Bvutfu\" → +2 days → Bvutfu\n- (11): \"The day before yesterday was Bvuŋka\" → -2 days → Bvuŋka\n- (8): \"Tomorrow is Bvuŋkaden\" → +1 day → Bvuŋkaden\n\nSo the days are cyclic. We can infer that:\n\n- Bvutfu → reference point\n- Bvusɔw → one day after Bvutfu? Let's check.\n\nFrom (1): Yesterday = Bvumbon \nFrom (5): Day after tomorrow = Bvutfu → so today = day before that → Bvutfu is +2 → today = Bvutfu - 2 → thus today is Bvutfu - 2\n\nBut (1) says \"Yesterday was Bvumbon\" → so the day before today = Bvumbon\n\nThen today = Bvumbon +1 \nDay after tomorrow = Bvutfu → so today +2 = Bvutfu → Bvumbon +1 +2 = Bvutfu → Bvumbon +3 = Bvutfu → so Bvutfu = Bvumbon +3\n\nSimilarly, (11): \"The day before yesterday was Bvuŋka\" → -2 days = Bvuŋka → today = Bvuŋka +2\n\nBut from above: today = Bvumbon +1 → so Bvumbon +1 = Bvuŋka +2 → Bvumbon - Bvuŋka = 1\n\nNow, (8): \"Tomorrow is Bvuŋkaden\" → so today = Bvuŋkaden -1\n\nSo now:\n\n- today = Bvuŋkaden -1 \n- today = Bvumbon +1 → so Bvumbon +1 = Bvuŋkaden -1 → Bvumbon +2 = Bvuŋkaden\n\nFrom earlier: Bvutfu = Bvumbon +3 → so Bvuŋkaden = Bvumbon +2 → so Bvutfu = Bvumbon +3 → so Bvutfu = Bvuŋkaden +1\n\nThus, sequence (in order): \nBvumbon → Bvuŋkaden → Bvutfu → Bvusɔw → Bvuzhi → back?\n\nBut we have day markers used:\n\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nWe also see from (8): \"Tomorrow is Bvuŋkaden\" — so tomorrow = Bvuŋkaden → thus today = Bvuŋkaden -1\n\nWe now need to determine how the time markers work.\n\n---\n\n**Step 2: Decode temporal markers**\n\nLook at expressions like:\n\n- \"On X, Y\" — refers to event on day X\n- \"The day after tomorrow\" — +2\n- \"The day before yesterday\" — -2\n- \"Tomorrow\" — +1\n- \"Today\" — now\n- \"The day after\" — +1? Not directly, but “the day after tomorrow” = +2\n\nIn (5): \"The day after tomorrow is Bvutfu\" → +2 → Bvutfu\n\nIn (11): \"The day before yesterday was Bvuŋka\" → -2 → Bvuŋka\n\nIn (8): \"Tomorrow is Bvuŋkaden\" → +1 → tomorrow → Bvuŋkaden\n\nSo temporal shift markers:\n\n- \"tɔ̀ nɔ̂ː\" = \"the day after tomorrow\" → +2\n- \"nú\" = \"on\" → used with day names\n- \"yɛ᷅n\" = \"he saw\", \"she saw\", etc. → a verb of perception\n- \"bèsèn\" = \"the thief\" → used in object\n- \"me\" = \"I\"\n- \"wvù\" = \"he\"\n- \"kwɔ᷆ːn\" = \"the woman\"\n- \"nǔ\" = \"you (sg)\"\n- \"cǐ\" = \"that\"\n- \"fɔ̀ shě\" = \"the day after tomorrow\"\n\nSequences like \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\"\n\nSo all temporal expressions use a standard structure:\n\n- [time expression] + [day name] → e.g., \"The day after tomorrow is Bvutfu\"\n\nOR:\n\n- [time expression] + [day name] — for events on that day\n\nNow, in the sentences we are to translate (16–19), they are spoken on **Bvuŋkaden**.\n\nSo all are from the perspective of **Bvuŋkaden**.\n\nWe now decode each sentence.\n\n---\n\n**Sentence 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː**\n\nBreak down:\n\n- \"bvúsɔ̀w\" → a day name? Possibly \"Bvusɔw\"\n- \"nǔ\" → \"you (sg)\"\n- \"fɔ̀ shě\" → \"the day after tomorrow\"\n- \"ntfǔː\" → \"is\"\n\nSo: \"You (sg) will be on the day after tomorrow?\" — doesn’t make sense.\n\nWait: is \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\"?\n\nYes, from (5): \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, you (sg) are on the day after tomorrow\" — no.\n\nWait — more likely: \"On Bvusɔw, the day after tomorrow is\" — no.\n\nAlternative: is it \"you will be on the day after tomorrow\"? But \"on Bvusɔw\" is a day.\n\nWait: maybe \"bvúsɔ̀w\" is not a day name but a verb?\n\nLook at (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you(sg) will steal the yam\"\n\nSo \"bvúsɔ̀w\" is used as a day name — like \"on Bvusɔw\"\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" → \"On Bvusɔw, the day after tomorrow is\" → doesn’t make sense.\n\nBut in (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" → followed by a day name?\n\nNo — in (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo it is: [day after tomorrow] + [is] + [day name]\n\nSo yes: \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\"\n\nBut the sentence is: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" = \"you\"\n\nSo \"you (sg) the day after tomorrow is\" — no.\n\nPerhaps \"bvúsɔ̀w\" is not a day name? But in (2) it is.\n\nAlternative: could it be \"you will be on the day after tomorrow\"?\n\nBut in (2): \"On Bvusɔw, you will steal\" — so \"on Bvusɔw\" is the day.\n\nSo perhaps the structure is: [day name] + [subject] + [verb phrase]\n\nBut here: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — missing a verb?\n\nAlternatively, is there a verb for \"to be\"?\n\nCompare with (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\"\n\n\"yɛ᷅n wáy\" = \"saw\"\n\nSo verbs are attached to subjects.\n\nIn (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"They saw me at the market just now\"\n\nSo \"yɛ᷅n\" = \"saw\"\n\nSo in (16): \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — is \"fɔ̀ shě\" a verb?\n\nNo — \"fɔ̀ shě\" = \"the day after tomorrow is\"\n\nThus, structure: [day name] + [subject] + [time expression]\n\nBut without a verb?\n\nWait — could \"fɔ̀ shě\" be a verb?\n\n\"yɛ᷅n\" = \"saw\", \"cɔ́ŋ\" = \"steal\", \"bɛ̂ː\" = \"killed\"\n\nNo \"fɔ̀ shě\" as a verb.\n\nAlternatively, is \"fɔ̀ shě ntfǔː\" a time phrase meaning \"on the day after tomorrow\"?\n\nNo — the full phrase \"fɔ̀ shě ntfǔː\" is used in (5) with \"is\" — it's \"the day after tomorrow is\"\n\nSo likely, the sentence is: \"On Bvusɔw, the day after tomorrow is...\" — but what?\n\nBut the sentence structure is \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"nǔ\" = you\n\nSo it must be: \"You (sg) the day after tomorrow is\"\n\nNo.\n\nAlternative: is \"bvúsɔ̀w\" a verb?\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal the yam\"\n\nSo \"bvúsɔ̀w\" is a day name.\n\nSo must be day name.\n\nTherefore, likely misordering.\n\nWait — could it be \"On Bvusɔw, (you) are the day after tomorrow\"? No.\n\nAnother possibility: could \"fɔ̀ shě\" be a verb meaning \"to be\" or \"to happen\"?\n\nIn (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\"\n\nSo \"fɔ̀ shě\" is part of time expression.\n\nConclusion: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" likely means: \"On Bvusɔw, you (sg) are on the day after tomorrow\" — but that’s contradictory.\n\nAlternatively, is it \"You (sg) will be on the day after tomorrow\" — and \"on Bvusɔw\" is misread?\n\nNo.\n\nWait — perhaps \"nǔ\" is not \"you\" but a structure?\n\nMaybe \"nǔ\" is a verb — check.\n\nIn (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"On Bvusɔw, you will steal...\"\n\nSo \"nǔ\" = you — subject.\n\nSo in (16), \"nǔ\" = you.\n\nSo likely: \"On Bvusɔw, you will be the day after tomorrow\" — nonsense.\n\nAnother idea: is \"fɔ̀ shě ntfǔː\" a temporal expression that modifies the verb?\n\nBut no verb.\n\nUnless it's a zero verb construction.\n\nCompare with (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\"\n\nSo \"will\" is implied in \"fí\" — \"fí\" may be future auxiliary.\n\nBut in (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\" — past\n\nIn (14): \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\" — future\n\nNo such particle in (16)\n\nBut in (5): \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — \"The day after tomorrow is Bvutfu\" — so \"fɔ̀ shě\" is attached to \"ntfǔː\"\n\nSo in (16), \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — maybe it's \"On Bvusɔw, you are the day after tomorrow\" — still odd.\n\nWait — could \"fɔ̀ shě\" mean \"on\" or \"in\"?\n\nIn (5): \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː\" is \"the day after tomorrow is\"\n\nSo \"fɔ̀ shě ntfǔː\" = a phrase meaning \"the day after tomorrow is\" — followed by day name.\n\nSo in sentence 16, it’s \"On Bvusɔw, you (sg) [time expression]\" — but what?\n\nUnless it’s: \"On Bvusɔw, you will (be) the day after tomorrow\" — grammatically incorrect.\n\nWait — could it be a typo or misreading?\n\nLook at our earlier day sequence.\n\nWe have:\n\n- Bvutfu (day 0)\n- Bvusɔw (day +1?) → in (2)\n- Bvuzhi (day +2?) → (3)\n- Bvuŋka (day +3?) → (4)\n- Bvuŋkaden (day +4?) → tomorrow from Bvusɔw? (8)\n\nFrom (1): \"Yesterday was Bvumbon\"\n\nSo:\n\n- Today = Bvutfu → no.\n\nFrom (1): \"Yesterday was Bvumbon\" — so yesterday = Bvumbon → today = Bvumbon +1\n\nFrom (5): \"The day after tomorrow is Bvutfu\" → today +2 = Bvutfu → so Bvutfu = Bvumbon +1 +2 = Bvumbon +3\n\nSo Bvutfu = Bvumbon +3\n\n(11): \"The day before yesterday was Bvuŋka\" → today -2 = Bvuŋka → Bvuŋka = today -2\n\nToday = Bvumbon +1 → so Bvuŋka = Bvumbon +1 -2 = Bvumbon -1\n\nNow (8): \"Tomorrow is Bvuŋkaden\" → tomorrow = Bvuŋkaden → today +1 = Bvuŋkaden → Bvuŋkaden = Bvumbon +1 +1 = Bvumbon +2\n\nSo now we have:\n\n- Bvumbon → 0\n- Bvumbon +1 → today\n- Bvumbon +2 → Bvuŋkaden\n- Bvumbon +3 → Bvutfu\n- Bvumbon -1 → Bvuŋka\n\nSo days:\n\n- Bvumbon: 0\n- Bvusɔw: ? (not directly given)\n\nBut in (2): \"On Bvusɔw, you will steal\" — so Bvusɔw is a day.\n\nWhere is it?\n\nNot in the list yet.\n\nBut in (13): \"On Bvutfu, the woman saw the market\" → on Bvutfu\n\nSo Bvusɔw must be a day in between.\n\nWith the sequence:\n\n0: Bvumbon \n1: today (Bvuŋkaden -1) \n2: Bvuŋkaden \n3: Bvutfu \n-1: Bvuŋka\n\nWe are to translate on Bvuŋkaden (day 2)\n\nSo relative to Bvuŋkaden:\n\n- Bvusɔw → possibly day 1? (Bvumbon +1)\n\nBut Bvumbon +1 = today = Bvuŋkaden -1 = day 1\n\nSo day 1 = Bvumbon +1\n\nSo if Bvusɔw is at day 1 → Bvusɔw = day 1\n\nSo on Bvuŋkaden (day 2), \"On Bvusɔw\" → refers to day 1 → one day before.\n\nNow sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\"\n\n\"bvúsɔ̀w\" = day Bvusɔw → day -1 from today\n\n\"nǔ\" = you (sg)\n\n\"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is\" — but what?\n\nUnless it's a verb: \"you will be the day after tomorrow\" — incorrect.\n\nAnother possibility: could \"fɔ̀ shě\" be a past tense?\n\nBut in (", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10503.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Analyze the verb forms in the examples to detect patterns.\n\nLook at the verb roots and their inflections.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n\"takujaa-\" (saw) → \"takujaa-tit\" → past tense, 3rd person, possibly marked for object (you). \nBut \"takujaatit\" ends in -vit (past tense, 3rd person), and \"takujaa\" is the verb root. \nNote: \"Qingmivit\" = \"your dog\" = possessive noun (subject). \n\"takujaatit\" = \"saw you\" = verb in past tense, marked for object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n\"inuuhukt\" → \"shot\", \"up\" = marker for subject? \n\"iluaqhaiji\" = \"the doctor\" \n\"qukiqtanga\" = \"shot\" → verb with -tanga suffix → past tense, transitive \n\"qukiqtanga\" = \"shot\" → root \"qukiq\" + -tanga → past tense, transitive verb\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself\" \n\"aanniqt\" → root of \"hurt\" → \"aanniqtutit\" = past, 3rd person (you), reflexive \nBut \"you hurt yourself\" → subject (you), object (yourself)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" \n\"aarqijaa\" → \"cure\" → \"aarqijaatit\" → past tense, transitive → object (you)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog\" \n\"iputuj\" → \"speared\", root \"iputuj\" → \"iputujait\" → past tense, transitive \n\"Qingmiq\" = \"you\" (subject) \nSo \"you speared the dog\" → subject (you), object (dog)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = \"the shaman\" \n\"iluaqhaijimik\" = \"a doctor\" (possessive or noun with genitive?) \n\"aarqisijuq\" = \"cured\" → root \"aarqi\" + -sijuq → past tense, transitive → verb \"cure\" with object\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came\" \n\"nanuq\" = \"polar bear\" (subject) \n\"qaijuq\" = \"came\" → verb root \"qaij\" → past tense (marked by -q)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy\" \n\"iluaqhaijivit\" = \"your doctor\" (subject) \n\"inuuhuktuit\" = \"your boy\" (object) \n\"aarqijanga\" = \"cured\" → verb form, past tense\n\nSo verb morphology:\n- Past tense marker: often -vit, -tanga, -it, -anga, -q\n- Transitive verbs: have object\n- Reflexive: self-related object (e.g., \"you hurt yourself\")\n- Possession: marked by -up or -it (e.g., \"iluaqhaijivit\" = \"your doctor\")\n\nPattern: Transitive verbs end in -tanga, -it, -anga, -vit? Let's check:\n- \"qukiqtanga\" = \"shot\" → past transitive → ends in -tanga\n- \"aarqijaatit\" = \"cured you\" → ends in -it → transitive\n- \"iputujait\" = \"speared\" → ends in -ait → transitive\n- \"aanniqtutit\" = \"hurt yourself\" → reflexive → ends in -utit\n- \"aarqisijuq\" = in example 6 → \"cured a doctor\" → ends in -ijuq → transitive\n\nBut in example 3: \"aanniqtutit\" → reflexive → object = subject → self\nIn example 4: \"aarqijaatit\" → \"cured you\" → transitive → object = you\n\nSo when object is not self, transitive verb ends in -it, -tanga, or -aqua?\n\nBetter: Tense and causative/marking patterns.\n\nObserve that:\n- \"hurt\" appears as:\n - \"aanniqtutit\" → reflexive (you hurt yourself)\n - \"aanniqtanga\" would be non-reflexive? Not present\n- \"cure\" is:\n - \"aarqijaatit\" → cured you\n - \"aarqisijuq\" → cured a doctor\n\nSo: \"aarqi\" + suffix → \"aarqijaatit\" → \"cured you\", \"aarqisijuq\" → \"cured a doctor\"\n\nSo object is marked by noun + genitive or possessive ending?\n\nLook at object marking:\n- In 1: \"takujaatit\" → your dog saw you → object is \"you\" → marked by -tait?\n- In 2: \"qukiqtanga\" → shot the doctor → doctor is object → \"iluaqhaiji\"\n- In 4: \"aarqijaatit\" → \"cured you\" → \"you\" marked by -tait?\n- In 5: \"iputujait\" → you speared the dog → dog is object → \"iluaqhaiji\" → not clear\n\nMore precisely, notice:\n- In 8: \"iluaqhaijivit\" → your doctor (subject), \"inuuhuktuit\" → your boy → object, \"aarqijanga\" → cured → so object is marked by -uit?\n\nPossessive suffix: -up, -it, -vit\n- \"inuuhuktuup\" → \"the boy\" (subject) in example 2\n- \"iluaqhaiji\" → \"the doctor\"\n- \"iluaqhaijivit\" → \"your doctor\" → possessor \"your\" + doctor → -vit\n- \"inuuhuktuit\" → \"your boy\" → -uit → so suffix -uit → \"your boy\"\n\nIn example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n\"Qingmiup\" = \"the dog\" (subject) \n\"ilinniaqtitsijiit\" = \"your teacher\" → possessive → \"ilinniaqtitsijiit\" → -sijiit → indicates object\n\"aaniiqtanga\" → \"hurt\" → root \"aanniqt\" + -tanga\n\nSo verb \"hurt\" appears with:\n- \"aanniqtutit\" → reflexive → you hurt yourself\n- \"aanniqtanga\" → you hurt someone → \"hurt someone\" verb form\n\nIn example 3: \"aanniqtutit\" → \"You hurt yourself\" → reflexive\nIn example 10: \"aanniqtanga\" → \"the dog hurt your teacher\" → transitive → object = your teacher\n\nSo \"aanniqt\" + -tanga → transitive \"hurt\"\n\"aanniqt\" + -utit → reflexive \"hurt yourself\"\n\nSimilarly, \"cure\": \n- \"aarqijaatit\" → cured you → \"you\" with -tait?\n- \"aarqisijuq\" → cured a doctor → \"a doctor\" → genitive?\n\nIn example 6: \"aarqisijuq\" → \"cured a doctor\" → object is \"a doctor\"\n\nIn example 8: \"aarqijanga\" → \"cured your boy\" → object is \"your boy\" → marked as -uit?\n\nSo pattern: \n- Object marked by possessive suffix: -up, -it, -vit, -uit, -sijiit?\n- Verb root + tense marker + optional object marker\n\nNow translate:\n\n19. The shaman hurt you.\n\nFrom example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\"\n\n\"angatkuq\" = shaman → subject \n\"aarqisijuq\" = cured → verb \n\"iluaqhaijimik\" = a doctor → object\n\nSo \"hurt\" is like \"cure\" but different root.\n\nIs there a verb for \"hurt\"? \nExample 3: \"aanniqtutit\" → you hurt yourself → reflexive \nExample 10: \"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → transitive\n\nSo verb root \"aanniqt\" → \"hurt\"\n\nThus: \"The shaman hurt you\" → subject = \"Angatkuq\" (shaman) \nverb = \"aanniqt\" + past tense → transitive → \"aanniqtanga\" \nobject = \"you\" → \"takujaa\" → but in example 1, \"your dog saw you\" → \"you\" is object\n\nIn example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takujaatit\" → saw you → so object = \"you\"\n\nSo in any transitive verb, object is in accusative form.\n\nIn this case, \"you\" → \"takujaa\" → but in other examples, how is \"you\" formed?\n\n\"takujaa\" → \"see\" \nBut in example 1, \"takujaatit\" = \"saw you\" → so possible that \"you\" is not marked in the verb, but in the object?\n\nBut example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → \"iluaqhaiji\" is object → not marked with -up or -it\n\nBut example 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"your boy\" → possessive -uit\n\nSo when object is specific, possessive ending appears.\n\nBut \"you\" → in singular, unpossessed? How?\n\nLook at example 1: \"Qingmivit takujaatit\" → your dog saw you → object = \"you\" → \"you\" is not marked as \"your\"\n\nIn other cases, object is marked with -it (e.g., \"takujaa-tit\" → saw you → object \"you\" may be in base form)\n\nSo perhaps the object is in base form — no possessive.\n\nBut in example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" \n\"ilinniaqtitsijiit\" → your teacher → possessive → -sijiit\n\nSo when object is a class, it may get possessive.\n\nBut \"you\" — when object, is it base?\n\nIn example 3: \"Aanniqtutit\" → you hurt yourself → reflexive → object = self\n\nSo for \"you\" — direct object, not reflexive → base?\n\nSo \"the shaman hurt you\" → \nsubject = \"Angatkuq\" \nverb = \"aanniqtanga\" — transitive \"hurt\" \nobject = \"you\" → \"takujaa\" — but no possessive?\n\nBut in example 1, \"takujaatit\" — \"you\" is object, and the verb is \"takujaa\" + -tait?\n\nWait: \"takujaa\" + \"it\" or \"tait\"?\n\nIn example 1: \"takujaatit\" → verb = \"takujaa-tit\"? \n\"takujaatit\" = \"saw you\" → so \"takuja\" is root, \"-a\" is object?\n\nBut \"takujaa\" → \"see\" → \"takujaa\" + -t it?\n\nBut in example 4: \"aarqijaatit\" → cured you → object \"you\"\n\nSo likely: \"aanniqtanga\" = hurt (transitive), object = \"you\" → base form?\n\nBut no word for \"you\" in examples except in object.\n\nIn example 1: object = \"you\" → \"takujaatit\" → verb = \"takujaa-tit\"\n\nSo base object \"you\" → verb root with -t it?\n\nSimilarly, \"aanniqtanga\" = hurt (transitive)\n\nThus: \"Angatkuq aanniqtanga takujaa\" → better?\n\nBut in example 1: \"Qingmivit takujaatit\" → your dog saw you → subject \"Qingmivit\", verb \"takujaatit\"\n\nSo verb ends in -it → so \"aanniqtanga\" → should end in -anga?\n\nBut in example 10: \"aanniqtanga\" → used for \"hurt\" — transitive\n\nYes: \"ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → direct object = \"your teacher\" → marked with -sijiit\n\nSo verb root + tense marker → after object?\n\nNo — in this case, object before verb?\n\nStructure: subject + object + verb?\n\nIn example 1: \"Qingmivit takujaatit\" → subject then verb → object not marked?\n\nActually, in Inuktitut, the object is marked on the verb.\n\nObserve:\n\n- Example 1: \"Qingmivit takujaatit\" → subject = your dog, verb = saw you → object = you → marked in verb?\n \"takujaatit\" — \"saw you\" — is this marking \"you\" in the verb?\n\nIn example 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → object = your boy → is \"inuuhuktuit\" the object?\n\nYes, \"inuuhuktuit\" = \"your boy\" → possessive → object is marked with -uit\n\nSimilarly, in example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → object = \"your teacher\" → marked with -sijiit\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → object = \"you\" → \"takujaa\" = verb? But \"aarqijaatit\" = \"cured you\"\n\nSo \"aarqijaatit\" → \"cured you\" → object \"you\" → not possessive\n\n\"you\" → base object?\n\nIn example 1: \"takujaatit\" → saw you → object \"you\" → verb ends in -tait?\n\n\"takujaa\" + -tait → yes?\n\nIn example 4: \"aarqijaatit\" → cured you → ends in -tait?\n\n\"aarqijaatit\" → yes — ends in -tait\n\nIn example 1: \"takujaatit\" → ends in -tait\n\nIn example 10: \"aanniqtanga\" → transitive hurt → roots end in -anga → \"hurt\" → transitive?\n\nBut in example 3: \"aanniqtutit\" → reflexive → ends in -utit\n\nSo pattern:\n- Transitive verb: root + -anga or -tait?\n- Reflexive: root + -utit\n\nExample 2: \"qukiqtanga\" → shot → transitive → -tanga\nExample 4: \"aarqijaatit\" → cured you → -tait\nExample 5: \"iputujait\" → speared → -ait (not -tait?)\n\n\"iputujait\" = \"you speared the dog\" → verb = \"iputujait\" → so transitive? Object = dog → not marked with possessive?\n\nBut in this form, object is not marked with -it — so verb ends in -ait?\n\nCompare:\n- \"qukiqtanga\" = shot → -tanga\n- \"aarqijaatit\" = cured you → -tait\n- \"iputujait\" = speared the dog → -ait\n\nSo inconsistent?\n\nBut \"qukiqtanga\" → object = doctor → not possessive → verb ends in -tanga\n\n\"aarqijaatit\" → object = you → verb ends in -tait\n\n\"iputujait\" → object = dog → verb ends in -ait\n\nNo consistent suffix?\n\nBut perhaps suffixes are determined by root.\n\nRoot \"qukiq\" → shot → -tanga\nRoot \"aarqij\" → cure → -tait or -anga?\n\"aarqijaatit\" → -tait → for you\n\"aarqisijuq\" → \"cured a doctor\" → -ijuq → not -tait\n\nSo object marking may be on the noun, not the verb.\n\nConclusion: In Inuktitut, object is marked by a possessive suffix on the noun.\n\nSo:\n- In example 1: \"Qingmivit takujaatit\" → subject = your dog, object = you → \"you\" is not marked with possessive? But \"takujaa\" verb ends in -tait? → so verb may not mark object\n\nIn example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → doctor is object → \"iluaqhaiji\" → base form → not possessive\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → \"you\" → not marked with possessive\n\nIn example 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"your boy\" → marked with -uit\n\nIn example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher → \"your teacher\" → -sijiit\n\nIn example 5: \"Qingmiq iputujait\" → you speared the dog → object = dog → base form? \"the dog\" → \"iluaqhaiji\"\n\nSo general rule:\n- Object is marked with", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11535.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Start by analyzing the provided examples to identify patterns in subject, object, verb forms, and agreement.\n\nKey observations from the examples:\n\nExample 1: \"Qingmivit takujaatit.\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (possessive + subject) \n- \"takujaatit\" = saw you → verb form for \"see\" with object \"you\" \n→ Structure: [subject] + [verb] + [object] \n→ \"see\" is transitive: \"saw you\" → verb is -it (past tense), and object is marked after verb with suffix or independent particle?\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga.\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (subject) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (verb) \n→ \"qukiqtanga\" = past tense of \"shoot\" \n→ Verb agrees with subject? Yes: \"inuuhuktuup\" (subject) → \"qukiqtanga\" (verb) \nBut: Does the object take a specific form? iluaqhaiji → not modified \n→ Subject: inuuhuktuup → \"the boy\" \n→ Object: iluaqhaiji → \"the doctor\" \n→ Verb: qukiqtanga → past of \"shoot\"\n\nExample 3: \"Aanniqtutit.\" → \"You hurt yourself.\" \n→ \"Aanniqtutit\" → \"you hurt yourself\" \n→ Self-reference: object is \"yourself\" → \"self\" is incorporated into verb \n→ \"aanniqtutit\" → verb with reflexive form \n→ \"tut\" = past tense; 'aanni' = hurt; with reflexive suffix \n→ So verb shows reflexive form for self-objects\n\nExample 4: \"Iluaqhaijiup aarqijaatit.\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor (subject) \n- \"aarqijaatit\" = cured you \n→ \"aarqi\" = cure; \"-jaatit\" = past tense + object \"you\" \n→ Verb uses object suffix: -jaatit → for \"you\" \n→ \"aarqijaatit\" = cured you \n→ So verb takes object with suffix\n\nExample 5: \"Qingmiq iputujait.\" → \"You speared the dog.\" \n- \"Qingmiq\" = you \n- \"iputujait\" = speared the dog \n→ \"iputujait\" = past tense of \"speared\" → verb with object \n→ \"iputujait\" = speared (dog) → object is \"dog\" \n→ So verb forms like \"iputujait\" have object incorporated\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq.\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured (verb) \n→ Verb \"aarqisijuq\" = cured + object \"a doctor\" \n→ Object marked: \"iluaqhaijimik\" → \"a doctor\" \n→ Verb ends with \"-ijuq\" → suggests intransitive or transitive form \n→ But it has object: \"aarqisijuq\" — here, verb has object suffix? \n→ \"aariq\" = cure; \"-si\" = aspect/other; \"-juq\" = object marker? — may be that verb has -q suffix with object marking \n\nWait: \"iluaqhaijimik\" = a doctor → is \"mik\" a plural or definite? \n\"mik\" = a (article), so likely \"a doctor\" → definite article implied \n\nExample 7: \"Nanuq qaijuq.\" → \"The polar bear came.\" \n- \"Nanuq\" = the polar bear \n- \"qaijuq\" = came → verb \n→ No object → verb is intransitive \n→ \"qaijuq\" = past tense of \"come\" → no object needed \n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga.\" → \"Your doctor cured your boy.\" \n- \"Iluaqhaijivit\" = your doctor (subject) \n- \"inuuhuktuit\" = your boy (object) \n- \"aarqijanga\" = cured \n→ \"aarqijanga\" = past tense of \"cure\" with object \n→ \"inuuhuktuit\" = your boy → possessive form \n→ Object marked in form → verb + object = \"aarqijanga\" \n→ Verb takes object suffix → similar to \"aarqijaatit\" or \"aarqisijuq\"\n\nExample 9: \"Angunahuktiup amaruq iputujanga.\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter \n- \"amaruq\" = the wolf (object) \n- \"iputujanga\" = speared \n→ \"iputujanga\" = past tense of \"speared\" with object \n→ Object is marked → verb has object suffix → like \"iputujait\" → now with \"anga\" instead of \"ait\"? \n→ Aix and \"anga\" may indicate different aspect or state?\n\nBut look: \"iputujait\" → \"you speared the dog\" \n→ \"iputujanga\" → \"the hunter speared the wolf\" \n→ So same verb root, different subject/object \n→ \"it\" vs \"anga\" → possible tense/aspect difference?\n\nWait: Example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga.\" → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog (subject) \n- \"ilinniaqtitsijiit\" = your teacher (object) \n- \"aanniqtanga\" = hurt \n→ Verb \"aanniqtanga\" → hurts → past tense, with object \n→ \"aanniqtanga\" = past tense of \"hurt\" with object \nSo verb form: root + past suffix + object suffix \n\nExample 11: \"Ukiakhaqtutit.\" → \"You fell.\" \n→ \"Ukiakhaqtutit\" → you fell → verb with reflexive or no object → self-action \n→ \"utit\" = past tense → \"qut\" → may be root \n→ \"Ukiakha\" → \"fall\" → no object \n→ Intransitive → verb form → \"utit\" attachment\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq.\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter \n- \"nanurmik\" = a polar bear (object) \n- \"qukiqsijuq\" = shot \n→ So verb \"qukiqsijuq\" = shot with object \n→ Root: \"qukiq\" = shoot → past with object → \"qukiqsijuq\" \n→ Object appears before verb? → \"nanurmik\" → \"a polar bear\" → object \n→ Verb: \"qukiqsijuq\" → full form — includes object suffix? \n→ But in Example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" — object first, then verb \nWait: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → subject, object, verb \nSimilarly: \"Angunahukti nanurmik qukiqsijuq\" → subject, object, verb \n→ So order: subject, object, verb\n\nBut in Example 1: \"Qingmivit takujaatit\" → subject, verb, object? \n\"Qingmivit\" = your dog \n\"takujaatit\" = saw you → verb with object? \n→ \"takujaatit\" = saw you → object \"you\" embedded in verb? \n→ In that case: verb: \"takuj\" + \"a\" + \"t\" → suffix for object?\n\nIn Example 3: \"Aanniqtutit\" → you hurt yourself — no object marked — reflexive incorporated\n\nIn Example 5: \"Qingmiq iputujait\" → you speared the dog → here, \"Qingmiq\" is subject, \"iputujait\" is verb with object\n\nSo movie-type pattern:\n\n- Transitive verbs: verb forms include object suffix \n- Intransitive verbs: verb stands alone \n- Reflexive verbs: verb includes self-object\n\nSo for verb derivation, we need to identify: \n- Verb root (e.g., \"hurt\" → aanniqt, \"see\" → takuj, \"shoot\" → qukiq, \"cure\" → aarqi, \"fall\" → ukiakha) \n- Tense: all seem past tense → suffix -it, -anga, -tanga, -juq, etc. \n- Agreement: subjects are marked with possessive or determiner → \"your\", \"the\", etc. \n- Object: marked with suffix or particle?\n\nNow list known verb roots from examples:\n\n- hurt → aanniqt (e.g., aanniqtutit = you hurt yourself) \n- see → takuj (takujaatit = saw you) \n- shoot → qukiq (qukiqtanga = shot doctor) \n- cure → aarqi (aarqijaatit = cured you) \n- spear → iputuj (iputujait = speared dog) \n- come → qaiju (qaijuq = came)\n\nIn Example 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → doctor is subject, verb with object “you” → aarqijaatit → aarqi + j + aat + it? \n\"aarqijaatit\" → root aarqi, suffix j (object?), aat, it (past)? \n\nWait: in \"iluaqhaijimik aarqisijuq\" → \"a shaman cured a doctor\" → \"aarqisijuq\" → likely aarqi + si + juq → object marker in -juq?\n\nBut in Example 2: \"qukiqtanga\" → qukiq + t + a + ng? \n\nLet’s determine pattern of object marking.\n\nIn all transitive verbs, the object is marked in the verb form. \nExample 2: \"qukiqtanga\" — \"qukiq\" + \"t\" + \"a\" + \"ng\"? — simplified as \"qukiqtanga\" → verb with object \nExample 4: \"aarqijaatit\" → \"aarqi\" + \"ja\" + \"at\" + \"it\"? \nBut in Example 8: \"aarqijanga\" → cured your boy → same verb root → aarqi + \"ja\" + \"anga\"? \nIn 8: \"aarqijanga\" — cured your boy \nIn 4: \"aarqijaatit\" — cured you \n→ Different object → \"you\" vs \"your boy\" \n→ Object marked via vowel or suffix: \"ja\" appears in both \n→ \"atit\" vs \"anga\" → different suffixes → may indicate different object types\n\nBut in Example 12: \"qukiqsijuq\" → \"shot a polar bear\" → object suffix \"juq\"? \n\"qukiq\" → shoot → \"qukiqsijuq\" → qukiqsij + uq → may be object suffix \"-juq\"\n\nExample 5: \"iputujait\" → speared the dog → \"iputujait\" → \"iputuj\" + \"ait\"? → \"ait\" = object suffix?\n\nExample 9: \"iputujanga\" → speared wolf → \"anga\" → object suffix?\n\nSo verb forms:\n\n- hurt → aanniqt + ut + it → aanniqtutit \n- see → takuj + a + t + it → takujaatit \n- shoot → qukiq + t + a + ng? → qukiqtanga \n- cure → aarqi + j + a + a + t + it → aarqijaatit → forest? \n- spear → iputuj + a + it → iputujait \n- come → qaijuq → no object\n\nPattern: \nTransitive verbs end in -it, -anga, -tanga, -juq — all past tense with object \nVerb root + object marker + tense suffix \n\nObject marker varies per verb: \n- For \"hurt\": aanniqt → aanniqtutit (reflexive) \n- For \"see\": takuj → takujaatit → object \"you\" \n- For \"cure\": aarqi → aarqijaatit (you), aarqijanga (your boy) \n→ \"ja\" seems common → possibly object marker? \n- For \"spear\": iputujait → object \"the dog\", iputujanga → object \"wolf\" \nSo: object suffix seems to be either -ait, -anga, -juq — depending on verb \n\nNow, check possessive marking:\n\n- \"your\" → implies possessive marker: \n - \"qingmivit\" → your dog \n - \"iluaqhaijivit\" → your doctor \n - \"inuuhuktuit\" → your boy \n - \"ilinniaqtitsijiit\" → your teacher → \"ilinniaqtitsijiit\" \n→ Pattern: noun + \"vit\" → possessive marker \n\"vit\" = your → used after subject noun \n\"up\" = the → definite \n\"mik\" = a → in example 6: \"iluaqhaijimik\" → a doctor \nSo possessive: \n- \"Xvit\" = your X \n- \"Xup\" = the X \n- \"Xmik\" = a X\n\nNow solve the translation:\n\n19. \"The shaman hurt you.\" \n→ Subject: \"the shaman\" → \"Angatkuq\" (from example 6) \n→ Verb: \"hurt\" → \"aanniqt\" → past form? \n→ From example 3: \"aanniqtutit\" = you hurt yourself → one person, reflexive \n→ For \"you\" as object → object suffix needed \nLook for comparable: \nExample 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → subject = doctor, object = you, verb = aarqijaatit \n→ So \"cure you\" = aarqijaatit \n→ But \"cure\" = aarqi → hurt = aanniqt → likely aanniqt + object suffix \n\nIn example 3: \"you hurt yourself\" = aanniqtutit → reflexive \n→ For \"you\" as object, non-reflexive → must use object suffix? \nBut in example 3, object is \"self\" — incorporated \n\nNow, is there a transitive form of \"hurt\" with object?\n\nExample 10: \"the dog hurt your teacher\" = \"Qingmiup ilinniaqtitsijiit aanniqtanga\" \n→ \"aanniqtanga\" = hurt (with object) \n→ Object: \"your teacher\" → ilinniaqtitsijiit \n→ Verb: aanniqtanga → root aanniqt + object suffix \"anga\"? \n→ \"aanniqtanga\" = hurt + object (your teacher)? \n→ Compare to \"aanniqtutit\" → hurt yourself — reflexive → \"ut\" suffix? \n\nSo: \n- aanniqtutit = you hurt yourself \n- aanniqtanga = you hurt your teacher (transitive, non-reflexive) \n→ Object suffix = \"anga\"? \n\nSo for \"hurt you\" → must be aanniqt + \"a\" + \"t\" + \"it\"? → \"aanniqtatit\"? \nBut no such pattern.\n\nIn \"aanniqtanga\", object is \"your teacher\" → marked as \"ilinniaqtitsijiit\" → a possessed noun? \nBut \"aanniqtanga\" = verb with object incorporated \n\nSimilarly, \"qukiqtanga\" = shot doctor → object \"doctor\" not marked in noun — verb has object suffix \n\nTherefore: in all cases, transitive verbs have object incorporated in verb via suffix, not in noun.\n\nSo we need to find the verb form of \"hurt\" with object \"you\".\n\nFrom examples:\n\n- hurt yourself → aanniqtutit \n- hurt your teacher → aanniqtanga (in example 10) \n→ So: \n- \"utit\" = reflexive (self) \n- \"anga\" = object → \"your teacher\" \n\nSo for \"hurt you\", object is \"you\" → not \"yourself\" \n\nIs there a form for \"hurt you\"? \n\nIn example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"takuj\" = see → \"takujaatit\" → object \"you\" → suffix \"a\" + \"t\" + \"it\"? \n\nIn that case: \"a\" + \"t\" + \"it\" → \"aait\"? → \"takujaatit\" → takuj + a + ja + at + it? \n\nWait — more likely: \"takuj\" + \"a\" + \"at\" + \"it\"? → no — perhaps \"a\" is object marker \n\nBut in \"aanniqtanga\" → \"a\" in \"anga\" — may be object marker \n\nSimilarly, in \"aarqijaatit\" — \"a\" in \"jaat\"? → \"jaat\" → possibly object suffix \n\nIn example 2: \"qukiqtanga\" → \"qukiq\" + \"t\" + \"anga\"? → \"tanga\" → ? \n\nIn example 9: \"iputujanga\" → \"spear wolf\" → object suffix -anga \n\nSo object suffix varies: \n- hurt: aanniqt + ut → reflexive (utit) \n- hurt (object): aanniqt + a + ng → aanniqtanga? \n- shoot: qukiqtanga → qukiq + t + a + nga? \n- cure: aarqijaatit → aarqi + ja + aat + it? \n- spear: iputujait, iputujanga → object suffix -ait, -anga \n\nSo object suffix appears to be attached", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11938.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Identify core verbs and their forms in the examples.\n\nFrom example 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" is the verb \"to hurt\" in third person (he/she) or reflexive. \n→ the suffix \"-ut\" indicates past tense, and \"-t\" suggests verb conjugation for first person (you). \n→ \"aanniqtutit\" = \"you hurt yourself\" → so \"aanniqt\" is root of \"hurt\", and \"-utit\" = past tense, first person (you), marked for reflexive.\n\nFrom example 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = \"cured you\" → verb “aarqijaat” = “to cure”, with \"-it\" = past tense, recipient (you), third person. \n→ \"aarqijaatit\" = past tense, active, with patient (you).\n\nFrom example 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = you speared → verb “iputuj” = \"to spear\", past tense, first person. \n→ \"iputujait\" = past tense, first person, active.\n\nFrom example 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n→ \"takujaatit\" = \"saw you\" → verb \"takuj\" = \"to see\", past tense, with object (you). \n→ \"takujaatit\" = past tense, verb \"see\", object marked.\n\nFrom example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = \"cured a doctor\" → \"aarqisijuq\" must be \"cured\" + object \"a doctor\" → object is \"iluaqhaijimik\" = \"a doctor\" (note: iluaqhaiji = doctor, -mik = singular definite). \n→ \"aarqisijuq\" = cured, past tense, third person, object \"a doctor\".\n\nBut in 19: \"The shaman hurt you.\" \n→ Should be “shaman + hurt + you” → “Angatkuq aanniqtutit”?\n\nCheck: \"Angatkuq\" = shaman (from example 6: Angatkuq iluaqhaijimik aarqisijuq → shaman cured a doctor) \n→ so \"Angatkuq\" is subject, third person.\n\nHurt you → from example 3: \"aanniqtutit\" = you hurt yourself → but that’s reflexive. \nWe need “hurt you” → object is “you”, so object must be marked.\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" → “the doctor cured you” → object is “you” — so \"aarqijaatit\" with object marker.\n\nSo object marker: in \"aarqijaatit\" — the \"it\" is the past tense and the patient. \nBut in example 3: \"aanniqtutit\" — you hurt yourself → you is both subject and object.\n\nSo for “the shaman hurt you” → subject = “Angatkuq”, verb = “aanniqt” (to hurt), tense = past, object = “you”.\n\nIn Inuktitut, verbs are often marked for subject and object.\n\nLook at example 3: \"Aanniqtutit\" — you hurt yourself → subject and object are one → reflexive.\n\nExample 1: \"Qingmivit takujaatit\" → your dog (subject) saw you (object) → so \"takujaatit\" includes object marker (you).\n\nSo \"takujaatit\" = saw (past) + you (object)\n\nSimilarly, \"iputujait\" = you speared (dog) → object is dog.\n\nSo in general: verb + object (determined by affix or ending) → past tense.\n\nSo for 19: \"The shaman hurt you\" → subject: \"Angatkuq\", verb: \"aanniqt\", object: \"you\" → must be “Angatkuq aanniqtutit”?\n\nBut in example 3: \"aanniqtutit\" = you hurt yourself → first person.\n\nSo for third person (the shaman), and object (you), we need a past tense form with object marked.\n\nCheck example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman + doctor + cured → “aarqisijuq” = cured something → object is marked by -mik.\n\nIn this form, “iluaqhaijimik” is object → doctor (with -mik), and “aarqisijuq” = past tense of cure.\n\nSo verb form for \"cured\" → “aarqisijuq” → past tense, object marked.\n\nSimilarly, \"hurt\" in example 3 is \"aanniqtut\" — but only with reflexive.\n\nSo what is the correct form for \"hurt someone\"?\n\nExample 11: \"Ukiakhaqtutit\" → “You fell.” → so “ukiakhaqtut” = fall, past tense, first person.\n\nSo patterns:\n\n- Past tense: often ends in -it\n- Subject: definite possessive or third person\n- Object: marked in verb stem\n\nExample 4: \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → \"aarqijaatit\" = cured + you → patient = you → object marker = -it\n\nSo in 19: \"The shaman hurt you\" → subject = \"Angatkuq\", verb = \"aanniqt\", object = \"you\"\n\n→ so \"Angatkuq aanniqtuyit\" or \"Angatkuq aanniqtutit\"?\n\nBut in example 3: \"aanniqtutit\" = you hurt yourself → first person, reflexive.\n\nWe need third person subject + object → must be \"aanniqtutit\" with object?\n\nBut in example 4: \"aarqijaatit\" = cured + you → which is third person subject (doctor) + object \"you\"\n\nSo similar structure: verb form has past tense suffix -it and object marker.\n\nSo generic pattern: [Subject] + [Verb-root] + [past tense suffix] + [object marker if needed]\n\nBut in Inuktitut, object marking is often internal to the verb.\n\nCompare:\n\n- Example 4: iluaqhaijiup aarqijaatit → \"doctor\" + verb \"cured you\" → so \"aarqijaatit\" = verb with patient \"you\"\n\n- Example 6: Angatkuq iluaqhaijimik aarqisijuq → shaman + doctor + cured → \"aarqisijuq\" = past tense of cure → without object marker? But \"iluaqhaijimik\" is object.\n\nSo object is marked separately — no verb object affix.\n\nBut in 4: \"aarqijaatit\" has \"it\" and \"you\" is marked in the verb.\n\nWait: \"aarqijaatit\" — \"ita\" is not present — \"aarqijaatit\" — ending is -it → past tense → and \"a\" might be object marker?\n\nNo: \"iluaqhaijiup\" = the doctor → subject, \"aarqijaatit\" = cured you → verb with object.\n\nSo the verb \"aarqijaat\" has a form that includes object marking.\n\nSimilarly, “aanniqt” should have object marking.\n\nBut which form?\n\nIn example 3: \"Aanniqtutit\" = you hurt yourself → reflexive → both subject and object are \"you\"\n\nIn other cases, object is marked separately?\n\nLook at example 5: \"Qingmiq iputujait\" → you speared the dog → \"iputujait\" = you (subject) + speared + dog (object)\n\n→ so \"iputujait\" has object \"dog\" → must have object marker.\n\nSimilarly, \"takujaatit\" = saw you → object marked.\n\nSo in general: verb stem + object marker (in affix) → past tense.\n\nSo for \"hurt you\", verb base \"aanniqt\" + object marker for \"you\" → what is that?\n\nIn example 1: \"takujaatit\" → saw you → object is \"you\"\n\n\"takuj\" + \"a\" + \"ait\"? No.\n\nBorrowed from example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"takujaatit\"\n\n→ verb root \"takuj\" → see → with affix \"-a\" (patient?) and \"-it\" (past)\n\nSimilarly, \"aanniqt\" → hurt → would be \"aanniqt\" + marker → \"aanniqtutit\" → but only reflexive.\n\nWhere is object marker?\n\nPossibility: the object marker is \"a\" for \"you\" or \"y\"?\n\nIn example 1: \"takujaatit\" — \"takujaat\" → \"takuj\" + \"a\" + \"at\"? Unlikely.\n\nNote: in example 4: \"aarqijaatit\" — cured you → here \"ja\" is a marker?\n\n\"aarqijaatit\" → pattern: \"aariq\" + \"ja\" + \"aatit\"? No.\n\nBut in example 6: \"aaruqisijuq\" — \"cured a doctor\" — here \"iluaqhaijimik\" is object → so object is marked by suffix -mik.\n\nSo object is marked separately.\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" → \"doctor\" + cured you → the verb is \"aarqijaat\" with object \"you\", so verb has object marker.\n\nIn example 4: \"aarqijaatit\" — \"a\" might be object marker?\n\nYes — compare: \n- in 4: \"aarqijaatit\" = cured you \n- in 6: \"aarqisijuq\" = cured a doctor → \"aarqisijuq\" — \"sij\" might be object marker?\n\n\"aarqisijuq\" → \"isijuq\" — \"sij\" could be object marker?\n\nCompare: \n- \"iluaqhaijimik\" = a doctor — with -mik → definite singular object \n- \"aarqijaatit\" = cured you → \"you\" = first person, so marker might be -it?\n\nNo — in 4, object is you → first person, so different.\n\nBut in 4, the verb is \"aarqijaatit\" — has \"it\" ending, and object is \"you\".\n\nSo may be verb ends in -it and carries patient marking.\n\nIn 5: \"Qingmiq iputujait\" → you speared the dog → \"iputujait\" → verb with object implied.\n\nIn 11: \"Ukiakhaqtutit\" → you fell → first person.\n\nConclusion: Object marking is in the verb stem or suffix.\n\nSpecifically:\n\n- For \"see you\" → \"takujaatit\" \n- For \"cure you\" → \"aarqijaatit\" \n- For \"cure a doctor\" → \"aarqisijuq\" with object \"iluaqhaijimik\" → object marked with -mik\n\nSo object markers are:\n- -it: for \"you\" (subject or object?)\n- -mik: for \"a doctor\", definite singular\n\nBut \"it\" in verb is tense.\n\nTherefore, for \"the shaman hurt you\" → subject: \"Angatkuq\", verb: \"aanniqt\" → to hurt, same as in \"aanniqtut\" → but needs object marking.\n\nIn example 3: \"aanniqtutit\" — you hurt yourself → reflexive → both subject and object are you.\n\nSo for \"the shaman hurt you\" → subject: shaman (third person), object: you → so verb must be \"aanniqtutit\"?\n\nBut \"aanniqtutit\" is in first person.\n\nThus, it must be that the verb form has object marker.\n\nIn fact, likely: object is marked by -it if it's \"you\", or by -mik for \"a doctor\".\n\nBut in example 4: \"aarqijaatit\" = cured you → object \"you\" with -it\n\nIn example 6: \"aarqisijuq\" = cured a doctor → object marked by -mik (iluaqhaijimik)\n\nSo verb form \"aarqisijuq\" does not have object marker — object is marked separately.\n\nSimilarly, in example 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\"\n\n\"aarqijanga\" = cured → \"anga\" is object marker for \"boy\"?\n\n\"aarqijanga\" → \"cure\" + object → \"anga\" = boy?\n\n\"ajaranga\" → base?\n\nFrom context: \"iluaqhaijivit\" = your doctor (subject), \"inuuhuktuit\" = shot you (exact match earlier), \"aarqijanga\" = cured boy → object is \"your boy\"\n\nSo \"aarqijanga\" = cured boy → object marker is \"anga\"?\n\nBut in example 4: \"aarqijaatit\" = cured you → object \"you\"\n\nSo possible object markers:\n- -it: for \"you\"\n- -anga: for \"boy\"\n- -mik: for \"a doctor\"\n\nThis is inconsistent.\n\nBetter: in 6: \"iluaqhaijimik\" — \"a doctor\" with -mik → object\n\nIn 4: \"aarqijaatit\" — verb form implies object \"you\"\n\nSo the object is marked in the object noun, not in the verb.\n\nIn 4: subject = doctor, object = you → you is unmarked? But \"you\" only appears as object.\n\nIn example 3: \"Aanniqtutit\" — you hurt yourself → you is both subject and object, marked by reflexive.\n\nSo for \"the shaman hurt you\" → subject = shaman, object = you → object is marked by verb form?\n\nBut in 1: \"takujaatit\" = saw you → object marked\n\nIn 5: \"iputujait\" = speared the dog → object marked\n\nSo both object and verb are involved.\n\nThus, in all cases, the object is marked in the verb via an affix.\n\nPossible pattern:\n\n- \"you\" → affix -it (e.g., aarqijaatit, takujaatit)\n- \"a doctor\" → affix -mik (e.g., iluaqhaijimik)\n- \"boy\" → affix -anga (e.g., aarqijanga)\n\nThus, verb root + object marker + past tense suffix\n\nNow:\n\n19. The shaman hurt you → \"Angatkuq aanniqt [object marker for you] [tense]\"\n\n→ object: you → marker = -it → then past tense = -it → so \"aanniqtutit\"?\n\nBut \"aanniqtutit\" = you hurt yourself → reflexive.\n\nWe need non-reflexive — shaman hurt you.\n\nBut in the examples, is there a form for third person?\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman + doctor + cured\n\nVerb is \"aarqisijuq\" — past tense, no object marker in verb — object is marked with -mik.\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" — doctor cured you → verb has -it for object.\n\nSo inconsistency.\n\nAlternative: object marker is embedded in the verb stem.\n\nBut for \"hurt you\", what is the base?\n\nExample 3: \"aanniqtutit\" — you hurt yourself\n\nSo if we remove \"yourself\", we have \"aanniqtut\" — but it's not a standalone verb.\n\nBut in example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → verb \"qukiqtanga\" = shot?\n\n\"qukiqtanga\" — \"qukiqt\" = shoot, \"anga\" = patient?\n\nSo \"anga\" is object marker.\n\nSimilarly, in 22: \"You shot a dog\" → \"you\" + shot + dog → likely \"iputujait\" is \"you speared\", so \"qukiqtanga\" = shot + person?\n\nIn 2: \"qukiqtanga\" = shot doctor → doctor object → so \"anga\" object marker.\n\nSimilarly, in 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf → \"iputujanga\" = speared wolf → object \"wolf\"\n\nSo \"anga\" = object marker for animal/thing.\n\nIn 11: \"Ukiakhaqtutit\" = you fell → \"you\" subject, no object.\n\nSo in verb form:\n\n- When object is a person: -it or -a?\n- When object is thing: -anga?\n\nIn 4: \"aarqijaatit\" = cured you → \"you\" → using \"it\"\n\nIn 6: \"aarqisijuq\" = cured doctor → object “doctor” marked by -mik → not -anga.\n\nSo two systems?\n\nThus: in Inuktitut, object is marked with:\n- -it: for \"you\" (first person patient)\n- -mik: for \"a doctor\" (definite singular)\n- -anga: for \"boy\", \"wolf\", etc.\n\nSo for a general \"hurt you\" → verb = \"aanniqt\" + \"it\" + \"it\" → \"aanniqtutit\" — but this is reflexive.\n\nWait — perhaps \"aanniqt\" + \"u\" + \"t\" → no.\n\nPerhaps the object marker is on the verb, and \"it\" is tense.\n\nSo for \"hurt you\" → \"Angatkuq aanniqtutit\" — but this is first person.\n\nAlternatively, the verb form for \"hurt\" is \"aanniqt\" with past tense -it, and object marked by -it or by other.\n\nBut from example 3: only reflexive.\n\nSo is there a form for third person?\n\nIn example 8: \"Iluaqhaijivit inuuhuktuit aarqij", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12324.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are given English sentences and their Inuktitut translations, and we must translate five new sentences into Inuktitut based on observed patterns.\n\n---\n\nStep 1: Identify verb patterns and argument structure.\n\nLook at the given pairs:\n\n1. Qingmivit takujaatit → Your dog saw you. \n → \"saw\" = takujaatit (3rd person, past, verb with object) \n → Subject: \"your dog\" (Qingmivit — Qingmi- + your? + -v-?) \n → \"saw\" is marked with -vit (past tense) and takes object → takujaatit \n → \"takujaatit\" = saw YOU, indicating object is second person \n → So: subject + -vit (past) + verb + object (in -a**t**it form) \n\n2. Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor \n → \"shot\" = qukiqtanga → verb with object (qukiqtanga) \n → subject: Inuuhuktuup (boy) → \"Inuuhukt- + -uup\" \n → verb: qukiqtanga → \"qukiq\" (shot) + -tanga → object: iluaqhaiji (doctor) \n\n3. Aanniqtutit → You hurt yourself \n → \"hurt\" = aanniqtutit \n → subject: \"you\" (implied) \n → \"aanniqt- + -utit\" → object = yourself → implied reflexive \n → verb: aanniqtutit → past, reflects self \n\n4. Iluaqhaijiup aarqijaatit → The doctor cured you \n → \"cured\" = aarqijaatit \n → subject: iluaqhaijiup → doctor \n → verb: aarqijaatit → \"aarqi\" (cure) + -jaatit → object = you \n\n5. Qingmiq iputujait → You speared the dog \n → \"speared\" = iputujait \n → subject: you → implied \n → verb: iputujait → \"iputu\" (to spear) + -jait → object: dog (implied) \n → So: subject (you) + verb (iputujait) with object = dog \n\n6. Angatkuq iluaqhaijimik aarqisijuq → The shaman cured a doctor \n → verb: aarqisijuq → \"aarqi\" (cure) + -sijuq \n → object: iluaqhaijimik → iluaqhaiji + -mik → \"a doctor\" (definite, singular) \n → subject: Angatkuq → shaman \n\n7. Nanuq qaijuq → The polar bear came \n → \"came\" = qaijuq \n → subject: Nanuq \n → verb: qaijuq → simple past, no object \n\n8. Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy \n → verb: aarqijanga → aarqi + -janga → \"cured\" \n → subject: iluaqhaijivit → \"your doctor\" → iluaqhaiji + -vit \n → object: inuuhuktuit → \"your boy\" → inuuhukt + -uit \n → so → verb is aarqijaatit → but here → aarqijanga → different ending? \n\nWait: structure in 8: \n- iluaqhaijivit → your doctor → subject \n- inuuhuktuit → your boy → object \n- aarqijanga → cured → past tense, object as \"your boy\" → suffix -janga \nCompare to 4: iluaqhaijiup aarqijaatit → doctor cured you → object = you → -jaatit \nBut in this case: doctor cured your boy → object = your boy → -janga \n\nSo suffix changes based on object? \n\nLook at verb forms:\n\n- aarqijaatit → cured you \n- aarqijanga → cured your boy \n\nPossibility: suffix -jaatit = \"you\" (object), -janga = \"your boy\" (object) → object-specific form? \n\nBut is that a pattern? \n\nNow 9: Angunahuktiup amaruq iputujanga → The hunter speared the wolf \n→ ver: iputujanga → \"speared\" + object → wolf \n→ subject: Angunahuktiup → hunter \n→ object: amaruq → wolf \n→ verb: iputujanga → iputuj + -anga \n\nCompare with 5: Qingmiq iputujait → you speared the dog \n→ iputujait → iputuj + -ait \n\nSo verb suffix varies with object?\n\n- object = you → iputujait \n- object = wolf → iputujanga \n\nSo perhaps suffix indicates object? \n\nBut in 4: iluaqhaijiup aarqijaatit → doctor cured you → cured you → aarqijaatit → -jaatit → object = you \nIn 8: doctor cured your boy → aarqijanga → -janga \n\nIn 9: hunter speared the wolf → iputujanga → -anga \nIn 5: you speared the dog → iputujait → -ait \n\nSo the suffix changes based on object. \n\nLet’s collect verb patterns:\n\n| Verb | Object | Suffix |\n|------|--------|-------|\n| takujaatit | you | -jaatit |\n| aarqijaatit | you | -jaatit |\n| iputujait | dog | -ait |\n| iputujanga | wolf | -anga |\n| aarqijanga | your boy | -janga |\n\nWait — \"your boy\" → inuuhuktuit → inuuhukt + -uit \n\"your doctor\" → iluaqhaijivit → iluaqhaiji + -vit \n\nSo object noun has a possessive or clarifying marker. \n\nBut verb endings: \n- -ait: dog \n- -anga: wolf \n- -jaatit: you \n- -janga: boy (your boy) \n\nSo is the verb suffix agreeing with the object noun in some way?\n\nAlternatively, perhaps the suffix is inflected based on object noun class or number?\n\nAlternatively, maybe the suffix is determined by the object noun’s root form.\n\nLook at verb: iputuj + suffix → object root may be part of pattern.\n\nBut also, in 10: \nQingmiup ilinniaqtitsijiit aanniqtanga → The dog hurt your teacher \n→ \"hurt\" = aanniqtanga → verb: aanniqt + -anga → object = your teacher → so -anga \n\nIn 11: Ukiakhaqtutit → You fell → \"fell\" = ukiakhaqtutit → verb with no object, subject = you \n\nIn 12: Angunahukti nanurmik qukiqsijuq → The hunter shot a polar bear \n→ \"shot\" = qukiqsijuq → qukiq + -sijuq → object = nanurmik (polar bear) \n\nSo verbs:\n- aanniqtanga → hurt your teacher → -anga \n- aarqijaatit → cured you → -jaatit \n- aarqijanga → cured your boy → -janga \n- iputujait → speared dog → -ait \n- iputujanga → speared wolf → -anga \n\nNow look at the object:\n\n| Object | Verb suffix |\n|--------|-------------|\n| you | -jaatit |\n| your teacher | -anga |\n| your boy | -janga |\n| dog | -ait |\n| wolf | -anga |\n| doctor | -jaatit (in 6: Angatkuq iluaqhaijimik aarqisijuq → cured a doctor → aarqisijuq → suffix -sijuq) |\n\nWait — 6: Angatkuq iluaqhaijimik aarqisijuq → cured a doctor → verb = aarqisijuq → -sijuq \n→ But 4: cured you → aarqijaatit → -jaatit \n→ 8: cured your boy → aarqijanga → -janga \n\nSo three forms of same verb \"cure\": \n- aarqi + -jaatit → you \n- aarqi + -janga → your boy \n- aarqi + -sijuq → a doctor \n\nSo suffix depends on object noun:\n\n- -jaatit → you \n- -janga → your boy \n- -sijuq → a doctor (singular, definite) \n- -anga → wolf, teacher (maybe different class) \n\nIn 5: you speared the dog → iputujait → object = dog → -ait \nIn 9: hunter speared wolf → iputujanga → -anga \nIn 10: dog hurt your teacher → aanniqtanga → -anga \n\nSo a generic pattern seems to emerge: \nThe verb stem is combined with a suffix that indicates the specific object.\n\nAlso, note that:\n- Subject is often marked with possessive or definite form (e.g., \"your\", \"a\", \"the\")\n- Verb is past tense, marked with -it or -uit or -anga, etc.\n\nNow focus on translation of required sentences.\n\n---\n\n19. The shaman hurt you.\n\n\"shaman\" → Angatkuq (from sentence 6) \n\"hurt\" → aanniqt (also seen in 3: aanniqtutit) \n→ The shaman hurts you → so verb: aanniqt + object suffix → object = you → -jaatit \n→ So verb: aanniqt + -jaatit → aanniqtjaatit? \nBut check: 3. Aanniqtutit → you hurt yourself → aanniqtutit → aanniqt + -utit \n→ Reflexive, self \n\nBut here: \"hurt you\" → object = you → is it aanniqtjaatit? \n\nBut look at 4: iluaqhaijiup aarqijaatit → doctor cured you → aarqi + -jaatit \nSo \"cure\" → -jaatit for you \nSimilarly, 10: Qingmiup ilinniaqtitsijiit aanniqtanga → dog hurt your teacher → aanniqtanga → -anga \n\nBut \"you\" → object → in other cases, -jaatit used.\n\nIn 3: you hurt yourself → aanniqtutit → -utit → reflexive \n\nBut \"hurt you\" → subject = shaman, object = you → not reflexive → should use -jaatit?\n\nBut is -jaatit used in all \"you\" objects?\n\nCompare:\n- 4: doctor cured you → aarqijaatit → -jaatit \n- 10: dog hurt your teacher → aanniqtanga → -anga (teacher) \n- 3: you hurt yourself → aanniqtutit → -utit (reflexive)\n\nSo for non-reflexive \"you\", use -jaatit?\n\nBut in 4, \"cured you\" → -jaatit \nIn other verbs, \"you\" → what?\n\nCheck sentence 1: Qingmivit takujaatit → your dog saw you → takujaatit → \"saw you\" → -jaatit → same suffix\n\nSo \"you\" object → verb suffix -jaatit\n\nTherefore, for \"hurt you\" → verb = aanniqt + -jaatit → aanniqtjaatit?\n\nBut wait: 3 has aanniqtutit — with -utit → reflexive\n\nBut here, not reflexive → object is other person → so -jaatit?\n\nYes — confirmed in 1 and 4.\n\nSo: \"The shaman hurt you\" → Angatkuq aanniqtjaatit\n\nBut is object marked as \"you\"? \n\nYes — \"you\" is direct object.\n\nSo subject: shaman → Angatkuq \nVerb: aanniqtjaatit → hurt you\n\nBut in sentence 6: Angatkuq iluaqhaijimik aarqisijuq → shaman cured a doctor → object = a doctor → -sijuq\n\nSo object matters.\n\nBut for you → -jaatit\n\nSo 19: Angatkuq aanniqtjaatit\n\nBut wait — is \"aanniqtjaatit\" a real form? \n\nWe have aanniqtutit (you hurt yourself) → reflexive \nBut aanniqtjaatit → not in examples.\n\nBut we have:\n\n- takujaatit → saw you → -jaatit → so verb + -jaatit → object you \n- aarqijaatit → cured you → -jaatit → object you \n→ So yes, -jaatit is used for \"you\" object\n\nSo aanniqtjaatit → hurt you\n\nTherefore, 19: Angatkuq aanniqtjaatit\n\nBut is \"you\" marked? In all cases when object is \"you\", it’s -jaatit — even if subject is first or third.\n\nSo yes.\n\n---\n\n20. The teacher saw the boy.\n\n\"teacher\" → not in examples directly \nBut in 10: Qingmiup ilinniaqtitsijiit aanniqtanga → the dog hurt your teacher → so \"your teacher\" → ilinniaqtitsijiit → ilinniaqti + -tsijiit\n\nBut in 8: iluaqhaijivit inuuhuktuit aarqijanga → your doctor cured your boy → so \"your boy\" = inuuhuktuit → inuuhukt + -uit\n\nSo possessive → inuuhuktuit → your boy \n\nSimilarly, \"your teacher\" → ilinniaqtitsijiit → becomes ilinniaqti + -tsijiit → likely \"teacher\" = ilinniaqti\n\nSo \"teacher\" = ilinniaqti\n\n\"boy\" = inuuhukt → inuuhuktuit → \"your boy\"\n\nSo \"the teacher saw the boy\" → object = boy → verb = saw\n\nSaw → in sentence 1: takujaatit → saw you\n\nBut here: saw the boy → object = boy\n\nWhich suffix?\n\nIn 1: saw you → takujaatit → -jaatit \nIn 8: cured your boy → aarqijanga → -janga\n\nNo direct saw with boy.\n\nBut look at sentence 8: iluaqhaijivit inuuhuktuit aarqijanga → your doctor cured your boy → verb is aarqijanga → -janga\n\nBut for \"saw\", do we have such a form?\n\nSentence 1: Qingmivit takujaatit → your dog saw you → takujaatit → object = you → -jaatit\n\nNo saw with boy.\n\nBut verb \"saw\" = taku- + -jaatit?\n\nPossible — so verb stem = taku-?\n\nThen for \"saw the boy\", if object = boy → what suffix?\n\nIn 8: \"cured your boy\" → aarqijanga → -janga\n\nIn 9: \"speared the wolf\" → iputujanga → -anga\n\nIn 5: \"speared the dog\" → iputujait → -ait\n\nSo object-specific suffix.\n\nPossibly: suffix determined by object noun root.\n\nBut roots:\n\n- dog → qingmiq → qingmi? → or qingmivit → qingmiv- \n- wolf → amaruq → amar- \n- boy → inuuhukt → inuuhukt \n- teacher → ilinniaqti → ilinniaqti\n\nNo direct form for \"saw + boy\"\n\nBut could we generalize?\n\nIn sentence 4: doctor cured you → aarqijaatit → -jaatit (you) \nIn 9: hunter speared wolf → iputujanga → -anga \nIn 5: you speared dog → iputujait → -ait\n\nIn 8: doctor cured your boy → aarqijanga → -janga\n\n→ So suffix appears to be based on object noun form:\n\n- you → -jaatit \n- boy → -janga \n- wolf → -anga \n- dog → -ait \n- teacher → ? \n\nSo for boy → -janga \nFor wolf → -anga \nFor dog → -ait \nFor you → -jaatit\n\nThen \"saw the boy\" → takujaat + suffix → word for boy is inuuhukt → so does it use -janga?\n\nIn 8: \"cured your boy\" → aarqijanga → -janga → suggests -janga for boy\n\nSo perhaps saw + boy → takujaat + -janga → takujaatjanga?\n\nBut in 1: \"your dog saw you\" → takujaatit → -jaatit → object = you → so -jaatit\n\nSimilarly, if object = boy → -janga?\n\nIs there a pattern with object root?\n\n- dog → qingmi → root: qingmi- → verb: iputujait → -ait \n- wolf → amaruq → root: amaru- → verb: iputujanga → -anga \n- boy → inuuhukt → root inuuhukt → verb: aarqijanga → -janga \n\nSo the suffix seems to match something in the object’s root?\n\nBut no clear pattern.\n\nBut wait — no saw sentence with boy.\n\nBut the verb \"saw\" appears only in one example: 1 → saw you → takujaatit\n\nSo in absence of another, we must infer pattern from verb structure.\n\nThe verb stem is taku- → for \"see\"\n\nObject = you → now → tackujaatit → -jaatit\n\nObject = boy → likely → takujaat + -janga → takujaatjanga\n\nHence, \"the teacher saw the boy\" → ilinniaqti takujaatjanga\n\nBut subject: teacher — what form?\n\nIn 8: \"your doctor\" = iluaqhaijivit → iluaqhaiji + -vit \nIn 10: \"your teacher\" = ilinniaqtitsijiit → ilinniaqti + -tsijiit → unusual\n\nIs \"teacher\" ilinniaqti?\n\nIn ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11902.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are given a series of Nooni sentences spoken on different days of the Nooni “week,” and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to extract linguistic patterns from the given examples, especially regarding:\n\n- Time reference (e.g., today, tomorrow, yesterday, the day after tomorrow, etc.)\n- Verbs and their aspect (e.g., \"will,\" \"just now,\" \"heard,\" \"killed\")\n- Subject–object order (especially whether it's SOV or otherwise)\n- Tense and aspect markers (e.g., \"just now\" → present perfect or past with aspect)\n- Specific time expressions (e.g., “on Bvusɔw” vs “today” vs “tomorrow”)\n\n---\n\n**Step 1: Identify time expressions and their forms**\n\nFrom the data:\n\n- \"Yesterday was Bvumbon\" → (1) \"fɔgò cǐ nú bvúmbòn\" \n → \"fɔgò\" = yesterday; \"cǐ\" = was; \"nú\" = [day]; \"bvúmbòn\" = Bvumbon \n → So, \"yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\"\n\n- \"On Bvusɔw, you(sg) will steal the yam\" → (2) \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \n → \"wɔ̀\" = you(sg); \"nǔ\" = will; \"yúː\" = steal; \"kèŋkfǔ\" = yam; \"bvúsɔ̀w\" = on Bvusɔw \n → So: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\n- \"On Bvuzhi, the woman will help me\" → (3) \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" \n → \"kwɔ᷆ːn\" = woman; \"nǔ\" = will; \"bóy\" = help; \"fí\" = me; \"bvúzhí\" = on Bvuzhi \n → So: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\n→ Pattern: time is marked by \"on [day]\" and the Day name comes at the end.\n\n→ In past or specific time, \"on X\" = \"bvuxxx\" at the end.\n\n→ For \"today\", see:\n\n- \"Today, he killed the woman\" → (6) \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" \n → \"wvù\" = he; \"bɛ̂ː\" = killed; \"yo᷅kwɔ᷆ːn\" = woman; so \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" \n → \"ɛ̀bɛ̀n\" = today \n → Structure: subject + verb + object + day (today)\n\n- \"Today, I chose the book\" → (9) \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" \n → \"me\" = I; \"mbɛ̂ː\" = chose; \"nca᷅w\" = book; \"ŋwà\" = the; \"ɛ̀bɛ̀n\" = today \n → So \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\"\n\n→ Pattern: \"today\" is marked by \"ɛ̀bɛ̀n\" at the end.\n\nSimilarly:\n\n- \"The day after tomorrow is Bvutfu\" → (5) \"fɔ̀ shě ntfǔː nú bvútfu᷅\" \n → \"fɔ̀\" = the day after tomorrow; \"shě\" = is; \"ntfǔː\" = Bvutfu \n → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" \n → So \"fɔ̀ shě\" + day name → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nNote: \"fɔ̀\" = day after tomorrow \n\"shě\" = is \n\"ntfǔː\" = Bvutfu \n\"nú\" = [day] \n→ This suggests: \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\n→ So \"fɔ̀ shě\" + day name is used for future days.\n\nAlso:\n\n- \"Tomorrow is Bvuŋkaden\" → (8) \"ntfǔː nú bvûŋka᷆ːde᷆n\" \n → \"ntfǔː\" = tomorrow; \"nú\" = is; \"bvûŋka᷆ːde᷆n\" = Bvuŋkaden \n → So \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n\n→ So future time markers:\n- tomorrow → ntfǔː nú day\n- day after tomorrow → fɔ̀ shě nú day\n- yesterday → fɔgò cǐ nú day (already seen)\n\n- \"The day before yesterday was Bvuŋka\" → (11) \"kefwé cí nú bvûŋka\" \n → \"kefwé\" = day before yesterday; \"cí\" = was; \"nú\" = [day]; \"bvûŋka\" = Bvuŋka \n → So \"kefwé cí nú bvûŋka\"\n\n→ So: \n- \"day before yesterday\" → kefwé cí nú day \n- \"yesterday\" → fɔgò cǐ nú day \n- \"today\" → ɛ̀bɛ̀n \n- \"tomorrow\" → ntfǔː nú day \n- \"day after tomorrow\" → fɔ̀ shě nú day\n\nThus, we know time reference patterns.\n\n---\n\n**Step 2: Identify aspect markers**\n\nWhich aspect corresponds to \"just now\"?\n\n- \"You(sg) heard the thief a long time ago\" → (7) \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" \n → \"wɔ̀\" = you; \"tɔ̀\" = heard; \"nɔ̂ː\" = a long time ago; \"yo᷅w\" = the thief; \"cɔ̌ŋ\" = (a long time ago) \n → \"tɔ̀\" = heard; \"nɔ̂ː\" = long time ago → past with distance\n\n- \"Just now\" → occurs in (15): \"They saw me at the market just now\" \n → (15) \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" \n → \"bɔ́\" = saw; \"nɔ̂ː\" = just now; \"yɛ᷅n\" = them; \"me\" = I; \"lé\" = at; \"fɔ̀wǎy\" = market \n → So \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n→ \"nɔ̂ː\" = just now (present) \n→ So \"nɔ̂ː\" = just now → used in past tense with present aspect\n\n→ So for \"just now\", use \"nɔ̂ː\" as aspect marker.\n\nAlso:\n\n- \"On Bvutfu, the woman saw the market\" → (13) \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" \n → \"kwɔ᷆ːn\" = woman; \"cǐ\" = saw; \"nɔ̂ː\" = the market; \"yɛ᷅n\" = market? → \"wáy\" = market; \"é\" = the; \"bvútfu᷅\" = on Bvutfu \n → Actually: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → may be \"woman saw the market on Bvutfu\" \n → But \"cǐ\" = saw; \"nɔ̂ː\" → what? \n → \"nɔ̂ː\" = a long time ago? But here it's in middle of sentence.\n\nWait: \"cǐ nɔ̂ː yɛ᷅n wáy\" → \"cǐ\" = saw; \"nɔ̂ː\" = the market? But \"nɔ̂ː\" is better translated as \"just now\", not \"the market\".\n\nBut in (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"saw just now me at market\"\n\n→ So \"nɔ̂ː\" = just now\n\n→ Thus, \"nɔ̂ː\" = just now → used as aspect marker for recent past.\n\nTherefore:\n\n- \"just now\" → nɔ̂ː (as aspect)\n\n---\n\n**Step 3: Identify subject and object order**\n\n- Example (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \n → \"you(sg) will steal the yam on Bvusɔw\" \n → Subject → \"wɔ̀\" → you \n → Verb → \"nǔ yúː\" → will steal \n → Object → \"kèŋkfǔ\" → yam \n → Time → \"bvúsɔ̀w\" \n → Order: subject + verb + object + day\n\n- Example (3): \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" \n → \"woman will help me on Bvuzhi\" \n → \"kwɔ᷆ːn\" = subject (woman) \n → \"nǔ bóy\" = will help \n → \"fí me\" = me (object) \n → \"bvúzhí\" = on Bvuzhi \n → So: subject + verb + object + day\n\n→ So verb-object order is consistent.\n\n- Example (6): \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" \n → \"he killed the woman today\" \n → \"wvù\" = he \n → \"bɛ̂ː\" = killed \n → \"yo᷅kwɔ᷆ːn\" = the woman \n → \"ɛ̀bɛ̀n\" = today \n → Subject + verb + object + time\n\n→ So all cases: subject + verb + object + time/day\n\n→ So in translation, we will follow: subject + verb + object + time\n\n---\n\n**Step 4: Analyze verbs and their forms**\n\n- Verbs: \n - \"help\" → \"bóy\" (e.g., \"kwɔ᷆ːn nǔ bóy fí me\") \n - \"steal\" → \"yúː\" (e.g., \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\") \n - \"killed\" → \"bɛ̂ː\" (e.g., \"wvù bɛ̂ː yo᷅kwɔ᷆ːn\") \n → So \"steal\" = yúː → adopt as \"cɔ́ŋ\" → yam \n → \"kill\" = bɛ̂ː → kill someone \n → \"hear\" → not directly, but \"heard\" = tɔ̀ (e.g., (7): \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\")\n\n- \"hear\" → verb is \"tɔ̀\" → heard \n- \"see\" → \"bɔ́\" → saw (e.g., (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé\") → saw just now \n- \"choose\" → \"mbɛ̂ː\" (e.g., \"me mbɛ̂ː nca᷅w ŋwà\") → chose book\n\n→ So:\n- \"help\" = bóy \n- \"steal\" = yúː \n- \"kill\" = bɛ̂ː \n- \"see\" = bɔ́ \n- \"hear\" = tɔ̀ \n\n---\n\nNow translate each sentence **spoken on Bvumbon**.\n\nWe must place the time reference at the end.\n\n---\n\n**20. On Bvusɔw, I helped the man.**\n\n- Subject: I → \"me\" \n- Verb: helped → \"nǔ bóy\" (will help) → from (3): \"nǔ bóy\" = will help \n- Object: the man → \"dìɛ̀msɛ̌n\" (man) → from (12): \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\" → so \"dìɛ̀msɛ̌n\" = man \n- Time: On Bvusɔw → \"bvúsɔ̀w\" \n\n→ So: me nǔ bóy dìɛ̀msɛ̌n bvúsɔ̀w\n\nNote: no \"fí\" for object, since \"dìɛ̀msɛ̌n\" is the man, not \"me\" → object is \"dìɛ̀msɛ̌n\"\n\nSo: me nǔ bóy dìɛ̀msɛ̌n bvúsɔ̀w\n\n---\n\n**21. The thief stole the yam just now.**\n\n- Subject: thief → \"yo᷅w\" → from (7): \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"you heard the thief\" → \"yo᷅w\" = thief \n → Also (13): \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → woman saw the market → \"yɛ᷅n wáy\" → market \n → So \"yo᷅w\" = thief \n- Verb: stole → \"yúː\" (from (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\") → stole \n- Object: the yam → \"kèŋkfǔ\" (from (2)) \n- Aspect: just now → \"nɔ̂ː\" → used as aspect marker in middle \n\n→ So: yo᷅w yúː kèŋkfǔ nɔ̂ː\n\n→ Order: subject + verb + object + aspect/time\n\nBut is \"nɔ̂ː\" attached to the end? In (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé\" → saw just now me at market\n\n→ So yes, \"nɔ̂ː\" marks \"just now\" and appears at the end.\n\nBut is this part of time or aspect?\n\nFrom context, \"just now\" is a time reference ⇒ so we can place it at end.\n\n→ So: yo᷅w yúː kèŋkfǔ nɔ̂ː\n\nNote: no day marker because \"just now\" is not tied to a specific day.\n\nIn fact, in (15): \"They saw me at the market just now\" → no day, just now.\n\nSo this sentence has no day — just \"just now\".\n\n→ So it's not on a specific day — just a moment in time.\n\nThus: yo᷅w yúː kèŋkfǔ nɔ̂ː\n\n---\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- Subject: I → \"me\" \n- Verb: will hear → \"nǔ tɔ̀\" → from (7): \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"heard\" = tɔ̀ → \"nǔ tɔ̀\" = will hear \n- Object: the car → \"mutù\" → from (14): \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"we will steal the car\" → \"mutù\" = car \n- Time: on Bvuŋkaden → \"bvûŋka᷆ːde᷆n\" \n → From (8): \"ntfǔː nú bvûŋka᷆ːde᷆n\" → tomorrow is Bvuŋkaden → so \"bvûŋka᷆ːde᷆n\" = Bvuŋkaden \n\n→ So: me nǔ tɔ̀ mutù bvûŋka᷆ːde᷆n\n\n---\n\n**23. Today, the woman will kill the man.**\n\n- Subject: woman → \"kwɔ᷆ːn\" \n- Verb: will kill → \"nǔ bɛ̂ː\" → from (6): \"wvù bɛ̂ː yo᷅kwɔ᷆ːn\" → killed the woman \n- Object: the man → \"dìɛ̀msɛ̌n\" \n- Time: today → \"ɛ̀bɛ̀n\"\n\n→ So: kwɔ᷆ːn nǔ bɛ̂ː dìɛ̀msɛ̌n ɛ̀bɛ̀n\n\n---\n\n**24. Today, the man saw you(sg).**\n\n- Subject: man → \"dìɛ̀msɛ̌n\" \n- Verb: saw → \"bɔ́\" → from (15): \"bɔ́ nɔ̂ː yɛ᷅n me lé\" → saw \n- Object: you(sg) → \"wɔ̀\" → from (2): \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\" → you \n- Time: today → \"ɛ̀bɛ̀n\"\n\n→ So: dìɛ̀msɛ̌n bɔ́ wɔ̀ ɛ̀bɛ̀n\n\nNote: \"wɔ̀\" = you(sg), so object", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8787.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are to translate five sentences into Nooni, spoken on **Bvumbon**, using the patterns observed in the provided examples.\n\nStep 1: Identify grammatical patterns from the examples.\n\nWe examine time expressions and verb usage across days.\n\nTime markers:\n- \"On Bvusɔw\" → appears in 2, 4, 6, 20\n- \"Yesterday\" → fɔgò cǐ nú → 1\n- \"Tomorrow\" → ntfǔː nú → 8\n- \"The day after tomorrow\" → fɔ̀ shě ntfǔː → 5\n- \"Today\" → wvù → 4, 6, 9, 14\n- \"The day before yesterday\" → kefwé cí → 11\n- \"On Bvuŋkaden\" → 8, 22\n\nVerb alignment:\n- \"I came to the market\" → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn → me + verb + object\n- \"you will steal\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → wɔ̀ (you) + yúː (will) + cɔ́ŋ (steal) + object\n- \"the woman will help me\" → kwɔ᷆ːn nǔ bóy fí me bvúzhí → kwɔ᷆ːn (woman) + nǔ (will) + bóy (help) + me (me)\n\nSubject-object order:\n- In \"I came to the market\" → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy → subject before verb, object after\n- In \"you will steal\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ → subject, auxiliary, verb, object\n- In \"the woman will help me\" → kwɔ᷆ːn nǔ bóy fí me → subject, auxiliary, verb, object\n\nSo: **Subject + auxiliary (if any) + verb + object**\n\nTense markers:\n- Future: \"will\" → yúː (in 2, 3), nǔ (in 3), nǔ (in 14)\n- Present: \"today\" → wvù (in 4, 6, 9, 14)\n- Recently: \"just now\" → in 15: \"they saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n - \"just now\" → modifies past (immediate past)\n - \"saw me\" → bɔ́ nɔ̂ː yɛ᷅n me lé → verb + object\n\n\"just now\" → bɔ́ nɔ̂ː yɛ᷅n → in 15 → \"they saw me\" with immediate time marker\n\nIn 7: \"You(sg) heard the thief a long time ago\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → past with \"a long time ago\"\n\nSo time markers:\n- \"just now\" → appears with bɔ́ nɔ̂ː yɛ᷅n in 15\n- \"a long time ago\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w → subject + past marker + object\n- \"today\" → wvù (preferred for present)\n- \"on X day\" → \"nú\" + day name\n\nFor \"I helped the man\" → in 12 → me nú nfí dìɛ̀msɛ̌n → me (I) + nú (will) + nfí (help) + dìɛ̀msɛ̌n (man)\n\nSo present/future: auxiliary \"nú\" (will) or no auxiliary for present.\n\n\"Today\" = wvù, so present tense uses \"wvù\"\n\n\"on X day\" = \"nú\" + day name\n\nNow check object marking:\n- In \"the woman will help me\" → bóy fí me → fí = help, me = object → object marked\n- In \"I came to the market\" → fɔ̀wǎy → market is object, post-verbal\n\nIn \"I will help the man\" → me nú nfí dìɛ̀msɛ̌n → object after verb\n\nSo verb-object order → verb + object\n\nVerb aspect:\n- Immediate past → bɔ́ nɔ̂ː yɛ᷅n → found in 15\n- Future → cɔ́ŋ (steal) + kèŋkfǔ (yam) → in 2\n- Present → \"on today\" → wvù → 14\n\nNow for translation:\n\n20. On Bvusɔw, I helped the man.\n\n→ Day: Bvusɔw → \"nú bvúsɔ̀w\" \n→ I → me \n→ helped → nfí (from 12: me nú nfí dìɛ̀msɛ̌n) \n→ man → dìɛ̀msɛ̌n \n\nSo: me nú nfí dìɛ̀msɛ̌n nú bvúsɔ̀w? \n\nBut \"on\" is \"nú\" — so: \"nú bvúsɔ̀w\" = on Bvusɔw \n\"me nú nfí dìɛ̀msɛ̌n\" = I will help the man? But \"nú\" is \"will\", not present.\n\nBut in 12: \"me nú nfí dìɛ̀msɛ̌n\" = I am about to help the man → \"nú\" = about to? Yes — in 10: dìɛ̀msɛ̌n nú yɛ́n wvù lě → \"the man is about to see him\"\n\nSo \"nú\" = about to / future tense? But 12 says \"I am about to help\" → so \"nú\" is used for future or immediate future.\n\nIn 14: \"today, we will steal\" → bèsèn nǔ géː cɔ́ŋ mutù → \"nǔ\" = will\n\nSo \"nú\" is not always \"will\".\n\n10: dìɛ̀msɛ̌n nú yɛ́n wvù lě → man is about to see him\n\n→ \"nú\" + verb = about to\n\nSo \"about to\" = \"nú\" applied to present verb → implies future action\n\nSo \"I helped the man\" — if it's immediate past, we need a marker.\n\nBut sentence says: \"On Bvusɔw, I helped the man\" → past or present?\n\n\"helped\" = past tense? But no past tense marker.\n\nCompare to 15: \"they saw me just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé → \"just now\" uses \"bɔ́\" (immediate past)\n\nSimilarly, 7: \"heard the thief a long time ago\" → uses \"tɔ̀ nɔ̂ː\" (a long time ago)\n\nSo no \"just now\" in 20.\n\nSo likely past tense.\n\nBut in Nooni, how is past tense marked?\n\nWe don't have explicit past tense marker except via time phrases.\n\n\"Yesterday was Bvumbon\" → fɔgò cǐ nú → past reference\n\nBut in 1: \"Yesterday was Bvumbon\" → fɔgò cǐ nú bvúmbòn\n\nSo \"fɔgò\" = yesterday → past reference\n\nSimilarly, 11: \"The day before yesterday was Bvuŋka\" → kefwé cí nú bvûŋka\n\nSo \"kefwé cí\" = day before yesterday → past\n\n\"on Bvusɔw\" → must be a past day relative to Bvumbon.\n\nSo \"I helped the man\" → likely past action on a past day.\n\nBut is there a past auxiliary?\n\nIn 4: \"On Bvuŋka, he found the book\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà → \"wvù\" = on, \"tɔ̀ nɔ̂ː\" = found → \"he found\" → past tense with \"wvù\"\n\nSo verb form is simple past: \"tɔ̀ nɔ̂ː\" — found\n\nIn 6: \"Today, he killed the woman\" → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n → \"wvù\" + \"bɛ̂ː\" = killed\n\nSo \"wvù\" = on today → present\n\nBut on a past day, \"on Bvusɔw\" → \"nú bvúsɔ̀w\"\n\nAnd verb is in past form or simple?\n\nIn 5: \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅ → future\n\nIn 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → future\n\nSo \"is\" = \"nú\"\n\nFor past day: \"on Bvusɔw\" → just a temporal reference, no tense marker.\n\nSo verb should be in past if \"helped\"\n\nBut we have no explicit past auxiliary.\n\nIn 13: \"On Bvutfu, the woman saw the market\" → kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅ → \"cǐ nɔ̂ː yɛ᷅n\" = saw? → \"nɔ̂ː\" is a verb form?\n\n\"nɔ̂ː\" = to see? In 15: \"saw me\" → bɔ́ nɔ̂ː yɛ᷅n me lé → \"nɔ̂ː\" as past of see?\n\nYes: in 13: \"the woman saw the market\" → kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy → \"cǐ nɔ̂ː\" = saw?\n\ncǐ = on, nɔ̂ː = saw? → probably \"nɔ̂ː\" = see (past form)\n\nSimilarly, in 15: bɔ́ nɔ̂ː yɛ᷅n me lé → \"bɔ́\" = just now, \"nɔ̂ː\" = saw\n\nSo verb \"nɔ̂ː\" is used in past (with time marker or present)\n\nSo \"helped\" → what is the past form?\n\nIn 12: \"I am about to help\" → me nú nfí dìɛ̀msɛ̌n\n\nnfí = help\n\nSo \"help\" = nfí\n\n\"helped\" = past form?\n\nIs there a past form of \"help\"?\n\nWe don't see a direct past form, but \"helped\" would be \"nfí\" with past marker?\n\nNot seen.\n\nIn 3: \"the woman will help me\" → kwɔ᷆ːn nǔ bóy fí me → \"bóy\" = help, future\n\nNo past form.\n\nBut in 13: \"saw\" = nɔ̂ː\n\nSo \"helped\" may be \"nfí\" with past tense marker?\n\nNo such form.\n\nAlternative: in time phrases like \"on Bvusɔw\", the verb is in past tense by default?\n\nIn 4: \"he found\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà → found\n\nSo on a date, the verb is past.\n\nSo likely, \"I helped\" → me + verb in past + object\n\nPast form of \"help\"? Not directly provided.\n\nBut in 12: \"I am about to help\" → me nú nfí → future\n\nSo \"nfí\" = help, present/future\n\nIn 13: saw → nɔ̂ː → past\n\nSo perhaps \"helped\" is \"nfí\" with a past auxiliary?\n\nBut no such auxiliary.\n\nAlternatively, \"helped\" → same as \"help\" with time adverb.\n\nSo: on Bvusɔw, I helped → me cǐ nfí dìɛ̀msɛ̌n nú bvúsɔ̀w?\n\nBut \"cǐ\" = on → so \"cǐ\" is used for time?\n\nIn 1: fɔgò cǐ nú bvúmbòn → \"cǐ\" after \"yesterday\" → not \"on\"\n\nIn 4: wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka → \"wvù\" = on\n\nIn 13: kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅ → \"cǐ\" = on\n\nSo \"cǐ\" = on\n\nSo \"on Bvusɔw\" → cǐ bvúsɔ̀w\n\nNow, verb: \"helped\" → what is the form?\n\nWe have \"help\" in future: \"bóy\" in 3 → \"nǔ bóy fí me\"\n\n\"nfí\" in 12 → \"me nú nfí dìɛ̀msɛ̌n\"\n\nSo \"help\" = nfí or bóy?\n\nIn 12: \"help\" = nfí\n\nIn 3: \"help\" = bóy\n\nbóy in 3: \"nǔ bóy fí me\" → \"nǔ\" = will, \"bóy\" = help\n\nSo \"bóy\" = future help\n\n\"nfí\" = present/future in 12, with \"nú\"\n\nBut no past form.\n\nHowever, in 13: \"the woman saw the market\" → \"cǐ nɔ̂ː yɛ᷅n wáy\" → \"nɔ̂ː\" = saw, past\n\nSo perhaps \"helped\" is not needed as a separate past form — rather, the date implies past, so verb is simple past.\n\nBut we have no past tense marker.\n\nConclusion: In Nooni, when a time phrase is used with \"on X day\", the verb can be in the simple past (without auxiliary).\n\nSo \"I helped\" → me nfí dìɛ̀msɛ̌n — but \"nfí\" is present\n\nNot convincing.\n\nWait: in 5: \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅ → future time\n\nIn 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → future\n\nIn 11: \"day before yesterday was Bvuŋka\" → kefwé cí nú bvûŋka → past\n\nSo for \"on X day\", the verb is in past if X is in past.\n\nSo for 20: \"On Bvusɔw, I helped the man\" → Bvusɔw was in the past (since spoken on Bvumbon), so past verb.\n\nWe need a past form of \"help\".\n\nWe don't have it.\n\nBut in 12: \"I am about to help\" → me nú nfí dìɛ̀msɛ̌n → future\n\nIn 3: \"will help\" → nǔ bóy fí\n\nNo past.\n\nAlternative: perhaps \"helped\" = \"nfí\" with \"cǐ\" and no auxiliary.\n\nBut still, tense mismatch.\n\nWait — in 10: \"the man is about to see him\" → dìɛ̀msɛ̌n nú yɛ́n wvù lě → \"nú\" for about to\n\nSo \"nú\" = future, not past.\n\nFor past, no marker.\n\nSo perhaps \"helped\" is just \"nfí\", and the time phrase makes it past.\n\nSo: me nfí dìɛ̀msɛ̌n cǐ bvúsɔ̀w\n\nBut order? \"on Bvusɔw\" = cǐ bvúsɔ̀w\n\nSo me nfí dìɛ̀msɛ̌n cǐ bvúsɔ̀w\n\nBut in 3: \"you will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → Subject + auxiliary (yúː = will) + verb (cɔ́ŋ) + object (kèŋkfǔ)\n\nSo for past, no auxiliary.\n\nSo verb base = parent.\n\nIn 4: \"he found the book\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà → no auxiliary\n\nSo verb is in past form with time.\n\nSimilarly, \"I helped\" → me nfí dìɛ̀msɛ̌n cǐ bvúsɔ̀w\n\nBut in 13: \"on Bvutfu, the woman saw\" → kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy → only past verb\n\nSo pattern: subject + verb in past (noun form) + object? No object — here, \"saw the market\" → \"yɛ᷅n wáy\" → object\n\nSo in 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\" → woman saw market\n\nSo verb + object → \"nɔ̂ː yɛ᷅n\"\n\nSimilarly, in 3: \"nǔ yúː cɔ́ŋ kèŋkfǔ\" → will steal yam\n\nSo verb + object\n\nSo for \"I helped the man\" → me nfí dìɛ̀msɛ̌n\n\nOrder: subject + verb + object?\n\nIn 13: \"woman saw market\" → subject → kwɔ᷆ːn, then verb + object → cǐ nɔ̂ː yɛ᷅n wáy\n\nSo verb-object?\n\nIn 12: \"I am about to help the man\" → me nú nfí dìɛ̀msɛ̌n → subject + auxiliary + verb + object\n\nSo when \"about to\" is present, auxiliary \"nú\"\n\nOtherwise, basic form.\n\nSo \"helped\" = past → no auxiliary, just verb\n\nSo me nfí dìɛ̀msɛ̌n cǐ bvúsɔ̀w\n\nBut is \"nfí\" past of help?\n\nWe don't have", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9683.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "We are given sentences in Nooni from different days of the week, and we must translate five sentences (20–24) spoken on **Bvumbon**, using the linguistic patterns observed from the examples.\n\nWe must deduce the morphological and syntactic patterns for:\n\n- Time references (yesterday, today, tomorrow, etc.)\n- Aspect (past, future, present, just now)\n- Subject-verb-object order\n- Tense markers and time indicators\n- Possession, verbs with objects\n\nLet’s go sentence by sentence and build up patterns.\n\n---\n\n**Step 1: Time expressions**\n\nFrom the data:\n\n- \"Yesterday was Bvumbon\" → *fɔgò cǐ nú bvúmbòn* \n→ \"Yesterday\" is expressed with *fɔgò cǐ*, which is \"yesterday\" as a past time marker.\n\n- \"The day after tomorrow is Bvutfu\" → *fɔ̀ shě ntfǔː nú bvútfu᷅* \n→ \"The day after tomorrow\" is *fɔ̀ shě ntfǔː* (literally: \"the next day after tomorrow\"?) \nBut *fɔ̀ shě* = \"the next day\" / \"tomorrow\" → *fɔ̀ shě* = tomorrow? \nBut \"the day after tomorrow is Bvutfu\" → implies *fɔ̀ shě ntfǔː* = \"the day after tomorrow\"\n\nThen: *ntfǔː* = 'tomorrow', so *fɔ̀ shě ntfǔː* = \"the day after tomorrow\"\n\nBut in sentence 8: \"Tomorrow is Bvuŋkaden\" → *ntfǔː nú bvûŋka᷆ːde᷆n* \n→ *ntfǔː* = \"tomorrow\", *bvûŋka᷆ːde᷆n* = \"Bvuŋkaden\" (day)\n\nSimilarly, sentence 11: \"The day before yesterday was Bvuŋka\" → *kefwé cí nú bvûŋka* \n→ *kefwé cí* = \"the day before yesterday\"\n\nSo:\n\n- kewfé cí = day before yesterday \n- fɔgò cǐ = yesterday \n- ntfǔː = tomorrow \n- fɔ̀ shě = day after tomorrow (from sentence 5: \"The day after tomorrow is Bvutfu\") \n→ *fɔ̀ shě ntfǔː* = day after tomorrow\n\nAlso, sentence 15: \"They saw me at the market just now\" → *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* \n→ *fɔ̀wǎy* = \"market\" \n→ *just now* appears as *fɔ̀*? Or *fɔ̀*? But here: *just now* is implied in temporal phrase.\n\nBut in sentence 7: \"You(sg) heard the thief a long time ago\" → *wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ* \n→ \"a long time ago\" → *tɔ̀ nɔ̂ː* → \"a long time ago\"\n\nSo: time expressions:\n\n- *fɔgò cǐ* → yesterday \n- *kefwé cí* → day before yesterday \n- *ntfǔː* → tomorrow \n- *fɔ̀ shě* → day after tomorrow \n- *tɔ̀ nɔ̂ː* → a long time ago \n- *fɔ̀* → just now (sentence 15: \"just now\" → *fɔ̀*) \nAlso: sentence 13: \"On Bvutfu, the woman saw the market\" → implies \"saw\" is past \nSentence 15: \"They saw me at the market just now\" → \"just now\" → *fɔ̀* \n\nSo: temporal particle *fɔ̀* = \"just now\"\n\nAlso: \"Today\" appears as:\n- sentence 4: \"On Bvuŋka, he found the book\" → not explicitly \"today\"\n- sentence 6: \"Today, he killed the woman\" → *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n* \n→ \"Today\" is marked in the sentence as the time frame\n\nSimilarly, sentence 9: \"Today, I chose the book\" → *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n* \n→ *mbɛ̂ː* = \"chose\", \"today\" is contextual\n\nSentence 12: \"I am about to help the man\" → *me nú nfí dìɛ̀msɛ̌n* → *nú* = \"about to\"\n\nSo:\n\n- *mbɛ̂ː* = to choose (past or present?)\n- *bɛ̂ː* = to kill (sentence 6: \"he killed the woman\")\n- *wvù* = he / he found\n- *kwɔ᷆ːn* = the woman / subject\n\nBack to the verbs:\n\n**Step 2: Verbs and aspect**\n\nNote: In Nooni, verbs may have aspect markers. We see:\n\n- \"On Bvusɔw, you(sg) will steal the yam\" → *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* \n→ *yúː* = to steal, *cɔ́ŋ* = will? or a future marker?\n\nBut: *cɔ́ŋ* is used with future: \"you will steal\" \nSimilarly: sentence 3 → \"On Bvuzhi, the woman will help me\" → *kwɔ᷆ːn nǔ bóy fí me bvúzhí* \n→ *fí* = to help → *fí* is used with \"will help\"\n\nSo: *cɔ́ŋ* is a future tense or aspect marker.\n\nSimilarly, sentence 14: \"Today, we will steal the car\" → *bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n* \n→ *cɔ́ŋ* = will\n\nSo: *cɔ́ŋ* = future / will\n\nBut in sentence 5: *fɔ̀ shě ntfǔː nú bvútfu᷅* → \"The day after tomorrow is...\" → no *cɔ́ŋ*, but a state: future date \nSo *cɔ́ŋ* is not used in indicating the timing of a day, but of an event.\n\nSo: future = *cɔ́ŋ*\n\nAlso: \"just now\" → *fɔ̀* appears in sentence 15: \"just now\" → *fɔ̀* \nAnd in sentence 13: \"On Bvutfu, the woman saw the market\" → *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* \n→ saw → *cǐ*? But this is \"saw\" (past)\n\nWait: *cǐ* is used in \"On Bvutfu, the woman saw the market\" \nBut in other places:\n\n- \"Yesterday was Bvumbon\" → *fɔgò cǐ nú bvúmbòn* → *cǐ* = \"was\" (past)\n\n- \"On Bvuzhi, the woman will help me\" → *kwɔ᷆ːn nǔ bóy fí me* → no *cǐ*, but *fí* → \"help\" (present or future)\n\nSo: *cǐ* = past tense (e.g., \"was\", \"saw\")\n\n*ŋ* or *cɔ́ŋ* = future\n\nAlso: sentence 13: \"the woman saw the market\" → *kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅* \n→ *cǐ* = saw\n\nSo *cǐ* = past tense marker \n*cɔ́ŋ* = future tense marker\n\nAlso: \"I am about to\" → *me nú nfí dìɛ̀msɛ̌n* → *nú* = about to\n\nSo: *nú* = future, immediate (to be about to)\n\nSo:\n\n- past → *cǐ* \n- future → *cɔ́ŋ* \n- present/future immediate → *nú* \n\nIn sentence 12: \"I am about to help the man\" → *me nú nfí dìɛ̀msɛ̌n* → *nú* = about to\n\nSo *nú* = present or imminent future (futurity)\n\nNow, **subject-object order**:\n\nIn sentence 1: \"On Bvumbon, I came to the market\" → *me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn* \n→ *me* (subject), *ncí* (came), *nɔ̂ː* (to), *ntɔ᷅* (market), *bvúmbòn* (time)\n\nSo structure: Subject + verb + preposition + object + time\n\nSimilarly: sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w* \n→ *wɔ̀* (you), *yúː* (steal), *cɔ́ŋ* (will), *kèŋkfǔ* (the yam), *bvúsɔ̀w* (time)\n\nSo: Subject + verb + future + object + time\n\nSentence 3: \"On Bvuzhi, the woman will help me\" → *kwɔ᷆ːn nǔ bóy fí me bvúzhí* \n→ *kwɔ᷆ːn* (woman), *nǔ* (will), *bóy* (help), *me* (object), *bvúzhí* (time)\n\nSo verb-object: *bóy fí me* → object after verb\n\nSo in all examples, **object follows verb**, subject before verb.\n\nThus, structure: [subject] + [verb] + [object] + [time]\n\nAlso, **time** is usually placed at the end, and serves as a time reference.\n\nSo we use:\n\n- *[subject]* \n- *verb (past/future)* \n- *object* \n- *time (day)*\n\nNow, the **time markers**:\n\nWe need to map the days.\n\nKnown:\n\n- Bvumbon: day of the speaking event\n- Bvusɔw: spoken on Bvusɔw → sentence 2,4,6,7\n- Bvuŋka: spoken on Bvuŋka → sentence 4,5,6,7,12,13,14,15\n- Bvukema: spoken on Bvukema → 8,9,10,11\n\nIn sentence 1 (Bvumbon): \"Yesterday was Bvumbon\" → *fɔgò cǐ nú bvúmbòn* \nSo *fɔgò cǐ* = \"yesterday\" → the day before today (today = Bvumbon)\n\nSo the days are sequential.\n\nWe now go to the target translations.\n\n---\n\n**(20) On Bvusɔw, I helped the man.**\n\n- subject: \"I\" → *me* \n- verb: \"helped\" → past → *fí*? \n- object: \"the man\" → *dìɛ̀msɛ̌n* (from sentence 12: \"I am about to help the man\" → *dìɛ̀msɛ̌n* = man) \n- time: \"On Bvusɔw\" → *bvúsɔ̀w*\n\nNow, is the verb \"help\" marked with past? \nSentence 3: \"On Bvuzhi, the woman will help me\" → *kwɔ᷆ːn nǔ bóy fí me* → *fí* = help \nSo *fí* = help, present or future — but without *cɔ́ŋ*, so not future, may be present or past.\n\nBut in sentence 12: \"I am about to help\" → *me nú nfí dìɛ̀msɛ̌n* → *nú* = about to, *nfí* = help \nSo *fí* is the base verb.\n\nSo \"helped\" = past of *fí*?\n\nDo we have a past form?\n\nIn sentence 1: \"I came to the market\" → *me ncí nɔ̂ː* → *ncí* = came (past)\n\nIn sentence 13: \"The woman saw the market\" → *cǐ* = saw (past)\n\nSo past tense is *cǐ*\n\nSo \"helped\" → *fí cǐ*? Or *fí* with *cǐ*?\n\nIn sentence 3: \"the woman will help me\" → *fí me* → no *cǐ* → present/future\n\nIn sentence 12: \"I am about to help\" → *nú nfí* → future\n\nBut \"helped\" → past\n\nSo we need *fí* with past morpheme?\n\nBut no explicit past form seen.\n\nWait: sentence 1: \"I came\" → *me ncí* → *ncí* is past\n\nDo we have a past version of *fí*?\n\nNot directly. But in the pattern of verbs:\n\n- \"saw\" → *cǐ* \n- \"came\" → *ncí* \n- \"killed\" → *bɛ̂ː* (in sentence 6: \"he killed\") — *wvù bɛ̂ː yo᷅kwɔ᷆ːn* → *bɛ̂ː* = killed\n\nSo \"killed\" is base form.\n\nSimilarly, \"steal\" = *yúː cɔ́ŋ* → future\n\nSo perhaps *fí* = help, and past is not marked by morpheme — contextually inferred?\n\nWait: sentence 15: \"They saw me at the market just now\" → *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* \n→ \"saw\" = *bɔ́*, and *fɔ̀* = just now → present\n\nBut *bɔ́ nɔ̂ː* = \"they saw\" → *bɔ́* = saw\n\nSo *bɔ́* = saw, present (no *cǐ*), but *fɔ̀* attached — just now\n\nSo in past, sometimes seen with *cǐ*\n\nBack: in sentence 3: \"the woman will help me\" → *fí me* → future without *cǐ*\n\nIn sentence 12: \"I am about to help\" → *nú nfí*\n\nSo only *cǐ* is used with past, not with *fí*\n\nBut in sentence 13: \"the woman saw the market\" → *cǐ* = saw → past\n\nSo perhaps only verbs with a past marker (like *cǐ*) are past.\n\nSo \"helped\" must be marked with *cǐ* → *fí cǐ*\n\nSo: \"I helped the man\" → *me fí cǐ dìɛ̀msɛ̌n*\n\nBut is there evidence?\n\nSentence 12: \"I am about to help\" → *me nú nfí* → no object, no time → in present/future\n\nBut in absence of *cǐ*, it's not past.\n\nSo when verb is past, we use *cǐ*.\n\nSimilarly, in \"saw\" → *cǐ*\n\nSo we infer: past = *cǐ* after verb.\n\nThus: \"helped\" = *fí cǐ*\n\nSo full sentence: *me fí cǐ dìɛ̀msɛ̌n bvúsɔ̀w*\n\nBut time: \"on Bvusɔw\" → *bvúsɔ̀w* at end\n\nPattern from sentence 1: *me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn* → subject + verb + object + time\n\nSo here: *me fí cǐ dìɛ̀msɛ̌n bvúsɔ̀w*\n\nYes.\n\nSo (20) → *me fí cǐ dìɛ̀msɛ̌n bvúsɔ̀w*\n\n---\n\n**(21) The thief stole the yam just now.**\n\n- subject: \"the thief\" → *yo᷅kwɔ᷆ːn* (from sentence 6: \"he killed the woman\" → *yo᷅kwɔ᷆ːn*) \n- verb: \"stole\" → past → *yúː cǐ*? \n- object: \"the yam\" → *kèŋkfǔ* (sentence 2: \"you will steal the yam\" → *kèŋkfǔ*) \n- time: \"just now\" → *fɔ̀*\n\nPattern: subject + verb (past) + object + time\n\nSo: *yo᷅kwɔ᷆ːn yúː cǐ kèŋkfǔ fɔ̀*\n\nIs *yúː cǐ* = stole?\n\nIn sentence 2: \"you will steal the yam\" → *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ* → *yúː cɔ́ŋ* = will steal\n\nSo past: *yúː cǐ* = stole\n\nYes — *cǐ* = past\n\nConfirm: in sentence 13: \"saw\" = *cǐ*\n\nSo \"stole\" = *yúː cǐ*\n\nSo sentence: *yo᷅kwɔ᷆ːn yúː cǐ kèŋkfǔ fɔ̀*\n\nYes.\n\n---\n\n**(22) On Bvuŋkaden, I will hear the car.**\n\n- subject: *me* \n- verb: \"will hear\" → future → *cɔ́ŋ* \n- verb root: \"hear\" → from sentence 8: \"the thief will find us\" → *cɔ̌ŋ nú bóy bɔ́ŋ* → *cɔ̌ŋ* = will \n- \"hear\" → not found directly\n\nSentence 8: \"On Bvuŋkaden, the thief will find us\" → *cɔ̌ŋ nú bóy bɔ́ŋ* \n→ *bóy*", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9953.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are translating into Nooni, a Beboid language with specific temporal expressions and verb morphology. The key is to extract patterns from the provided examples based on time reference, verb aspect, subject, and object.\n\nStep 1: Identify time markers and their functions.\n\nFrom the examples:\n\n- \"Yesterday was Bvumbon\" → 1 → \"fɔgò cǐ nú bvúmbòn\" → past reference (yesterday)\n- \"On Bvusɔw, you(sg) will steal the yam\" → 2 → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"On Bvuzhi, the woman will help me\" → 3\n- \"On Bvuŋka, he found the book\" → 4 → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\"\n- \"The day after tomorrow is Bvutfu\" → 5 → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n- \"On Bvutfu, I will choose the car\" → 6 → \"me nú mbóy ncáw mutù bvútfu᷅\"\n- \"Today, he killed the woman\" → 6 → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n- \"You(sg) heard the thief a long time ago\" → 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\"\n- \"Tomorrow is Bvuŋkaden\" → 8 → \"ntfǔː nú bvûŋka᷆ːde᷆n\"\n- \"On Bvuŋkaden, the thief will find us\" → 8 → \"cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n\"\n- \"Today, I chose the book\" → 9 → \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\"\n- \"The man is about to see him\" → 10 → \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\"\n- \"The day before yesterday was Bvuŋka\" → 11 → \"kefwé cí nú bvûŋka\"\n\nWe observe:\n\n- Time expressions: \"Yesterday\", \"Today\", \"Tomorrow\", \"The day after tomorrow\", \"The day before yesterday\", \"On X-day\"\n- These map to specific temporal adverbials, and the day names (e.g., Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvuŋkaden) are used with prepositions or at the end of clauses.\n- The structure \"On X-day, S-V-O\" implies event on a specific day.\n- \"I will choose\" = future, \"I chose\" = past, \"I am about to help\" = present progressive.\n- \"Just now\" — appears in example 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nStep 2: Identify aspectual markers.\n\n- \"just now\" → appears in 15 → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = present, \"nɔ̂ː\" = action, \"yɛ᷅n\" = watch, \"me lé\" = me, \"fɔ̀wǎy\" = market\n- So, \"bɔ́\" = \"just now\" or \"recently\", present aspect, so likely used for recent completed action.\n\n\"Today\" — 6, 9, 14 → \"Today, he killed\", \"Today, I chose\", \"Today, we will steal\"\n\n\"Tomorrow\" → 8\n\n\"Yesterday\" → 1\n\n\"We will steal\" → future, with \"cɔ́ŋ\" (steal), e.g., 2, 14\n\n\"He found the book\" → past, e.g., 4\n\nSo verb aspect is grammaticalized and tied to time markers.\n\nStep 3: Subject/object roles.\n\nIn example 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n- \"wɔ̀\" = you\n- \"yúː\" = will\n- \"cɔ́ŋ\" = steal\n- \"kèŋkfǔ\" = the yam\n- \"bvúsɔ̀w\" = on Bvusɔw\n\nSo: subject (you), verb (steal), direct object (yam)\n\nExample 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n- \"kwɔ᷆ːn\" = woman\n- \"cǐ\" = saw\n- \"nɔ̂ː\" = action\n- \"yɛ᷅n\" = see (watch)\n- \"wáy\" = market\n- \"é\" = at\n- \"bvútfu᷅\" = Bvutfu\n\nSo: subject (woman), verb (saw), object (market)\n\nThis suggests that verbs like \"see\", \"hear\", \"help\", \"steal\", \"kill\" take object directly after the verb, and the temporal expression is usually at the end.\n\nNote: \"the car\" = \"mutù\" (in 6), \"the book\" = \"ŋwà\", \"the woman\" = \"yo᷅kwɔ᷆ːn\", \"the man\" = \"dìɛ̀msɛ̌n\"\n\nStep 4: Handling of days (temporal expressions)\n\n- \"On X-day\" → \"nú\" + day name, in the clause → e.g., \"me nú mbóy ncáw mutù bvútfu᷅\"\n- \"Tomorrow is X-day\" → \"ntfǔː nú X-day\" → e.g., 8\n- \"Yesterday was X-day\" → \"fɔgò cǐ nú X-day\" → 1\n- \"The day after tomorrow is X-day\" → \"fɔ̀ shě ntfǔː nú X-day\" → 5\n- \"The day before yesterday was X-day\" → \"kefwé cí nú X-day\" → 11\n\nSo we have:\n\n- Tomorrow → ntfǔː nú X-day\n- Yesterday → fɔgò cǐ nú X-day\n- Day after tomorrow → fɔ̀ shě ntfǔː nú X-day\n- Day before yesterday → kefwé cí nú X-day\n- Today → just present, no temporal marker, or \"today\" implied\n\nThus, in all cases, the day is specified with \"nú\" or \"ntfǔː\" (tomorrow) or \"kefwé\" (day before yesterday)\n\nStep 5: Translate the requested sentences, with time reference \"spoken on Bvumbon\"\n\n20. On Bvusɔw, I helped the man.\n\nWe need \"On Bvusɔw, I helped the man\"\n\nFrom example 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\"\n\nStructure: [subject] [nǔ] [verb] [object] [on day]\n\n\"help\" = \"bóy\" or \"fí\" — in 3: \"bóy fí me\" → \"help me\"\n\nSo \"help\" = \"fí\" (to help someone), or \"bóy\" (to help)\n\nCheck: \"bóy\" = to help? In 3: \"the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\"\n\n\"nǔ\" = will (future), \"bóy\" = help, \"fí me\" = help me\n\nSo \"bóy\" is the verb of helping, with \"fí\" indicating \"to help someone\"\n\nBut \"fí\" is more like \"help to\" — so \"bóy fí me\" = \"will help me\"\n\nSo \"I helped the man\" → \"me nǔ bóy fí dìɛ̀msɛ̌n\"\n\nBut \"spoken on Bvumbon\" → so time reference is not future; it's a past statement.\n\nWait: the day is “Bvusɔw” — so the event is on Bvusɔw.\n\nBut the speaker is now on Bvumbon — so the event is in the past.\n\nSo the past tense is needed.\n\nLook at example 4: \"On Bvuŋka, he found the book\" → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\"\n\n\"tɔ̀\" = found (past), \"nɔ̂ː\" = (action), \"bɔ᷅ŋ\" = book\n\nSo past tense uses \"tɔ̀\", \"nɔ̂ː\"\n\nIn 1: \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → \"fɔgò\" = yesterday, \"cǐ\" = was\n\nSo \"was\" = \"cǐ\", \"is\" = ?\n\nWe need to find the past tense of \"help\".\n\nIn example 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\" → \"nǔ\" = will\n\nSo future = \"nǔ\"\n\nThen past of \"help\" → probably \"bóy\" without \"nǔ\"? But \"bóy\" appears as verb.\n\nIn sentence 4: \"he found the book\" → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\"\n\n\"found\" = \"tɔ̀\"\n\nSo past tense is marked by \"tɔ̀\"\n\nTherefore, \"I helped\" = \"me bóy fí dìɛ̀msɛ̌n\" → but past?\n\nBut in 3: \"the woman will help me\" → uses \"nǔ\"\n\nSo not just \"bóy\" as base.\n\nPossibility: the verb for \"help\" is \"bóy\", and aspect/tense is marked by auxiliary.\n\nBut in 4: \"found\" is \"tɔ̀\"\n\nSo verb \"help\" is likely \"bóy\", and in past, it would be \"bóy\" with an auxiliary.\n\nIn 5: \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\"\n\nThis is a state of future — \"is\" = \"ntfǔː\"\n\n\"will\" = \"nǔ\"\n\n\"heard\" → example 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\"\n\n\"heard\" = \"tɔ̀\"\n\nSo \"heard\" = \"tɔ̀\", \"will steal\" = \"nǔ cɔ́ŋ\"\n\nTherefore, \"helped\" = past of \"help\" → must be \"bóy\" or \"tɔ̀\"?\n\nIn 3: \"will help\" → \"nǔ bóy fí me\"\n\nIn 4: \"found\" → \"tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\"\n\nSo \"bóy\" is used in future as \"nǔ bóy\", so past would be without \"nǔ\"\n\nBut we don’t have a past form of \"help\"\n\nPossibility: the verb \"bóy\" takes the particle \"fí\" to mean \"help someone\"\n\nSo \"I helped the man\" = \"me bóy fí dìɛ̀msɛ̌n\"\n\nBut is it past?\n\nAll other verbs in past use \"tɔ̀\" — e.g., \"found\", \"heard\", \"killed\"\n\nIn 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n\n\"bɛ̂ː\" = killed? (past)\n\nYes — \"he killed\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n\nSo \"killed\" = \"bɛ̂ː\"\n\nSimilarly, \"heard\" = \"tɔ̀\"\n\nSo \"helped\" — likely \"bóy\" with past tense marker?\n\nBut only with \"tɔ̀\" used in other verbs.\n\nBut in 3: \"will help\" → \"nǔ bóy\"\n\nSo \"bóy\" is a verb, with tense markers.\n\nSo \"I helped\" = \"me tɔ̀ bóy fí dìɛ̀msɛ̌n\" — but that would be awkward.\n\nAlternatively, is there a verb for \"help\" that uses \"bóy\" only?\n\nWait — in 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\n\"seen\" = \"cǐ\" — past?\n\nYes — \"cǐ\" = saw (past)\n\nIn 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\n\"bɔ́\" = just now, recent\n\nSo \"saw\" = \"yɛ᷅n\"\n\nTherefore, \"helped\" may be \"bóy\", and the past tense is marked by context or by \"cǐ\" or \"tɔ̀\"\n\nBut \"bóy\" is used in future with \"nǔ\"\n\nSo perhaps the past tense of \"help\" is \"bóy\" without auxiliary, and \"tɔ̀\" is not required?\n\nBut no other verbs use \"bóy\" without aspect.\n\nAnother possibility: \"bóy\" = to help, and tense is expressed via the time reference.\n\nSince the event is on \"Bvusɔw\", which is a prior day (already spoken about), and speaker is now on Bvumbon, it must be past — so verb should be in past.\n\nIn example 4: past event → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\"\n\nSo past tense = \"tɔ̀\"\n\nSo perhaps \"helped\" = \"tɔ̀ bóy fí dìɛ̀msɛ̌n\"\n\nYes — this seems plausible.\n\nSo 20: \"On Bvusɔw, I helped the man\" → \"me tɔ̀ bóy fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nBut in 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\"\n\nSo \"nǔ\" = will → future\n\n\"tɔ̀\" = past — used for past events\n\nSo yes.\n\nStructure: [subject] [tɔ̀] [verb] [object] [on day]\n\nSo \"me tɔ̀ bóy fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nBut \"bóy\" is the verb, and \"fí\" is the complement.\n\nIn 13: \"the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy\"\n\n\"yɛ᷅n\" = saw — so \"yɛ᷅n\" is the verb.\n\nSimilarly, \"helped\" must be a verb.\n\nIn 3: \"help me\" = \"bóy fí me\"\n\nSo \"help the man\" = \"bóy fí dìɛ̀msɛ̌n\"\n\nWith past: \"me tɔ̀ bóy fí dìɛ̀msɛ̌n\"\n\nWith time: \"nú bvúsɔ̀w\"\n\nThus: 20 → \"me tɔ̀ bóy fí dìɛ̀msɛ̌n nú bvúsɔ̀w\"\n\nNow 21. The thief stole the yam just now.\n\n\"just now\" → example 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nSo \"bɔ́\" = just now\n\nSo \"just now\" is marked by \"bɔ́\"\n\n\"thief\" = \"yo᷅kwɔ᷆ːn\" (from 6: \"he killed the woman\" → \"yo᷅kwɔ᷆ːn\")\n\n\"stole\" → example 2: \"you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n\n\"cɔ́ŋ\" = steal\n\nSo \"stole\" = past of \"cɔ́ŋ\" → likely \"cɔ̌ŋ\" (as in 6: \"killed\" = \"bɛ̂ː\", \"heard\" = \"tɔ̀\")\n\nIn 7: \"you heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\"\n\n\"heard\" = \"tɔ̀\", \"cɔ̌ŋ\" = thief?\n\nWait — \"yo᷅w\" = the thief?\n\nIn 2: \"you will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ\"\n\n\"cɔ́ŋ\" = steal, \"kèŋkfǔ\" = yam\n\nIn 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\"\n\n\"yo᷅kwɔ᷆ːn\" = woman? No — \"yo᷅kwɔ᷆ːn\" = woman (killed), so \"yo᷅kwɔ᷆ːn\" = woman\n\nIn 7", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9397.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Identify patterns from given examples.\n\nWe are given a set of Jaqaru words and their English translations.\n\nFrom the examples:\n\n- aq”ipsa = the cave too → \"the cave\" + \"too\" (additional)\n- aq”na = in the cave → \"in\" + \"the cave\"\n- qucxap”a = through the lake → \"through\" + \"the lake\"\n- qucxst”psa = from our1+2 lake too → \"from\" + \"our1+2 lake\" + \"too\"\n- chushp”a = his corner → \"his\" + \"corner\"\n- chushuntxi = is it in the corner? → \"is it\" + \"in\" + \"the corner?\"\n- marka = the town\n- markp”t”a = from his town → \"from\" + \"his\" + \"town\"\n- markstxi = is it our1+2 town? → \"is it\" + \"our1+2\" + \"town?\"\n- ishinhna = in my bed → \"in\" + \"my\" + \"bed\"\n- ishma = your bed → \"your\" + \"bed\"\n- p”ak”u = the pot\n- p”ak”unhpsa = my pot too → \"my\" + \"pot\" + \"too\"\n- qaqat”a = from the cliff → \"from\" + \"the cliff\"\n- yapsanpsa = in our1+2 field too → \"in\" + \"our1+2\" + \"field\" + \"too\"\n\nNow analyze each word for structure:\n\nPattern 1: Possession and numerals\n\n- \"our1+2\" is used as a determiner meaning \"mine and yours\" → appears in:\n - qucxst”psa: from our1+2 lake too\n - markstxi: is it our1+2 town?\n - yapsanpsa: in our1+2 field too\n\nPattern 2: Determiner + noun\n\n- \"in the cave\" = aq”na\n- \"in my bed\" = ishinhna → \"in\" + \"my\" + \"bed\"\n- \"in your corner\" = ? → likely \"in\" + \"your\" + \"corner\"\n- \"in your corner too\" = ? → \"in\" + \"your\" + \"corner\" + \"too\"\n\nPattern 3: \"from\" construction\n\n- from his town = markp”t”a\n- from the cliff = qaqat”a\n- from our1+2 lake too = qucxst”psa → \"from\" + \"our1+2\" + \"lake\" + \"too\"\n\nPattern 4: Questions with \"is it\" + location\n\n- chushuntxi = is it in the corner?\n- markstxi = is it our1+2 town?\n→ So \"is it in the [possessed noun]\" → \"is it\" + \"in\" + \"[determiner]\" + \"[noun]?\"\n\nPattern 5: \"too\" is added after the noun in both affirmative and negative forms?\n\n- aq”ipsa = the cave too → suggests \"too\" is a suffix or post-noun marker\n- p”ak”unhpsa = my pot too → same: \"my pot\" + \"too\"\n- yapsanpsa = in our1+2 field too → same: \"in our1+2 field\" + \"too\"\n\nTherefore, \"too\" is a post-noun marker, not necessarily independent.\n\nNow solve each part:\n\n4. our1+2 cliff \n→ From \"from the cliff\" = qaqat”a \n→ \"our1+2 cliff\" = \"from\" + \"our1+2\" + \"cliff\"? No → but \"from\" is used with \"cliff\", not \"our1+2 cliff\" \n\"our1+2 cliff\" is a noun phrase: “the cliff” belonging to both.\n\nBut in the gloss: “from the cliff” = qaqat”a \nSo “the cliff” is a noun phrase. \nIn \"from our1+2 lake\" → qucxst”psa → shows that \"our1+2\" modifies the lake.\n\nSo likely: “our1+2 cliff” = qaqat”a → but with \"our1+2\" attached? \nBut qaqat”a is “from the cliff” — no possessive.\n\nSo to form “our1+2 cliff” → likely similar to “our1+2 field”?\n\n\"yapsanpsa\" = in our1+2 field too → so “our1+2 field” is a noun phrase.\n\nSo “our1+2 cliff” = would be just \"qqa\" (cliff) + \"our1+2\"? But do we have a word?\n\nNo separate word for “cliff” in possession.\n\nBut “from the cliff” is qaqat”a → so “the cliff” is a base.\n\nSo “our1+2 cliff” = ? → likely formed by “our1+2” + “cliff” → just like “our1+2 field” is implied.\n\nCheck: no example directly has “our1+2 cliff” → but similar pattern.\n\nWe have “our1+2 lake” in qucxst”psa → only as part of “from our1+2 lake too”\n\nBut “in our1+2 field too” → yapsanpsa → “in” + “our1+2 field” + “too”\n\nSo “our1+2 field” is a unit.\n\nSimilarly, “our1+2 lake” is a unit in “from our1+2 lake too”\n\nTherefore, “our1+2 cliff” = should be derived by adding “our1+2” to “cliff” → but what is the word for cliff?\n\n“from the cliff” = qaqat”a → “the cliff” → qaqat”a\n\nSo “our1+2 cliff” → likely qaqat”a with “our1+2” attached? But where?\n\nWe see in “our1+2 lake” → in “from our1+2 lake too”, possession appears before the noun? But “lake” is not preceded by “our1+2” in the word form — it's in the context.\n\nBut in “our1+2 field” → “in our1+2 field too” → “our1+2” modifies “field”\n\nSimilarly, “our1+2 lake” → in “from our1+2 lake too” → so “our1+2” modifies the noun.\n\nIn “from our1+2 lake too” → \"from\" + \"our1+2\" + \"lake\" + \"too\"\n\nSimilarly, “from his town” → markp”t”a → \"from\" + \"his\" + \"town\"\n\nSo “from your corner” would be “from” + “your” + “corner”\n\nBut “our1+2 cliff” → likely “our1+2” + “cliff” → but no base word?\n\nBut “cliff” is not in a base form.\n\nThe base forms are: cliff → qaqat”a → “from the cliff”\n\nSo to say “our1+2 cliff”, the structure is just “our1+2” + “cliff”\n\nBut in the word list, do we see \"our1+2 cliff\"?\n\nWe have “our1+2 lake” in “from our1+2 lake too” → meaning “our1+2 lake” is a noun phrase.\n\nSimilarly, “our1+2 field” is used in “in our1+2 field too”\n\nThus, “our1+2 cliff” = ??? → likely “qqa” + “our1+2”? But we don't know.\n\nBut the base for cliff is “the cliff” = qaqat”a → perhaps “our1+2 cliff” = qaqat”a with “our1+2” prepended?\n\nBut in previous constructions, for possession, it's attached to the noun with “our1+2” modifying.\n\nTherefore, “our1+2 cliff” = qaqat”a → but with “our1+2” attached?\n\nNo — we have no such form.\n\nInstead, look for parallel structures.\n\nWe have:\n\n- the cave → aq”ipsa\n- in the cave → aq”na\n→ so “the cave” is a noun phrase.\n\nSimilarly:\n\n- from the cliff → qaqat”a → “the cliff” as a noun\n\nSo “our1+2 cliff” → must be “the cliff” with “our1+2” → so qaqat”a with “our1+2” → likely not the base.\n\nBut in examples, when \"our1+2\" modifies a noun, it comes before the noun.\n\nFor example:\n\n- from our1+2 lake too → so “our1+2 lake” as the object\n- in our1+2 field too → “in our1+2 field”\n\nSo for \"our1+2 cliff\" → it would be in the same form: “our1+2 cliff”\n\nBut we don’t have a word for it.\n\nBut since the pattern is consistent, and no other form is given, we assume that “our1+2 cliff” is formed by replacing “the” with “our1+2” and keeping the noun.\n\nBut “from the cliff” is qaqat”a → so “from our1+2 cliff” would be analogous to “from our1+2 lake” → which is qucxst”psa\n\nSo instead of “cliff”, use a rule: the determiner goes before the noun.\n\nThus, “our1+2” modifies the noun directly.\n\nTherefore, “our1+2 cliff” = qqa (cliff) with “our1+2” → but we don’t have a word.\n\nBut the only base is qaqat”a = from the cliff\n\nSo likely, “our1+2 cliff” is not a standalone noun, but a possessive phrase.\n\nBut the question asks for “our1+2 cliff” — a noun phrase.\n\nFrom the patterns, in “in our1+2 field too”, we see “our1+2 field” used.\n\nSimilarly, “is it our1+2 town?” → “our1+2 town”\n\nSo “our1+2” + noun (with noun base)\n\nWe have \"cliff\" — the word is missing, but the base must be \"cliff\" = qaqat”a → “from the cliff”\n\nBut “cliff” itself is the noun; “the” is implicit.\n\nSo “our1+2 cliff” = “our1+2” + “cliff” = like “our1+2 field”\n\nSo it should be “our1+2 cliff” → no article.\n\nIn “in our1+2 field too” → not “in the our1+2 field”\n\nSimilarly, “from our1+2 lake too” → “from our1+2 lake”\n\nSo yes — “our1+2 cliff” = just “our1+2 cliff” → pattern matches.\n\nWe do not have a word in the list, but we can infer the form.\n\nSo answer to 4: our1+2 cliff → **qqa** → but we don’t have qqa\n\nWait — qaqat”a = from the cliff → so the word for “cliff” is qaqat”a with “from”?\n\nNo.\n\nThe word for “cliff” is not directly given. The phrase “from the cliff” is qaqat”a.\n\nSo the root is “the cliff” = qaqat”a\n\nSo “our1+2 cliff” → similar to “our1+2 lake” → which is used in “from our1+2 lake too”\n\nBut “from our1+2 lake too” → the noun “lake” is after “our1+2”\n\nSo “our1+2 lake” is a phrase.\n\nSimilarly, “our1+2 cliff” is just “our1+2 cliff”\n\nWe don’t have the word, but since “our1+2 field” is in “in our1+2 field too”, we know that the structure is “our1+2” + noun.\n\nTherefore, “our1+2 cliff” = “our1+2” + “cliff” → but what is the Jaqaru form?\n\nWe don’t have a standalone word — but from “from our1+2 lake” → “our1+2 lake” is part of “from our1+2 lake too”\n\nSimilarly, “from the cliff” = qaqat”a → so if “our1+2 cliff” were “from our1+2 cliff”, it would be like “from our1+2 lake”\n\nSo what is the form?\n\n“cliff” is “cliff” → likely attached after “our1+2”\n\nBut the base word for “cliff” is not given directly.\n\nBut from “from the cliff” = qaqat”a, and “our1+2” is used like in “our1+2 lake” → the noun is modified.\n\nSo we assume that “our1+2 cliff” = **qqa** — no.\n\nPerhaps the base word for “cliff” is the same as in “cliff” → and we just form “our1+2” + “cliff”\n\nBut no such word.\n\nAlternatively, “our1+2 cliff” is **qqa** with “our1+2” — still missing.\n\nWait — in qaqat”a → the “q” is a consonant, “a” is vowel.\n\nPerhaps the stem is “q” + “a” + “t” + “a” → but no.\n\nBetter: look at other attached forms.\n\nWe have:\n\n- in the cave = aq”na\n- in my bed = ishinhna\n- in your corner = ? → likely “in” + “your” + “corner”\n\n“corner” = chushp”a = his corner → so “corner” is chushp”a\n\n“your corner” = ? → likely like “your bed” = ishma → ishma = your bed\n\n“your” → ishma (bed) → so “your” = ish?\n\nBut “your” in “your bed” = ishma → “isha” + “ma”?\n\n“ish” = in? no — ishinhna = in my bed → so ish is part of “in”\n\nAlternatively, “your” in “your bed” is ishma — “ishma”\n\n“my” in “in my bed” = ishinhna → “ish” + “inh” + “na”? \n\nIshinhna = in my bed → “in” + “my” + “bed”\n\n“my” → ish? → ishinhna → “ish” in first part?\n\nBut “ish” is in “in my bed” → “in” is separate.\n\n“in” = ish or in?\n\n“in” appears with:\n\n- in the cave → aq”na\n- in my bed → ishinhna\n- in your corner → ?\n- in your corner too → ?\n- in our1+2 field → yapsanpsa\n\nSo “in” is the preposition.\n\nSo “in your corner” = “in” + “your” + “corner”\n\n“your” → from “your bed” = ishma → ishma = your bed → so “your” = ish? → ishma → “ishma”\n\nBut ishma → “ish” + “ma” → “ma” = bed?\n\nBut chushp”a = his corner → “chush” + “p” + “a” → so “chush” = his?\n\nSimilarly, “your” = ? → from ishma → perhaps “ish” — but only in “bed”\n\nNo clear word.\n\nBut “your corner” → likely “ish” + “p” + “a” or similar to chushp”a?\n\nBut chushp”a = his corner → chush → his\n\nSo “your” → ? → ish → your? isha?\n\nBut ishma = your bed → so “ishma” = your bed → “ish” + “ma”\n\nSo “your” is “ish”?\n\nIn “in your corner” → “in” + “ish” + “p” + “a” = ish + chushp”a?\n\nBut “ish” is not in base.\n\nPerhaps “your corner” = “ish” + “chushp”a → but that’s not a word.\n\nBut in “from his town” = markp”t”a → from + his + town\n\nSo possessive markers are attached before the noun.\n\nSo “your corner” = “your” + “corner” → “ish” + “chushp”a\n\nBut “ish” is not a standalone word.\n\nUnless “ish” = your\n\nIn “your bed” = ishma → so “ish” + “ma” = your bed\n\nLikely, “your” = ish\n\nSo “your corner” = ish + chushp”a → ishchushp”a?\n\nBut no such form.\n\nBut look at “in your corner” → it is not a direct word.\n\nBut from “is it in the corner?” = chushuntxi → so “in the corner” is used.\n\nSo in “in your corner” → could be “in” + “your” + “corner” → so “in” + “your” + “corner” → but we don’t have “your” as a word.\n\nBut “your bed” = ishma — “ish” + “ma”\n\n“my bed” = ishinhna — “ish” + “inh” + “na”\n\n“my” and “your” both begin with “ish”, but different suffixes.\n\n“my” = ishinhna → “ish” + “inh” → “in” + “my” + “bed” — so “ish” = my?\n\nBut “in” is separate.\n\n“in” is separate in all cases.\n\nSo “in my bed” = ishinhna → “ish” is “my”\n\n“in your bed” = ishma → “ish” is “your”?\n\nBut “ish” is common.\n\nIn “in my bed” = ishinhna\n\nIn “your bed” = ishma\n\nSo “ish” appears in both.\n\n“in” is not in “your bed” — it is missing.\n\nSo “your bed” = ishma — no “in”\n\nSo “in” is only with “my” and “cave” and “corner”\n\nTherefore, “in your corner” = “in” + “your” + “corner” = “in” + “ish” + “chushp”a\n\nBut is there a form?\n\nNo direct example.\n\nBut we have “in our1+2 field” = yapsanps", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11315.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Step-by-step analysis of the Jaqaru examples and target translations:\n\nFirst, identify patterns from the given examples:\n\n1. \"aq”ipsa\" = \"the cave too\" \n → \"too\" is marked with a suffix, likely -psa \n → \"the cave\" is aq”, so \"the cave too\" = aq”ipsa\n\n2. \"aq”na\" = \"in the cave\" \n → \"in\" is a preposition, likely a prefix or infix; \"in the cave\" is prefixed or suffixed as aq”na\n\n3. \"qucxap”a\" = \"through the lake\" \n → \"through\" is likely a prepositional modifier; \"lake\" is \"qucx\" \n → \"qucxap”a\" → part of a pattern where \"through\" is attached to noun\n\n4. \"qucxst”psa\" = \"from our1+2 lake too\" \n → The structure “from our1+2 lake too” → \"qucxst”psa\" \n → “our1+2” appears in the base: “qucx” = lake, “st” = from, “psa” = too \n → Indicates that “from + our1+2 + lake + too” = qucxst”psa \n → So: from + our1+2 + noun + too → st + (our1+2) + noun + psa \n → Possible pattern: [st] + [our1+2] + [noun base] + [psa] = from our1+2 X too\n\n5. \"chushp”a\" = \"his corner\" \n → \"his\" = chush, \"corner\" = p”a → chushp”a\n\n6. \"chushuntxi\" = \"is it in the corner?\" → question form of “in the corner” \n → \"in the corner\" = chushuntxi → \"untxi\" likely indicates question form \n → so \"in\" + \"corner\" → \"chushuntxi\"\n\n7. \"marka\" = \"the town\" \n → base noun form: marka\n\n8. \"markp”t”a\" = \"from his town\" \n → \"from\" = mark + p”t”a? \n → \"his\" = chush, so \"from his town\" = mark + chush + town? \n But \"markp”t”a\" → probably mark + p”t”a → p”t”a = his town? \n → contradiction: chushp”a = his corner → so chush + corner \n → marka = the town → mark + town \n → markp”t”a = from his town → likely: mark + p”t”a → p”t”a = his town → possible \n → Indicates that possessive for “his” is shown in a derived form: p”t”a = his town \n → So possessive forms are attached to noun; possessive markers are embedded as infix or suffix \n → \"his town\" = chush + marka → but chush + marka is not given; markp”t”a is given → suggests “p”t”a” = “his town” \n → So “p”t”a” = his town? → yes \n → From “markp”t”a” = from his town → thus \"p”t”a\" = his town → so \"from + his town\" = markp”t”a\n\n9. \"markstxi\" = \"is it our1+2 town?\" \n → \"is it + our1+2 + town?\" → markstxi \n → \"stxi\" = question form? similar to \"chushuntxi\" = is it in the corner? \n → so \"stxi\" = question marker \n → \"our1+2\" = our1+2, present in \"markstxi\" \n → so “our1+2” appears before noun, and + stxi = question form \n → So: [our1+2] + [noun] + stxi = is it our1+2 town?\n\n10. \"utamt”a\" = \"from your house\" \n → \"your\" = uta? but we have \"utamt”a\" \n → \"your\" likely = uta; \"house\" = t”a? → \"utamt”a\" = from your house \n → \"from\" + \"your house\" = utamt”a \n → so \"from\" = uta + m? → possibly \"utam\" = from your + base \n → But \"p”ak”unhpsa\" = \"my pot too\" = my pot + too → \"unh\" = my pot? \n → \"p”ak”u\" = the pot → \"p”ak”unhpsa\" = my pot too \n → So \"unh\" = my → \"unhpsa\" = my pot too → \"unh\" is modifier for \"my\" \n → Thus, possession via prefix or suffix: \"my\" = unh \n → So \"your\" = uta → \"utamt”a\" = from your house → so \"utam\" + t”a\" → \"utamt”a\"\n\n11. \"utnha\" = \"my house\" → \"unh\" + \"t”a\" → unh + t”a\" = my house \n → confirms possession via unh = my \n → thus \"your house\" = uta + t”a → utat”a? \n But \"utamt”a\" = from your house → not utat”a \n\n → possibly the word is not direct: \"your house\" = \"utat”a\" \n But we have \"utamt”a\" = from your house → “from” is marked, possibly “utam” = from your \n → So “from” may be part of the form → \"utam\" = from your \n → So base form of house = t”a → \"my house\" = unh + t”a = utnha? \n → utnha = unh + t”a → yes \n → so \"your house\" = uta + t”a → utat”a? \n → but we have “from your house” = utamt”a → so utam + t”a → suggests “utam” = from your\n\n12. \"yaputxi\" = \"is it the field?\" \n → \"field\" = yap? → \"yaputxi\" = is it the field? \n → “is it” + “field” → stxi = question marker → yes \n → so “yap” = field → “yaputxi” = is it the field?\n\n13. \"yapsanpsa\" = \"in our1+2 field too\" \n → \"in\" + \"our1+2\" + \"field\" + \"too\" \n → structure: \"yapsanpsa\" → \"yap\" + \"sa\" + \"n\" + \"psa\"? \n → compare to “qucxst”psa” = from our1+2 lake too \n → “from” = st, “our1+2” = our1+2, “lake” = qucx → so st + our1+2 + qucx + psa \n → in our1+2 field too → likely \"in\" + \"our1+2\" + \"field\" + \"too\" \n → so “in” = ya? “yap” = field → “yap” + “s” + “an” + “psa”? \n → “yapsanpsa” → “yap” + “s” + “an” + “psa”? \n → “s” may be “in” → but in \"chushuntxi\" = in the corner → “untxi” \n → “untxi” = in + corner → in = un? \n → so “in” = un? \n → in “chushuntxi” → chush + un + txi → so in = un → then “un” = in \n → in “yapsanpsa” = in our1+2 field too → “un” + “our1+2” + “field” + “too” \n → “un” + “s” + “an” + “psa”? \n → “s” + “an” → perhaps “san” = our1+2? \n → “san” = our1+2? \n → In “qucxst”psa” → “st” = from → so “st” is a preposition \n → in “chushuntxi” → “un” = in → so in = un \n → in “yapsanpsa” → “un” + “san” + “yap” + “psa”? → not matching \n → instead, \"yapsanpsa\" = “yap” + “san” + “psa” \n → “san” may = our1+2 → because in “qucxst”psa” → “st” + “our1+2” + “qucx” → so the marker “san” may be for our1+2 \n → but “qucxst”psa” — “qucx” = lake, “st” = from, no “san” \n → “san” appears only in “yapsanpsa” \n → could be that “san” = our1+2 → used in “in our1+2 field too” → “yap” + “san” + “psa” → with “un” missing? \n → unless “yap” is “in the field” → so “yap” + something? \n\n → From “yaputxi” = is it the field? → so “yap” = field \n → In “chushuntxi” = is it in the corner? → “untxi” = in corner \n → So “in” = un → so “in the field” = un + yap → “unyap” \n → Then “in our1+2 field too” = un + our1+2 + yap + psa → un + san + yap + psa → “yapsanpsa” \n → So “san” = our1+2 \n → “psa” = “too” \n → So pattern: \n in + our1+2 + noun + too → un + san + noun + psa \n\n → Similarly, “from our1+2 lake too” = from + our1+2 + lake + too → st + san + qucx + psa → “qucxst”psa” \n → So “st” = from \n → “un” = in \n → “san” = our1+2 \n → “psa” = too \n\nNow apply to the target questions:\n\n4. our1+2 cliff \n→ no “in”, no “from”, no “is it” \n→ just “our1+2 cliff” \n→ Base word: cliff → “qaqat”a = from the cliff → so “qaqat”a” \n→ “qaq” = cliff → so “qaq” = cliff \n→ “qaqat”a” = from the cliff → “at” = from? → “at” = from? \n→ In “qucxst”psa” = from + our1+2 + lake → “st” = from \n→ So “from” = st \n→ “qaqat”a” = from the cliff → “qaq” + “at” → suggests “at” = from? \n→ But “st” = from → so “at” ≠ from \n→ So “qaq” = cliff? → “qaqat”a” → “qaq” + “at” → “at” = the? \n→ Compare: “marka” = the town → so “a” = the? \n→ “utnha” = my house → “t”a = house → “t”a = house \n→ So “qaqat”a” = from the cliff → “qaq” + “at” → “at” = the? → yes, “a” = the \n→ so “the” = a \n→ Therefore: “our1+2 cliff” = our1+2 + cliff \n→ “our1+2” = san \n→ “cliff” = qaq \n→ So: san + qaq → sanq”aq? \n→ But need to check if “cliff” = qaq \n→ “qaqat”a” = from the cliff → so “qaq” = cliff → yes \n→ So “our1+2 cliff” = san + qaq → sanq”aq \n\nBut is “san” at the beginning? Like in “sanpsa” → yes \n→ So 4. our1+2 cliff → sanq”aq \n\n5. in your corner \n→ “in” = un \n→ “your” = ? \n→ “corner” = chushp”a → chush = his, so maybe “chush” = corner? \n→ “chushp”a” = his corner → so “chush” = corner? \n→ So “corner” = chush \n→ “your” → where is “your” in the examples? \n→ “utamt”a” = from your house → “your” = uta \n→ “your house” = uta + t”a → utat”a \n→ So “your” = uta \n→ So “in your corner” = un + uta + chush → unutachush? \n→ But is there a suffix or infix? \n→ In “chushuntxi” = in the corner? → un + chush + txi → “untxi” \n→ So “in the corner” = un + chush + txi \n→ Therefore, “in your corner” = un + uta + chush? \n→ But the possessive “your” is not attached to “corner” — still in literal sense \n→ In “chushuntxi” → corner = chush → so “your” must be separate \n→ But in terms of marking: “his” = chush → so “your” = uta \n→ So “in your corner” = un + uta + chush → unutachush? \n→ But is this a compound? \n→ No data shows “in your + corner” as a unit \n→ Compare to “in the corner” = unchush + txi → but that's only in the question \n→ In “markstxi” = is it our1+2 town? → our1+2 = san → so “markstxi” → sanmarkstxi? \n→ No \n→ So likely: “in your corner” = un + uta + chush → unutachush \n\nBut is “your” a prefix or suffix? \nIn “utamt”a” = from your house → “utam” = from your → so “your” = uta → embedded \n→ So perhaps “your corner” = uta + chush → “utachush” \n→ Then “in your corner” = un + utachush → “unutachush” \n\nBut more likely: “in your corner” = un + chush + uta → no, because “your” is not a modifier of the corner in the same way as “his” \n→ In “chushp”a” = his corner → so corner is marked with chush \n→ So “your corner” would be uta + chush → “utachush” \n→ Then “in your corner” = un + utachush → “unutachush” \n\n6. in your corner too \n→ same as above, plus “too” \n→ “too” = psa \n→ So “unutachushpsa” \n\n7. from your corner too \n→ “from” = st \n→ “your corner” = utachush \n→ “too” = psa \n→ So “st + utachush + psa” → stutachushpsa \n\n8. is it from the cave? \n→ “is it from” + “the cave” \n→ “from” = st \n→ “the cave” = aq”ipsa = the cave too → so “the cave” = aq”ipsa \n→ But “aq”ipsa” = the cave too → so base = aq” → “cave” = aq” \n→ So “from the cave” = st + aq” → st + aq” → staq” \n→ “is it” = stxi \n→ So full: stxi + st + aq” → stxi staq” → but order? \n→ In “is it our1+2 town?” = markstxi → so “is it” + [noun] \n→ So “is it from the cave?” = stxi + [from the cave] → stxi + st + aq” → stxi staq” \n→ But no example with “is it from X”? \n→ “from our1+2 lake too” = qucxst”psa” → so “from” comes before noun? \n→ But “from the cave” = st + aq” \n→ So “is it from the cave?” = stxi + st + aq” → stxi staq” \n→ But examples show “from” before noun, not after \n→ “is it from the cave?” → the structure is “is it” + “from the cave” \n→ so likely: stxi + st + aq” → but perhaps the words are combined with “aq” as base \n→ aq”ipsa = the cave too → so “aq” = the cave \n→ “from the cave” = st + aq” \n→ So yes: stxi staq” \n\n9. is it the house? \n→ “is it” + “the house” \n→ “the house” = “utnha” = my house → so “t”a = house → “the” = a \n→ So “the house” = a + t”a → at”a \n→ So “is it the house?” = stxi + at”a → stxi at”a \n\nNow verify all:\n\n4. our1+2 cliff → san + qaq → sanq”aq \n5. in your corner → un + uta + chush → unutachush \n6. in your corner", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10403.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Identify the relevant patterns in the given data.\n\nFirst, from the given examples:\n\n- \"aq”ipsa\" = \"the cave too\" → \"too\" is a separate particle attached to the noun.\n- \"aq”na\" = \"in the cave\" → \"in\" is a locative prefix.\n- \"qucxap”a\" = \"through the lake\"\n- \"qucxst”psa\" = \"from our1+2 lake too\" → \"from\" is a preposition, \"our1+2\" is used, and \"too\" is attached.\n\nFrom this, we extract:\n\n- \"our1+2\" is used in constructions like \"our1+2 lake\" → appears in \"qucxst”psa\"\n- \"too\" is marked by the suffix -psa or -t”sa?\n - \"aq”ipsa\" → \"the cave too\" → so \"too\" is attached via suffix.\n - \"qucxst”psa\" → \"from our1+2 lake too\" → both \"from\" and \"too\" are attached.\n\nNow, look at the basic word forms:\n\n- \"chushp”a\" = \"his corner\"\n- \"chushuntxi\" = \"is it in the corner?\"\n- \"marka\" = \"the town\"\n- \"markp”t”a\" = \"from his town\"\n- \"markstxi\" = \"is it our1+2 town?\"\n- \"utamt”a\" = \"from your house\"\n- \"utnha\" = \"my house\"\n- \"p”ak”unhpsa\" = \"my pot too\" → so \"too\" is suffix -psa\n- \"yaputxi\" = \"is it the field?\"\n- \"yapsanpsa\" = \"in our1+2 field too\" → \"in\" + \"our1+2\" + \"field\" + \"too\"\n\nPattern:\n- \"too\" is marked by -psa or -t”sa? In \"aq”ipsa\", it's \"ipsa\" — possibly suffix.\n- In \"p”ak”unhpsa\" = \"my pot too\" → \"unhpsa\", not \"unh\" alone → so \"psa\" at end = \"too\"\n- In \"yapsanpsa\" = \"in our1+2 field too\" → \"psa\" at end = \"too\"\n- In \"qucxst”psa\" = \"from our1+2 lake too\" → again, \"psa\" at end\n\nThus, \"too\" = suffix -psa\n\nSo: verb form or noun form + -psa = \"too\"\n\nAlso:\n- \"in\" appears as \"na\" — \"aq”na\" = \"in the cave\", so \"na\" = \"in\"\n- \"from\" appears as \"qucx\" prefix (qucxap”a), \"markp”t”a\" = \"from his town\" → \"p”t”a\" = \"his town\", so \"from\" = \"mark\" prefix?\nWait — \"marka\" = \"the town\", \"markp”t”a\" = \"from his town\" → \"p”t”a\" = \"his town\" → so \"mark\" + possessive = from/possession?\n\nBut \"qucxst”psa\" = \"from our1+2 lake\" → \"qucx\" is \"through\"? Or base?\n\nWait — \"qucxap”a\" = \"through the lake\" → \"qucx\" + \"ap”a\" → \"through the lake\"\n\n\"qucxst”psa\" = \"from our1+2 lake too\" — so \"qucx\" may be \"through\", but it's used with \"from\"? Inconsistent?\n\nBut \"qucxst”psa\" = \"from our1+2 lake too\" — so \"qucx\" may not be \"through\" in that form.\n\nWait — is \"qucx\" used for \"through\" or \"from\"?\n\nLook: \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too\n\nPossibly \"qucx\" = \"through\" — and \"st”\" = \"from\"? Unlikely.\n\nAlternatively, maybe \"qucx\" is a root, and \"st\" is \"from\"?\n\nBut then \"st”psa\" → \"from our1+2 lake too\" — \"st”psa\" might be \"from the lake too\"?\n\nBut \"qucx\" is present.\n\nAlternative idea: Maybe \"qucx\" is the root, and the meaning shifts?\n\nYes — but the only consistent marker is:\n\n- \"in\" = \"na\"\n- \"from\" = appears in \"markp”t”a\" = \"from his town\", \"qucxst”psa\" = \"from our1+2 lake\"\n\nSo \"from\" is marked by a prefix? \"mark-\"? \"qucx-\"?\n\nBut \"mark\" + \"p”t”a\" = from his town → so \"mark\" = from?\n\n\"markstxi\" = is it our1+2 town? → so \"mark\" + \"stxi\" = is it our1+2 town?\n\nSo \"mark\" = town, and “mark” with possessive = from?\n\nBut \"marka\" = the town → \"mark\" = the town\n\n\"markp”t”a\" = from his town → possessive \"p”t”a\" = his town → so \"from his town\"\n\nThus: \"from X\" = \"mark\" + possessive of X\n\nBut \"qucxst”psa\" = \"from our1+2 lake too\"\n\n\"qucx\" + \"st”psa\" → \"st”psa\" = our1+2 lake?\n\nBut \"qucxap”a\" = through the lake → so \"ap”a\" = the lake?\n\nSo \"ap”a\" = the lake\n\nThen \"st”psa\" = our1+2 lake too → again, \"st”psa\" = our1+2 lake too?\n\nBut earlier: \"qucxst”psa\" = from our1+2 lake too → so \"from\" is not carried by \"qucx\"?\n\nPossibly, \"qucx\" is a preposition meaning \"through\", and \"st\" is a variant?\n\nAlternatively, the word \"st”\" might be a form of \"in\", but \"stxi\" appears in \"is it in the corner\" = \"chushuntxi\" → \"chush\" + \"untxi\" = is it in?\n\nWait — \"chushuntxi\" = \"is it in the corner?\" — so \"untxi\" = \"in the corner?\"\n\nBut \"markstxi\" = \"is it our1+2 town?\" — so \"stxi\" = “is it our1+2 town?”\n\nThus, \"stxi\" = \"is it in X?\" for a noun X\n\n\"chushuntxi\" = \"is it in the corner?\" → \"chushuntxi\" → \"chush\" = corner, \"untxi\" = is it in?\n\nSo \"untxi\" = \"is it in?\"\n\nSimilarly, \"markstxi\" = is it our1+2 town?\n\nSo \"stxi\" = \"is it (in) X?\"\n\nBut in \"chushuntxi\", \"chush\" is corner → \"chush\" + \"untxi\" → so \"untxi\" = is it in?\n\nBut in \"markstxi\", \"mark\" + \"stxi\" → \"markstxi\" → so \"stxi\" = \"is it in X?\"\n\nSo likely, \"stxi\" = \"is it in X?\" where X is the noun\n\nBut the noun is attached — \"chush\" is corner.\n\nSo form: [noun] + [stxi] = is it in [noun]?\n\nBut \"markstxi\" = is it our1+2 town → so \"mark\" is to be interpreted as \"our1+2 town\"?\n\nWait — \"mark\" = the town → \"our1+2 town\" would require \"our1+2\" prefix?\n\nBut \"markstxi\" = is it our1+2 town?\n\nYes — the \"our1+2\" is in the context → so \"mark\" = \"the town\" — when combined with \"stxi\", it's \"is it in the town?\" or \"is it our1+2 town?\"\n\nYes — so the structure is:\n\n- [Possessive] + [noun] → e.g. \"our1+2 lake\" → \"qucxst”psa\" → \"qucxst”psa\" = from our1+2 lake too\n\nBut how is \"our1+2\" incorporated?\n\nWe see:\n\n- \"qucxst”psa\" = from our1+2 lake too → so \"our1+2\" is used with lake → how?\n\n\"qucxap”a\" = through the lake → no \"our1+2\"\n\n\"qucxst”psa\" = from our1+2 lake too → so \"our1+2\" is attached to \"lake\"\n\nBut no explicit \"our1+2 lake\" = \"our1+2 lake\"\n\nSo likely, \"our1+2\" is a prefix that attaches to the noun.\n\nIn \"qucxst”psa\": \"st”psa\" → contains \"our1+2 lake\"?\n\nBut \"st”psa\" = \"our1+2 lake too\"? Or \"from our1+2 lake too\"?\n\nSo \"st”\" may be \"lake\"?\n\nBut \"ap”a\" = lake → \"qucxap”a\" = through the lake\n\nSo \"ap”a\" = lake\n\nThen \"st”psa\" = ? — so \"st”\" may be another form?\n\nPossibly, there is a root \"la\" or \"st\" for lake?\n\nBut only \"ap”a\" is used for lake.\n\n\"qucxst”psa\" = from our1+2 lake too → the \"our1+2\" is in the phrase → so the word form must contain it.\n\nSo likely, in Jaqaru, possessive is marked via prefix or suffix.\n\nFrom:\n\n- \"aq”na\" = in the cave → \"na\" = in\n- \"chushp”a\" = his corner → \"p”a\" = his?\n- \"chushuntxi\" = is it in the corner? → \"untxi\" = is it in?\n- \"markp”t”a\" = from his town → \"p”t”a\" = his town → so possessive suffix?\n\nThus, possessive is marked by suffix -p”a, -t”a, etc.\n\nSo:\n\n- \"his corner\" = chushp”a → chush + p”a\n- \"his town\" = markp”t”a → mark + p”t”a? But p”t”a → doesn't match \"p”a\"\n\n\"p”a\" vs \"p”t”a\" → different.\n\n\"chushp”a\" = his corner → \"p”a\"\n\"markp”t”a\" = from his town → \"p”t”a\"\n\nBut \"marka\" = the town → so \"a\" = the town\n\nSo possessive forms vary: corner → p”a, town → p”t”a\n\nPossibly, possessive suffix depends on the noun.\n\nBut \"p”a\" is for \"corner\", \"p”t”a\" for \"town\"?\n\nNow, for \"our1+2\", we see:\n\n- \"qucxst”psa\" = from our1+2 lake too → so \"st”psa\" = from our1+2 lake?\n\nBut \"st”\" — if \"st”\" = lake, then \"st”psa\" = lake too?\n\nBut “qucx” may be “from”, or “through”?\n\n\"qucxap”a\" = through the lake → so \"qucx\" + \"ap”a\" = through the lake\n\n\"qucxst”psa\" = from our1+2 lake too → so “qucx” is used with \"from\"?\n\nBut can't be both.\n\nPossibility: \"qucx\" is used for “through”, and separate prepositions for “from”?\n\nBut “qucxst”psa” = from\n\nAlternative: in Jaqaru, “from” = “mark” + possessive?\n\n- “marka” = the town\n- “markp”t”a” = from his town → so “mark” + (possessive of town) = from his town\n\nSimilarly, “from our1+2 lake” → would be “mark” + (our1+2 lake)\n\nBut “mark” + what? “mark” + “st”psa”?\n\nBut we don’t have “mark” + “lake”\n\nWe have “qucxst”psa” = from our1+2 lake too\n\nSo likely, “qucx” = from?\n\nBut “qucxap”a” = through the lake → so “qucx” cannot be both.\n\nThis is inconsistent.\n\nBut note: \"qucxst”psa\" has \"st”psa\" — perhaps \"st”\" = lake?\n\nBut \"ap”a\" = lake → \"qucxap”a\" = through the lake\n\n\"qucxst”psa\" = from our1+2 lake too → so \"st”psa\" = our1+2 lake?\n\nSo \"st”psa\" = our1+2 lake → so \"st”\" = lake?\n\nBut \"ap”a\" = lake → so why two forms?\n\nAnother idea: \"st”\" and \"ap”a\" are different forms of lake?\n\nBut \"qucxap”a\" = through the lake — so “ap”a” = lake\n\n\"qucxst”psa\" = from our1+2 lake → so \"st”psa\" = our1+2 lake → so \"st”\" = lake, with possessive?\n\nPossibly, the noun \"lake\" has two forms: \"ap”a\" (the lake), \"st”\" (the lake with possessive)?\n\nBut \"st”psa\" ends with \"psa\" — which is \"too\"\n\nSo “st”psa” = our1+2 lake too\n\nTherefore, “st”psa” = our1+2 lake too → so “st”” = lake, with possessive for \"our1+2\" and suffix \"too\"?\n\nBut how is “our1+2” attached?\n\nOnly in constructions with “psa”\n\nIn:\n\n- aq”ipsa” = the cave too → “ipsa” = cave too → suffix “psa” = too\n- p”ak”unhpsa = my pot too → “unhpsa” = my pot too → suffix “psa” = too\n- yapsanpsa = in our1+2 field too → “yapsanpsa” = in our1+2 field too → suffix “psa” = too\n\nSo –psa = too\n\nAlso:\n\n- aq”na = in the cave → “na” = in\n- ishinhna = in my bed → “inhna” = my bed? “inh” + “na”?\n- utamt”a = from your house → “utam” + “t”a”?\n- utnha = my house → “utn” + “ha”\n\nPossessive forms:\n\n- “his corner” = chushp”a → chush + p”a\n- “his town” = markp”t”a → mark + p”t”a\n- “your house” = utamt”a → utam + t”a\n- “my house” = utnha → utn + ha\n\nSo it seems:\n\n- possessive suffix varies by noun: for corner → p”a, town → p”t”a, house → t”a or ha?\n\n“utamt”a” — your house → “t”a” suffix\n“utnha” — my house → “ha” suffix?\n\nBut “utn” + “ha” — not consistent.\n\n“chushp”a” — his corner → “p”a\n“markp”t”a” — his town → “p”t”a”\n“utamt”a” — your house → “t”a”\n“utnha” — my house → “ha”\n\nNo clear pattern.\n\nPossibly, noun roots are used with specific possessive suffixes.\n\nBut for translation, we are to derive:\n\n4. our1+2 cliff → so “our1+2” + “cliff”\n\nWe have “cliff” — no direct word, but “cliff” is like “cliff” — “aq” = cave, “cq” = cliff?\n\nIn “qaqat”a” = from the cliff → “qaqat”a” = from the cliff\n\nSo “qaqat”a” → “qaqat”a” = from the cliff\n\n“qaqat”a” → likely “qaqat”” + “a” = from the cliff → so “qaqat”” = the cliff\n\nSo “qaqat”” = the cliff\n\nThus, “our1+2 cliff” = “our1+2” + “qaqat”a”?\n\nBut how is “our1+2” attached?\n\nIn “qucxst”psa” = from our1+2 lake too — so “st”psa” = our1+2 lake too → so possessive is embedded in the noun?\n\nSo “our1+2 lake” = lake with possessive?\n\nSimilarly, “our1+2 cliff” = cliff with “our1+2” prefix?\n\nBut in “from the cliff”, it's “qaqat”a” — so “qaqat”a” = from the cliff → so “qaqat”a” = from the cliff\n\nSo building “our1+2 cliff” = our1+2 + cliff → how?\n\nPossibly, “our1+2” is a prefix, like in “our1+2 lake”\n\nIn “qucxst”psa” = from our1+2 lake too → so “st”psa” = our1+2 lake too — so “st”psa” = our1+2 lake too\n\nThus, possessive is built into the noun by adding possessive suffix?\n\nBut “st”” — could be lake with possessive?\n\nBut “lake” is linked to “ap”a” in “ap”a” = lake\n\n“st”” is not “ap”a”\n\nPossibly, the form for “our1+2 lake” is “st”psa” — with “st”” = lake?\n\nBut “st”” appears in “qu", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10404.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Analyze the given translations to extract patterns.\n\nGiven:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- marka → the town \n- chushuntxi → is it in the corner? \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- qaqat”a → from the cliff \n- yapsanpsa → in our1+2 field too \n\nStep 2: Identify patterns for possession and direction.\n\nNotice that:\n\n- \"our1+2\" = mine and yours → appears in \"qucxst”psa\", \"markstxi\", \"yapsanpsa\" \n- \"his\" → chushp”a, markp”t”a \n- \"in my bed\" → ishinhna → “in” + “my” \n- \"your bed\" → ishma \n- \"my pot too\" → p”ak”unhpsa = p”ak”u (the pot) + “unhpsa” → “too” \n- \"our1+2 field too\" → yapsanpsa = “in our1+2 field too” \n\nPattern: \n- When “too” appears, it's attached to the root with a suffix like -unhpsa or -npsa \n- “in” appears in ishinhna, chushuntxi, yapsanpsa \n- “from” appears in qucxst”psa, markp”t”a, qaqat”a \n- “is it” appears in chushuntxi, markstxi \n\nStep 3: Build forms for each target.\n\n4. “our1+2 cliff” \n→ From “from the cliff” = qaqat”a \n→ So “our1+2 cliff” = “from the cliff” but with “our1+2” → likely “our1+2” prefixed or attached to “cliff” \n→ Look at: qucxst”psa = from our1+2 lake → qr “our1+2 + lake” \n→ Similarly, yapsanpsa = in our1+2 field too → “our1+2 + field” \n→ So “our1+2 cliff” = ? + cliff → likely \"qucxat”a\" with “our1+2” attached. But qaqat”a is “from the cliff” \n→ So “our1+2 cliff” would be like “our1+2 + cliff” = “qucxat”a” → no, that’s “from the cliff” \n→ Instead, look at “in our1+2 field too” = yapsanpsa \n→ “in our1+2 field” → yapsa (field) + “our1+2” → yapsanpsa \n→ So likely, “our1+2 cliff” = qaqat”a with “our1+2” inserted → qaqat”a → from the cliff \n→ Is there a form for “our1+2” + “cliff”? \n→ qucxst”psa = from our1+2 lake → “our1+2” + “lake” → lake is “qucx” \n→ So “our1+2 lake” = qucxst”psa → “st” might be a marker for “our1+2” \n→ Similarly, “our1+2 town” = markstxi → “mark” (town) + stxi \n→ “our1+2 field” = yapsanpsa → “yapsa” (field) + “npsa”? But yapsanpsa = “in our1+2 field too” \n→ Instead, note that “in our1+2 field too” = yapsanpsa \n→ “in” = “ya” or “is” or “yap”? \n→ In “yapsanpsa”, “yap” = field, “s” = in, “anpsa” = our1+2 too? \n→ But markstxi = is it our1+2 town → “is it” = “markstxi” \n→ markstxi → likely “mark” (town) + “stxi” → “stxi” = is it? \n→ chushuntxi → is it in the corner? → “chush” (corner) + “untxi” \n→ So “untxi” = is it? \n→ So “is it in the corner?” = chushuntxi \n→ So “is it in the corner” = chushuntxi \n→ Then “in your corner” = ? \n→ “in my bed” = ishinhna → “ishin” + “hna”? \n→ “your bed” = ishma \n→ “in my bed” = ishinhna → “ishin” + “hna” → so “in” + “my” → “ishin” = in + my \n→ “in your” = ishina? But no. \n→ “your bed” = ishma → “ish” + “ma” \n→ “in my” = ishinhna → “ishin” + “hna”? \n→ So “in” might be “ish” or “yap”? \n\nAlternative: \n“in my bed” = ishinhna \n“in your corner” → might be “ish” + “ma” (your) + “corner”? \n→ “corner” = chushp”a → his corner \n→ So “in your corner” → “ish” + “ma” + “chushp”a? → but no such word \n\nBut look at: \n- chushuntxi = is it in the corner? \n→ So “in the corner” = chushuntxi without “is it”? But it’s a question \n→ So “in the corner” → chushuntxi is “is it in the corner?” \n→ Thus “in the corner” is the content of the question \n→ So direct translation: “in your corner” → might be “ish” + “ma” + “chush” → but no form \n\nWait: “in my bed” = ishinhna \n→ So “in my” = ishin \n→ “in your” = ishima? \n→ But “your bed” = ishma → so “your” = ish → “ma” \n→ So “in your” might be ishima? \n\nBut ishinhna = in my bed → could be “ish” + “hin” + “hna”? \n\nNot clear. \n\nAlternative pattern: \n“from his town” = markp”t”a \n“from our1+2 town” = markstxi \n→ So “from” + “his” → markp”t”a \n→ “from” + “our1+2” → markstxi \n→ So “from your” → ? \n→ “your” = ish → “ma” \n→ “from your corner” → “from your” + “corner” → ish + ma + chushp”a? \n→ But in markp”t”a → “mark” + “p”t”a → “p”t”a = from his → so “t”a = his? \n→ chushp”a = his corner → so “p”a = his corner? → “p”a → agglutinated? \n\nTry: \n- chushp”a = his corner \n- marka = the town \n- markp”t”a = from his town → “mark” + “p”t”a → “t”a = his? \n→ So “his” = “t”? \n→ “markp”t”a” → “mark” (town) + “p”t”a” → “p”t”a” = his town → “t”a = his \n→ “chushp”a” → “chush” + “p”a” → “p”a = his corner → so “p”a = his \n→ Then “your” = ? → “ish” + “ma” \n→ “from your town” → ? \n→ If “from his town” = markp”t”a → “p”t”a” = his town \n→ So “from your town” = markp”ma” → “ma” = your? \n→ But no such word \n\nWait: “our1+2” forms: \n- from our1+2 lake → qucxst”psa → “qucx” is lake, “st” might be our1+2? \n- from our1+2 town → markstxi → “mark” town, “stxi” → is it? → not “our1+2” \n→ “markstxi” = is it our1+2 town? \n→ So “our1+2” is marked in “stxi” \n→ Similarly, “qucxst”psa = from our1+2 lake too → “st” + lake → “st” = our1+2? \n→ “st” is likely “our1+2” \n→ So “our1+2” = “st” \n\nNow, “in our1+2 field too” = yapsanpsa \n→ yapsa = field \n→ “anpsa” = in our1+2 too → “anpsa” = in + our1+2 + too \n→ So “too” = “unhpsa” in p”ak”unhpsa → “unhpsa” = too \n→ So “too” = unhpsa \n→ “in” = “an”? \n\n“in” appears in: \n- in my bed → ishinhna \n- in your corner — we want \n- in our1+2 field → yapsanpsa \n\nyapsanpsa → “yapsa” + “anpsa” → “in our1+2 field” \n→ So “anpsa” = in our1+2 \n→ “an” = in \n→ “psa” = our1+2? \n→ But “st” is used for “our1+2” in qucxst”psa and markstxi \n\nContradiction: both “st” and “psa” for “our1+2”? \n\nWait: \n- qucxst”psa = from our1+2 lake too → “st” before “lake” → so “our1+2” is “st” \n- markstxi = is it our1+2 town? → “st” in “stxi” → “st” for our1+2 \n- yapsanpsa = in our1+2 field too → “anpsa” → “an” + “psa” → “psa” for our1+2? \n\nInconsistency. \n\nBut look at yapsanpsa: “in our1+2 field too” \nPossibility: “yapsa” = field, “an” = in, “psa” = our1+2 → so our1+2 = psa \n\nBut in qucxst”psa = from our1+2 lake too → “st” not “psa”? \n\nUnless it's “st” and “psa” are different. \n\nBut “our1+2” is defined as ‘mine and yours’. \n\nPossibility: “our1+2” is marked by a suffix, and different constructions use different markers. \n\nBut in markstxi: “is it our1+2 town?” → “st” in “stxi” → so “st” = our1+2 \nIn yapsanpsa: “in our1+2 field too” → “anpsa” → “psa” = our1+2? \n\nPerhaps “psa” is a variant? \n\nWait: the word pattern might be that “our1+2” is attached via a suffix, and the root is modified. \n\nLook at “in my bed” = ishinhna → “ishin” + “hna” → “ishin” = in + my \n→ “in your” = ishima? But “your bed” = ishma → so “ish” + “ma” → “ma” = your \n→ So “in your” = ishima? \n\nSimilarly, “in your corner” = ishima + chushp”a → but would that be ishima chushp”a? \n\nBut in the list, “is it in the corner?” = chushuntxi → suggests “in the corner” = chushuntxi \n→ So “in the corner” = chushuntxi → “untxi” = in? \n\nNo: “untxi” is in is it? → chushuntxi = is it in the corner → “untxi” = in the corner? \n\nUnlikely. \n\nBetter: \n“is it in the corner?” = chushuntxi \n→ so “in the corner” = chushuntxi (without “is it”) — but it's a question \n→ The structure appears to be: [is it] + [in the X]? \n\nSo “in the corner” = chushuntxi — content \n→ So “in your corner” = ? \n→ “your” = ish → “ma” \n→ So “in your corner” = ish + ma + chushp”a = ishmacushp”a? \n\nBut in the examples, no compound form. \n\nAlternative: \n“in my bed” = ishinhna → “ish” + “hin” + “hna” — “hin” = my? \nBut “your” = ishma → “ma” = your → so “in” = “ish” — but “ish” + “ma” = your → so “ish” = in? \n\nNo — “ish” = your? \n\n“your bed” = ishma → “ish” + “ma” \n“in my bed” = ishinhna → “ish” + “hin” + “hna” — “hin” = my? \n\nSo “in” = ish, “my” = hin, “your” = ma \n\nSo for “in your corner” → ish + ma + chushp”a → ishmacushp”a? \n\nBut no such form given. \n\nWait — “is it in the corner?” = chushuntxi → “chush” (corner) + “untxi” → “untxi” = in the corner? \n\n“untxi” = in the corner? \n→ But “in our1+2 town?” = markstxi → “mark” + “stxi” → “stxi” = in our1+2 town? \n\nSo likely: \n- “in the corner” = chush + unt → “unt” = in? \n- “in our1+2 town” = mark + stxi → “stxi” = in our1+2 town \n→ So “in” = “unt” in corner, “st” in town? \n\nNo consistency. \n\nAlternative: \n“in” is not a separate word; the locational aspect is encoded. \n\nGo back to basics.\n\n4. our1+2 cliff \n→ qaqat”a = from the cliff \n→ “our1+2 cliff” = ? \n→ “in our1+2 field” = yapsanpsa \n→ “from our1+2 lake” = qucxst”psa \n→ So “our1+2” appears as a suffix or infix \n→ “qucxst”psa = qucx + st”psa → st”psa = our1+2 lake too \n→ The form is “qucx” + “st” (our1+2) + “psa” (too) \n→ “markstxi” = is it our1+2 town? → “mark” + “st” + “xi” \n→ So “st” = our1+2 \n→ “yapsanpsa” = “yap” (field) + “an” (in) + “psa” (our1+2) + “sa”? \n→ “yapsanpsa” = “yap” + “s” + “anpsa” — “anpsa” = in our1+2 \n→ So “an” = in, “psa” = our1+2 \n→ But “st” is used in other places for our1+2 \n\nConflict. \n\nPerhaps “st” and “psa” are not both “our1+2” — or perhaps it's a typo or error. \n\nBut in the problem: “our1+2 = ‘mine and yours’” — one unit. \n\nLook at: \n- “in our1+2 field too” = yapsanpsa \n- “from our1+2 lake too” = qucxst”psa \n- “is it our1+2 town?” = markstxi \n\nIn all, “our1+2” is marked with “st” or “psa”? \n\nqucxst”psa → “st” \nmarkstxi → “st” \nyapsanpsa → “anpsa” — “psa” \n\nSo possibly “st” is for “our1+2” in most cases, and “anpsa” is a different construction. \n\nBut “yapsanpsa” = in our1+2 field too → so “anpsa” = in our1+2 → so “an” = in, “psa” = our1+2 \n\nSo “our1+2” = “st” or “psa”? \n\nUnless the pattern is inconsistent, which is unlikely. \n\nAlternative: perhaps the “our1+2” is attached as a suffix with a specific form. \n\nIn “qucxst”psa” → “st” attached to “qucx” (lake) \nIn “markstxi” → “st” attached to “mark” (town) \nIn “yapsanpsa” → “anpsa” → “an” + “psa” → “an” is in, “psa” is our1+2 \n\nBut “yapsanpsa” = in our1+2 field too → so “anpsa” = in our1+2 → so “psa” = our1+2 \nSo “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9969.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We analyze the Inuktitut sentences to extract grammatical patterns, especially regarding verb form, subject, object, and aspect.\n\nStep-by-step pattern identification:\n\nExample 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject, possessive marker \"your\" + \"dog\") \n- \"takujaatit\" = saw you (passive verb: \"saw\", with \"you\" as object) \n→ \"takujaatit\" is the verb \"to see\" in past tense, with object \"you\"\n\nExample 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (subject) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot → verb in past tense, agentive \n→ \"qukiqtanga\" = past tense of \"to shoot\", object marked\n\nExample 3: \n\"Aanniqtutit\" → \"You hurt yourself.\" \n- Subject: \"you\" (implied) \n- Object: \"yourself\" → reflexive \n→ \"aanniqtutit\" = you hurt yourself → verb root \"aanniqtu\" + past tense marker \"-tut\"\n\nExample 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor (subject) \n- \"aarqijaatit\" = cured you → verb with object \"you\" \n→ \"aarqijaatit\" = cured + object marked \n→ \"aarqisijaat\" → cured (base) → past tense with object clause\n\nExample 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"qingmiq\" = you \n- \"iputujait\" = speared the dog → verb \"to spear\", object marked \n→ \"iputujait\" = past tense of \"to spear\", object marked\n\nExample 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman (subject) \n- \"iluaqhaijimik\" = a doctor (object) → \"iluaqhaiji\" + plural/object marker \"-mik\" \n- \"aarqisijuq\" = cured → past tense form \n→ \"aarqisijuq\" = past tense of \"cure\", object marked\n\nExample 7: \n\"Nanuq qaijuq\" → \"The polar bear came.\" \n- \"nanuq\" = the polar bear \n- \"qaijuq\" = came → verb root \"qaij\" + past tense \"-uq\" \n→ \"qaijuq\" = past tense of \"to come\"\n\nExample 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"iluaqhaijivit\" = your doctor (subject) \n- \"inuuhuktuit\" = your boy (object, possessive + noun) \n- \"aarqijanga\" = cured → past tense, object marked \n→ \"aarqijanga\" = past tense of \"cure\", with object marked\n\nExample 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter \n- \"amaruq\" = the wolf \n- \"iputujanga\" = speared → verb with object \n→ \"iputujanga\" = past tense of \"spear\", object marked\n\nExample 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"qingmiup\" = the dog (subject) \n- \"ilinniaqtitsijiit\" = your teacher (object) → possessive + noun \n- \"aanniqtanga\" = hurt → past tense of \"hurt\", object marked \n→ \"aanniqtanga\" = hurt, with object marked\n\nExample 11: \n\"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you + \"fell\" in past tense → verb root \"ukiakhaq\" + tense marker \"-tut\"\n\nExample 12: \n\"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter \n- \"nanurmik\" = a polar bear → object with marker \"mik\" \n- \"qukiqsijuq\" = shot → past tense \n→ \"qukiqsijuq\" = past tense of \"to shoot\", object marked\n\nPattern observation:\n- All verbs are in past tense and have a marked object.\n- The pattern is: [subject] + [verb] + [object]\n- Objects are marked with possessive or plural markers (e.g., -mik, -vit, -up, -it)\n- Subjects often include possessive markers (e.g., \"your\", \"your boy\") or definite articles\n- Verb form ends with a suffix indicating the past tense and object marking\n- Reflexive forms (e.g., \"you hurt yourself\") use a self-object marker (implied)\n\nNow, translate the requested sentences:\n\n13. Amaruup angatkuit takujanga \n- \"Amaruup\" = the wolf \n- \"angatkuit\" = saw (verb root \"angatk\" + past tense \"-uit\") \n- \"takujanga\" = (see) + object marker → \"you\" or \"someone\"? \n→ \"takujanga\" = saw → object is missing? But in example 1, we see \"takujaatit\" = saw you \n→ \"takujanga\" → past tense of \"to see\", object likely implied or marked? \nCompare: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"takujanga\" likely = saw [someone], with object implied or missing.\n\nBut \"angatkuit\" = saw → past tense of \"takuj\" \nSo \"Amaruup angatkuit takujanga\" → \"The wolf saw you\"? \nBut \"takujanga\" → does it take object?\n\nIn example 1: \"takujaatit\" = saw you → object-marked \nIn example 4: \"aarqijaatit\" = cured you → object-marked \nSo verb form ends with \"a\" + \"t\" + \"it\" → object marker added later?\n\nWait: \"takujanga\" → ends with -anga → could be object marker? \n\"takujanga\" → likely past tense of \"to see\" with object? \nBut in example 1: \"takujaatit\" → \"you\" as object → tonal or suffix?\n\nWait: \"takujaatit\" → ends with \"-aatit\"? \nCompare: \n- takujaatit → \"saw you\" \n- aarqijaatit → \"cured you\" \n→ pattern: verb root + \"j\" + \"a\" + \"it\" → object marker \"a\" + \"it\"\n\nBut \"takujanga\" → ends with \"-anga\" → not \"-aatit\"\n\nIn example 1: \"takujaatit\" → \"to see\" + object reference \nIn example 7: \"qaijuq\" = came (no object)\n\nSo perhaps the verb + object suffix is altered by grammar.\n\nAlternative: verb root + passive structure?\n\nWait — in sentence 1: \"Qingmivit takujaatit\" → subject: your dog, verb: saw you \n→ \"takuj\" + suffix \"a\" + \"at\" + \"it\" → object marker\n\nBut in sentence 13: \"Amaruup angatkuit takujanga\" → \n\"Amaruup\" = the wolf \n\"angatkuit\" = the verb \"saw\" → past tense? \n\"takujanga\" = \"saw\" → but is this a second verb? No.\n\nPossibility: misanalysis.\n\nWait — is \"angatkuit\" the verb? \n\"angatkuq\" = the shaman (example 6) \n\"angatkuit\" → past tense? From example 6: \"Angatkuq\" = the shaman → no tense \nSo \"angatkuit\" → could be past tense of \"to see\"?\n\nBut \"takuj\" = to see \n\"angatkuit\" → \"angatk\" + \"uit\" → \"to see\" with object?\n\nOr is \"takujanga\" the verb?\n\nCompare sentence 2: \"inuuhuktuup iluaqhaiji qukiqtanga\" → \"shot\" verb is \"qukiqtanga\" \nQukiqtanga — root qukiq + past tense mark?\n\nLook for verb endings:\n\n- qukiqtanga → past tense of \"to shoot\" \n- aarqijaatit → past tense of \"to cure\" \n- iputujait → to spear \n- aanniqtutit → to hurt (reflexive)\n\nCommon pattern: verb root + -(i) + t + a + it → past with object\n\nBut not consistent.\n\nAlternative: consider that the verb stem is modified by a suffix indicating object or direction.\n\nBack to sentence 13: \n\"Amaruup angatkuit takujanga\" \nSuppose \"angatkuit\" is the object? \"the wolf\" is subject → can't be.\n\n\"angatkuit\" → could be \"saw\" with object?\n\nBut in example 1: verb is \"takujaatit\" = saw you → root \"taku\", verb agrees.\n\nSo perhaps the verb is \"takuj\" + past tense marker.\n\nBut \"takujanga\" — does it have a past marker?\n\nCompare:\n- takujaatit → ends with \"aatit\" → past with object? \n- aarqijaatit → ends with \"aatit\" \n- qukiqtanga → ends with \"anga\" → distinct\n\nSo a pattern: \n- verbs like \"takuj\", \"aarq\", \"iputuj\", \"aanniqt\", \"qukiq\" → all go with a past tense ending \n- \"takujanga\" → matches \"takuj\" + \"anga\"? But not in examples.\n\nWait — sentence 1: \"takujaatit\" → present or past?\n\nAll examples are past tense.\n\n\"takujanga\" — compare with sentence 13.\n\nSuppose: \n\"Amaruup\" = the wolf (subject) \n\"angatkuit\" = saw (verb) \n\"takujanga\" = [object]?\n\nBut there's no object pronoun. \nIn example 1: \"takujaatit\" = saw you → object \"you\" is marked via suffix\n\nSo likely: \"takujanga\" = saw [someone], with object marked.\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object marked\n\nSo verb + object suffix → object is included in suffix\n\nThus: \"Amaruup angatkuit takujanga\" → \n\"angatkuit\" = past tense of \"to see\"? \nBut \"takujanga\" is the verb root?\n\nWait: \"angatkuit\" is a form of \"to see\"?\n\nIn example 1: \"Qingmivit takujaatit\" — verb is \"takujaatit\" \nSo verb stem is \"takuj\" → verb root\n\nIn sentence 13: \"angatkuit\" — root \"angat\" → meaning \"to see\"?\n\nPossibly: \"angat\" = to see \nThen \"angatkuit\" = saw (past tense)\n\nThen \"takujanga\" — is this a second verb?\n\nUnlikely.\n\nAlternative: the structure is [subject] + [verb root + past tense] + [object]\n\nBut \"angatkuit\" might be verb, \"takujanga\" object?\n\n\"takujanga\" could be \"you\" → but in example 1: \"takujaatit\" → \"you\" marked\n\nSo \"takujanga\" might be \"you\"\n\nBut \"takujanga\" not present in any example.\n\nIn sentence 1: \"takujaatit\" → verb \"saw you\"\n\nIn sentence 4: \"aarqijaatit\" → cured you\n\nIn sentence 5: \"iputujait\" → speared the dog → object is \"the dog\"\n\nSo \"takujanga\" likely = saw you → object \"you\"\n\nBut spelling: \"anga\" vs \"aatit\"?\n\n\"anga\" is not in the object suffix.\n\nWait — all object-marked verbs in examples end with \"-aatit\" or \"-anga\"?\n\nExample 4: \"aarqijaatit\" → ends with \"aatit\" \nExample 1: \"takujaatit\" → ends with \"aatit\" \nExample 5: \"iputujait\" → ends with \"ait\" → not full\n\n\"iputujait\" → ends with \"ait\" → could be base form?\n\nBut that's with object.\n\nConclusion: object in past tense verb is marked by suffix like -aatit or -anga?\n\nIn sentence 13: \n\"Amaruup\" = the wolf \n\"angatkuit\" = saw? \nBut \"angatkuit\" — root \"angat\" = to see? \nThen \"takujanga\" must be object?\n\nOnly object marker in Inuktitut is marked on the verb.\n\nSo likely the verb form includes object marking.\n\nThus: \"angatkuit takujanga\" → is one verb form?\n\nBut \"angat\" and \"takuj\" are different roots.\n\nPossibility: a typo or misreading.\n\nWait — is it \"Amaruup angatkuit takujanga\" → \"the wolf saw you\"?\n\nBut \"takujanga\" = saw → impossible.\n\nAnother idea: perhaps \"takujanga\" is the past tense of \"to see\", and \"angatkuit\" is subject?\n\nBut \"angatkuit\" is not typically a noun.\n\nIn example 12: \"nanurmik qukiqsijuq\" → \"a polar bear\" + \"shot\"\n\nSo noun + verb with object.\n\nIn sentence 13: \"Amaruup\" = the wolf (subject) \n\"angatkuit\" = ? \n\"takujanga\" = ?\n\nCompare to sentence 2: \"inuuhuktuup iluaqhaiji qukiqtanga\" → boy (subject), doctor (object), shot (verb)\n\nSo verb is at end.\n\nSo sentence 13: likely \"the wolf saw you\" → verb is \"takujanga\", object is \"you\"?\n\nBut no \"you\" in form.\n\nIn sentence 1: \"takujaatit\" = saw you → so verb has object suffix\n\nSo \"takujanga\" must be an object-marked verb.\n\nBut \"takujanga\" ends in \"anga\" → not in example.\n\nCompare to example 4: \"aarqijaatit\" → \"cured you\" → ends in \"aatit\"\n\nSo suffix -aatit = past tense with object\n\n\"takujanga\" ends in \"anga\" — not matching.\n\nDifference: in example 5: \"iputujait\" — object \"the dog\" — ends in \"ait\"\n\n\"iputujait\" — is that object-marked?\n\nIn sentence 5: \"Qingmiq iputujait\" → you speared the dog → verb is \"iputujait\"\n\nSo verb form includes object.\n\nThus, verb form = root + object suffix\n\nSo in 13: \"takujanga\" = a verb form → but not found in examples.\n\nBut \"takujanga\" might be a variant of \"takujaatit\"?\n\nPerhaps typo: \"takujanga\" is \"takujaatit\" missing 'a'?\n\nNo.\n\nAnother: in sentence 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" → past tense of \"cure\" with object → ends with \"anga\"\n\nIn example 4: \"aarqijaatit\" → ends with \"aatit\"\n\nIn example 8: \"aarqijanga\" → ends with \"anga\"\n\nInconsistency.\n\nWait — \"aarqijaatit\" → in example 4: \"doctor cured you\" \n\"aarqijanga\" → in example 8: \"doctor cured your boy\"\n\nSo both have object markers.\n\nBut suffixes differ: aatit vsanga.\n\nPattern: could be number or aspect?\n\n\"aatit\" and \"anga\" — both object-marked past tense verbs.\n\nSo likely both are valid.\n\nThus \"takujanga\" is likely \"saw you\" — past tense with object.\n\nSo sentence 13: \"Amaruup angatkuit takujanga\" → the wolf saw you?\n\nBut \"angatkuit\" — if it's a verb, why two verbs?\n\nUnless \"angatkuit\" is a noun? Like \"the seeing\"?\n\nNo.\n\nPossibility: misreading of words.\n\nOriginal: \"Amaruup angatkuit takujanga\"\n\nIs it \"Amaruup\" + \"angatkuit takujanga\"?\n\nPerhaps \"angatkuit\" is the verb \"to see\" in past, and \"takujanga\" is object?\n\nBut no object mark.\n\nAnother idea: perhaps \"takujanga\" is the object \"you\"?\n\nIn example 1: \"takujaatit\" — \"you\" is marked in verb\n\nSo in 13, \"takujanga\" cannot be object.\n\nTherefore, must be that \"angatkuit takujanga\" is one verb form.\n\nBut no example matches.\n\nLook at sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\"\n\n\"qukiqsijuq\" = shot → verb with object\n\nSo object is in noun phrase.\n\nIn sentence 13: \"Amaruup\" = subject \n\"angatkuit\" = verb? \n\"takujanga\" = object?\n\nBut \"takujanga\" not a noun.\n\nIn sentence 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nSo possessive marker.\n\nBack to sentence ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12180.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Step 1: Analyze the given sentences to identify patterns in verb stems, agreement, and object/subject marking.\n\nLook at sentence 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject), \"takujaatit\" = saw (past tense, 3rd person). \n- \"takuj\" is the verb root meaning \"to see\", and the suffix -aatit is past tense. \n- \"Qingmivit\" = \"your dog\", where \"qingmi\" = dog, \"v\" is possessive (your), \"vit\" is suffix marking third person subject? Or perhaps a transitive verb with object.\n\nSentence 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (subject), \"iluaqhaiji\" = the doctor (object), \"qukiqtanga\" = shot (past tense). \n- \"qukiq\" is root of \"to shoot\", \"-tanga\" past tense. \n- \"iluaqhaiji\" is a noun phrase with possessed form? Appears to be direct object.\n\nSentence 3: \n\"Aanniqtutit\" → \"You hurt yourself.\" \n- \"aanniqtutit\" = you hurt yourself. \n- \"aanniqt\" = hurt, with \"utit\" as past tense. \n- \"yourself\" suggests reflexive, possibly marked by internal agreement.\n\nSentence 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor (subject), \"aarqijaatit\" = cured you. \n- \"aarqi\" = cure, \"-jaatit\" past tense. \n- Object \"you\" is marked by \"you\" in the object clause. So object appears as subject of the verb clause.\n\nSentence 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"Qingmiq\" = you (subject), \"iputujait\" = speared the dog. \n- \"iputuj\" = to spear, \"-jait\" past tense. \n- So \"qingmiq\" = you, with \"qingmi\" = dog, but here \"you\" acts as subject, so subject is \"you\", object is \"the dog\".\n\nSentence 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman (subject), \"iluaqhaijimik\" = a doctor (object), \"aarqisijuq\" = cured. \n- \"aarqisijuq\" = cured, with \"sij\" possibly marking undergone action? But \"aarqi\" remains cure root.\n\nSentence 7: \n\"Nanuq qaijuq\" → \"The polar bear came.\" \n- \"Nanuq\" = the polar bear, \"qaijuq\" = came. \n- \"qaij\" = to come, \"-uq\" is past tense? Seems minimal word.\n\nSentence 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"Iluaqhaijivit\" = your doctor (subject), \"inuuhuktuit\" = your boy (object), \"aarqijanga\" = cured. \n- \"aarqijanga\" = past tense of cure. \n- Possessive markers: \"your\" appears as \"vi-\" before noun (iluaqhaijivit, inuuhuktuit).\n\nSentence 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter (subject), \"amaruq\" = the wolf (object), \"iputujanga\" = speared. \n- \"iputujanga\" = past tense of \"to spear\" — matches sentence 5 verb.\n\nSentence 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog (subject), \"ilinniaqtitsijiit\" = your teacher (object), \"aanniqtanga\" = hurt. \n- \"aanniqtanga\" = hurt, past tense. \n- \"ilinniaqtitsijiit\" = your teacher. \"ilinniaqt\" = teacher, \"sijiit\" = possessive?\n\nSentence 11: \n\"Ukiakhaqtutit\" → \"You fell.\" \n- \"Ukiakhaqtutit\" = you fell. \n- \"ukiak\" = to fall, \"qut\" + \"it\" = past tense? Base verb with past suffix.\n\nSentence 12: \n\"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter, \"nanurmik\" = a polar bear, \"qukiqsijuq\" = shot. \n- \"qukiqsijuq\" = shot, past tense. \n- \"qukiq\" = to shoot, \"-sijuq\" = past tense.\n\nNow, observe consistent verb patterns:\n\n- Verbs are often root + suffix indicating tense (e.g., -tanga, -jait, -juq, -it).\n- Possessions: \"vi-\" (your), \"mi-\" (his/her), \"na-\" (a), \"up\" (a common marker for indefinite)\n- Object markers: in many cases, object noun is marked by possessive or demonstrative.\n- Reflexive: \"aanniqtutit\" → \"you hurt yourself\" → when subject and object are the same person.\n\nNow analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" = a wolf or the wolf? \nFrom sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \nSo \"amaruq\" = the wolf. \nThus \"amaruup\" = a wolf (indefinite, \"up\" = a) → \"a wolf\" \n\"angatkuit\" = ? \nFrom sentence 7: \"Nanuq qaijuq\" → \"the polar bear came.\" \n\"angatkuq\" = the shaman? From sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" \nSo \"angatkuq\" = the shaman. \nThen \"angatkuit\" = the shaman (past tense?) \n\"takujanga\" → past tense of \"to see\"? \nFrom sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"takuj\" root + past tense. \n\"takujanga\" = past tense of \"to see\" → saw \nSo: \"Amaruup\" = a wolf, \"angatkuit\" = the shaman, \"takujanga\" = saw \nBut \"angatkuit\" = the shaman, \"takujanga\" = saw, so the wolf saw the shaman? \nBut grammar: subject-verb-object? \n\"Amaruup\" is likely subject → \"a wolf saw the shaman\" \nBut \"angatkuit\" is not \"the shaman\" as object — no object clearly marked. \nWait — in sentence 1, \"takuj\" root with \"-aatit\" past tense. \nSentence 1: \"takujaatit\" → saw you. \nSo \"takujanga\" → past tense of \"see\" → saw. \nAnd \"angatkuit\" → the shaman? \n\"angatkuq\" = shaman, so \"angatkuit\" = shaman in past tense — likely same form, tense suffix. \nSo: \"a wolf saw the shaman\" → \"Amaruup angatkuit takujanga\" \n\"angatkuit\" is the shaman (object), but it's NOT marked with \"vi-\" or \"inuuhuk\"-type. \nPossibility: \"angatkuit\" is object of \"takujanga\"? \nBut \"takujanga\" is not transitive in that way — in sentence 1, \"takuj\" is transitive: \"dog saw you\". \nSo \"wolf saw shaman\" → yes. \nSo: a wolf saw the shaman.\n\n14. Nanuit inuuhukturmik aanniqsijuq. \n- \"Nanuit\" = the polar bear? \nFrom sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\". \n\"nanuit\" = past tense of \"came\"? \n\"qaijuq\" = came → \"qaij\" root → \"nanuit\" = polar bear came → \"nanuit\" = past tense of \"come\"? \nBut \"nanuit\" may be subject → the polar bear. \n\"inuuhukturmik\" → \"a boy\"? \n\"inuuhuk\" = boy → \"inuuhuktuit\" = your boy → \"inuuhukturmik\" = a boy? \n\"m\" = plural or mark of \"a\"? \n\"inuuhukturmik\" = \"a boy\" → object. \n\"aanniqsijuq\" = ? \n\"aanniqt\" = hurt → \"aanniqsijuq\" = hurt (past tense). \nSo: \"the polar bear hurt a boy\" \n\"nanuit\" = subject, \"inuuhukturmik\" = object, \"aanniqsijuq\" = hurt. \nMatches pattern.\n\n15. Angunahuktiit aarqijuq. \n\"Angunahuktiit\" → the hunter (with possessive? or past tense?) \nFrom sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"angunahukti\" = hunter (subject). \n\"it\" suffix → past tense? \nSo \"Angunahuktiit\" = the hunter (past tense?) \n\"aarqijuq\" → \"cured\" \n\"aarqi\" = cure → \"aarqijuq\" = cured. \nSo the hunter cured? \nBut object missing. \nIn sentence 4: \"Iluaqhaijiup aarqijaatit\" → doctor cured you. \nSo \"aarqijaatit\" = cured you. \nSo \"aarqijuq\" = cured someone → the hunter cured someone. \nBut who? \nPossibly missing object. \nBut in sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear. \nSo \"angunahukti\" is subject. \n\"angunahuktiit\" = the hunter (past tense), so likely subject of verb. \n\"aarqijuq\" = cured — implying cured someone. \nBut no object. \nIn sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy. \nSo \"cured\" is transitive. \nThus \"angunahuktiit aarqijuq\" likely means \"the hunter cured [someone]\" — but who? \nPossibly implies \"he cured himself\"? No reflexivity. \nIs it reflexive? \nNo reflexive marker. \nMore likely: \"the hunter cured someone\" — but translation must be full. \nBut in Inuktitut, absence of object may imply a default. \nBut look at sentence 3: \"Aanniqtutit\" → \"you hurt yourself\" → reflexive. \nNo reflexive marker here. \nThus probably not reflexive. \nBut all examples with \"cure\" or \"hurt\" show object. \nSo likely this is \"the hunter cured [a person]\" — but who? \nWait: in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor. \nSo \"aarqisijuq\" = cured a doctor. \nThus \"aarqijuq\" = cured someone → \"the hunter cured someone\" \nBut who? Possible omission. \nBut sentence 8: \"your doctor cured your boy\" — specific. \nHere, no object → perhaps more natural to say \"the hunter cured [a person]\" — but no word in context. \nWait — in sentence 14, subject is \"polar bear\", object is \"a boy\" — structured. \nIn 15, \"angunahuktiit\" = hunter (subject), \"aarqijuq\" = cured → likely transitive. \nBut object not present. \nUnless \"it\" in \"angunahuktiit\" is possessive? \n\"angunahuktiit\" — could be \"your hunter\"? \nNo — \"inuuhuktuit\" = your boy. \n\"it\" is suffix — past tense. \nMost likely: \"the hunter cured\" → implied object. \nBut no object — so perhaps \"cured himself\"? \nBut no reflexive marker. \nLook at sentence 3: \"aanniqtutit\" = you hurt yourself → reflexive. \n\"aanniqt\" + \"utit\" = hurt yourself. \nSo reflexive must have internal marker. \nHere, no such marker. \nThus likely not reflexive. \nBut perhaps in context, it's just \"the hunter cured [someone]\" — but translation should be precise. \nWait — sentence 15: \"Angunahuktiit aarqijuq\" \nIn sentence 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you. \nSo \"cure\" verb with impersonal object? \nNo — \"you\" is object. \nSo here, \"the hunter cured\" — but no object — missing? \nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" — shaman cured a doctor. \nSo object is explicitly marked. \nSo lack of object → not intended. \nPossibility: \"Angunahuktiit\" = the hunter (subject) and \"aarqijuq\" = cured → but no object. \nUnless \"it\" refers to an implied object. \nBut \"it\" is marking past tense, not possession. \nAlternative: \"aaruq\" is not cured — maybe a different verb? \nNo, in sentence 4, \"aarqijaatit\" = cured you. \nSo likely \"the hunter cured someone\" — but we have no person. \nIs it possible that \"aaruq\" is short for \"aarqijaatit\"? \nNo — no possessive. \nBut look at sentence 18: \"Angunahuktimik aarqisijutit\" → likely similar, with object. \nSo back — 15 might be \"the hunter cured himself\" — but no reflexive marker. \nNot supported. \nPerhaps \"Angunahuktiit\" is not a subject — but object? \nBut \"angunahukti\" is a noun referring to hunter. \nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → subject is hunter. \nSo likely subject. \nThus must be \"the hunter cured [someone]\" — default translation: \"The hunter cured someone.\" \nBut that is vague. \nWait — compare to 14: \"Nanuit inuuhukturmik aanniqsijuq\" → has object → \"the polar bear hurt a boy\" \n15: no object → \"the hunter cured\" — incomplete. \nBut perhaps it's \"the hunter cured himself\"? \nNo evidence. \nWait — sentence 3: \"Aanniqtutit\" → \"you hurt yourself\" → reflexive. \nNo object → but reflexive — so when no object, could be reflexive. \nBut \"aarqijuq\" — not same structure. \n\"aarqijaatit\" has object \"you\". \nSo object must be present. \nTherefore, possibly a missing noun. \nBut in the sentence, it's not given. \nSo perhaps the verb is intransitive? \nBut \"cure\" is not intransitive. \nThus, likely the intended translation is \"The hunter cured himself\" — though not supported. \nAlternatively, perhaps \"aaruq\" is a minimal form. \nBut in sentence 4, \"aarqijaatit\" = cured you → object marked. \nSo no — object is missing. \nPerhaps the structure is different. \nWait — look at sentence 16: \"Ilinniaqtitsiji qukiqtait\" \n\"Ilinniaqtitsiji\" → your teacher → \"ilinniaqtitsiji\" = your teacher \n\"qukiqtait\" → shot? \n\"qukiq\" = to shoot → \"qukiqtait\" = past tense of shoot → shot \nSo \"your teacher shot [someone]\" — object missing. \nSimilarly, sentence 17: \"Qaijutit\" → literally \"qaijutit\" — \"qaij\" = to come → \"utit\" past tense → \"came\" \nSo \"came\" — no object. \n\"Qaijutit\" → \"he came\" → implied subject. \nSo likely \"the polar bear came\" (as in sentence 7). \nSo \"Qaijutit\" → \"It came\" or \"he came\"? \nBut no subject. \nIn sentence 7: \"Nanuq qaijuq\" → \"the polar bear came\" → \"nanuq\" = the polar bear. \nSo \"qaijutit\" = came — past tense. \nSo if no subject, then \"someone came\" — but likely implies subject is missing. \nSimilarly, \"Qaijutit\" likely is \"It came\" or \"The polar bear came\" — but no noun. \nBut in context, it's a standalone sentence. \nSo must be \"It came\" or \"Came\" — but with subject implied. \nBut in Inuktitut, such minimal forms may be used. \nSimilarly, in 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured\" → likely \"The hunter cured someone\" — but not full. \nBut perhaps the pattern from sentence 3:", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12162.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze the given sentences to identify grammatical patterns, especially regarding verb forms, possessive markers, and subject/object markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject), \"takujaatit\" = saw you (verb + object) \n→ So \"takujaatit\" = saw (past tense), \"you\" is the object. \n→ \"vit\" suffix may indicate possession (your) or verb aspect.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (subject), \"iluaqhaiji\" = the doctor (object), \"qukiqtanga\" = shot \n→ \"qukiqtanga\" is the past tense of \"shoot\" with object (doctor) \n→ Verb \"qukiqtanga\" = shot (past), so verb form ends with \"-anga\" \n→ Name and role assignment: \"iluaqhaiji\" = doctor (object)\n\nSentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n- \"Aanniqtutit\" = you hurt yourself \n→ \"aanniqt\" = hurt, \"utit\" = past tense? \n→ \"aanniqt\" + \"utit\" = hurt yourself → reflexive \n→ Possession via self (reflexive), no external object\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor (subject), \"aarqijaatit\" = cured you \n→ \"aarqijaatit\" = cured (past tense), with object \"you\" \n→ \"aarqi\" = cure, \"jaatit\" = past tense with object \n→ Possible suffix \"-jaatit\" = past tense + object \n→ \"up\" = possessive marker? → in \"iluaqhaijiup\", \"up\" likely marks possession of subject (the doctor)\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"Qingmiq\" = you (subject), \"iputujait\" = speared the dog \n→ \"iputujait\" = speared (past), \"the dog\" as object \n→ \"iputujait\" likely built from \"iputuj\" = spear + \"ait\" = past tense (object)\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"Angatkuq\" = the shaman (subject), \"iluaqhaijimik\" = a doctor (object), \"aarqisijuq\" = cured \n→ \"aarqisijuq\" = cured + object \n→ \"mik\" = a (definite article or indefinite) \n→ \"aarqisijuq\" = cured (past tense) \n→ So \"aarq\" + past tense suffix + object marker?\n\nSentence 7: \"Nanusq qaijuq\" → \"The polar bear came.\" \n- \"Nanusq\" = the polar bear, \"qaijuq\" = came \n→ \"qaijuq\" = came (past tense), no object \n→ Possessive pattern?\n\nSentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"Iluaqhaijivit\" = your doctor (subject), \"inuuhuktuit\" = your boy (object), \"aarqijanga\" = cured \n→ \"aarqijanga\" = cured (past), with object \n→ \"vit\" = your (possessive), \"uit\" = your (possessive on object) \n→ \"aarqijanga\" = cured + object → appears to be past tense + object with possession\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"Angunahuktiup\" = the hunter, \"amaruq\" = the wolf, \"iputujanga\" = speared \n→ \"iputujanga\" = speared (past) with object \n→ \"up\" = possessive (the hunter) \n→ \"amaruq\" = wolf (object)\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"Qingmiup\" = the dog, \"ilinniaqtitsijiit\" = your teacher (object), \"aanniqtanga\" = hurt \n→ \"aanniqtanga\" = hurt (past) with object \n→ \"up\" = your (possession on object?) or on subject? \n→ \"ilinniaqtitsijiit\" = your teacher → \"it\" = your, \"sijiit\" = teacher?\n\nSentence 11: \"Ukiakhaqtutit\" → \"You fell.\" \n- \"Ukiakhaqtutit\" = you fell → \"utit\" = past tense \n→ \"ukiakhaq\" = fell (base verb)\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"Angunahukti\" = the hunter, \"nanurmik\" = a polar bear, \"qukiqsijuq\" = shot \n→ \"qukiqsijuq\" = shot (past tense + object) \n→ \"mik\" = a (indefinite) \n→ \"qukiqsijuq\" = shot\n\nNow derive the verb patterns:\n\n- Past tense verbs often end in \"-anga\", \"-ait\", \"-jaatit\", \"-sijuq\", \"-tutit\"\n- Possessive: -vit, -uit, -up\n- Objects are marked with possessive or article markers (mik, it, etc.)\n\nNow look at the target sentences:\n\n13. Amaruup angatkuit takujanga \nBreak it down: \n- \"Amaruup\" = the wolf? (Possibly \"amaru\" = wolf, \"up\" = possessive) \n- \"angatkuit\" = came? → \"angat\" = come, \"kuit\" = past tense? \n→ In sentence 7: \"Nanusq qaijuq\" = polar bear came → \"qaijuq\" = came \n→ In sentence 12: \"qukiqsijuq\" = shot → so \"qukiq\" = shoot \n→ \"angat\" + \"kuit\"? Is \"angatkuit\" = came? \n→ Compare to sentence 7: \"qaijuq\" = came \n→ So possibly \"angatkuit\" = came (past tense with object?) \nBut \"angatak\" is not seen. \nBut sentence 12: \"qukiqsijuq\" = shot → uses \"-sijuq\" \nSentence 4: \"aarqijaatit\" = cured you → uses \"-jaatit\" \nSentence 5: \"iputujait\" = speared → ends in \"-ait\" \nSentence 3: \"aanniqtutit\" = hurt → ends in \"-utit\" \nSentence 11: \"ukiakhaqtutit\" = fell → ends in \"-utit\" \nSentence 1: \"takujaatit\" = saw → ends in \"-jaatit\" \n\nSo verb endings: \n- -jaatit = saw / cured / hurt? \n- -utit = hurt / fell \n- -ait = speared \n- -sijuq = shot \n- -anga = shot? (sentence 2: \"qukiqtanga\" = shot)\n\nWait — sentence 2: \"qukiqtanga\" → \"shot\" \nSentence 12: \"qukiqsijuq\" → \"shot\" \n→ \"qukiqtanga\" and \"qukiqsijuq\" both mean \"shot\" \n→ Possibly different forms with different object or possession?\n\nBut in sentence 11: \"Ukiakhaqtutit\" = fell → \"utit\" \nSentence 3: \"Aanniqtutit\" = hurt → \"utit\" \nSo \"utit\" = hurt or fell — both transitive or intransitive?\n\nBut sentence 10: \"aanniqtanga\" = hurt → so \"aanniqtanga\" = hurt (like sentence 3 but not reflexive)\n\nSo:\n- \"aanniqtutit\" → hurt (past, reflexive) \n- \"aanniqtanga\" → hurt (past, object?) → in sentence 10: \"aanniqtanga\" → hurt your teacher\n\nSo \"aanniqt\" + \"utit\" = hurt yourself; \"aanniqt\" + \"anga\" = hurt someone\n\n→ So verb root + \"utit\" = reflexive, \"anga\" = transitive\n\nSimilarly:\n- \"takujaatit\" → saw you → \"takuj\" + \"jaatit\" = saw (object) \n\"takuj\" = see \n- \"iputujait\" → speared → \"iputuj\" + \"ait\" \n- \"qukiqtanga\" → shot → \"qukiq\" + \"tanga\" \n- \"qukiqsijuq\" → shot → \"qukiq\" + \"sijuq\" \n→ So \"tanga\" and \"sijuq\" both mean \"shot\"? \n→ But \"tanga\" = intransitive? or with object?\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → the boy shot the doctor → object present \n→ So \"qukiqtanga\" = shot + object \n→ But in sentence 12: \"qukiqsijuq\" = shot a polar bear → also object \n→ So both forms are verbs with object?\n\nBut \"tanga\" and \"sijuq\" may differ in object marking.\n\nNow back to 13: \"Amaruup angatkuit takujanga\" \n→ \"Amaruup\" = the wolf (subject) → \"amaru\" + \"up\" \n→ \"angatkuit\" = came? \n→ \"takujanga\" = saw? \n→ \"takujanga\" → \"takuj\" + \"anga\" → is \"anga\" used in \"saw\"?\n\nIn sentence 1: \"Qingmivit takujaatit\" → saw → ends in \"jaatit\" \n→ \"takujanga\" → ends in \"anga\" → different from \"jaatit\" \nSo \"takujanga\" might mean \"saw\" with a different form? But no full example.\n\nWait: sentence 4: \"Iluqaahi jiip aarqijaatit\" → the doctor cured you → \"aarqijaatit\" = cured → object + past tense \nSentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → \"aarqijanga\" = cured \nSo both \"jaatit\" and \"anga\" are past tense with object?\n\nBut in sentence 1: \"takujaatit\" → \"saw you\" → so \"jaatit\" \nIn sentence 13: \"takujanga\" → \"saw\"? → possible\n\nBut \"angatkuit\" → came? \nSentence 7: \"Nanusq qaijuq\" → polar bear came → “qaijuq” \nSo “qaij” + “uq” = came \nSo “angatkuit” → “angat” + “kuit” → is “angat” = come?\n\nPossibly \"angat\" = came, \"kuit\" = past tense? But in sentence 7: “qaijuq” → “qaij” = came, “uq” = past\n\nSimilarly:\n- \"qaijuq\" → came (past)\n- \"angatkuit\" → possibly came (past)\n\nBut \"kuit\" vs \"uq\" — different past markers?\n\nIn sentence 3: \"aanniqtutit\" → hurt (past) \nSentence 11: \"ukiakhaqtutit\" → fell (past) \nSo past tense suffix: -utit, -anga, -ait, -sijuq, -jaatit\n\n\"Jaatit\", \"utit\", \"ait\", \"sijuq\", \"tanga\"\n\nDo they correspond to different verbs?\n\nCheck if past tense suffix rules:\n\n- verifica: verb root + past suffix\n\nPossessive markers:\n- \"vit\" = your (subject)\n- \"uit\" = your (object)\n- \"up\" = the (subject or object?) → in \"Amaruup\" = the wolf?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" \n\"Angunahuktiup\" = the hunter, \"amaruq\" = the wolf → no \"up\" on object\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher → \"up\" on subject\n\nIn sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → \"vit\" on subject, \"uit\" on object\n\nSo:\n- \"vit\" → subject possession (your)\n- \"uit\" → object possession (your)\n- \"up\" → subject (the)\n\nSo \"Amaruup\" → the wolf (subject) — \"up\" on subject\n\nNow verb: \"angatkuit\" → came? \nCompare to sentence 7: \"Nanusq qaijuq\" → came → \"qaij\" + \"uq\" → \"uq\" = past tense \nSo \"angatkuit\" → \"angat\" + \"kuit\" → perhaps \"kuit\" = past tense?\n\nBut sentence 3: \"aanniqtutit\" — \"utit\" = past \nSentence 1: \"takujaatit\" — \"jaatit\" = past \nSentence 2: \"qukiqtanga\" — \"tanga\" = past \nSo different past markers exist.\n\nSo possible past markers:\n- -utit: hurt, fell\n- -jaatit: saw, cured\n- -ait: speared\n- -sijuq: shot\n- -tanga: shot\n\nBut sentence 2 and 12 both use \"shot\" — sentence 2 has \"qukiqtanga\", sentence 12 has \"qukiqsijuq\"\n\nSo different past suffixes for the same verb?\n\nYes — perhaps different suffixes for different objects or possession?\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → object is \"iluaqhaiji\" (specific) \nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear → object is \"nanurmik\" (a polar bear)\n\nSo both show \"shot\" with object, but different suffixes.\n\nSo: verb root + past suffix → different suffixes for different meanings?\n\nBut \"qukiqtanga\" and \"qukiqsijuq\" may be different past forms.\n\nNow sentence 13: \"Amaruup angatkuit takujanga\" \n→ Subject: \"Amaruup\" = the wolf \n→ Verb 1: \"angatkuit\" → came? \n→ Verb 2: \"takujanga\" → saw?\n\nBut do \"angatkuit\" and \"takujanga\" use past markers?\n\nFor \"came\": sentence 7 has \"qaijuq\" → \"qaij\" + \"uq\" \nNo \"kuit\" in any verb.\n\nIs \"angat\" = came? \nYes — no direct example, but \"angat\" = come, common in Inuktitut. \nAnd \"kuit\" could be a past tense variant.\n\nBut in English, \"came\" is equivalent.\n\nSo \"angatkuit\" = the wolf (subject) came\n\nThen \"takujanga\" = saw?\n\nIn sentence 1: \"takujaatit\" = saw you → \"jaatit\" \nSo \"takujanga\" → different form? But no example.\n\nAre there examples of \"takujanga\"?\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → dog hurt teacher → no \"takuj\"\n\nSentence 16: \"Ilinniaqtitsiji qukiqtait\" → the teacher was shot? → \"qukiqtait\" = shot?\n\nIn sentence 5: \"iputujait\" = speared \nIn sentence 16: \"qukiqtait\" → shot?\n\n\"qukiqtait\" → \"qukiq\" + \"tait\"? What is \"tait\"?\n\nBut no \"tait\" in earlier verbs — all are \"anga\", \"sijuq\", \"utit\", \"jaatit\", \"ait\"\n\nMissing \"tait\"?\n\nPossibility: misreading.\n\n\"qukiqtait\" — is it \"qukiq\" + \"tait\"?\n\nBut in sentence 12: \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" — shot\n\nIn sentence 2: \"qukiqtanga\" — shot\n\nSo both \"tanga\" and \"sijuq\" = shot?\n\nBut \"tait\" not seen.\n\nCould \"qukiqtait\" be a typo or misreading?\n\nSentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\nCompare with sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"your teacher\" hurt → so \"ilinniaqtitsijiit\" = your teacher\n\nSo \"ilinniaqtitsiji\" = teacher → without \"it\"? But in sentence 10, \"it\" is attached to object.\n\nIn sentence 16: \"Ilinniaqtitsiji qukiqtait\" → \"the teacher\" shot?\n\nPossibly \"qukiqtait\" = shot\n\nBut \"tait\" is not seen in any verb.\n\nUnless it's a different verb.\n\nPossibility: \"qukiqtait\" = shot (past) with object → may be based on \"tait\" = past?\n\nBut earlier only -utit, -jaatit, -ait, -sijuq, -tanga exist.\n\nWait —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11313.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "First, analyze the given Inuktitut sentences and their translations to detect patterns in case, verb form, and argument structure.\n\nLook at verb forms and how subjects and objects are marked.\n\nSentence 1: Qingmivit takujaatit → Your dog saw you. \n- “Qingmivit” (your dog) + “takujaatit” (saw you) → verb suffix “-vit” is a past tense marker; verb root “takuj” = see; marked object “you” via object suffix “-aatit” (you, accusative). \n\nSentence 2: Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor. \n- “Inuuhuktuup” (the boy) → subject, possible marker “-tuup” (accusative?) or present form. \n- “iluaqhaiji” → doctor (object) \n- “qukiqtanga” → shot (past tense verb “qukiqt-” + “-anga” = past form, signaling action) \n→ “qukiqtanga” = shot → verb form with object marking.\n\nSentence 3: Aanniqtutit → You hurt yourself. \n- “Aanniqtutit” → “aanniqt-” = hurt, “-utit” = past, reflexive (self) → object is subject (yourself). So reflexive form.\n\nSentence 4: Iluaqhaijiup aarqijaatit → The doctor cured you. \n- “iluaqhaijiup” → doctor (subject) \n- “aarqijaatit” → cured + you (object, marked by -aatit). “aarq-” = cure. So verb with object marked.\n\nSentence 5: Qingmiq iputujait → You speared the dog. \n- “Qingmiq” = you (subject) \n- “iputujait” = speared the dog → verb root “iputuj” + “-ait” = past tense, object marked by “-ait” → likely object marker.\n\nSentence 6: Angatkuq iluaqhaijimik aarqisijuq → The shaman cured a doctor. \n- “Angatkuq” = the shaman (subject) \n- “iluaqhaijimik” = a doctor (object) → object marked by “-mik” (genitive or object?) \n- “aarqisijuq” = cured → verb “aarq-” + “-isijuq” = past tense with object? \nWait — in sentence 4, “aarqijaatit” is cured + you, so object marked by “-aatit”. But here, “aarqisijuq” — object marker is missing? Might be genitive or object implied.\n\nWait: “iluaqhaijimik” — “-mik” is a common object marking in Inuktitut: possessive or object case.\n\nAlso, “angatkuq” = shaman, likely subject.\n\nSo, “cured a doctor” — verb with object marked via “-mik”.\n\nSentence 7: Nanuq qaijuq → The polar bear came. \n“Nanuq” = polar bear (subject) \n“qaijuq” = came (past) → verb with no object, so simple event.\n\nSentence 8: Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy. \n- “iluaqhaijivit” = your doctor (subject) \n- “inuuhuktuit” = your boy (object?) \n- “aarqijanga” = cured → so verb “aarqi-” + “-janga” = past + object marked. \nObject is “your boy” — “inuuhuktuit” has “-uit” (object case), and “-uit” appears in sentence 2 as “inuuhuktuit” (boy) — so object marker.\n\nSentence 9: Angunahuktiup amaruq iputujanga → The hunter speared the wolf. \n- “Angunahuktiup” = the hunter (subject) \n- “amaruq” = the wolf (object) \n- “iputujanga” = speared → verb “iputuj” + “-anga” = past tense, object marked by “-anga”?\n\nBut sentence 5: “iputujait” = you speared the dog → object marked by “-ait” → seems inconsistent.\n\nWait — sentence 9: “iputujanga” — ending “-anga” → could be past tense. \nSentence 5: “iputujait” — “-ait” — specific.\n\nBut in (2), “qukiqtanga” — shot → past tense. \n(4): “aarqijaatit” — cured + you → object marked by “-aatit” \n(8): “aarqijanga” — cured + your boy → object marked by “-anga”?\n\nSo two different object markers? \nPossibly based on case.\n\nNow, look for regularities:\n\nSubject usually marked with a suffix like:\n- “-up” (accusative?) — no\n- “-it” — in “Qingmivit” → it could be possessive or object form?\n\nWait — in sentence 1: “Qingmivit” — “Qingmi” + “-vit” → “-vit” could be past tense? \nBut “takujaatit” ends with “-aati” — object.\n\nIn sentence 5: “Qingmiq iputujait” → “Qingmiq” is “you”, not “Qingmi” + suffix. \nIn sentence 1: “Qingmivit” — “your dog” as subject, verb is “takujaatit” → object “you”.\n\nIn sentence 8: “iluaqhaijivit” → “your doctor” — “-vit” ends with -vit → use of “-vit” suggests the subject is marked with -vit (possessive or object case?)?\n\nWait — in sentence 4: “iluaqhaijiup” → “doctor” → object? but in sentence 8: “iluaqhaijivit” = your doctor → subject. \nSo the suffix on the subject changes from “-up” to “-vit” when possessive?\n\nIn sentence 2: “Inuuhuktuup” → “the boy” — not possessive. \nSentence 9: “Angunahuktiup” → “the hunter” — subject. \nSentence 6: “Angatkuq” → subject.\n\nSo “-up” and “-vit” may be grammatical markers of subject or object.\n\nBut in sentence 4: “iluaqhaijiup” → doctor → likely object? \nBecause in sentence 8: “iluaqhaijivit” → your doctor → subject.\n\nSo:\n- “iluaqhaijiup” → doctor as object \n- “iluaqhaijivit” → doctor as subject\n\nThus, object marker = “-up” or “-vit”? \nNo — “vit” is in “iluaqhaijivit” — possession? \nPossibly: \n- “-up” = object \n- “-it” = subject?\n\nNo — in sentence 9: “Angunahuktiup” → hunter → subject, not object. \n“-up” is used in both subject and object?\n\nNeed another clue.\n\nLook at verb forms:\n\nVerb in past tense often ends with:\n- “-vit” (e.g., sentence 1: “takujaatit” — “takuj” + “-aati”?) — no \nActually, “takuj” + “-aati” — “aati” = object \nThe verb itself may carry one suffix.\n\nFrom sentence 1: “takujaatit” — “takuj” + “-aati” → object \nFrom sentence 5: “iputujait” — “iputuj” + “-ait” → object \nFrom sentence 9: “iputujanga” — “iputuj” + “-anga” → object \nSo different object markers: -aati, -ait, -anga?\n\nBut sentence 4: “aarqijaatit” → “aarqi” + “-aati” → cured you \nSentence 8: “aarqijanga” → cured your boy → “-anga” \nSentence 6: “aarqisijuq” → cured a doctor → “-sijuq”?\n\n“aarqisijuq” — likely derived from “aarqis-” “-ijuq”?\n\nIn sentence 4: “aarqijaatit” → verb with object “you” \nSentence 8: “aarqijanga” → cured your boy \nSentence 6: “aarqisijuq” → cured a doctor → object “a doctor” — marked by “-mik” (genitive), not direct object?\n\nThis suggests that object marking in verbs is inconsistent — depends on the verb or structure.\n\nNow, look for who does what.\n\nNotice: \nIn sentence 5: “Qingmiq iputujait” → you speared the dog → subject = “you” (Qingmiq), object = the dog → marked by “-ait”\n\nSentence 9: “Angunahuktiup amaruq iputujanga” → hunter speared wolf → subject “Angunahuktiup”, object “amaruq”, verb “iputujanga” → verb with object.\n\nSo object markers vary.\n\nNow, where do we see prepositional/possessive forms?\n\nSentence 3: “Aanniqtutit” — you hurt yourself → reflexive — subject is marked as both agent and patient.\n\nSentence 11: “Ukiakhaqtutit” → you fell → same structure.\n\nSo marked by object suffix “-utit” — reflexive?\n\nIn sentence 1: “takujaatit” → object “you” → not reflexive.\n\nSo “-utit” may mark reflexive (subject = object).\n\nIn sentence 13: Amaruup angatkuit takujanga \nBreak down:\n\nAmaruup — likely \"the wolf\" (from sentence 9: \"amaruq\" = wolf) \nangatkuit — “angatkuq” is the shaman → “angatkuit” = the shaman (object?) or subject?\n\nIn sentence 3: “Aanniqtutit” — you hurt yourself → reflexive.\n\nNow, sentence 13: “Amaruup angatkuit takujanga” \n→ Amaruup = wolf (subject?) \n→ angatkuit = shaman (object?) \n→ takujanga = saw?\n\n“takuj” = see → past tense “takujanga”\n\nBut in sentence 1: “takujatit” — saw you → object “you”\n\nSo verb “takujanga” + object?\n\nBut where is the object?\n\nNo object marker after verb.\n\nSo is “takujanga” seen or witnessed?\n\nPossibly: “Amaruup” (wolf) saw the shaman?\n\nOr “shaman” saw the wolf?\n\n“angatkuit” — likely the object of the verb?\n\nSo “wolf saw shaman”?\n\nBut “angatkuit” — in sentence 2: “iluaqhaiji qukiqtanga” → doctor shot → object is doctor.\n\nSimilarly, here — “angatkuit” is likely the object.\n\nSo “wolf saw shaman” → does this make sense?\n\nBut in sentence 8: “iluaqhaijivit inuuhuktuit aarqijanga” → your doctor cured your boy → doctor is subject.\n\nSo subject first.\n\nIn sentence 13: “Amaruup angatkuit takujanga” → subject = wolf? verb = saw, object = shaman?\n\nSo “the wolf saw the shaman”\n\nBut is “angatkuit” object?\n\nYes — similar to sentence 2: “iluaqhaiji” is object, verb “qukiqtanga” → shot.\n\nSo here: “angatkuit” is object → “wolf saw [shaman]”\n\nSo translation: The wolf saw the shaman.\n\nBut is there a case?\n\nNow sentence 14: Nanuit inuuhukturmik aanniqsijuq \n“Nanuit” = the bear? (from sentence 7: “nanuq” = polar bear) \n“-uit” → object? but in sentence 7: “nanuq qaijuq” → bear came — no object\n\n“inuuhukturmik” → boy with “-mik” (object or genitive) \n“aanniqsijuq” → hurt?\n\n“aanniqtutit” = you hurt yourself → “aanniqt” + “-utit” = past, reflexive\n\n“aanniqsijuq” — similar but “-sijuq” instead of “-utit” — likely object marker?\n\nSo “aanniqsijuq” = hurt someone?\n\n“inuuhukturmik” — likely “your boy” → “inuuhuk” = boy, “-turmik” — possessive or object?\n\n“-turmik” → may be object form.\n\nSo “the bear hurt your boy”?\n\n“nanuit” = bear (subject) \n“inuuhukturmik” = your boy (object) \n“aanniqsijuq” = hurt → so bear hurt your boy\n\nYes.\n\nSo → The bear hurt your boy.\n\nNow sentence 15: Angunahuktiit aarqijuq \n“Angunahuktiit” — hunter (subject?) — “-it” suffix \nFrom sentence 9: “Angunahuktiup” = the hunter \nSo “-it” = subject form? \n“aarqijuq” — cure → “aarq-” + “-ijuq” = past tense, likely verb with object?\n\nBut no object marker — so perhaps object is implicit or absent?\n\nCompare to sentence 4: “iluaqhaijiup aarqijaatit” → doctor cured you → object marked by “-aati”\n\nHere, “aarqijuq” — no object suffix → so object missing?\n\nBut in sentence 6: “Angatkuq iluaqhaijimik aarqisijuq” — shaman cured a doctor → object marked by “-mik” → object is doctor.\n\nIn sentence 8: “iluaqhaijivit inuuhuktuit aarqijanga” — cured your boy → object marked by “-uit”\n\nSo object suffix present in some cases, absent in others.\n\nIn this one: “aarqijuq” — no object marking → so maybe the verb stands alone, or object is the subject?\n\nBut subject is “angunahuktiit” — hunter.\n\nSo “the hunter cured” — cured what?\n\nPossibly cured the bear? Or the bear was cured?\n\nBut “aarqijuq” = cured → so likely “the hunter cured [someone]” — missing object?\n\nBut in example 6: “cured a doctor” — object marked by “-mik”\n\nIn example 8: “cured your boy” — object marked by “-uit”\n\nHere no object marking → so maybe object is omitted, or it's a reflexive?\n\nBut no reflexive marker.\n\nPossibility: “aarqijuq” = cured someone — object implied?\n\nBut sentence 16: “Ilinniaqtitsiji qukiqtait” \n“Ilinniaqtitsiji” — teacher? (from sentence 10: “Qingmiup ilinniaqtitsijiit aanniqtanga” → dog hurt your teacher)\n\nSentence 10: “Qingmiup ilinniaqtitsijiit aanniqtanga” → dog hurt your teacher → verb “aanniqtanga” → hurt + you (reflexive?) — no\n\n“aanniqtanga” — from “aanniqtutit” → “-utit” is reflexive → “-anga” is past tense → so “hurt” in past tense with object?\n\nIn that sentence: “ilinniaqtitsijiit” — “your teacher” — object?\n\nSo object marked by “-sijiit”?\n\nIn sentence 10: “ilinniaqtitsijiit” — your teacher, object.\n\nSo object form ends with “-it” or “-sijiit”?\n\nIn sentence 16: “Ilinniaqtitsiji” — possibly subject? But “qukiqtait” → shot.\n\n“qukiqtait” — from sentence 2: “qukiqtanga” → shot → so “-ait” object marker.\n\nSo “ilinniaqtitsiji” → likely subject? → your teacher?\n\nThen “qukiqtait” → shot — object?\n\nSo “your teacher shot [someone]”?\n\nBut who?\n\nObject missing.\n\nSo “your teacher shot” — something?\n\nBut no object.\n\nCompare with sentence 12: “Angunahuktimik aarqisijutit” → hunter shot a doctor → object marked.\n\nIn sentence 16: “Ilinniaqtitsiji qukiqtait” — object missing → perhaps object is implied, or not stated?\n\nBut the structure is similar to sentence 2: “Inuuhuktuup iluaqhaiji qukiqtanga” → boy shot doctor → subject then object then verb.\n\nHere: “ilinniaqtitsiji” → subject → your teacher? \n“qukiqtait” → shot → object?\n\nSo object not there — so perhaps it's “your teacher shot him” — but what?\n\nAlternatively, maybe “qukiqtait” has object?\n\nBut verb form “qukiqtait” — same as in sentence 2 “qukiqtanga” — “-ait” could be object marker.\n\nSo the object must be missing — but in that case, the sentence is incomplete?\n\nNo — must be a logical translation.\n\nPossibility: “Ilinniaqtitsiji” is object? — but then “qukiqtait” would be verb with subject?\n\nBut “qukiqtait” ends with “-ait” → object marker → so cannot be subject.\n\nSo “ilinniaqtitsiji” must be subject.\n\nThus, “your teacher shot [someone]” — unknown object.\n\nBut is there an implicit object?\n\nLikely not — must be derived from pattern.\n\nWait — sentence 17: “Qaijutit” → alone\n\n“qaijutit” — from sentence 7: “qaijuq”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12190.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are asked to write out the numbers 42 and 494 in Nahuatl, based on the given linguistic patterns in the examples.\n\nWe begin by analyzing the provided equations in Nahuatl and Arammba to extract numerical patterns, especially those involving multiplication, addition, and number construction.\n\n---\n\n### Step 1: Identify known multiplicative structures\n\nLook at equation (1): \n**mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli**\n\n- \"mahtlactli\" appears twice on the left: one as multiplier, one as multiplicand.\n- The result is **mäcuïl-pöhualli-om-mahtlactli**\n\nThis resembles a multiplication structure where a number (mahtlactli) times itself yields a compound form.\n\nBut we must test what \"mahtlactli\" might represent.\n\nConsider equation (4): \n**mäcuïlli + öme = chicöme**\n\nThis suggests that a unit (mäcuïlli) and öme combine to form chicöme.\n\nIf we assume that öme = 1, then mäcuïlli + 1 = chicöme → mäcuïlli = chicöme – 1 \nBut we don’t yet know values.\n\nEquation (2): \n**cem-pöhualli × öme = öm-pöhualli**\n\nThis looks like a multiplicative identity — a number times 1 equals itself.\n\nSo **öme = 1**\n\nAlso, mäcuïlli × öme = chicöme (equation 4): \n→ mäcuïlli × 1 = chicöme → mäcuïlli = chicöme\n\nSo **mäcuïlli = chicöme**\n\nWait: equation (4) says: mäcuïlli + öme = chicöme → mäcuïlli + 1 = chicöme → mäcuïlli = chicöme – 1\n\nSo this contradicts above.\n\nBut in (4): addition, not multiplication.\n\nSo which is it?\n\nEquation (4): mäcuïlli + öme = chicöme → with öme = 1 → mäcuïlli + 1 = chicöme → chicöme = mäcuïlli + 1\n\nSo chicöme is one more than mäcuïlli.\n\nNow equation (5): \n**mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui**\n\nThis is a multiplication: (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nAlso note: (6): mäcuïlli × ëyi = caxtölli\n\nThis is a key pattern: mäcuïlli × ëyi = caxtölli\n\nSo multiplication of mäcuïlli by ëyi gives caxtölli → suggests ëyi is a multiplier or unit.\n\nEquation (5): multiplication of (mahtlactli-om-ëyi) × ëyi → produces a compound involving cem-pöhualli and caxtölli.\n\nBut equation (6): mäcuïlli × ëyi = caxtölli\n\nSo we can speculate: mäcuïlli × ëyi = caxtölli → caxtölli is the product of mäcuïlli and ëyi.\n\nThus, if we assume that:\n- ëyi = 10 (a common base in Mesoamerican number systems), then mäcuïlli × 10 = caxtölli\n\nSo caxtölli = 10 × mäcuïlli\n\nBut equation (4): mäcuïlli + öme = chicöme → mäcuïlli + 1 = chicöme\n\nSo chicöme = mäcuïlli + 1 → thus, chicöme is the successor of mäcuïlli.\n\nThis is consistent with a base-20 system with units.\n\nNow look at equation (3): \n**yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë**\n\nWe might interpret this as: (yë-pöhualli-on-chicöme) + (mahtlactli-on-nähui) = näuh-pöhualli-on-cë\n\nNote that \"on\" likely means \"of\" or \"in\", and the structure resembles compound numbers.\n\nBut it's tricky.\n\nNow consider the equation (13):\n\n**yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno**\n\nWe are told this equals ndamno. Possibly a specific number.\n\nWe are to find 42 and 494.\n\nSo what are the base units?\n\nWe know from equation (6): \nmäcuïlli × ëyi = caxtölli\n\nIf we suppose that this is a multiplication of a number by 10, then ëyi = 10.\n\nThen caxtölli = 10 × mäcuïlli\n\nThen from (4): mäcuïlli + 1 = chicöme → so chicöme = mäcuïlli + 1\n\nSo the base units may be:\n- 1 = öme\n- 10 = ëyi\n- 20 = ? (perhaps mahtlactli or something else)\n\nFrom equation (1): \n**mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli**\n\nLeft side: mahtlactli × mahtlactli\n\nRight side: mäcuïl-pöhualli-om-mahtlactli\n\nWe can infer: mahtlactli × mahtlactli = something → maybe 20×20?\n\nBut 20×20 = 400, which is close to 42 or 494.\n\nAlternatively, maybe mahtlactli = 20.\n\nTry this:\n\nAssume:\n- öme = 1\n- ëyi = 10\n- mahtlactli = 20\n\nThen:\n- mahtlactli × mahtlactli = 20×20 = 400\n\nNow, equation (1) right-hand side: mäcuïl-pöhualli-om-mahtlactli\n\nWe now examine where \"mäcuïl\" and \"pöhualli\" might sit.\n\nFrom equation (2): \ncem-pöhualli × öme = öm-pöhualli → cem-pöhualli × 1 = öm-pöhualli → so cem-pöhualli = öm-pöhualli\n\nBut cem is likely a number, and öm is opposite or variant.\n\nNot useful directly.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli-om-ëyi = 20 - 10? No — “om” might mean “of” or “by”, so mahtlactli-om-ëyi = 20 of 10?\n\nAlternatively, could be a compound meaning 20 × 10? But that's 200.\n\nCompute:\nmahtlactli-om-ëyi = 20-10? Maybe not.\n\nAlternatively, interpret \"mahtlactli-om-ëyi\" as a number, possibly \"20 × 10\"?\n\nBut it's being multiplied by ëyi (10) → so (20 × 10) × 10 = 2000? Unlikely.\n\nBut the result is cem-pöhualli-on-caxtölli-on-nähui\n\nWe know from (6) that mäcuïlli × 10 = caxtölli → so if mäcuïlli = 2, then caxtölli = 20\n\nSo maybe mäcuïlli = 2?\n\nThen:\n- mäcuïlli = 2\n- ëyi = 10 → caxtölli = 20\n\nThen from (4): mäcuïlli + öme = chicöme → 2 + 1 = 3 → chicöme = 3\n\nNow, 20 = 1×10 + 10 → 10 + 10 = 20? But we have only 2 units.\n\nWe need to build number 42 and 494.\n\nNow observe equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe suspect this is a representation of a number.\n\nLet’s break down:\n\n- yë-tzontli: possibly related to tens or units?\n- on-näuh-pöhualli: “on” likely means “of”\n- on-caxtölli-on-cë\n\nWe know caxtölli = 20 → so “on-caxtölli” = 20\n\ncë may be a unit.\n\nAlso, “näuh-pöhualli” may be a base unit.\n\nIf caxtölli = 20, then “on-caxtölli” = 20\n\n“on-cë” might be unit 1.\n\nSo: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë → “tzontli” may be a unit, possibly 20?\n\nMaybe yë-tzontli = 20?\n\nThen yë-tzontli = 20\n\nSo the whole thing is: 20 (on something) + 20 + 1?\n\nBut it's: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nThis structure might mean: (tzontli) × (something) + (something)\n\nAlternatively, think of it as: 20 × 1 + (20) × 1 + 1 → 20 + 20 + 1 = 41?\n\nBut it's equal to ndamno — perhaps a known number.\n\nAlso, equation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe are told this equals yànparo tarumba.\n\nBut also equation (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nThis is important.\n\nIt says: cen-tzontli = tarumba tambaroy fete asàr\n\nBut from equation (11): nimbo × fete = tarumba\n\nEquation (8): ngámbi + asàr = tambaroy\n\nEquation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → fete = 1? Or tied to yanparo?\n\nBut from (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe are trying to build numbers in Nahuatl.\n\nBack to Nahuatl equations.\n\nFrom equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe now suppose:\n- cë = 1\n- caxtölli = 20\n- näuh-pöhualli → may be 1 or 10?\n- yë-tzontli → may be 20 or 10?\n\nTry to interpret the structure.\n\n\"yë-tzontli-on-näuh-pöhualli\" → might mean (tzontli) on (näuh-pöhualli) → multiplier or base?\n\nBut \"on\" is a prepositional particle.\n\nPerhaps it's a compound number: A-on-B means A is multiplied by B?\n\nBut need evidence.\n\nFrom equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nAssume:\n- chicöme = 3\n- mahtlactli = 20\n- nähui = 1 (unit)\n\nThen: (yë-pöhualli-on-3) + (20-on-1) = näuh-pöhualli-on-1\n\nThis might mean that \"on\" is a multiplication operator.\n\nSo:\n- yë-pöhualli-on-chicöme = yë-pöhualli × 3\n- mahtlactli-on-nähui = 20 × 1 = 20\n- sum = (yë-pöhualli × 3) + 20 = näuh-pöhualli × 1\n\nThat is: (yë-pöhualli × 3) + 20 = näuh-pöhualli\n\nBut this would mean that näuh-pöhualli is a number that is 20 more than 3×yë-pöhualli.\n\nStill not clear.\n\nNow go back to the most promising one: equation (6) \n**mäcuïlli × ëyi = caxtölli**\n\nIf we suppose:\n- ëyi = 10\n- caxtölli = 20 → then mäcuïlli = 2\n\nSo 2 × 10 = 20\n\nThen from (4): mäcuïlli + öme = chicöme → 2 + 1 = 3 → chicöme = 3\n\nSo we have:\n- 1 = öme\n- 2 = mäcuïlli\n- 3 = chicöme\n- 10 = ëyi\n- 20 = caxtölli\n\nNow what about 20? Is mahtlactli = 20?\n\nCheck equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nLeft: mahtlactli × mahtlactli\n\nIf mahtlactli = 20 → 20×20 = 400\n\nRight: mäcuïl-pöhualli-om-mahtlactli\n\nmäcuïl → is mäcuïlli with l? Possibly same as mäcuïlli = 2\n\nSo mäcuïl-pöhualli → perhaps 2 × 10? Or 2 × pöhualli?\n\n\"pöhualli\" might be a base unit.\n\nIf pöhualli = 20, then mäcuïl-pöhualli = 2 × 20 = 40?\n\nThen 40 + mahtlactli = 40 + 20 = 60 ≠ 400\n\nNo.\n\nAlternatively, \"mäcuïl-pöhualli\" might be 2 × pöhualli, and pöhualli = 10?\n\nThen 2×10 = 20 → 20 + 20 = 40\n\nStill not 400.\n\nSo maybe mahtlactli = 10?\n\nThen 10×10 = 100\n\nright side: mäcuïl-pöhualli-om-mahtlactli → 2×10 + 10 = 30 → no.\n\nmahtlactli = 40?\n\nThen 40×40 = 1600 — too big.\n\nWait — perhaps \"mahtlactli\" is not a number, but a unit of counting, and “on” means part of.\n\nAlternative approach: look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe assume:\n- cë = 1\n- caxtölli = 20\n- näuh-pöhualli = ? \n- yë-tzontli = ?\n\nSuppose “on” means “times” or “multiplied by”.\n\nThen:\n- yë-tzontli-on-näuh-pöhualli = yë-tzontli × näuh-pöhualli\n- on-caxtölli = × 20\n- on-cë = × 1\n\nBut structure is: A-on-B-on-C-on-D → may mean A×B + C×D\n\nOr: A×(B + C×D)\n\nBut likely a composite number.\n\nSuppose: (yë-tzontli × näuh-pöhualli) + (caxtölli × cë) = ndamno\n\ncaxtölli × cë = 20 × 1 = 20\n\nSo (yë-tzontli × näuh-pöhualli) + 20 = ndamno\n\nNow, if ndamno is a known number, what could it be?\n\nWe are to find 42 and 494.\n\n42 = 30 + 12 → 3×10 + 2×1 → 3×10 + 2 = 32 → no.\n\n42 = 20 + 20 + 2 → 20+20+2 = 42\n\nOr 4×10 + 2\n\nWe have units:\n- 1 = öme\n- 2 = mäcuïlli\n- 3 = chicöme\n- 10 = ëyi\n- 20 = caxtölli\n\nSo 42 = 2×20 + 2 → but 2 is mäcuïlli\n\nOr 2×20 + 2 = 42\n\nThat is: two 20s and two units.\n\nBut what about tzontli?\n\nIn (13), we have: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nPerhaps “tzontli” is 3?\n\nThen tzontli = 3\n\nnäuh-pöhualli = 10?\n\nThen: 3×10 + 20 + 1 = 30 + 20 + 1 = ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9689.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are to write out the numbers 42 and 494 in Nahuatl, based on the provided linguistic examples. We must derive the pattern from the given equations, without assuming known numerals or relying on external knowledge.\n\n---\n\nStep 1: Understand the structure of the given equations.\n\nWe look for patterns in addition, multiplication, and number formation.\n\nFrom (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nWe see that \"mahtlactli-on-cë\" × \"mahtlactli\" = \"mäcuïl-pöhualli-om-mahtlactli\"\n\nNote: \"mahtlactli\" appears on both sides. The left has \"on-cë\" attached — possibly a modifier or a unit. \n\"on-cë\" likely marks a specific operation or quantifier. \n\"pöhualli\" appears again in other equations — appears to be a base unit. \n\"mäcuïl\" appears in both (1) and (4).\n\n(4): mäcuïlli + öme = chicöme \n→ Addition: mäcuïlli + öme = chicöme\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6): mäcuïlli × ëyi = caxtölli\n\nIn (6): mäcuïlli × ëyi = caxtölli → multiplication of mäcuïlli (a unit) and ëyi produces caxtölli.\n\nSo, \"mäcuïlli × ëyi = caxtölli\" → suggests that \"ëyi\" is a count unit, and \"mäcuïlli\" is a base.\n\nSimilarly, in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli — this seems to be multiplication.\n\nAlso, (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ addition involving \"pöhualli\" and \"chicöme\"\n\nNow look at the number 42.\n\nIn the Arammba system, we have:\n(7): ngámbi + ngámbi = ngámbi × yànparo \n→ Addition of ngámbi = multiplication form\n\n(8): ngámbi + asàr = tambaroy \n→ suggests that ngámbi + asàr = tambaroy (like 1 + 2 = 3)\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ seems like a distributive or scaling operation\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ multiplication with a modifier \"tàxwo\"\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe are to map 42 and 494 in Nahuatl. So, we need to know how numbers are formed.\n\nNotice that in the final equations (13) and (14), both involve long compound forms with tzontli, cem-pöhualli, etc.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nNote that in (15): cen-tzontli = tarumba tambaroy fete asàr \n→ \"cen-tzontli\" is equal to a compound: tarumba + tambaroy + fete + asàr\n\nBut tambaroy = ngámbi + asàr (from (8)) \nfete = from (10) or (11) \ntarumba = nimbo × fete\n\nSo \"cen-tzontli\" = tarumba + tambaroy + fete + asàr\n\nNow, this is in Arammba. But Nahuatl equations involve similar compounds.\n\nLook at (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \nSo \"cen-xiquipilli\" is a compound number.\n\nIn Nahuatl, numbers are often formed via multiplicative or additive components.\n\nWe observe:\n\nIn (4): mäcuïlli + öme = chicöme → addition of a unit and another gives a compound\n\nIn (6): mäcuïlli × ëyi = caxtölli → multiplication\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli → this seems like (A × A) = B\n\nSo perhaps \"mahtlactli\" is a base unit, and squaring it produces a compound.\n\nWe suspect that Nahuatl uses a vigesimal (base-20) system, common in Mesoamerican languages.\n\nAlso, \"pöhualli\" appears as a base unit — likely \"20\"\n\n\"öme\" appears in (2) and (4): cem-pöhualli × öme = öm-pöhualli\n\nc-pöhualli × öme = om-pöhualli → this looks like 20 × 5 = 100? No, 20×5=100, but 5×20=100, 100 in vigesimal is 5×20.\n\nWait:\n\n(2): cem-pöhualli × öme = öm-pöhualli \ncem-pöhualli → likely 20 \nöme → likely 5 \nThen 20 × 5 = 100 → but “öm-pöhualli” is 5×20 → i.e., öme × pöhualli\n\nSo: (20 × 5) = (5 × 20) → commutative → suggests the operation is multiplicative and commutative.\n\nBut also: in (4): mäcuïlli + öme = chicöme → mäcuïlli is likely \"1\" or \"2\"? Or a base?\n\nPossibly, \"mäcuïlli\" is 1, \"öme\" is 5, and 1+5=chicöme? But 6?\n\nAlternatively, mäcuïlli = 1 (base unit), öme = 5, so 1+5=6.\n\nBut then in (6): mäcuïlli × ëyi = caxtölli \n→ 1 × ëyi = caxtölli → implies caxtölli = ëyi → so ëyi is a unit.\n\nBut in (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nLet’s try to extract:\n\nmahtlactli-om-ëyi → likely \"mahtlactli\" + \"ëyi\"\n\nWe suppose that \"mahtlactli\" represents a unit like “1” or “20”, and \"ëyi\" is a count.\n\n(5): (mahtlactli + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nNow, (6): mäcuïlli × ëyi = caxtölli → 1 × ëyi = caxtölli → so caxtölli = ëyi\n\nThen from (5): (mahtlactli + ëyi) × ëyi = (20 + ëyi) × ëyi → equals cem-pöhualli-on-caxtölli-on-nähui\n\nBut cem-pöhualli = 20, caxtölli = ëyi, nähui = ? (likely 1)\n\nThen the right-hand side: 20 + (ëyi × ëyi) → 20 + (ëyi²)\n\nSo: (mahtlactli + ëyi) × ëyi = 20 + (ëyi²)\n\nLeft: mahtlactli × ëyi + ëyi² = 20 + ëyi² → so mahtlactli × ëyi = 20\n\nAssume mahtlactli is a base. If mahtlactli = 20, then 20 × ëyi = 20 → ëyi = 1\n\nBut then (6): mäcuïlli × ëyi = caxtölli → 1 × 1 = caxtölli → caxtölli = 1\n\nThen (5): (20 + 1) × 1 = 21 → should equal 20 + (1²) = 21 → works.\n\nSo this suggests:\n\n- mahtlactli = 20\n- ëyi = 1\n- caxtölli = 1\n- mäcuïlli = 1 (from equation 6: 1 × 1 = 1)\n\nBut in (4): mäcuïlli + öme = chicöme → 1 + öme = chicöme\n\nIn (2): cem-pöhualli × öme = öm-pöhualli → 20 × öme = öme × 20 → consistent\n\nFrom (2): 20 × öme = öme × 20 → commutative → doesn't fix value.\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (20 + cë) × 20 = mäcuïl-pöhualli-om-20\n\nRight side: mäcuïl-pöhualli-om-mahtlactli → likely a compound of mäcuïl (a unit) and pöhualli (20)\n\nAssume mäcuïl = 1 → then 1 × 20 = 20 → but left side is (20 + cë) × 20\n\nSo if (20 + cë) × 20 = 1 × 20 + 20? No.\n\nWait: (a + b) × c = a×c + b×c\n\nSo (20 + cë) × 20 = 400 + 20×cë\n\nRight side: mäcuïl-pöhualli-om-mahtlactli → perhaps (1 × 20) + 20 = 40? But 400 + 20×cë = 40? No.\n\nAlternatively, “on-cë” may not be additive.\n\nAlternatively, “on-cë” means “one” — so mahtlactli-on-cë = “20-one” = 19?\n\nThen 19 × 20 = 380\n\nRight side: mäcuïl-pöhualli-om-mahtlactli\n\nIf mäcuïl = 1, pöhualli = 20 → 1×20 = 20 → so 20 + 20 = 40 — not 380.\n\nDoesn’t work.\n\nAnother idea: perhaps “mahtlactli-on-cë” means the number ‘one’ in a different base.\n\nBut more promising: look at (13):\n\nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe are to write 42 and 494.\n\nTry to find a multiplicative base.\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo, \"cen-tzontli\" is equal to \"tarumba jam\" — but also in (14), it is part of a compound.\n\nBut in (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nFrom earlier:\n\n- tambaroy = ngámbi + asàr → from (8)\n- fete = from (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → so (x × x) = fete × x → implies fete = x\n- so if yenówe = 2, then fete = 2\n- (12): nimbo + yànparo tàxwo = yenówe tàxwo\n- (11): nimbo × fete = tarumba\n\nIf fete = 2, and tarumba = nimbo × 2\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nAnd from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → so addition with modification\n\nBut in (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nWe don’t yet have numeric values.\n\nBut consider that in Nahuatl, numbers are often built using:\n\n- 20 × (a) + (b)\n\nFor example, 42 = 2×20 + 2 → 40 + 2\n\n494 = 24×20 + 14 → 480 + 14\n\nSo we need to express 2×20 + 2 and 24×20 + 14.\n\nWe need to find which units mean 20, 2, 1, etc.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli\n\nIf we assume pöhualli = 20, then:\n\n20 × öme = öme × 20 → valid.\n\nNow, if it's 20 × 1 = 20 → so öme = 1?\n\nBut then (2) says 20 × 1 = 1 × 20 → holds.\n\nBut in (4): mäcuïlli + öme = chicöme → 1 + 1 = chicöme → 2?\n\nBut 2 may be part of a unit.\n\nIn (6): mäcuïlli × ëyi = caxtölli → 1 × ëyi = caxtölli → so caxtölli = ëyi\n\nSo if ëyi = 2, then caxtölli = 2\n\nIn (5): (mahtlactli + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli = 20 (assumed)\n\nëyi = 2\n\nThen (20 + 2) × 2 = 22 × 2 = 44\n\nRight side: cem-pöhualli-on-caxtölli-on-nähui = 20 + (caxtölli) + nähui = 20 + 2 + 1 = 23 — not 44.\n\nNo.\n\nWhat if the multiplication is not direct?\n\nBack to (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose mahtlactli = 20\n\nmahtlactli-on-cë = 20 + 1 = 21\n\n21 × 20 = 420\n\nRight side: mäcuïl-pöhualli-om-mahtlactli\n\nmäcuïl-pöhualli = 1 × 20 = 20\n\nthen 20 + 20 = 40 — not 420.\n\nNo.\n\nPerhaps \"on-cë\" means \"to the power of 1\"?\n\nAnother idea: perhaps the base is 20, and numbers are formed using multiplicative components.\n\nLook at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSo yë-tzontli is the \"one\" or \"ten\" or \"base\" component.\n\n\"tzontli\" may be 20, or 1.\n\n\"yë\" may mean \"one\" or \"first\".\n\n\"on-näuh\" may be \"on-näuh\" as in \"with näuh\" — maybe \"näuh\" = 1\n\n\"pöhualli\" = 20\n\n\"caxtölli\" = ? from (6): mäcuïlli × ëyi = caxtölli\n\nWe have no direct values.\n\nBut from (4): mäcuïlli + öme = chicöme\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli\n\nIf we suppose öme = 5, then 20 × 5 = 100 → and 5 × 20 = 100 → so öme = 5\n\nThen in (4): mäcuïlli + 5 = chicöme\n\nIf mäcuïlli = 1, then 1+5=6 → chicöme = 6\n\nIn (6): 1 × ëyi = caxtölli → so caxtölli = ëyi\n\nIn (5): (mahtlactli + ëyi) × ëyi = 20 + (ëyi) + (nähui)\n\nRight side: cem-pöhualli-on-caxtölli-on-nähui = 20 + (ëyi", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9306.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "We are given a series of equations in two languages: Nahuatl and Arammba. The task is to deduce the numerical system of Nahuatl (specifically how numbers are formed), and then write **42** and **494** in Nahuatl.\n\nWe proceed step by step, using only the given equations to infer patterns, focusing on syntactic and semantic patterns, particularly how numbers are formed.\n\n---\n\n**Step 1: Look for number patterns in Nahuatl**\n\nWe analyze each line:\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\n- This looks like: (A × A) = B\n- \"mahtlactli\" appears on both sides — possibly a base unit\n- \"on-cë\" may be a suffix, possibly indicating multiplication or addition\n- Product: `mäcuïl-pöhualli-om-mahtlactli`\n\nCompare with (4): `mäcuïlli + öme = chicöme`\n\n- Addition of `mäcuïlli` and `öme` yields `chicöme`\n- So `mäcuïlli + öme = chicöme` → likely \"15\" or \"16\", since 15 + 1 = 16?\n\nAlso (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\n- Complex addition involving compound terms.\n\nBut look at (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\n- Product of `mahtlactli-om-ëyi` and `ëyi`\n- Result: `cem-pöhualli-on-caxtölli-on-nähui`\n\nNow (6): `mäcuïlli × ëyi = caxtölli`\n\n- This is key: `mäcuïlli × ëyi = caxtölli`\n\n- So multiplication of two units gives a larger number term.\n\nWe suspect `mäcuïlli` = 15, since 15 × something = a compound.\n\nAlso, (2): `cem-pöhualli × öme = öm-pöhualli`\n\n- `cem-pöhualli × öme = öm-pöhualli`\n\n- Here, the product is `öm-pöhualli`, which is just a suffix reordering — could indicate that the operation is \"addition\" or \"multiplication\" without change.\n\nBut more interesting: (4) `mäcuïlli + öme = chicöme`\n\n- So `15 + 1 = 16` → `chicöme`\n\nNow look at equations (2) and (1):\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nWhat does \"mahtlactli\" likely represent?\n\nCheck (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\n- Perhaps `mahtlactli` is 20; \"on-cë\" or \"om\" might be a multiplier?\n\nNote: In some Mesoamerican systems (especially Nahuatl), base-20 is common. 20 is a key number.\n\nTry assuming:\n- `mahtlactli` = 20\n\nThen (1): `mahtlactli-on-cë × mahtlactli = ...`\n\nWhat is \"on-cë\"? Possibly a marker.\n\nBut (1): (20 × 20) = `mäcuïl-pöhualli-om-mahtlactli`\n\nIf 20×20 = 400, then that might be a key.\n\nAlso (6): `mäcuïlli × ëyi = caxtölli`\n\nSuppose `mäcuïlli` = 15, `ëyi` = 1 → then product = 15×\n\nWait — (4): `mäcuïlli + öme = chicöme` → 15 + 1 = 16 → so `chicöme` = 16\n\nNow look at (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nIf `mahtlactli = 20`, and `ëyi = 1`, then `mahtlactli-om-ëyi` = 20 + 1 = 21\n\nThen 21 × 1 = 21 → product is `cem-pöhualli-on-caxtölli-on-nähui`\n\nBut from (6): `mäcuïlli × ëyi = caxtölli`\n\nSo 15 × 1 = caxtölli → caxtölli = 15?\n\nBut 15×1 = 15, so that fits.\n\nNow in (5), the product is `cem-pöhualli-on-caxtölli-on-nähui`\n\nWe know caxtölli = 15 → so caxtölli-on-nähui = 15 + 1 = 16? But that's the same as chicöme.\n\nBut the product is 21 → so likely 21 = cem-pöhualli + something.\n\nWait: what about `cem-pöhualli`?\n\nFrom (2): `cem-pöhualli × öme = öm-pöhualli`\n\nIf öme = 1, then multiplication gives the same term — suggests that `cem-pöhualli × 1 = cem-pöhualli` — consistent with öme = 1.\n\nSo assume:\n- `öme` = 1\n\nThen (4): `mäcuïlli + öme = chicöme` → 15 + 1 = 16 → chicöme = 16\n\n(6): `mäcuïlli × ëyi = caxtölli` → 15 × e = caxtölli → if e = 1 → caxtölli = 15\n\nNow from (5): (20 + 1) × 1 = 21 → cem-pöhualli-on-caxtölli-on-nähui\n\nSo 21 = cem-pöhualli-on-caxtölli-on-nähui\n\nBut what is on-nähui? Possibly indicates +1?\n\nSo maybe: A-on-B means A+B\n\nSimilarly, in (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThis would be: (A + 16) + (20 + 1) = ?\n\nSo 16 + 21 = 37 → result is näuh-pöhualli-on-cë\n\nSo on-cë may be a +1 tag.\n\nBut from (1): (20 × 20) = mäcuïl-pöhualli-om-mahtlactli\n\n20×20 = 400 → so mäcuïl-pöhualli-om-mahtlactli = 400\n\nBut mäcuïl? Could be a variant of mäcuïlli? Possibly \"15\" with an added element.\n\nmäcuïlli = 15 → so mäcuïl-pöhualli → maybe 15 × 20 = 300?\n\nBut 15 × 20 = 300 → could be 300 → matches 400? No.\n\nWait — perhaps mäcuïl-pöhualli = 300?\n\nThen mäcuïl-pöhualli-om-mahtlactli = 300 + 20 = 320 → not 400.\n\nAlternative: maybe \"mahtlactli\" = 1?\n\nNo — repeated in (1), product with self grows.\n\nAlternative: maybe the base is 20, and numbers are formed as:\n\nNumber = (a × 20) + b, where a is the \"upper\" digit, b is the \"lower\"\n\nIn Nahuatl, traditional counting is base-20.\n\nWe have evidence:\n- 1 = öme\n- 15 = mäcuïlli\n- 16 = chicöme\n- 20 = mahtlactli\n\nThen:\n\n(6): mäcuïlli × ëyi = caxtölli → 15 × 1 = 15 → caxtölli = 15\n\nSo multiplication: 15 × 1 = 15\n\n(5): (20 + 1) × 1 = 21 → cem-pöhualli-on-caxtölli-on-nähui\n\nIf the structure is: A-on-B = A + B → then 21 = cem-pöhualli-on-caxtölli-on-nähui\n\nBut caxtölli = 15, on-nähui = +1 → 15+1=16? But 21 ≠ 16\n\nUnless cem-pöhualli is a multiplier?\n\nCompare (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1 → product = cem-pöhualli → so it's invariant under multiplication by 1.\n\nSo cem-pöhualli × 1 = cem-pöhualli → consistent with being a base.\n\nNow, in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nLeft: (20 × 20) = 400\n\nRight: mäcuïl-pöhualli-om-mahtlactli\n\nIf mäcuïl-pöhualli = 300 → 300 + 20 = 320 → not 400\n\nBut 400 = 20 × 20\n\nSo perhaps mäcuïl-pöhualli = 20 × 20 = 400?\n\nBut mäcuïlli = 15 → why would mäcuïl be 20?\n\nNot likely.\n\nAlternative idea: the forms with \"-on\" are additive.\n\nSo in equation (5): mahtlactli-om-ëyi is 20 + 1 = 21, times ëyi = 1 → so 21 × 1 = 21 → gives cem-pöhualli-on-caxtölli-on-nähui\n\nSo 21 = cem-pöhualli-on-caxtölli-on-nähui\n\nSo if caxtölli = 15, then caxtölli-on-nähui = 15 + 1 = 16 → not 21.\n\nSo not additive.\n\nBut what if the structure is: A × B → A × B = compound with multiplicative elements.\n\nFrom (6): mäcuïlli × ëyi = caxtölli → so 15 × 1 = 15 → caxtölli = 15\n\nSo \"multiplication\" works.\n\nThen (5): (mahtlactli-om-ëyi) × ëyi = 21 × 1 = 21 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nSo unless \"cem-pöhualli\" is 21, it's strange.\n\nWait: perhaps \"cem-pöhualli\" is the product value?\n\nBut from (2): cem-pöhualli × öme = öm-pöhualli → suggests cem-pöhualli × 1 = cem-pöhualli → so it's unchanged.\n\nSo probably cem-pöhualli is a base.\n\nNow look at (13) and (14), which are the target-related equations.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe need to interpret the components.\n\nFirst, let’s find what \"yë-tzontli\" might be.\n\nFrom the earlier patterns:\n\nWe have:\n- 1 = öme\n- 20 = mahtlactli\n- 15 = mäcuïlli\n- 16 = chicöme\n- caxtölli = 15\n- on-cë → likely +1\n- on-nähui → possibly +1, similar to on-cë?\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n→ (A + 16) + (20 + 1) = (A + 16 + 21) = A + 37 = näuh-pöhualli-on-cë\n\nSo the sum is like A + 37 = result with +1 at end.\n\nBut we don't know A.\n\nBut (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSo yë-tzontli-on-(näuh-pöhualli-on-caxtölli-on-cë)\n\ncaxtölli = 15 → on-cë = +1 → so caxtölli-on-cë = 15 + 1 = 16 = chicöme\n\nSo näuh-pöhualli-on-caxtölli-on-cë = näuh-pöhualli-on-chicöme\n\nSo entire expression: yë-tzontli-on-(näuh-pöhualli-on-chicöme) = ndamno\n\nNow, the left side has a \"on\" structure.\n\nPossibility: \"X-on-Y\" = X + Y\n\nThen: yë-tzontli + (näuh-pöhualli-on-chicöme) = ndamno\n\n→ yë-tzontli + (näuh-pöhualli + 16) = ndamno\n\nWe don’t know yë-tzontli.\n\nBut we have equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis looks like a sum of three items.\n\nCompare to (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nWe suspect this is 20×20 = 400 → so mäcuïl-pöhualli-om-mahtlactli = 400\n\nSo mäcuïl-pöhualli = 400 - 20 = 380? Unlikely.\n\nAlternative: the \"on\" might represent addition, and \"om\" might represent multiplication.\n\nLook at (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n\"om\" might be \"×\", and \"on\" might be \"+\".\n\nSo mahtlactli × ëyi = 20 × 1 = 20\n\nBut left is (mahtlactli-om-ëyi) × ëyi → (mahtlactli × ëyi) → so would be (20 × 1) = 20\n\nBut multiplied by ëyi = 1 → still 20\n\nProduct is 20 → but result is cem-pöhualli-on-caxtölli-on-nähui\n\nNot 20.\n\nBut (6): mäcuïlli × ëyi = caxtölli → 15 × 1 = 15 → fits\n\n(4): mäcuïlli + öme = chicöme → 15 + 1 = 16 → fits\n\nSo perhaps:\n- 1 = öme\n- 15 = mäcuïlli\n- 16 = chicöme\n- 20 = mahtlactli\n- 15 × 1 = 15 = caxtölli\n- 20 + 1 = 21 → but not represented simply\n\nNow from (5): (20 + 1) × 1 = 21 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nSo 21 is represented as cem-pöhualli-on-caxtölli-on-nähui\n\nBut caxtölli = 15 → on-nähui = +1 → 15 + 1 = 16 → not 21\n\nSo inconsistency.\n\nUnless cem-pöhualli is not 1.\n\nAlternatively, cem-pöhualli might be 20?\n\nBut (2): cem-pöhualli × öme = öm-pöhualli → so if cem-pöhualli = 20, and öme = 1, product = 20 → equals öm-pöhualli? Only if öm-pöhualli = 20.\n\nSo maybe öm-pöhualli = 20\n\nThen, cem-pöhualli × 1 = öm-pöhualli → so cem-pöhualli = öm-pöhualli\n\nThus cem-pöhualli = 20\n\nSo now (5): (20 + 1) × 1 = 21 → result = cem-pöhualli-on-caxtölli-on-nähui = 20-on-15-on-1\n\nSo 20 + 15 + 1 = 36 → not 21\n\nNo.\n\nWhat if the structure is: A-on-B means A × B?\n\nFor example, mäcuïlli-on-öme = 15 × 1 = 15? But not in any example.\n\nWe have only multiplication of mäcuï", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9336.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are to write out the numbers 42 and 494 in Nahuatl, using the given linguistic equations as clues to deduce the number system.\n\nStep 1: Identify the structure of Nahuatl number expressions.\n\nLook at the equations:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(2) cem-pöhualli × öme = öm-pöhualli \n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n(4) mäcuïlli + öme = chicöme \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli \n\nWe observe recurring components:\n\n- \"mahtlactli\" appears frequently — likely a base number (e.g., 20)\n- \"öme\" appears in equations (2), (4), (6) — likely 1\n- \"pöhualli\" is a base unit — appears in multiplication and addition\n- \"cem-pöhualli\" appears in (2) and (5), and in (14)\n\nFrom (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"mahtlactli-on-cë\" likely means \"20 + 1\" = 21 \nThen 21 × 20 = mäcuïl-pöhualli-om-mahtlactli \nBut 21 × 20 = 420 — not helpful directly.\n\nWait — look at (4): mäcuïlli + öme = chicöme \nLikely: 20 + 1 = 21 → mäcuïlli = 20, öme = 1 → chicöme = 21\n\nSo mäcuïlli = 20, öme = 1\n\nThen (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli \nSo if ëyi = 1 → caxtölli = 20 — no \nBut if ëyi = 1 and 20×1 = 20 → caxtölli = 20 → then ëyi = 1? But 1 is öme.\n\nWait — what if ëyi = 1? Then (6) says 20×1 = caxtölli → caxtölli = 20\n\nBut look at (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nIf mahtlactli = 20, ëyi = 1 → 20 + 1 = 21 \nThen 21 × 1 = 21 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nSo 21 × 1 = 21 → is that cem-pöhualli-on-caxtölli-on-nähui?\n\nBut caxtölli-on-nähui → 20 + ? \nIf caxtölli = 20, nähui = ? → maybe 1?\n\nWait — this doesn't give a consistent value.\n\nBut what about equation (2): \ncem-pöhualli × öme = öm-pöhualli \nIf we suppose öme = 1 → then cem-pöhualli × 1 = öm-pöhualli\n\nThis suggests that cem-pöhualli = öm-pöhualli? Or a standard number?\n\nBut multiplication by 1 gives same result → likely öme = 1\n\nThus, öme = 1\n\nNow (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → so mäcuïlli = 20, chicöme = 21\n\nSo, likely, the base is 20, and units are built on that.\n\nNow (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nmahtlactli-on-cë = 20 + 1 = 21 \nmahtlactli = 20 \nLeft side: 21 × 20 = 420 \nRight side: mäcuïl-pöhualli-om-mahtlactli\n\nNote: mäcuïl-pöhualli → could be 20 × 1 = 20? But \"pöhualli\" is likely a unit.\n\nWait — look at (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \nand (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo in (15), cen-tzontli = tarumba tambaroy fete asàr \nIf we assume that the right-hand side is a compound number, and \"tarumba\" is a base, but from (11): nimbo × fete = tarumba → so tarumba = nimbo × fete? \nBut (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nBut in Arammba, \"yànparo\" appears in (7): ngámbi + ngámbi = ngámbi × yànparo → suggests multiplication → perhaps yànparo = 1?\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \nSo (left): 2ngámbi = 1ngámbi × yànparo → implies ngámbi × 2 = ngámbi × yànparo → so 2 = yànparo → so yànparo = 2\n\nThus in Arammba, yànparo = 2\n\nSimilarly, in Nahuatl, could we find a corresponding value?\n\nNow (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLeft: (20+1) × 20 = 21 × 20 = 420 \nRight: mäcuïl-pöhualli-om-mahtlactli → likely structure: (some number) × pöhualli + 20?\n\nWait — what if pöhualli = 1? \nThen mäcuïl-pöhualli → 20 × 1 = 20? But mäcuïl → likely 20?\n\nIf mäcuïl = 20, then 20×pöhualli → 20×1 = 20 → plus om-mahtlactli = plus 20 → total 40?\n\nBut we got 420 → contradiction.\n\nWait — perhaps the \"pöhualli\" is a base unit, and \"mäcuïl-pöhualli\" = 20×pöhualli → if pöhualli = 1 → 20\n\nThen mäcuïl-pöhualli-om-mahtlactli → 20 + 20 = 40 → still not 420\n\nAlternatively, maybe \"mahtlactli\" is not 20? But (4): mäcuïlli + öme = chicöme — if this is 20 + 1 = 21, then both mäcuïlli and mahtlactli are 20?\n\nNote: \"mahtlactli\" and \"mäcuïlli\" — probably variants.\n\nPossibility: \"mahtlactli\" = 20, \"mäcuïlli\" = 20 → same?\n\nBut in (1): (20+1) × 20 = 420 → right side: mäcuïl-pöhualli-om-mahtlactli → perhaps 20×21?\n\nIs there a pattern where multiplication occurs in a structure?\n\nEquation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSome addition.\n\nBut let's turn to (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe need to find how numbers are expressed.\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr \nand (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSo left-hand side: cen-tzontli + cem-pöhualli-om-mahtlactli-om-öme\n\nSo the expression is: (number) + (some compound)\n\nBut in (14), the result is yànparo tarumba\n\nWe know from Arammba (7): ngámbi + ngámbi = ngámbi × yànparo → yànparo = 2\n\nSo in Nahuatl, what is the pattern?\n\nLook at (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis looks like: cen-tzontli + (cem-pöhualli-om-mahtlactli-om-öme) = yànparo tarumba\n\nSo, the sum of two terms equals a compound.\n\nNow, yànparo tarumba — could yànparo be 2, tarumba be a unit?\n\nIn Arammba, (11): nimbo × fete = tarumba → so tarumba is a product → suggests tarumba is a composite number.\n\nLikely, in Nahuatl, \"tarumba\" is a number, and from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = tarumba + tambaroy + fete + asàr\n\nThus, cen-tzontli is a compound number expressed as sum of components.\n\nSo the addition of components builds numbers.\n\nNow, in (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSo cen-tzontli is a unit — likely 100 or 1000?\n\nBut we are to write 42 and 494.\n\nWe assume that the Nahuatl number system is base 20, and numbers are formed as:\n\n[a × 20 + b] where a and b are digits.\n\nSo 42 = 2×20 + 2 = 2×20 + 2\n\nSo we need the form of \"2×20 + 2\"\n\nWhat is the notation?\n\nFrom (4): mäcuïlli + öme = chicöme → 20 + 1 → 21 → so 20 + 1 is possible.\n\nSo 20 + 2 → 22 → would be mäcuïlli + öme + öme → but we don't have evidence for multiple öme.\n\nBut (1): (20+1) × 20 = 420 → 420\n\n420 = 21 × 20 → so could be related to multiplication.\n\nWe need an expression for 42.\n\n42 = 2×20 + 2\n\nSo structure: (2 × 20) + 2\n\nNow, what is the form of multiplication?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli → suggests cem-pöhualli × 1 = öm-pöhualli → so if cem-pöhualli = 20, then 20×1 = 20 → forms öm-pöhualli → so öm-pöhualli = 20\n\nBut (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe suppose ëyi = 1 → then left = mahtlactli-om-1 = 20+1 = 21\n\nThen 21 × 1 = 21 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nSo 21 × 1 = cem-pöhualli-on-caxtölli-on-nähui\n\nBut if cem-pöhualli = 20, caxtölli = 20, nähui = 1 → then 20 + 20 + 1 = 41? Not 21.\n\nContradiction.\n\nWait — perhaps the left side is not 21×1, but (20+1) × (20+1)? No.\n\nWait — equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nLeft: (mahtlactli + ëyi) × ëyi\n\nSuppose ëyi = 1 → (20+1) × 1 = 21 → result is cem-pöhualli-on-caxtölli-on-nähui\n\nBut 21 = 20 + 1 → so result should be 20+1 → but it is written as a compound of three elements.\n\nSo perhaps the number 21 is expressed as cem-pöhualli-on-caxtölli-on-nähui → meaning (20) + (20) + (1)? That's 41 — too big.\n\nAlternatively, maybe cem-pöhualli = 1, caxtölli = 20, nähui = 1 → 1+20+1=22 — still not 21.\n\nAlternatively, cem-pöhualli means 1? From (2): cem-pöhualli × öme = öm-pöhualli → if öme = 1 → cem-pöhualli = öm-pöhualli\n\nSo cem-pöhualli = öm-pöhualli\n\nSo they are equal.\n\nNow (2): cem-pöhualli × öme = öm-pöhualli → so (cem-pöhualli) × 1 = (cem-pöhualli) → consistent.\n\nSo no new info.\n\nBut what about (6): mäcuïlli × ëyi = caxtölli\n\nIf mäcuïlli = 20, then 20 × ëyi = caxtölli\n\nSo if ëyi = 1 → caxtölli = 20\n\nIf ëyi = 2 → caxtölli = 40\n\nSo it seems that “×” operation stands for multiplication, and \"×\" is used to combine a base and a multiplier.\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nLeft: (20+1) × 20 = 420\n\nRight: mäcuïl-pöhualli-om-mahtlactli\n\nIf mäcuïl = 20, pöhualli = 1 → 20×1 = 20 → then 20 + 20 = 40 → still not 420\n\nWait — what if \"mäcuïl-pöhualli\" = 20 × 21?\n\nThen 20 × 21 = 420\n\nSo perhaps \"pöhualli\" is not 1, but a multiplier.\n\nAlternative interpretation: the expression is formed as a product: [a × b] → written as a-pöhualli-b or something.\n\nIn (1): mahtlactli-on-cë × mahtlactli → result is mäcuïl-pöhualli-om-mahtlactli\n\n\"on\" may mean \"plus\", \"om\" may mean \"and\", \"pöhualli\" is a multiplier.\n\nBut (4): mäcuïlli + öme = chicöme → clear addition.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo addition of two terms.\n\nNow, equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe need to find 42 and 494.\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli is a number made of sum of four components.\n\nLikely, in Nahuatl, the number system uses base 20, and numbers are built as:\n\nX = a×20 + b, where a and b are numbers (often single digits)\n\nSo 42 = 2×20 + 2\n\nSo how is it written?\n\nWe need the form for \"2×20 + 2\"\n\nFrom (4): mäcuïlli + öme = chicöme → 20 + 1 → 21\n\nSo to get 2×20 + 2, we need:\n\n(2 × 20) + 2\n\nWhat is \"2 × 20\"?\n\nFrom (6): mäcuïlli × ëyi = caxtölli → if mäcuïlli = 20, then 20 × ëyi = caxtölli\n\nSo if ëyi = 2 → caxtölli = 40\n\nSo \"20 × ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9364.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are given equations in Nahuatl and Arammba, and we are to derive how to write \"43; 569\" in Arammba, based on the patterns.\n\nWe begin by analyzing the equations to determine number patterns, especially how numbers are formed and how operations (like addition, multiplication) are expressed.\n\n---\n\n### Step 1: Analyze Nahuatl examples to find number patterns\n\nLook at equation (1): \n**mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli** \nThis appears to be multiplication. \n\"mahtlactli\" likely stands for \"1\", and \"cë\" may be a unit or modifier. \n\"mahtlactli-on-cë\" may be \"1 × cë\" — possibly \"cë\" is not a number but a unit. \nBut here: \"mahtlactli × mahtlactli\" → \"mäcuïl-pöhualli-om-mahtlactli\" \nThis may represent 1 × 1 = 1 → result is 1? But it has a complex form.\n\nBut note that in equation (4): \n**mäcuïlli + öme = chicöme** \nThis is addition. \nSimilarly, (3): \n**yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë**\n\nBut consider (4): mäcuïlli + öme = chicöme \nPossibility: \n- mäcuïlli = 2 \n- öme = 1 \n- chicöme = 3 \n\n(From standard Nahuatl numeral systems, mäcuïl is \"two\", öme is \"one\", chicöme is \"three\") — common in Nahuatl numerals.\n\nEquation (2): \n**cem-pöhualli × öme = öm-pöhualli** \nNote: “cem-pöhualli” × “öme” = “öm-pöhualli” \nIf öme = 1, then this is multiplication by 1 → identity. \nSo cem-pöhualli × 1 = cem-pöhualli. \nBut here, result is “öm-pöhualli” — which may be a different form. \n“öm” vs “cem” — possibly a different spelling?\n\nWait: “cem” and “öm” — could be regional variants? Or perhaps “cem” = 2, “öm” = 1?\n\nBut in (2): cem-pöhualli × öme = öm-pöhualli \nThat would mean 2 × 1 = 1? — absurd.\n\nAlternative: do not take it as multiplication of values. Consider structure.\n\nLook at equations (5) and (6): \n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6) mäcuïlli × ëyi = caxtölli\n\nFrom (6): 2 × y = caxtölli — so if y = ëyi, then 2 × ëyi = caxtölli → caxtölli = 2 × ëyi \nSo ëyi = ? → caxtölli = 2 × ëyi → ëyi = caxtölli / 2\n\nIn (5): (1 × ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nSo (ëyi) × (ëyi) = cem-pöhualli-on-caxtölli-on-nähui \nSo (ëyi)² = cem-pöhualli-on-caxtölli-on-nähui\n\nBut from (6), 2 × ëyi = caxtölli → ëyi = caxtölli / 2\n\nThus (caxtölli / 2)² = cem-pöhualli-on-caxtölli-on-nähui\n\nIf caxtölli = 4, then ëyi = 2 → 2² = 4 → should be 4 \nBut output is cem-pöhualli-on-caxtölli-on-nähui — which is longer.\n\nSo likely the structure implies a place-value system.\n\nNotice equation (13): \n**yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno**\n\nTry to interpret:\n\n\"yë-tzontli\" — appears in other forms.\n\nFrom (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nPossibly \"yë-pöhualli-on-chicöme\" = 3 × (something), plus 1 × (nähui) → result is näuh-pöhualli-on-cë\n\nBut let’s instead focus on the **Arammba** side and find how numbers are constructed.\n\n---\n\n### Step 2: Analyze Arammba equations for number formation\n\nWe are to write 43 and 569 in Arammba.\n\nKey equations in Arammba:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \nSo 1 + 1 = 1 × yànparo → 2 = yànparo → yànparo = 2\n\n(8) ngámbi + asàr = tambaroy \nSo 1 + x = y → tambaroy = 1 + x → x = asàr → asàr = ? \nSo asàr = tambaroy - 1 — if tambaroy is 2, then asàr = 1? \nBut ngámbi = 1, so 1 + asàr = tambaroy → if asàr = 1 → tambaroy = 2 → consistent.\n\nSo possibly: \n- ngámbi = 1 \n- asàr = 1 \n- tambaroy = 2\n\nBut (7): 1 + 1 = 1 × yànparo → 2 = yànparo \nSo yànparo = 2 → consistent.\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \nNote the \"tàxwo\" suffix. \nPossibly \"tàxwo\" = \"plus\" or \"and\"? Or indicates additive operation.\n\nSo: (2 + asàr) with \"tàxwo\" → 2 + 1 = 3? But result is \"yànparo fete\" = 2 fete? \nSo if fete is a value, this may be a base addition or multiplication.\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo yenówe × (yenówe) with \"tàxwo\" → result is \"fete yenówe tàxwo\" \nLikely, \"yenówe\" is a number, and \"×\" with \"tàxwo\" means multiplication, and result is \"fete\" + \"yenówe\" with \"tàxwo\"\n\nSo: A × A = fete A → so fete A = A²? \nSo fete represents multiplication.\n\nTherefore, \"fete\" = \"times\" or \"multiplies\".\n\nThus: A × A → \"fete A\"\n\nSimilarly, (11) nimbo × fete = tarumba \nSo nimbo × (fete) = tarumba → nimbo × (times) → tarumba\n\n(12) nimbo + yànparo tàxwo = yenówe tàxwo \nSo nimbo + (2) with \"tàxwo\" = yenówe with \"tàxwo\" \n→ nimbo + 2 = yenówe\n\nSo now we can assign values:\n\nFrom (12): nimbo + 2 = yenówe → yenówe = nimbo + 2 \nFrom (10): yenówe × yenówe = fete yenówe → (nimbo+2)² = fete (nimbo+2)\n\nFrom (11): nimbo × fete = tarumba → nimbo × (fete) = tarumba\n\nNow, (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nCompare to (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nAnd (15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nWe see that “cen-tzontli” appears in (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nThat is, one number equals a combination of others.\n\nWe already have:\n\n- ngámbi = 1 \n- yànparo = 2 \n- asàr = 1? (from 1 + 1 = 2 → tambaroy = 2) \n- from (12): nimbo + 2 = yenówe \n- from (10): yenówe² = fete yenówe → so if yenówe = 3, then 3² = 9 → fete 3 = 9 \n- from (11): nimbo × fete = tarumba → so nimbo × 9 = tarumba \n- from (15): cen-tzontli = tarumba + tambaroy + fete + asàr \n- tambaroy = 2, asàr = 1 → so cen-tzontli = tarumba + 2 + 9 + 1 = tarumba + 12\n\nBut from (15): cen-tzontli = tarumba + 12\n\nThus, consistent.\n\nNow, we suspect that numbers in Arammba are formed using composition: \n- base units: ngámbi = 1 \n- then combinations: addition, multiplication \n\nNow, let’s go back to (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nThis is: (2 + fete) with \"tàxwo\" = 2 fete \nSo: 2 + fete = 2 fete? \nOnly if fete = 0? Doesn’t work.\n\nWait — may be parsing: \n\"yànparo tàxwo\" = 2 + ? \n\"asàr\" = 1 \nSo: (2 + 1) with \"tàxwo\"? But the output is \"yànparo fete\"\n\nNote: “yànparo” is 2, “fete” is a multiplier.\n\nSo if “fete” means “times”, then could it be that:\n\n(2 + 1) × something = 2 × something?\n\nBut left side is (2 + 1) × ? and right is 2 × fete → unclear.\n\nBut (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ yànparo + fete + asàr? No.\n\nPerhaps \"tàxwo\" is a verb: \"plus\" or \"and\"\n\nSo: yànparo + fete(asàr) = yànparo + fete\n\n→ 2 + (fete × 1) = 2 + fete → valid, only if numbers are additive, and \"fete\" is a number.\n\nBut then why result is \"yànparo fete\" — which is 2 × fete?\n\nSo if output is 2 × fete, then 2 + fete = 2 × fete?\n\nSo 2 + fete = 2fete → 2 = fete\n\nSo fete = 2\n\nThen from (10): yenówe × yenówe = fete yenówe → yenówe² = 2 × yenówe → yenówe² - 2 yenówe = 0 → yenówe(yenówe - 2) = 0 → yenówe = 0 or 2\n\nSo yenówe = 2\n\nThen from (12): nimbo + 2 = yenówe = 2 → nimbo = 0 — not plausible.\n\nAlternative: fete = 3?\n\nThen 2 + fete = 5, 2 × fete = 6 → not equal.\n\nOnly if 2 + fete = 2 × fete → fete = 2 → contradiction with earlier.\n\nSo perhaps \"fete\" is a noun, and “asàr” modifies it.\n\nTry: fete asàr = fete × 1 → could be a product.\n\nSo left side: (yànparo tàxwo) + (fete asàr tàxwo) → (2 + fete) + (fete × 1)? \n\nBut then output is yànparo fete → which is 2 × fete\n\nSo: 2 + fete + fete = 2 × fete \n→ 2 + 2fete = 2fete → 2 = 0 — contradiction.\n\nAlternative: \"tàxwo\" marks a number as used in multiplication.\n\nTry reading (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nSo: A × (A with \"tàxwo\") = fete A with \"tàxwo\"\n\nSo A × A = fete A → so fete A = A² → so fete means \"times\", and \"fete A\" = A²\n\nThus: multiplication is \"fete\"\n\nSo in general, multiplication is marked by \"fete\"\n\nAlso, addition seems to be via \"tàxwo\" or just addition, with optional attachment.\n\nNow equation (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (2) = yenówe → yenówe = nimbo + 2\n\nEquation (11): nimbo × fete = tarumba → nimbo × (times) = tarumba → so tarumba = nimbo × (some value)\n\nBut from (10): yenówe × yenówe = fete yenówe → (nimbo + 2)² = fete (nimbo + 2)\n\nSo fete (nimbo + 2) = (nimbo + 2)²\n\nFrom (11): nimbo × fete = tarumba → nimbo × (nimbo+2)² = tarumba\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nWe have: \ntambaroy = 2 \nasàr = 1 \nfete = (nimbo+2)² \ntarumba = nimbo × (nimbo+2)²\n\nSo cen-tzontli = [nimbo × (nimbo+2)²] + 2 + (nimbo+2)² + 1 \n= (nimbo + 1)(nimbo+2)² + 3\n\nNow look at (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nBut in Nahuatl, there is (1): mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli → 1×1 = 2? Not.\n\nAlternatively, look at (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis seems to be a compound.\n\nBreak down: \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme \n→ seems to be \"cen-tzontli\" + \"cem-pöhualli\" + \"mahtlactli\" + \"öme\"\n\nIn Nahuatl (1), mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nSo mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nLikely: multiplication is involved.\n\nBut (14) in Arammba: \n\"cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\" = yànparo tarumba\n\nThis may mean: (cen-tzontli) × (cem-pöhualli-om-mahtlactli-om-öme) = yànparo tarumba\n\nBut we don't know the values.\n\nWe suspect that numbers are built from base units with multiplication and addition.\n\nBut in (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis suggests that “cen-tzontli” is equal to the sum: tarumba + tambaroy + fete + asàr\n\nSo it's a sum, not a product.\n\nSimilarly, in (16): cen-xiquipilli = weremeke tarumba nimbo yànparo — again, a sum.\n\nSo likely, all operations are additive; multiplication is denoted by \"fete\".\n\nNow, we try to reverse-engineer 43 and 569 using base units.\n\nWe already have:\n\n- ngámbi = 1 \n- yànparo = 2 \n- asàr = 1 (from 1 + 1 = 2) \n- fete = multiplication operator \n\nNow, let’s find a multiplication pattern.\n\nFrom (10): yenówe × yenówe = fete yenówe → so fete A = A²\n\nSo multiplication is denoted by fete.\n\nNow, (12): nimbo + 2 = yenówe → so yenówe = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba → nimbo × (value) = tarumba\n\nBut from (10): fete yenówe = yenówe² → so fete is used for multiplication.\n\nBut how is a number written?\n\nPossibility: place value", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10097.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We are to write out in Arammba: 43; 569.\n\nWe are given several equations in Nahuatl and Arammba. We must deduce the numeral system of Arammba from the equations and use it to derive the forms for 43 and 569.\n\n---\n\n### Step 1: Analyze Nahuatl equations for numeral patterns\n\nLook at the equations and identify known numerals.\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ This looks like \"x × x = mäcuïl-pöhualli-om-x\" \n\"mahtlactli\" is likely a base numeral, perhaps 2 or 1. \nBut \"mahtlactli\" appears on both sides, so “x² = (mäcuïl-pöhualli-om-x)” \nThis may suggest that \"mahtlactli\" is a base numeral, and the product has a structure of \"A-om-x\", with A being a derived form.\n\nEquation (2): \ncem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × öme = öm-pöhualli \nNote: \"öme\" likely means 2. \n\"cem-pöhualli\" × 2 = \"öm-pöhualli\" \nSo if öme = 2, then cem-pöhualli × 2 = öm-pöhualli → suggests cem-pöhualli = 1/2 of öm-pöhualli → but in integers, that would mean öm-pöhualli = 1? Not likely.\n\nWait. Equation (4): \nmäcuïlli + öme = chicöme \n→ mäcuïlli + 2 = chicöme \nIf öme = 2, and mäcuïlli is some numeral, then chicöme = mäcuïlli + 2\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nThis is complex. \"on\" may indicate addition or derivative.\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (x × y) = some compound \nEquation (6): \nmäcuïlli × ëyi = caxtölli \n→ suggests multiplication: mäcuïlli × ëyi = caxtölli \n\nFrom (6): mäcuïlli × ëyi = caxtölli \nFrom (4): mäcuïlli + öme = chicöme \nSo mäcuïlli is added to öme → then multiplied?\n\nIn addition: (A + B) × C = D\n\nBut equation (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"mahtlactli-on-cë\" may be \"2\", because \"on-cë\" may represent \"2\", and \"mahtlactli\" on its own is \"1\"?\n\nTry: \nLet mahtlactli = 1 \nThen mahtlactli-on-cë = 2 \nThen (2) × (1) = mäcuïl-pöhualli-om-1 \nSo 2 × 1 = 2 → so 2 = mäcuïl-pöhualli-om-1\n\nAlternatively, maybe \"mahtlactli-on-cë\" = 2, and 2 × 1 = ? \nBut result is mäcuïl-pöhualli-om-mahtlactli → which may be \"a number\" such that 2×1 = ?\n\nBut in other equations, we have multiplication: \n(2) cem-pöhualli × öme = öm-pöhualli \nSuppose öme = 2 → then cem-pöhualli × 2 = öm-pöhualli → implies öm-pöhualli = 2 × cem-pöhualli \nSo unless cem-pöhualli = 1, then öm-pöhualli > cem-pöhualli\n\nEquation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n\"mahtlactli-om-ëyi\" suggests (1 - something) × ëyi → but \"mahtlactli-om-ëyi\" could be 1 - ëyi?\n\nAlternatively, structure: A × B = C \nIn (6): mäcuïlli × ëyi = caxtölli \nIn (4): mäcuïlli + öme = chicöme \nSo adding and multiplying — could be using a base 20 system?\n\nLook at equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis looks like a large number formed by combining base numerals.\n\nPossibly, numerals are built using a base (e.g., 20), with place values via \"on\" or \"om\".\n\nWe observe that in (13) and (14), compound forms suggest multiplication or composition.\n\nNow, equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nWe need to interpret what this means.\n\nAlternate approach: from equation (4): \nmäcuïlli + öme = chicöme \nSuppose öme = 2 → so if mäcuïlli = ? then chicöme = mäcuïlli + 2\n\nEquation (6): mäcuïlli × ëyi = caxtölli \nSo mäcuïlli × ëyi = caxtölli\n\nEquation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nAgain, mahtlactli-om-ëyi may represent 1 - ëyi? Unlikely.\n\nAlternatively, \"om\" might mean \"plus\" or \"and\", or just a structural connector.\n\nWait — from (2): cem-pöhualli × öme = öm-pöhualli \nSuppose öme = 2 → then cem-pöhualli × 2 = öm-pöhualli \nSo öm-pöhualli = 2 × cem-pöhualli\n\nSuppose cem-pöhualli = 1 → then öm-pöhualli = 2 \nSo öm-pöhualli = 2 \nThen öme = 2\n\nNow from (4): mäcuïlli + 2 = chicöme → so mäcuïlli + öme = chicöme\n\nFrom (6): mäcuïlli × ëyi = caxtölli \nSuppose mäcuïlli = 1 → then 1 + 2 = chicöme = 3 \nAnd 1 × ëyi = caxtölli → so caxtölli = ëyi\n\nBut in (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nIf mahtlactli = 1, then 1-om-ëyi → maybe 1 - ëyi?\n\nIf ëyi = 2, then 1-2 = -1? Unlikely.\n\nPerhaps \"mahtlactli-om-ëyi\" = (1 × something)\n\nAlternatively, the \"on\" and \"om\" are structural markers.\n\nIn (1): (A-on-cë) × A = B\n\nIf A = mahtlactli = 1, A-on-cë = 2 → 2 × 1 = 2\n\nResult: mäcuïl-pöhualli-om-mahtlactli → could be a fixed form for 2?\n\nBut “mäcuïl-pöhualli” might be a base.\n\nEquation (1): 2 × 1 = mäcuïl-pöhualli-om-1 → so 2 = mäcuïl-pöhualli-om-1?\n\nThen in (2): cem-pöhualli × 2 = öm-pöhualli \nSo (cem) × 2 = (öm) → if öm = 4, then cem = 2\n\nBut earlier we had öm-pöhualli = 2? Contradiction.\n\nWait, from (2): cem-pöhualli × öme = öm-pöhualli\n\nSuppose öme = 2 → cem × 2 = öm → so öm = 2 × cem\n\nNow suppose that cem = 1 → öm = 2\n\nBut in (1), 2 × 1 = mäcuïl-pöhualli-om-1 → so 2 is represented as mäcuïl-pöhualli-om-1\n\nSo if öm = 2, it’s represented as öm-pöhualli → so öm-pöhualli = 2\n\nSo öm = 2\n\nThen from (2): cem × 2 = 2 → cem = 1\n\nSo cem = 1\n\nNow equation (4): mäcuïlli + 2 = chicöme\n\nEquation (6): mäcuïlli × ëyi = caxtölli\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nSince cem-pöhualli = 1 → the right-hand side is 1-on-caxtölli-on-nähui\n\nSo (A) × ëyi = 1-on-caxtölli-on-nähui\n\nIf ëyi = 3 → then A × 3 = something involving 1, caxtölli, nähui\n\nSuppose A = mahtlactli-om-ëyi → if mahtlactli = 1, then 1-om-3 → not clear.\n\nAlternative idea: in (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nyë-pöhualli-on-chicöme: could be \"x on chicöme\" → \"x + chicöme\"? \nIf yë = 1 → then 1-on-chicöme → could be 1 + chicöme?\n\nThen plus mahtlactli-on-nähui → 1 + chicöme + 1 + nähui = näuh-pöhualli-on-cë?\n\nNot clear.\n\nBut notice from (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe are told to write 43; 569 in Arammba.\n\nThe structure (a-on-b-on-c-on-d) appears in Nahuatl — perhaps indicating a base-20 system with digits.\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe need to extract what each component might mean.\n\nIn the Arammba equations, we have:\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ 2 × ngámbi = ngámbi × yànparo\n\nLet ngámbi = A \nThen 2A = A × yànparo → so if A ≠ 0 → 2 = yànparo\n\nSo yànparo = 2\n\n(8) ngámbi + asàr = tambaroy \n→ A + asàr = tambaroy\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (yànparo) tàxwo + (fete asàr) tàxwo = yànparo fete\n\n\"tàxwo\" means \"times\"? or \"with\" or \"and\"?\n\nBut: (2) × (asàr) + (fete × asàr) = 2 × fete? \nLeft: (2) + (asàr) → no.\n\nWait: (yànparo tàxwo) = (2) × (towards)? \n\"tàxwo\" may mean \"multiplied by\" or \"combined with\"\n\nSo (yànparo tàxwo) = 2 × (something)? \nBut the equation: (yànparo tàxwo) + (fete asàr tàxwo) = yànparo fete\n\nThis suggests: (2 × X) + (fete × asàr) = 2 × fete\n\nUnclear.\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (Y) × (Y tàxwo) = (fete Y tàxwo)\n\nSo Y × (Y with \"tàxwo\") = (fete with Y with \"tàxwo\")\n\nLet Y = yenówe\n\nThen Y × (Y × something) = fete Y something\n\nThis suggests: Y × (Y × X) = fete (Y × X)\n\nSo Y² × X = fete (Y × X) → implies Y² = fete? Only if X cancels.\n\nThen Y² = fete\n\nSo fete = (yenówe)²\n\n(11) nimbo × fete = tarumba \nSo nimbo × (Y²) = tarumba\n\n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (2 × something) = (yenówe × something)\n\nNow, from (10): Y × (Y × X) = fete × (Y × X) \nSo Y² X = fete Y X → so Y² = fete\n\nSo fete = Y²\n\nThen (11): nimbo × Y² = tarumba\n\n(12): nimbo + (2 × X) = (Y × X) → wait, \"yànparo tàxwo\" = 2 × X? or 2?\n\nFrom (7): yànparo = 2\n\n\"yànparo tàxwo\" = 2 × (something)? Or is it 2?\n\nAssume \"tàxwo\" means \"multiplied by\" or \"with\".\n\nSo \"yànparo tàxwo\" = 2 × (some unit), perhaps.\n\nBut (9): (yànparo tàxwo) + (fete asàr tàxwo) = yànparo fete\n\nLet’s suppose that \"asàr\" is a number — perhaps 1 or 3.\n\n(8): ngámbi + asàr = tambaroy → so A + asàr = tambaroy\n\n(7): 2A = A × yànparo → yànparo = 2\n\nSo yànparo = 2\n\n(9): (2 × X) + (fete × asàr) = 2 × fete\n\nWe don’t know X or asàr.\n\n(10): yenówe × (yenówe × asàr) = fete × (yenówe × asàr) \nWait, the structure is: \nyenówe × (yenówe tàxwo) = fete × (yenówe tàxwo)\n\nSo Y × (Y) = fete × Y → so Y = fete\n\nBut earlier we said Y² = fete → contradiction.\n\nUnless \"tàxwo\" means \"times\"\n\nSo (10): Y × (Y × asàr) = fete × (Y × asàr)\n\nSo Y² × asàr = fete × (Y × asàr)\n\nDivide both sides by (Y × asàr) → Y = fete\n\nSo fete = Y\n\nBut previously from (10), we had Y × (Y × asàr) = fete × (Y × asàr) → so Y = fete\n\nSo fete = yenówe\n\nThen (11): nimbo × fete = nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nNow yànparo = 2\n\n\"yànparo tàxwo\" = 2 × (something)? or is it 2?\n\nSuppose \"yànparo tàxwo\" = 2 (unit), then (12): nimbo + 2 = yenówe (with \"tàxwo\")\n\n\"yenówe tàxwo\" = yenówe × something?\n\nIf \"tàxwo\" means \"multiplied by\", then \"yenówe tàxwo\" = yenówe × X\n\nSo: nimbo + 2 = (yenówe × X)\n\nBut we don't know X.\n\nFrom (8): ngámbi + asàr = tambaroy → A + asàr = tambaroy\n\nNo values.\n\nNow, from (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe need to find the value of this expression.\n\nSimilarly, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nNow let’s try to deduce the structure.\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nThis suggests that \"cen-tzontli\" is a compound form equal to the product or sum of several values.\n\nSimilarly, (16): cen-xiquipilli = weremeke tarumba", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9555.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Identify the number systems in both languages.\n\nIn Nahuatl, the examples show operations involving numerals and their combinations. Look for patterns in the structure and composition of numbers.\n\nExample (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ \"on-cë\" may mean \"plus one\", \"unit\", or \"increment\", possibly indicating a number structure involving addition.\n\nBut more interestingly, observe structure of (4): \nmäcuïlli + öme = chicöme \nThis may represent a number combining units and a base.\n\nSimilarly, (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuggests additive formation.\n\nHowever, in (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nThis appears to be multiplication with a base, possibly modular, and formed as direct product.\n\nWe now examine equations for number patterns in Nahuatl and map them to Arammba via (13)-(16), which directly give translations.\n\nStep 2: Use the translation equations (13)-(16) to extract number structures.\n\nEquation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nBreak it down: \n\"yë-tzontli\" may be a base unit (e.g., 1 or 10). \n\"on-cë\" likely means \"plus one\" → possibly a unit increment. \n\"pöhualli\" is a recurring element in Nahuatl: in (1), (2), (4), it appears in compound numerals.\n\nLook at (2): cem-pöhualli × öme = öm-pöhualli \nHere: cem-pöhualli × öme → öm-pöhualli \nseems like multiplication may assimilate or simplify. \nBut: cem-pöhualli = 2 × pöhualli? cem = two? \nSo, 2 × öme = öm-pöhualli → suggests öme is a unit (e.g., one), and \"öm-pöhualli\" is 2×1? \n\nContradiction: left side: 2 × öme → right: öm-pöhualli \nIf öme = 1, then left = 2 → right = 2×pöhualli → so öm-pöhualli = 2×pöhualli? \nSo öm = 2? → thus \"öm\" is a numeral for two.\n\nIn (4): mäcuïlli + öme = chicöme \nIf mäcuïlli = 1 (from (1), mäcuïl-pöhualli=1), then 1 + 2 = 3 → chicöme = 3 \nSo we can start assigning:\n\n- öme = 2 \n- mäcuïlli = 1 \n- mäcuïl-pöhualli = 1 (as in (1)) \n- cem = 2 \n- cem-pöhualli = 2 × pöhualli \n\nEquation (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"on-cë\" = \"plus one\" or \"unit\", so \"mahtlactli-on-cë\" = mahtlactli + 1 \nLet mahtlactli = x → (x+1) × x = mäcuïl-pöhualli-om-mahtlactli \nRight side: mäcuïl-pöhualli-om-mahtlactli → could be 1×pöhualli plus mahtlactli → 1×pöhualli + x \nBut this is not algebraically matching unless x is known.\n\nAlternatively, from earlier:\n(4): mäcuïlli + öme = chicöme → 1 + 2 = 3 → chicöme = 3 \n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nLet ëyi = y → (x–y) × y = cem-pöhualli-on-caxtölli-on-nähui \nBut hard to parse.\n\nBut look at (6): mäcuïlli × ëyi = caxtölli \nIf mäcuïlli = 1 → 1 × ëyi = caxtölli → ëyi = caxtölli \nSo, caxtölli = ëyi\n\nPlug into (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (x – ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nBut caxtölli = ëyi → so: (x – ëyi) × ëyi = cem-pöhualli-on-ëyi-on-nähui \nThis resembles multiplication with carries.\n\nNow, from (1): (x+1) × x = mäcuïl-pöhualli-om-mahtlactli \nRight: 1×pöhualli + x → so left = right → (x+1)x = x + 1×pöhualli \n→ x² + x = x + pöhualli \n→ x² = pöhualli \n\nThus, pöhualli = x²\n\nNow, if pöhualli = x², and cem-pöhualli = 2×pöhualli → 2x² \nThen in (2): cem-pöhualli × öme = öm-pöhualli \n→ (2x²) × 2 = öm-pöhualli → 4x² = öm-pöhualli \nBut öm-pöhualli = öm × pöhualli = öm × x² \nSo: 4x² = öm × x² → öm = 4\n\nThus: \nöme = 2 \nöm = 4 \npöhualli = x² \nx = mahtlactli → so x² = pöhualli\n\nNow equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n\nBreak this down: \n\"yë-tzontli\" → likely a base unit \n\"on-näuh-pöhualli\" → possibly 1 × pöhualli \n\"on-caxtölli\" → x? \n\"on-cë\" → +1 \n\nSo entire expression: yë-tzontli + (näuh × pöhualli) + caxtölli + 1?\n\nBut \"näuh-pöhualli\" might mean 1×pöhualli → so right-hand side ndamno is likely a numeral.\n\nWe now try to deduce what 43 and 569 are in Nahuatl numerals.\n\nWe have:\n- mäcuïlli = 1\n- öme = 2\n- cem = 2 (in cem-pöhualli)\n- pöhualli = x² (x = mahtlactli)\n- caxtölli = ëyi\n\nIn (13), \"yë-tzontli\" is likely the base unit — could it be 1?\n\nAssume yë-tzontli = 1 → then \"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\" → 1 + (näuh × pöhualli) + caxtölli + 1 → possible.\n\nBut \"on-cë\" is +1 — so possibly an additive unit.\n\nBut in (13), yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nNow balance: 43 and 569 must be expressible in this system.\n\nWe don’t have a full number system table — but from (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nCompare to (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSo both have \"cen-tzontli\" as base.\n\nIn Nahuatl: \n\"cen-tzontli\" = base\n\nThen in (14): cen-tzontli + cem-pöhualli + om-mahtlactli + om-öme → equals yànparo tarumba\n\nWe don’t have direct mapping — but in Arammba, (12): \nnimbo + yànparo tàxwo = yenówe tàxwo \n(11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × fete → multiplicative\n\nAlso (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (y × y) × tàxwo = fete × y × tàxwo → so y² × tàxwo = fete × y × tàxwo → y = fete \nSo yenówe = fete\n\n(11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo → so nimbo + yànparo = yenówe? (if tàxwo is a unit)\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nLeft: (yànparo + fete) asàr? But “tàxwo” appears only with yànparo and fete\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ if \"tàxwo\" is a unit, then: (yànparo + fete) × asàr = yànparo × fete? \nOnly if asàr = 1 → contradicts.\n\nAlternatively: \"tàxwo\" might be a prepositional particle or \"added to\" → “+” operator.\n\nSo: [yànparo + fete] asàr → [or a compound: yànparo-fete]?\n\nBut left: (yànparo tàxwo) + (fete asàr tàxwo) → is that (A + B) with suffix?\n\nEquation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ So addition: yànparo + fete = yànparo fete? \nWith a transformation?\n\n→ Suggests that fete is a unit: “asàr” is a multiplier?\n\nAssume: \n“asàr” = 2 \n“tàxwo” = a communal or associative particle.\n\nThen: yànparo + fete → considered as a compound with asàr? \nBut result is yànparo fete → no number.\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ left: y × y \nright: f × y \nso y × y = f × y → y = f → yenówe = fete\n\nSo fete = yenówe\n\nIn (11): nimbo × fete = tarumba → nimbo × yenówe = tarumba\n\nIn (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + yànparo = yenówe?\n\nThen from (12): nimbo = yenówe – yànparo\n\nBut from (11): tarumba = nimbo × yenówe = (yenówe – yànparo) × yenówe \n= yenówe² – yànparo × yenówe\n\nAlso (15): cen-tzontli = tarumba tambaroy fete asàr \n→ base = (tarumba) (tambaroy) (fete) (asàr)\n\nSimilarly, (16): cen-xiquipilli = weremeke tarumba nimbo yànparo \n→ base = weremeke tarumba nimbo yànparo\n\nNow back to (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nWe suspect \"yë-tzontli\" = 1 \n\"on-näuh-pöhualli\" = 1 × pöhualli \n\"on-caxtölli\" = caxtölli \n\"on-cë\" = +1\n\nSo total: 1 + pöhualli + caxtölli + 1 = ndamno\n\nBut earlier, pöhualli = x², x = mahtlactli\n\nWe need to assign number values.\n\nFrom (4): mäcuïlli + öme = chicöme → 1 + 2 = 3 → chicöme = 3 \nSo numerals: \n1 = mäcuïlli \n2 = öme \n3 = chicöme \n\nThen, from earlier: in (1), mahtlactli × (mahtlactli + 1) = mäcuïl-pöhualli-om-mahtlactli \nWe had: x(x+1) = pöhualli + x → so x² = pöhualli \n→ pöhualli = x² → so x² is the value of pöhualli\n\nBut x = mahtlactli → so x is the base\n\nTry x = 1 → pöhualli = 1 → then mahtlactli = 1 → so mahtlactli-on-cë = 2 → (1+1)×1 = 2 → equals 1×1 +1 = 2 → matches \n→ pöhualli = 1\n\nThen (2): cem-pöhualli × öme = öm-pöhualli \n→ 2×1 × 2 = 4 → so öm-pöhualli = 4 \n→ öm = 4 → since pöhualli = 1 \n\nThen (4): 1 + 2 = 3 → chicöme = 3\n\n(5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (1 – y) × y = 2×1 + caxtölli + nähui \n→ (1 – y)y = 2 + caxtölli + nähui \nBut left side: y – y² → if y=1 → 0 → not possible \nIf y=0 → undefined \nSo x ≠ 1\n\nTry x = 2 \nThen pöhualli = 4 \nmahtlactli = 2 \n(2+1)×2 = 6 \nRight: mäcuïl-pöhualli-om-mahtlactli = 1×4 + 2 = 6 → matches\n\n(2): cem-pöhualli = 2×4 = 8 \n× öme = 2 → 8×2 = 16 \nRight: öm-pöhualli = öm×4 → so 16 = 4×4 → öm = 4 → matches earlier\n\n(4): 1 + 2 = 3 → chicöme = 3\n\n(5): (mahtlactli-om-ëyi) × ëyi = (2 – y) × y = cem-pöhualli-on-caxtölli-on-nähui \n→ (2 – y)y = 8 + caxtölli + nähui \n(6): mäcuïlli × ëyi = caxtölli → 1 × y = caxtölli → caxtölli = y\n\nSo (2–y)y = 8 + y + nähui → \n2y – y² = 8 + y + nähui \n→ y – y² = 8 + nähui\n\nLeft: y(1 – y) \nMust be negative → right: 8 + nähui → positive → impossible\n\nSo contradiction.\n\nTry x = 3 \npöhualli = 9 \nmahtlactli = 3 \n(3+1)×3 = 12 \nRight: 1×9 + 3 = 12 → matches\n\n(2): 2×9 = 18 × 2 = 36 → öm×9 = 36 → öm = 4 → still works\n\n(5): (3 – y)y = 2×9 + y + nähui = 18 + y + nähui \n(6): caxtölli = y \nSo (3–y)y = 18 + y + nähui \n3y – y² = 18 + y + nähui \n2y – y² = 18 + nähui\n\nLeft: y(2 – y) \nMax at y=1 → 1 → too small → max 1 at y=1\n\nBut 18 + nähui ≥ 18 → impossible\n\nThus contradiction.\n\nSo pöhualli cannot be x².\n\nAlternative interpretation of (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n\"on-cë\" = \"added\", so left = (x+1)×x \nRight: mäcuïl-pöhualli-om-mahtlactli → = pöhualli + x\n\nSo (x+1)x = pöhualli + x → x² + x = pöhualli + x → x² = pöhualli\n\nMust be true → so pöhualli = x²", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9359.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to deduce how numbers are formed in Arammba, specifically to write **43** and **569** in Arammba.\n\nWe are to solve only part (c): write 43; 569 in Arammba.\n\n---\n\n**Step 1: Understand the structure of the numerical system via examples**\n\nWe first analyze the equations to deduce operations and number formation patterns.\n\n---\n\n**Look at Nahuatl equations:**\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nNote: \"mahtlactli\" is likely a unit of count. The result involves \"mäcuïl-pöhualli\" which may involve a compound structure.\n\n(2) cem-pöhualli × öme = öm-pöhualli \n→ cem-pöhualli × öme = öm-pöhualli \nPerhaps \"cem-pöhualli\" is a number (like 2), \"öme\" = 2, result = \"öm-pöhualli\" = 4? Possibly such a compound is associative.\n\n(3) yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nAddition of two numbers.\n\n(4) mäcuïlli + öme = chicöme \n→ Something like 1 + 2 = 3? Or 3 = 1 + 2.\n\n(5) mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ (X × Y) = Z\n\n(6) mäcuïlli × ëyi = caxtölli \n→ (1 × Y) = caxtölli? Perhaps caxtölli is \"Y\".\n\nWait — in (6): mäcuïlli × ëyi = caxtölli \nIf mäcuïlli is a unit (like 1), and × ëyi yields caxtölli, then caxtölli = ëyi \nSo ëyi is a numeral and caxtölli = ëyi.\n\nSimilarly, in (4): mäcuïlli + öme = chicöme \nSo 1 + öme = chicöme → chicöme = 1 + öme \nSo if öme = 2, then chicöme = 3.\n\nIn (2): cem-pöhualli × öme = öm-pöhualli \nSuppose cem-pöhualli = 2, öme = 2 → 2×2 = 4 → öm-pöhualli = 4 \nSo öm-pöhualli = 4 \nSo numbers: \nöme = 2 \nöm-pöhualli = 4 \nchicöme = 3 \nmäcuïl-pöhualli = ? from (1)\n\n(1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nPossibly (A × A) = (some number) \nmahtlactli is likely a base unit (e.g., 1)\n\nSo if mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ 1×1 = 1 → so the product is 1, but structured as mäcuïl-pöhualli-om-mahtlactli? That suggests mäcuïl-pöhualli = 1? Unlikely.\n\nAlternative: Perhaps the compound represents multiplication with a base.\n\nAnother idea: In Nahuatl, numbers are formed via compound expressions involving \"pöhualli\" (day), \"mahtlactli\" (day or count), etc.\n\nBut instead of focusing on Nahuatl numerals directly, observe the **Arammba equations**.\n\n---\n\n**Arammba equations:**\n\n(7) ngámbi + ngámbi = ngámbi × yànparo \n→ ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = x \nThen: x + x = x × yànparo \n→ 2x = x × yànparo \nDivide both sides by x (if x ≠ 0): \n2 = yànparo \n→ yànparo = 2\n\n(8) ngámbi + asàr = tambaroy \n→ x + asàr = tambaroy \nCould be 1 + 2 = 3 (if asàr = 2) → tambaroy = 3\n\n(9) yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (yànparo + fete) asàr × something? Wait.\n\n\"yànparo tàxwo\" = yànparo with \"täxwo\" (possibly a modifier like \"times\")\n\nSo: (yànparo × tàxwo) + (fete × asàr × tàxwo) = yànparo fete \n\nNot clear.\n\n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo \n→ (Y × Y tàxwo) = fete Y tàxwo\n\n→ Y × (Y × tàxwo) = fete Y tàxwo \n→ Y × Y × tàxwo = fete Y tàxwo \nSo Y² × tàxwo = fete × Y × tàxwo \nDivide both sides by Y × tàxwo (≠0): \nY = fete \n→ yenówe = fete\n\n(11) nimbo × fete = tarumba \n→ nimbo × fete = tarumba \nWe just got fete = yenówe → so nimbo × yenówe = tarumba\n\n(12) nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (yànparo × tàxwo) = yenówe × tàxwo\n\nWe know yànparo = 2 from (7). So:\n\nnimbo + (2 × tàxwo) = yenówe × tàxwo\n\nBut from (10), we deduced yenówe = fete\n\nSo: nimbo + 2×tàxwo = fete × tàxwo\n\nSo: nimbo = (fete × tàxwo) - 2×tàxwo = (fete - 2) × tàxwo\n\nSo nimbo depends on tàxwo.\n\nNow, (15): cen-tzontli = tarumba tambaroy fete asàr \n→ cen-tzontli = tarumba + tambaroy + fete + asàr \n(?) \nLikely meaning: a number (cen-tzontli) = sum of those compound terms.\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nWe may assume that \"cen-\" is a numeral prefix (possibly 100 or something).\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSo if cen-tzontli is 100, then:\ntarumba + tambaroy + fete + asàr = 100\n\nWe already suspect:\n- yànparo = 2\n- fete = yenówe\n- from (8): ngámbi + asàr = tambaroy\n- assume ngámbi = 1 → then tambaroy = 1 + asàr\n- from (10): fete = yenówe\n- from (10) and (12): both involve × tàxwo, so perhaps \"täxwo\" means \"times\" or \"multiply\"\n\nKey: Arammba seems to have a **multiplicative** and **additive** structure.\n\nNow, go to the joined equations:\n\n(13) yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14) cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15) cen-tzontli = tarumba tambaroy fete asàr \n(16) cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nOur goal: write 43 and 569 in Arammba.\n\nWe are told to derive from the pattern.\n\nLet’s examine equation (15): \ncen-tzontli = tarumba + tambaroy + fete + asàr \nAnd we are to interpret \"cen-tzontli\" — the prefix \"cen-\" likely means \"100\" (as in \"cent\" or \"hundred\") — this is a common pattern in numeral systems.\n\nSo \"cen-tzontli\" = 100 → so:\ntarumba + tambaroy + fete + asàr = 100\n\nLet’s now count the terms:\n\nWe have:\n- from (8): ngámbi + asàr = tambaroy → if ngámbi = 1, then tambaroy = 1 + asàr \n- from (10): yenówe = fete \n- from (11): nimbo × fete = tarumba \n- from (12): nimbo + 2×tàxwo = fete × tàxwo → nimbo = (fete - 2) × tàxwo\n\nWe have many variables, but perhaps the system is designed so that the number \"100\" is decomposed into:\ntarumba + tambaroy + fete + asàr = 100\n\nLet’s make substitutions.\n\nLet fete = x → yenówe = x \nThen from (12): nimbo = (x - 2) × tàxwo \nFrom (11): tarumba = nimbo × x = (x - 2) × tàxwo × x\n\nFrom (8): tambaroy = 1 + asàr\n\nSo total sum:\ntarumba + tambaroy + fete + asàr = \n(x-2)x tàxwo + (1 + asàr) + x + asàr \n= x(x-2) tàxwo + 1 + asàr + x + asàr \n= x(x-2) tàxwo + x + 1 + 2asàr\n\nSet this equal to 100:\n\nx(x-2) tàxwo + x + 1 + 2asàr = 100\n\nNow we also need consistent values. Perhaps we assume that \"täxwo\" is a multiplicative operator, and \"täxwo\" may represent a number (like 1), or it may be a functional operator.\n\nWait — in equation (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \nLeft: (2 × tàxwo) + (fete × asàr × tàxwo) = yànparo × fete = 2 × fete\n\nSo: \n2×tàxwo + (fete × asàr × tàxwo) = 2 × fete \nDivide both sides bytàxwo (≠0): \n2 + fete × asàr = 2 × (fete / tàxwo) → not consistent.\n\nWait, original (9): \n\"yànparo tàxwo + fete asàr tàxwo = yànparo fete\" \nLikely: (yànparo × tàxwo) + (fete × asàr × tàxwo) = yànparo × fete\n\nSo: \n2×tàxwo + x × asàr × tàxwo = 2 × x \nDivide both sides by tàxwo: \n2 + x × asàr = 2x / tàxwo → messy.\n\nAlternatively, suppose that \"täxwo\" means \"×\" — the multiplication operator.\n\nThen (9): \n(yànparo × tàxwo) + (fete × asàr × tàxwo) = yànparo × fete \n→ (2 × ×) + (x × asàr × ×) = 2 × x → not helpful.\n\nBut perhaps \"täxwo\" is just a modifier, like \"times\", and used in compounds.\n\nAlternatively, focus on known value from (15): \ncen-tzontli = sum of four terms = 100\n\nSo the idea is that 100 is composed as:\ntarumba + tambaroy + fete + asàr = 100\n\nWe suspect:\n- ngámbi = 1 (smallest unit)\n- asàr = a number\n- tambaroy = 1 + asàr\n- fete = x\n- tarumba = nimbo × x\n- nimbo = (x - 2) × (some base)\n\nBut back to (12): \nnimbo + 2×täxwo = x × täxwo \n→ nimbo = (x - 2) × täxwo\n\nNow assume that täxwo = 1 → simplest, then:\nnimbo = (x - 2) \ntarumba = nimbo × x = x(x - 2)\n\nThen from (15):\ntarumba + tambaroy + fete + asàr = x(x-2) + (1 + asàr) + x + asàr \n= x² - 2x + 1 + asàr + x + asàr \n= x² - x + 1 + 2asàr = 100\n\nSo:\nx² - x + 1 + 2asàr = 100 \n→ x² - x + 2asàr = 99 \n→ 2asàr = 99 - x² + x \n→ asàr = (99 - x² + x)/2\n\nasàr must be a positive integer. So 99 - x² + x must be even and positive.\n\nTry small integer values for x (fete):\n\nTry x = 3: \n99 - 9 + 3 = 93 → 93/2 = 46.5 → not integer\n\nx = 4: \n99 - 16 + 4 = 87 → 87/2 = 43.5 → no\n\nx = 5: \n99 - 25 + 5 = 79 → 79/2 = 39.5 → no\n\nx = 6: \n99 - 36 + 6 = 69 → 34.5 → no\n\nx = 7: \n99 - 49 + 7 = 57 → 28.5 → no\n\nx = 8: \n99 - 64 + 8 = 43 → 43/2 = 21.5 → no\n\nx = 9: \n99 - 81 + 9 = 27 → 13.5 → no\n\nx = 10: \n99 - 100 + 10 = -1 → negative → invalid\n\nNo solution for täxwo = 1\n\nTry täxwo = 2\n\nThen:\nnimbo = (x - 2) × 2 = 2x - 4 \ntarumba = nimbo × x = x(2x - 4) = 2x² - 4x\n\ntambaroy = 1 + asàr \nfete = x \n\nSum: 2x² - 4x + (1 + asàr) + x + asàr = \n2x² - 3x + 1 + 2asàr = 100 \n2x² - 3x + 2asàr = 99 \n→ 2asàr = 99 - 2x² + 3x \n→ asàr = (99 - 2x² + 3x)/2\n\nTry integer x.\n\nx = 3: \n99 - 18 + 9 = 90 → 90/2 = 45 → integer → asàr = 45\n\nValid.\n\nNow check if any equations support this.\n\nCheck (12): nimbo + 2×täxwo = fete × täxwo \ntäxwo = 2 \nnimbo = 2×3 - 4 = 2 \nLeft: 2 + 4 = 6 \nRight: 3 × 2 = 6 → yes.\n\n(11): nimbo × fete = tarumba \nnimbo = 2, fete = 3 → tarumba = 6 \nFrom above: tarumba = 2x² - 4x = 2×9 - 12 = 18 - 12 = 6 → yes.\n\n(8): ngámbi + asàr = tambaroy \nngámbi = 1 → tambaroy = 1 + 45 = 46 → consistent.\n\n(15): sum = tarumba (6) + tambaroy (46) + fete (3) + asàr (45) = 6+46+3+45 = 100 → good.\n\nSo the values work with:\n- fete = 3\n- asàr = 45\n- täxwo = 2\n- ngámbi = 1\n- nimbo = 2\n- yànparo = 2 → from earlier\n\nNow we know:\n- fete = 3\n- asàr = 45\n- nagmbi = 1 → unit\n- nimbo = 2\n- yànparo = 2\n- tarumba = 6\n\nNow, what about the base system?\n\nWe are to write **43** and **569** in Arammba.\n\nWe have:\n- \"cen-tzontli\" = 100\n- So 100", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9234.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We are given a set of Kunuz Nubian sentences and their English translations. The task is to translate five new sentences (11–15) into English, based on the linguistic patterns observed in the original examples.\n\nStep 1: Identify core grammatical patterns.\n\nLook at basic sentence structures:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu → We bought the camels for the neighbours. \n→ Subject + verb (past) + object + prepositional phrase (for X) \n\"kanarriːcciːg\" = bought (past, 3rd person, plural or generic) \n\"ar\" = we \n\"kamiːg\" = the camels \n\"jaːnticcirsu\" = for the neighbours \n\n→ Pattern: [Subject] [verb] [object] [preposition + recipient] \n\n2. tirt kadeːg allesu → The owner repaired the dress. \n\"tirt\" = repaired \n\"kadeːg\" = the dress \n\"allessu\" = (the) owner → so \"tirt\" is transitive verb (repair), \"kadeːg\" is object, \"allessu\" is subject → subject is mentioned last? Wait: \"tirt kadeːg allesu\" → The owner repaired the dress → So \"tirt\" is verb, \"kadeːg\" is object, \"allessu\" is subject. \n→ So structure: [Subject] [verb] [object] → \"allessu tirt kadeːg\" would be expected. But it’s \"tirt kadeːg allesu\" → verb-object-subject? That can’t be.\n\nWait: \"tirt kadeːg allesu\" → The owner repaired the dress → So \"tirt\" = repaired, \"kadeːg\" = the dress (object), \"allessu\" = the owner (subject), so likely structure: [verb] [object] [subject] — unusual.\n\nBut in sentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu → we bought the camels for the neighbours → ar = subject, kanarriːcciːg = verb, kamiːg = object, jaːnticcirsu = for neighbours → subject verb object prepositional phrase → so in 1: [S] [V] [O] [PP]\n\nNow check 2: tirt kadeːg allesu → the owner repaired the dress → if \"tirt\" is verb, \"kadeːg\" is object, \"allessu\" is subject → this suggests that subject is placed at end, and verb-object-subject is a pattern?\n\nBut in 3: jahali waliːg darbadki biticcirra → the young men will give the chicken to the dogs \n\"jahali\" = young men (subject), \"waliːg\" = will (future), \"darbadki\" = give, \"biticcirra\" = to the dogs → [S] [future] [V] [PP] → so verb stands between subject and object?\n\nIn 4: man jahalgi kadeːcciːg maːgtirsu → he stole the dresses for the young man \n\"man\" = he, \"jahalgi\" = stole, \"kadeːcciːg\" = the dresses, \"maːgtirsu\" = for the young man → [S] [V] [O] [PP] → again, subject-verb-object-for-recipient\n\nIn 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces \n\"ay\" = I, \"beyyeːcciːg\" = buying (present), \"ajaːnirri\" = the necklaces → [S] [V] [O] → simple\n\n6: wal aygi baːbiːg eldeːnsu → The dog found the doors for me \n\"wal\" = dog, \"aygi\" = found, \"baːbiːg\" = the doors, \"eldeːnsu\" = for me → [S] [V] [O] [PP]\n\n7: magas ikki waliːg ticcirsu → The thief gave you (pl.) the dogs \n\"magas\" = thief, \"ikki\" = you (pl.), \"ticcirsu\" = gave? But \"ticcirsu\" is past, \"gave\", and \"ikki\" is object? Wait: \"ikki waliːg\" = you (pl.), \"ticcirsu\" = gave → so likely: [S] [V] [O] → thief gave you the dogs → so object is \"ikki waliːg\" → so \"ikki\" = you (pl.), a pronoun for object\n\n8: iːdi magaski kamiːg tirsa → The men gave the camels to the thief \n\"iːdi\" = the men (subject), \"magaski\" = the camels (object), \"tirsa\" = to the thief → [S] [O] [to object] → so object is first, then \"to\" + recipient\n\nWait — now contradiction: in 1: ar kanarriːcciːg kamiːg jaːnticcirsu → subject-verb-object-for-recipient \nIn 8: iːdi magaski kamiːg tirsa → subject-object-to-recipient \nDifferent order.\n\nSo both can’t be correct unless the verb is not transitive.\n\nWait: verb in 8: \"tirsa\" = to give? \"tirsa\" likely means \"to give\", and \"magaski kamiːg\" = the camels (object), then \"tirsa\" = to give → so \"to the thief\" → so structure: [S] [O] [to R] → so object is before the recipient → different from 1.\n\nBut in 1: ar kanarriːcciːg kamiːg jaːnticcirsu → subject (we) + verb (bought) + object (camels) + for neighbours → object before for-phrase.\n\nIn 8: iːdi magaski kamiːg tirsa → subject (men) + object (camels) + to thief → object before prepositional phrase.\n\nBut in 7: magas ikki waliːg ticcirsu → thief gave you the dogs → \"ikki waliːg\" = you (pl.), \"ticcirsu\" = gave → so [S] [O] [V]? → no, \"ticcirsu\" is verb, so \"ikki waliːg\" is object → \"gave\" is verbal.\n\nSo 7: \"magas\" = thief (subject), \"ikki waliːg\" = you (pl.), \"ticcirsu\" = gave → so [S] [O] [V]? — no, verb is last.\n\nStructure: [S] [O] [V] → thief gave you the dogs → but \"ticcirsu\" = gave, so verb is at end → so verb is not transitive in the same way.\n\nThis suggests that in some cases, object comes before verb, in others, object comes after.\n\nWe need to find consistent patterns.\n\nAlternative idea: verb may carry a meaning that includes direction or recipient.\n\nFocus on verbs with object and recipient.\n\nLook at 8: iːdi magaski kamiːg tirsa → the men gave the camels to the thief \n→ s: men, o: camels, r: to thief\n\nSentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu → we bought the camels for the neighbours → o: camels, r: for neighbours → so structure: S V O for R\n\nSentence 2: tirt kadeːg allesu → the owner repaired the dress → S: owner, V: repaired, O: dress → verb with object only — no recipient\n\nSentence 3: jahali waliːg darbadki biticcirra → young men will give the chicken to the dogs → S: young men, V: will give, O: chicken, R: to dogs → [S] [V] [O] [to R]\n\nSentence 4: man jahalgi kadeːcciːg maːgtirsu → he stole the dresses for the young man → S: he, V: stole, O: dresses, R: for young man → S V O for R\n\nSentence 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces → S I, V am buying, O necklaces → S V O\n\nSentence 6: wal aygi baːbiːg eldeːnsu → the dog found the doors for me → S: dog, V: found, O: doors, R: for me → [S] [V] [O] [for R]\n\nSentence 7: magas ikki waliːg ticcirsu → thief gave you (pl.) the dogs → S: thief, O: you (pl.), V: gave? → or V: gave, O: you the dogs → likely [S] [V] [O] → but object is \"ikki waliːg\" = you?\n\nWait — \"ikki waliːg\" is likely \"you (pl.)\" — a pronoun — so meaning: thief gave you the dogs → S gave O to whom?\n\nBut no recipient — so is \"ticcirsu\" used as \"give\" and \"ikki waliːg\" as object — but who did it to?\n\nPerhaps the object is the recipient?\n\nCompare to sentence 8: iːdi magaski kamiːg tirsa → men gave the camels to the thief → \"magaski kamiːg\" = the camels → object, \"tirsa\" = to thief → recipient\n\nSo in sentence 7: \"magas ikki waliːg ticcirsu\" → \"ikki waliːg\" is object? Or is it recipient?\n\n\"ikki waliːg\" = you (pl.) — likely object of the verb \"give\" — so \"thief gave you the dogs\" → S (thief), V (gave), O (you), but what is the thing given? \"the dogs\" — missing.\n\n\"ticcirsu\" could mean \"gave\", and the object is \"ikki waliːg\", but the thing given is missing.\n\nWait — no: standard structure is \"give [object] to [recipient]\" — so subject gives object to recipient.\n\nIn 7: \"magas ikki waliːg ticcirsu\" → if \"ikki waliːg\" is object, then \"to whom\" is missing.\n\nBut in 8: \"iːdi magaski kamiːg tirsa\" → \"tirsa\" means \"to the thief\" → so recipient is expressed by the verb? Not likely.\n\n\"tirsa\" is likely \"give to\" — so structure: subject + object + give to recipient?\n\nBut in 8: \"iːdi magaski kamiːg tirsa\" → \"tirsa\" could be a verb like \"to give\" — so \"men gave the camels to the thief\"\n\nSo likely the verb is \"give to\", and the object comes before.\n\nSimilarly in 3: jahali waliːg darbadki biticcirra → \"darbadki\" = give, \"biticcirra\" = to dogs → so \"to dogs\" at end\n\nIn 1 and 4 and 6: \"for neighbours\", \"for young man\", \"for me\"\n\nBut in 3: \"to the dogs\"\n\nSo \"to\" or \"for\" depending on meaning.\n\n\"for\" = purpose or intended use \n\"to\" = recipient\n\nImportant: in 1: \"bought the camels for the neighbours\" → purpose: to use the camels for neighbours \nIn 6: \"found the doors for me\" → found doors for me → purpose \nIn 4: \"stole the dresses for the young man\" → for use \nIn 3: \"give the chicken to the dogs\" → recipient \nIn 7: \"thief gave you the dogs\" → object is \"you\", so \"you\" is recipient? But \"ikki waliːg\" = you (pl.) — likely recipient, not object.\n\nSo in 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs → the object is \"the dogs\", not \"you\"\n\nBut \"ikki waliːg\" is not \"the dogs\" — it's a pronoun.\n\nSo what is missing?\n\nPerhaps the object is \"the dogs\", and \"ikki waliːg\" is recipient.\n\nBut the structure is: subject + recipient + verb + object → not standard.\n\nPerhaps the verb \"ticcirsu\" = give, and \"ikki waliːg\" = to you.\n\nBut \"ikki waliːg\" is a pronoun meaning \"you\", not \"to you\".\n\nCompare with sentence 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces → subject + verb + object\n\nSentence 10: sarkaːyi aygi beyyeːcciːg adeːnda → the cowards are giving me the necklaces → \"sarkaːyi\" = cowards, \"aygi\" = are giving, \"beyyeːcciːg\" = the necklaces, \"adeːnda\" = to me → so [S] [V] [O] [to R]\n\nSo consistent pattern: [S] [V] [O] [to R] or [for R]\n\nNow look at the words involved:\n\nWe are to translate:\n\n11. magasi argi ajomirra \n12. ay kanarriːg baːbki alletirsi \n13. hanu tirtiːg elirsu \n14. tirti argi kamgi deːccirsa \n15. ay darbadki bijaːndi\n\nFirst, list frequent verbs and their meanings:\n\n- kanarriːcciːg = bought (1) \n- tirt = repaired (2) \n- darbadki = give (3) \n- jahalgi = stole (4) \n- beyyeːcciːg = buying (5) \n- aygi = found (6) \n- ticcirsu = gave (7) \n- magaski = the camels (8) \n- kamiːg = the camels (1) \n- kadeːg = the dress (2) \n- baːbiːg = the doors (6) \n- waliːg = young men (3) \n- ikki = you (pl.) (7) \n- hanu = I will strike (9) \n- alletirsi = for me? (6) — \"wal aygi baːbiːg eldeːnsu\" → for me → \"eldeːnsu\" = for me \n- jaːnticcirsu = for the neighbours (1) \n- maːgtirsu = for the young man (4) \n- biticcirra = to the dogs (3) \n- bijaːndi = strike? (9) \n- deːccirsa = to the camels? (14) \n- argi = to? or for? \n- ajomirra = strike? or donkey? \n- elirsu = to the donkey?\n\nLet’s now analyze each sentence.\n\nSentence 11: magasi argi ajomirra \n\"magasi\" — look for patterns: in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"magas\" = men/thief, \"magaski\" = the camels \n\"magasi\" — similar to \"magas\", likely same root — could be \"the thief\" or \"the men\" \n\"argi\" — appears in 14: \"tirti argi kamgi deːccirsa\" → \"argi\" likely a preposition meaning \"to\" \n\"ajomirra\" — look at sentence 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = strike the donkey \nSo \"bijomri\" = strike the donkey \n\"ajomirra\" — perhaps \"strike the donkey\" — same root? \nYes — \"bj\" → strike, \"omir\" → donkey? \nIn 9: \"hanuːg bijomri\" = I will strike the donkey → \"hanuːg\" = I will, \"bijomri\" = strike the donkey → so \"bijomri\" = strike the donkey \nThus \"ajomirra\" = strike the donkey? But \"a\" prefix? \n\nPossibility: \"argi\" = to \nSo \"magasi argi ajomirra\" = the thief to strike the donkey? — illogical\n\n\"argi\" could be a verb? But in 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" = repaired? → \"tirt\" = repaired, \"tirti\" = past tense? \n\"tirti\" = repaired (past) \n\"argi\" → if verb, but no verb like \"argi\" in list — only \"tirt\", \"kanarri\", etc.\n\n\"argi\" is likely a preposition — as in \"to\" — the same as \"deːccirsa\" or \"jaːnticcirsu\"\n\nIn 14: \"tirti argi kamgi deːccirsa\" → tirti (repaired) argi (to) kamgi (the camels) deːccirsa (to the camels)? — redundant?\n\nNo — \"kamgi\" = the camels, \"deːccirsa\" = to the camels → repetition?\n\nBut in 1: \"kanarriːcciːg kamiːg jaːnticcirsu\" → bought the camels for the neighbours → \"kamiːg\" = the camels, \"jaːnticcirsu\" = for the neighbours\n\nSimilarly, in 8: \"iːdi magaski kamiːg tirsa\" → men gave the camels to the thief → \"kamiːg\" = the camels, \"tirsa\" = to the thief\n\nSo \"kamgi\" likely = the camels\n\nSimilarly \"kadeːg\" = the dress\n\nIn 14: \"tirti argi kamgi deːccirsa\" → repaired to", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11522.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Step 1: Identify consistent patterns in the given sentences.\n\nLook at the verb structures and how they relate to meaning.\n\nSentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu \n\"We bought the camels for the neighbours.\" \n\"ar\" = subject (we) \n\"kanarriːcciːg\" = bought (past tense) \n\"kamiːg\" = the camels (object) \n\"jaːnticcirsu\" = for the neighbours (for + to whom)\n\n→ \"BUY\" = kanarriːcciːg \nSubject + verb + object + for + recipient\n\nSentence 2: tirt kadeːg allesu \n\"The owner repaired the dress.\" \n\"tirt\" = repaired (past tense) \n\"kadeːg\" = the dress (object) \n\"allesu\" = the owner (subject)\n\n→ \"REPAIR\" = tirt \nSubject + verb + object \nNo \"for\" or recipient, only object\n\nSentence 3: jahali waliːg darbadki biticcirra \n\"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men (subject) \n\"waliːg\" = will (future tense) \n\"darbadki\" = give \n\"biticcirra\" = to the dogs (to + object)\n\n→ \"GIVE\" = darbadki \nSubject + future marker + verb + to + object \nNote: \"to\" is marked by \"biticcirra\" — a form with \"to\"\n\nSentence 4: man jahalgi kadeːcciːg maːgtirsu \n\"He stole the dresses for the young man.\" \n\"man\" = he (subject) \n\"jahalgi\" = stole (past tense) \n\"kadeːcciːg\" = the dresses (object) \n\"maːgtirsu\" = for the young man (for + recipient)\n\n→ \"STEAL\" = jahalgi \nSubject + verb + object + for + recipient\n\nSentence 5: ay beyyeːcciːg ajaːnirri \n\"I am buying the necklaces.\" \n\"ay\" = I (subject) \n\"beyyeːcciːg\" = buying (present) \n\"ajaːnirri\" = the necklaces (object)\n\n→ \"BUY\" = beyyeːcciːg \nPresent tense: \"ay\" + verb + object\n\nSentence 6: wal aygi baːbiːg eldeːnsu \n\"The dog found the doors for me.\" \n\"wal\" = the dog (subject) \n\"aygi\" = found (past) \n\"baːbiːg\" = the doors (object) \n\"eldeːnsu\" = for me (for + recipient)\n\n→ \"FIND\" = baːbiːg \nSubject + verb + object + for + recipient\n\nSentence 7: magas ikki waliːg ticcirsu \n\"The thief gave you (pl.) the dogs.\" \n\"magas\" = the thief (subject) \n\"ikki\" = you (pl.) \n\"ticcirsu\" = gave (verb) \n→ \"GIVE\" = ticcirsu \nSubject + object + verb? Wait — order is: subject + object + verb? \nBut in sentence 3, it's subject + future + verb + to + object. \n\nWait — sentence 7: \"magas ikki waliːg ticcirsu\" \n→ \"magas\" = subject \n\"ikki\" = you (pl.) — this is object of \"gave\" \n\"ticcirsu\" = verb \"gave\"\n\nBut in sentence 3: \"jahali waliːg darbadki biticcirra\" → subject + future marker + verb + to + object \nSo \"waliːg\" is future, attached to verb \"darbadki\"\n\nIn sentence 7: “ticcirsu” is verb, no “to”, no future marker \nBut \"ikki\" is object — \"gave you the dogs\" \nSo likely: subject + object + verb?\n\nBut in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \n→ verb = kanarriːcciːg, object = kamiːg, for = jaːnticcirsu \n\"jaːnticcirsu\" = for the neighbours → structure: \"for + recipient\" \n\nIn sentence 8: iːdi magaski kamiːg tirsa \n\"The men gave the camels to the thief.\" \n\"iːdi\" = men (subject) \n\"magaski\" = the camels (object) \n\"tirsa\" = gave (verb) \n→ \"gave\" = tirsa \nSubject + object + verb — no \"to\", no \"for\"\n\nBut sentence 3: \"dalbadki biticcirra\" → \"to the dogs\" \n\"biticcirra\" = to + recipient\n\nSo verb forms with \"to\" are different from those with \"for\"?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" \n→ verb = aygi (found), object = baːbiːg, for = eldeːnsu\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" \n→ present tense verb with object.\n\nTense markers:\n- Present: beyyeːcciːg (in sentence 5)\n- Past: kanarriːcciːg (1), jahalgi (4), aygi (6), tirsa (8)\n- Future: waliːg (in 3)\n\nSo the future marker \"waliːg\" attaches to the verb “darbadki” in sentence 3.\n\nNow sentence 10: sarkaːyi aygi beyyeːcciːg adeːnda \n\"The cowards are giving me the necklaces.\" \n\"sarkaːyi\" = cowards (subject) \n\"aygi\" = are giving (present, active) \n\"beyyeːcciːg\" = verb \"give\" \n\"adeːnda\" = me (recipient) → so \"to me\"?\n\nIn sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → object only \nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → cowards are giving me the necklaces\n\nSo \"adeːnda\" = me — \"to me\" → \"to\" form?\n\nSo verb “give” (beyyeːcciːg) is used here with \"adeːnda\" (to me)\n\nSimilarly, sentence 3: darbadki biticcirra → to the dogs\n\nSo verbs ending in -cciːg are in different forms?\n\nNow look at standard verbs:\n\n- \"kanarriːcciːg\" = buy \n- \"beyyeːcciːg\" = buy (present) \n→ \"kanarriːcciːg\" = past, \"beyyeːcciːg\" = present\n\nAlso, \"tirt\" = repair \n\"tirsa\" = gave (past) \n\"tirtiːg\" = ? (in 13)\n\nSentence 13: hanu tirtiːg elirsu \n\"hanu\" = strike (base? or subject?) \n\"tirtiːg\" = ? \n\"elirsu\" = the doors?\n\n\"hanu\" = to strike? \n\nSentence 9: ay hanuːg bijomri \n\"I will strike the donkey.\" \n\"ay\" = I \n\"hanuːg\" = will strike (future) \n\"bijomri\" = the donkey (object)\n\nSo \"hanu\" = strike \n\"hanuːg\" = will strike (future form)\n\n→ Future of \"hanu\" is \"hanuːg\"\n\nNow in sentence 13: hanu tirtiːg elirsu \n\"hanu\" = strike? \nBut no \"will\", no object — \"tirtiːg\" = for the doors?\n\n\"tirtiːg\" — likely future form of \"tirt\" (repair)\n\n\"tirt\" = repair (past) \n\"tirtiːg\" — future form? \n\nSentence 3: \"waliːg\" = future marker \nSo future of \"tirt\" would be \"tirt waliːg\" or \"tirtiːg\"?\n\n\"tirtiːg\" — \"tirt\" with \"-iːg\" → possible future form?\n\nSimilarly, \"tirsa\" = past (gave)\n\nSo likely: \n- tirt → past of \"repair\" \n- tirtiːg → future of \"repair\" \n\nThus, in sentence 13: hanu tirtiːg elirsu \n\"hanu\" = strike (subject?) \nBut \"hanu\" is not a future verb — in sentence 9, \"hanuːg\" is future: \"I will strike\"\n\nSo \"hanu\" = base verb \"strike\"\n\n\"tirtiːg\" = future of \"repair\"\n\n\"elirsu\" = the doors?\n\nSo: \"I will strike the doors?\" → but \"hanu\" is subject?\n\nWait: “hanu tirtiːg elirsu” — subject = hanu (implying \"he\" or \"they\"?)\n\nBut in sentence 9: \"ay hanuːg bijomri\" = \"I will strike the donkey\"\n\nSo structure: subject + future verb + object\n\nIn sentence 13: hanu tirtiːg elirsu — only object \"elirsu\"? \nNo object? \"elirsu\" = the doors — could be object?\n\nSo perhaps: “he will repair the doors” — only if \"tirtiːg\" = future repair\n\nBut \"hanu\" = strike — not repair\n\nSo inconsistency?\n\nWait — in sentence 8: iːdi magaski kamiːg tirsa \n\"iːdi\" = men (subject) \n\"magaski\" = camels (object) \n\"tirsa\" = gave\n\n\"tirsa\" = past of \"give\"? \nBut earlier \"ticcirsu\" (sentence 7) = \"gave\"\n\nSo two verbs for \"give\"? \n- ticcirsu (sentence 7) \n- tirsa (sentence 8)\n\nIs that a problem?\n\nIn sentence 3: \"darbadki\" = give \nIn sentence 7: \"ticcirsu\" = gave \nIn sentence 8: \"tirsa\" = gave \n\nCould \"tirsa\" and \"ticcirsu\" be different forms?\n\nBut in sentence 14: tirti argi kamgi deːccirsa\n\n\"tirti\" — likely future of \"tirt\" (repair) \n\"argi\" — who? \n\"kamgi\" — the camels? \n\"deːccirsa\" — to whom?\n\n\"deːccirsa\" — looks like \"to the camels\"? But camels are object.\n\nStructure: future repair + object + to?\n\nPossibly: \"they will repair the camels for the owner\"?\n\nWait.\n\nNow attention to object and recipient markers.\n\nGeneral pattern:\n\n- When object is marked directly: subject + verb + object \n- When recipient is specified: subject + verb + for + recipient (e.g. jaːnticcirsu, eldeːnsu, adeːnda)\n\n- Future tense: verb base + \"waliːg\" (in sentence 3), or verb stem + \"iːg\" (in sentence 9: hanuːg)\n\nSo \"waliːg\" = future in some verbs, but in 3: \"waliːg\" is attached to \"darbadki\" for future.\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" — past verb, object, for recipient \nSentence 5: \"ay beyyeːcciːg ajaːnirri\" — present verb, object \nSentence 9: \"ay hanuːg bijomri\" — future verb, object\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" — present verb, recipient (to me)\n\n→ So verb \"beyyeːcciːg\" used with \"adeːnda\" = to me\n\n→ So recipients marked with a specific form like \"adeːnda\" = to me \n\"eldeːnsu\" = for me \n\"jaːnticcirsu\" = for neighbours\n\nSo \"deːccirsa\" → likely a recipient form?\n\nLook at sentence 14: tirti argi kamgi deːccirsa \n\"tirti\" — future of repair? \n\"argi\" — subject? \n\"kamgi\" — object? \n\"deːccirsa\" — recipient?\n\n→ \"they will repair the camels for the owner\"?\n\nBut \"deːccirsa\" may be \"to the owner\"?\n\nBack to sentence 11: magasi argi ajomirra\n\n\"magasi\" — likely a subject (\"the thief\")? \n\"argi\" — verb? \n\"ajomirra\" — object?\n\n\"ajomirra\" — similar to \"biticcirra\" (to the dogs) — likely recipient?\n\n\"biticcirra\" = to the dogs \n\"ajomirra\" = to the dogs? (same form?)\n\n\"biticcirra\" → \"to the dogs\" \n\"ajomirra\" → possibly \"to the dogs\"?\n\nBut \"argi\" — could be verb?\n\nIs \"argi\" a verb?\n\nLook at sentence 8: iːdi magaski kamiːg tirsa → no \"argi\"\n\nSentence 7: magas ikki waliːg ticcirsu → verb = ticcirsu (gave)\n\nCompare to sentence 11: magasi argi ajomirra\n\n\"magasi\" — likely subject (the thief) \n\"ajomirra\" — object or recipient? \n\n\"argi\" — possibly a verb form?\n\nUnlikely: in previous verbs, object is separate.\n\nAlternative: \"argi\" = verb, \"ajomirra\" = recipient?\n\nCheck if \"ajomirra\" = to the dogs?\n\nIn sentence 3: \"biticcirra\" = to the dogs \nSo \"ajomirra\" = to the dogs? Could be a different form.\n\nBut \"biticcirra\" and \"ajomirra\" — same root?\n\nPossibly, \"biticcirra\" and \"ajomirra\" are both to+object, and differ only in object.\n\nBut \"ajomirra\" may be \"to the dogs\".\n\nSo sentence 11: magasi argi ajomirra → the thief does something to the dogs?\n\nBut what verb is \"argi\"?\n\nIs \"argi\" = repair? \n\"tirt\" = repair \n\"tirti\" = future repair\n\n\"argi\" — not seen before.\n\nSentence 12: ay kanarriːg baːbki alletirsi \n\"ay\" = I \n\"kanarriːg\" = past of \"buy\"? (buy = kanarriːcciːg) \n\"baːbki\" = the doors? \n\"alletirsi\" = for me?\n\n\"alletirsi\" — likely \"for me\"\n\nSo: \"I bought the doors for me\"\n\n→ \"I bought the doors for myself\"\n\nSo \"kanarriːg\" = past of \"buy\" \n\"baːbki\" = object (the doors) \n\"alletirsi\" = for me (recipient)\n\nSentence 3: \"jalali waliːg darbadki biticcirra\" → young men will give the chicken to the dogs \nSo verb = darbadki → give\n\nIs \"argi\" a version of \"darbadki\"?\n\n\"argi\" vs. \"darbadki\" — different vowel?\n\nPerhaps a different verb.\n\nWhat about sentence 13: hanu tirtiːg elirsu \n\"hanu\" = strike (base) \n\"tirtiːg\" = future of repair? \n\"elirsu\" = the doors\n\nSo → \"he will repair the doors\"?\n\nBut \"hanu\" = strike, not repair.\n\nMistake.\n\nUnless \"hanu\" is not subject.\n\n\"hanu\" can be a verb or noun?\n\nIn sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\nSo \"hanu\" = verb \"strike\"\n\nSo in sentence 13: \"hanu tirtiːg elirsu\" — \"hanu\" as verb? \nBut no future marker.\n\n\"tirtiːg\" = future of repair\n\nSo could this be \"he will repair the doors\" — but \"hanu\" is strike.\n\nOnly if \"hanu\" is the subject.\n\nSo \"hanu\" = subject (he) \n\"tirtiːg\" = verb (will repair) \n\"elirsu\" = object (the doors)\n\nSo the structure is: subject + future verb + object\n\nYes — because \"tirtiːg\" is future of \"repair\"\n\nSo \"he will repair the doors\"\n\nSimilarly, sentence 14: tirti argi kamgi deːccirsa \n\"tirti\" = future of repair \n\"argi\" = verb? \n\"kamgi\" = object (the camels)? \n\"deːccirsa\" = recipient?\n\nBut \"argi\" not a known verb.\n\nUnless \"argi\" is a verb meaning \"give\"?\n\nBut \"ticcirsu\" = give \n\"darbadki\" = give\n\n\"argi\" — perhaps a variant?\n\nBut in sentence 11: magasi argi ajomirra\n\n\"magasi\" — thief \n\"argi\" — verb \n\"ajomirra\" — to the dogs?\n\nSo likely \"the thief will give the dogs to the dogs\"? No.\n\nOr \"argi\" = give — then \"magasi gives the dogs to the dogs\"?\n\nBut redundant.\n\nAlternatively, \"argi\" = repair?\n\nBut in sentence 14: \"tirti argi kamgi deːccirsa\" — \"repair the camels for the owner\"?\n\nBut \"tirti\" is already repair.\n\nOnly one verb per meaning?\n\nPerhaps \"argi\" is a different verb.\n\nBack to sentence 3: \"darbadki\" = give \nSentence 7: \"ticcirsu\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11493.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze the structure of the given sentences to identify consistent syntactic patterns, especially regarding verb morphology, object/subject markers, and verb particles.\n\nSentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu \n→ \"We bought the camels for the neighbours.\" \n- \"ar\" = subject (we) \n- \"kanarriːcciːg\" = verb form, likely \"buy\" \n- \"kamiːg\" = object (the camels) \n- \"jaːnticcirsu\" = \"for the neighbours\" → instrument or recipient → object complement\n\nPattern: Subject + [verb] + object + [for X] → \"buy X for Y\"\n\nSentence 2: tirt kadeːg allesu \n→ \"The owner repaired the dress.\" \n- \"tirt\" = subject (the owner) \n- \"kadeːg\" = verb \"repair\" \n- \"allesu\" = object (the dress) \n→ \"Subject repaired the dress\"\n\nSentence 3: jahali waliːg darbadki biticcirra \n→ \"The young men will give the chicken to the dogs.\" \n- \"jahali waliːg\" = subject (young men) \n- \"darbadki\" = verb stem (give) \n- \"biticcirra\" = object (chicken) \n- \"to the dogs\" → object of \"give\" → in a separate phrase\n\nBut the structure is: Subject + verb + object + to + recipient\n\nSentence 4: man jahalgi kadeːcciːg maːgtirsu \n→ \"He stole the dresses for the young man.\" \n- \"man\" = subject (he) \n- \"jahalgi\" = verb (steal) \n- \"kadeːcciːg\" = object (dresses) \n- \"maːgtirsu\" = \"for the young man\"\n\nPattern: Subject + verb + object + for + recipient\n\nSentence 5: ay beyyeːcciːg ajaːnirri \n→ \"I am buying the necklaces.\" \n- \"ay\" = subject (I) \n- \"beyyeːcciːg\" = verb \"buying\" (present progressive) \n- \"ajaːnirri\" = object (necklaces)\n\nVerb + object → subject + verb (progressive) + object\n\nSentence 6: wal aygi baːbiːg eldeːnsu \n→ \"The dog found the doors for me.\" \n- \"wal\" = subject (dog) \n- \"aygi\" = verb \"found\" \n- \"baːbiːg\" = object (doors) \n- \"eldeːnsu\" = \"for me\"\n\n→ subject + verb + object + for + me\n\nSentence 7: magas ikki waliːg ticcirsu \n→ \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = subject (the thief) \n- \"ikki waliːg\" = \"you (pl.)\" → object \n- \"ticcirsu\" = verb \"gave\"\n\n→ subject + object (you) + verb (gave)\n\n→ here, verb comes after object → object + verb\n\nSentence 8: iːdi magaski kamiːg tirsa \n→ \"The men gave the camels to the thief.\" \n- \"iːdi\" = subject (the men) \n- \"magaski\" = object (camels) \n- \"tirsa\" = verb (gave)\n\n→ subject + object + verb → not object + verb\n\nBut note: in (7), \"magas ikki waliːg ticcirsu\" → subject + object + verb \nIn (8), \"iːdi magaski kamiːg tirsa\" → subject + object + verb\n\nSo verb comes after object in both cases.\n\nSentence 9: ay hanuːg bijomri \n→ \"I will strike the donkey.\" \n- \"ay\" = subject (I) \n- \"hanuːg\" = verb (will strike) \n- \"bijomri\" = object (donkey)\n\nPresent tense, future, with object after verb.\n\nSentence 10: sarkaːyi aygi beyyeːcciːg adeːnda \n→ \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = subject (cowards) \n- \"aygi\" = verb (are giving) \n- \"beyyeːcciːg\" = object (necklaces) \n- \"adeːnda\" = \"to me\" → recipient\n\nSo verb is \"giving\", object after verb, and then \"to me\" → structure: subject + verb + object + to + recipient\n\nBut in sentence 3: jahali waliːg darbadki biticcirra \n→ \"young men will give the chicken to the dogs\" \n→ subject + verb + object + to recipient\n\nSo pattern holds: verb + object + to recipient (or for recipient)\n\nNow look at verb types:\n\n- \"kanarriːcciːg\" → buy → appears in 1, 4, 5 \n- \"kadeːg\" → repair → 2 \n- \"darbadki\" → give → 3 \n- \"jahalgi\" → steal → 4 \n- \"beyyeːcciːg\" → buy → 5, 10 \n- \"aygi\" → find → 6 \n- \"tirsa\" → give → 7,8 \n- \"hanuːg\" → strike → 9 \n- \"magaski\" → camels (object) \n- \"argi\", \"ajomirra\", \"baːbki\", \"alletirsi\", etc. are new forms in questions.\n\nNow analyze the new sentences.\n\n11. magasi argi ajomirra \nStructure: subject = \"magasi\" → likely \"the thief\" (from magas → thief) \n\"argi\" → verb? Likely stem of \"give\" (since \"tirsa\", \"tirsi\" appear) \n\"ajomirra\" → object? Possibly \"the donkey\" or \"the strike\"?\n\nCompare with 9: ay hanuːg bijomri → \"I will strike the donkey\" \n\"hanuːg\" → verb, \"bijomri\" → object (donkey)\n\nIn 11: \"argi\" → if \"give\", then \"argi\" = give? \nBut \"tirsa\" = give, \"tirsi\" = give → likely same root.\n\n\"argi\" → could be a variant of \"tirsi\"? Notice in 14: tirti argi kamgi deːccirsa \n\"tirti\" → \"the owner\" (from tirt) \n\"argi\" → verb \n\"kamgi\" → object? Perhaps \"camels\"? \n\"deːccirsa\" → \"to the thief\"? deːccir → deːccir → \"to the thief\" (from \"tirsa\"?) \n\nIn 1, \"kanarriːcciːg\" = buy \nIn 2, \"kadeːg\" = repair \nIn 3, \"darbadki\" = give \nIn 4, \"jahalgi\" = steal \nIn 5, \"beyyeːcciːg\" = buy \nIn 6, \"aygi\" = find \nIn 7, \"ticcirsu\" = give \nIn 8, \"tirsa\" = give \nIn 9, \"hanuːg\" = strike \nIn 10, \"aygi beyyeːcciːg\" = are giving\n\nSo \"argi\" likely is a form of \"give\".\n\n\"ajomirra\" → in 9: \"bijomri\" → object of strike → so \"omirri\" is likely \"donkey\"\n\nThus \"ajomirra\" = \"the donkey\"\n\nSo 11: \"The thief gives the donkey\"\n\nBut is it \"gives\" or \"strike\"? \"argi\" is not \"hanuːg\" → different form.\n\n\"argi\" = give → therefore \"magasi argi ajomirra\" = \"The thief gives the donky\"\n\nBut is \"ajomirra\" = \"donkey\"?\n\nYes — from sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = donkey\n\nSo \"ajomirra\" = same; likely same root + plural? But \"donkey\" is singular — so \"ajomirra\" = the donkey\n\nThus 11: \"The thief gives the donkey\"\n\nBut is the verb \"gives\" or is it \"will give\"? No tense marker.\n\nBut \"tirsa\" in 7 is past → \"gave\" \n\"tirsi\" could be informal form?\n\nIn 14: tirti argi kamgi deːccirsa → \"the owner gives the camels to the thief\" → gives to thief → \"deːccirsa\" → \"to the thief\" → matches deːccir from \"tirsa\" → likely deːccir = \"to the thief\"\n\nSo \"argi\" is \"give\"\n\nThus 11: magasi argi ajomirra → \"The thief gives the donkey\"\n\nBut is there a direction or subject? \"Magasi\" = thief → \"the thief\" → subject\n\nSo translation: \"The thief gives the donkey\"\n\n✅\n\n12. ay kanarriːg baːbki alletirsi \n\"ay\" = I \n\"kanarriːg\" = buy \n\"baːbki\" = object? Could be \"the doors\"? \n\"alletirsi\" = complement?\n\nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → buy X for Y \n\"jaːnticcirsu\" = for neighbours\n\nIn sentence 6: wal aygi baːbiːg eldeːnsu → dog found the doors for me → object + for + me\n\nIn sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"baːbki\" = doors? \"baːbiːg\" in 6 → \"doors\" → so \"baːbki\" = doors (same root)\n\n\"alletirsi\" → likely \"for me\" → from \"eldeːnsu\" → \"for me\" → \"eldeːnsu\"\n\n\"eldeːnsu\" = for me → \"alletirsi\" → likely same root — could be \"al-letirsi\" = for me?\n\nCompare: \n- \"eldeːnsu\" = for me → \"eldeː\" + \"nsu\" \n- \"alletirsi\" → \"al-\" = for? \"letirsi\" → could be variant of \"eldeːnsu\"?\n\nIn 10: \"adeːnda\" = to me → so \"to me\"\n\nIn 6: \"eldeːnsu\" = for me\n\nSo \"alletirsi\" → likely \"for me\" → same as \"eldeːnsu\"\n\nTherefore: \"I buy the doors for me\"\n\nThat sounds odd — buying doors for oneself?\n\nBut possible — possible self-reference.\n\nAlternatively, is \"alletirsi\" = to me?\n\nBut in 6, \"found the doors for me\" → for me.\n\nIn 12: \"ay kanarriːg baːbki alletirsi\" → I buy the doors for me.\n\nYes — consistent.\n\nSo translation: \"I buy the doors for myself\"\n\nBut \"alletirsi\" is likely \"for me\"\n\nThus 12: \"I buy the doors for me\"\n\n✅\n\n13. hanu tirtiːg elirsu \n\"hanu\" = I (from 9) \n\"tirtiːg\" → \"tirt\" = owner → \"tirti\" = owner? → \"tirtiːg\" = owner? \n\"tirtiːg\" = likely \"the owner\" \n\"elirsu\" → ? \n\nIn sentence 2: tirt kadeːg allesu → \"the owner repaired the dress\" \n\"el\" + \"irsu\"? → \"el\" + \"irsu\" → like \"eldeːnsu\" → \"el\" + \"irsu\"? \nDress? \"allesu\" = dress → so \"el\" + \"s\" → \"el\" + \"su\" → \"allesu\" → dress\n\n\"elirsu\" → could be \"dress\"? \"el\" + \"irsu\" → identical to \"allesu\"? → pattern?\n\n\"allesu\" = dress → \"elirsu\" → \"el\" + \"irsu\" → very similar; likely \"dress\"\n\nThus \"hanu tirtiːg elirsu\" → \"I the owner the dress\" → grammar?\n\nSubject: \"hanu\" → I \n\"tirtiːg\" → seems like object? \"the owner\" → but \"the owner\" is a noun\n\n\"hanu tirtiːg\" → I + owner?\n\nPossibility: subject + \"the owner\" + \"dress\"\n\nBut tense? \"hanu\" is in 9 → future \"will strike\"\n\nHere, no tense marker → present?\n\nBut \"hanu\" = I, not a verb.\n\n\"hanu\" is subject in 9 → \"I\" → here also → \"I\"\n\n\"tirtiːg\" → likely a noun phrase: \"the owner\"\n\n\"elirsu\" → dress\n\nSo structure: \"I the owner dress\" — doesn't work\n\nAlternative: \"hanu\" = verb? But in 9: \"hanuːg\" = verb, \"I will strike\"\n\n\"hanu\" alone = I, so likely subject.\n\nSo perhaps: \"I (am) buying\" → no verb\n\nBut no verb — no form like \"hanu\" as verb? In 9: \"hanuːg\" = strike\n\nHere: \"hanu tirtiːg elirsu\" → I owner dress\n\nBut in sentence 1, \"ar kanarriːcciːg kamiːg\" → we bought camels → no \"owner\" in object\n\nCould \"tirtiːg\" be the verb?\n\n\"tirt\" = repair → \"tirtiːg\" → could be \"repair\"?\n\nIn 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\"\n\nSo \"tirt\" = verb \"repair\"\n\n\"tirtiːg\" → could be \"repair\" → with \"g\" suffix → possessive or object marker?\n\nPossibly \"tirti\" = repair → \"tirtiːg\" = repair (g = object?) or stem?\n\nBut in sentence 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs → \"ticcirsu\" = gave\n\n\"tir\" roots: tirt → repair, tirsa → give, ticcirsu → give\n\nSo \"tirt\" and \"tir\" roots — likely \"repair\" and \"give\"\n\nSo \"tirtiːg\" = repair?\n\nBut \"tirt\" is subject in 2 → \"the owner\"\n\nSo if \"tirtiːg\" is verb, then \"hanu\" = subject, \"tirtiːg\" = verb?\n\nBut \"hanu\" → subject of agent — not verb.\n\nAlternatively: \"hanu\" is not subject → could be \"will strike\" — present tense?\n\nBut no object.\n\n\"elirsu\" → dress → so perhaps \"I repair the dress\"\n\nThus verb = \"repair\", root = \"tirt\" → \"tirtiːg\" = repair?\n\nYes — in 2: tirt kadeːg allesu → \"the owner repaired the dress\" → \"tirt\" verb\n\nSo \"tirtiːg\" → \"repair\" (with object marker? g?) → could be \"repair the\" → but no object at start\n\n\"hanu\" = subject → \"I\"\n\nSo \"hanu tirtiːg elirsu\" → \"I repair the dress\"\n\nYes — makes perfect sense.\n\n\"elirsu\" = dress → matches \"allesu\" → likely same root.\n\nThus 13: \"I repair the dress\"\n\n✅\n\n14. tirti argi kamgi deːccirsa \n\"tirti\" = the owner (from tirt) \n\"argi\" = give (verb) \n\"kamgi\" = camels? From 1 → \"kamiːg\" = camels → so \"kamgi\" = camels \n\"deːccirsa\" = to the thief? From 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"tirsa\" → verb → \"to the thief\" → \"deːccirsa\" → likely \"to the thief\"\n\n\"deːccir\" = to thief? From \"tirsa\" → \"to thief\" → so \"deːccirsa\" = to the thief\n\nThus: \"The owner gives the camels to the thief\"\n\n✅\n\n15. ay darbadki bijaːndi \n\"ay\" = I \n\"darbadki\" = verb → \"give\" (from sentence 3: \"jahali waliːg darbadki biticcirra\" → young men give chicken to dogs)\n\nSo \"darbadki\" = give \n\"bijaːndi\" = object?\n\nIn 3: \"biticcirra\" = chicken → object\n\nSo \"bijaːndi\" = chicken?\n\nYes — likely same root.\n\nSo \"I give the chicken\"\n\n✅\n\nFinal translations:\n\n11. The thief gives the donkey \n12. I buy the doors for me \n13. I repair the dress \n14. The owner gives the camels to the thief \n15. I give the chicken\n\n\\boxed{a.1: The thief gives the donkey; a.2: I buy the doors for me; a.3: I repair the dress; a.4: The owner gives the camels to the thief; a.5: I give the chicken}", + "generated_tokens": 4023, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: The thief gives the donkey; a.2: I buy the doors for me; a.3: I repair the dress; a.4: The owner gives the camels to the thief; a.5: I give the chicken", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 10841.0, + "ioling_final_answer_chars": 156.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Analyze core verb patterns and their argument structures in the provided sentences.\n\nSentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (verb, past tense) \n- \"kamiːg\" = the camels (object) \n- \"jaːnticcirsu\" = for the neighbours (prepositional phrase, recipient) \nStructure: [Subject] [verb] [object] [for (recipient)]\n\nSentence 2: tirt kadeːg allesu → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress (object) \n- \"allesu\" = (probably \"the dress\" is being repaired, no prepositional phrase) \nNo \"for\" or recipient here. But \"tirt\" is a verb of repair.\n\nSentence 3: jahali waliːg darbadki biticcirra → \"The young men will give the chicken to the dogs.\" \n- \"jahali waliːg\" = the young men (subject) \n- \"darbadki\" = give (verb, future) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" implied? But no explicit \"for\" or \"to\". \nHowever, \"darbadki\" = give, and it's followed by object and then recipient? Not clearly.\n\nWait — sentence 8: iːdi magaski kamiːg tirsa → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men (subject) \n- \"magaski\" = gave (verb) \n- \"kamiːg\" = the camels (object) \n- \"tirsa\" = to the thief (direction/recipient)\n\nSo, verb + object + to + recipient. \"tirsa\" = to the thief.\n\nThus, structure: S + V + O + to + R\n\nSimilarly, sentence 4: man jahalgi kadeːcciːg maːgtirsu → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past) \n- \"kadeːcciːg\" = the dresses (object) \n- \"maːgtirsu\" = for the young man (recipient)\n\nSo \"for\" = recipient.\n\n\"for\" and \"to\" seem to be synonymous, both marking recipient.\n\nIn sentence 5: ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present) \n- \"ajaːnirri\" = the necklaces (object)\n\nNo recipient — just action on an object.\n\nSentence 6: wal aygi baːbiːg eldeːnsu → \"The dog found the doors for me.\" \n- \"wal\" = the dog \n- \"aygi\" = found (verb) \n- \"baːbiːg\" = the doors (object) \n- \"eldeːnsu\" = for me (recipient)\n\n\"for me\" = recipient.\n\nSo recurring pattern: verb + object + for/to + recipient\n\nAlso, \"kanarriːg\" = bought (sentence 1), verb. \"kadeːg\" = dress (sentence 2). \"darbadki\" = give (sentence 3). \"jahalgi\" = stole (sentence 4). \"beyyeːcciːg\" = buying (5). \"aygi\" = found (6). \"magaski\" = gave (8). \n\nObservation: verbs of action (buy, give, steal, find) take object + recipient (for/to).\n\nNow look at any structural reversal.\n\nSentence 7: magas ikki waliːg ticcirsu → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n- verb is \"ticcirsu\" = gave → but here, the object is \"dogs\", the recipient is \"you\" \nBut the sentence says: \"gave you the dogs\" → so structure: [subject] [verb] [recipient] [object]?\n\nWait, no: \"gave you the dogs\" = recipient first, then object — that's anomalous.\n\nCompare to sentence 8: iːdi magaski kamiːg tirsa → \"the men gave the camels to the thief\" → object before recipient.\n\nSo in 7: magas ikki waliːg ticcirsu → the thief gave you the dogs → object \"the dogs\", recipient \"you\"?\n\nBut it's: \"ikki waliːg\" = you (pl.), \"ticcirsu\" = gave, object missing. But object is \"the dogs\"? Not stated.\n\nWait — original: magas ikki waliːg ticcirsu → likely word order: subject (magas), recipient (ikki waliːg), verb (ticcirsu), object (implied as \"the dogs\")? But object not stated.\n\nBut sentence 8: iːdi magaski kamiːg tirsa → \"men gave the camels to the thief\" — object \"kamiːg\", then \"tirsa\" = to thief.\n\nIn 7: verb is \"ticcirsu\", which is perhaps the same as \"magaski\" or \"tirsa\"? Only possibility is that \"ticcirsu\" is \"gave\" in a different form.\n\nBut \"tirsa\" = \"to the thief\", so \"tirsa\" = to + recipient.\n\nIn 3: jahali waliːg darbadki biticcirra → \"young men will give the chicken to the dogs\" → verb \"darbadki\" (give), object \"biticcirra\", recipient \"the dogs\" implied.\n\nSo verb + object + to + recipient.\n\nIn 8: iːdi magaski kamiːg tirsa → verb \"magaski\" + object \"kamiːg\" + \"tirsa\" = to thief.\n\nIn 7: magas ikki waliːg ticcirsu → if \"ticcirsu\" = gave, but recipient \"ikki waliːg\" is first, then verb — unusual.\n\nPerhaps object is missing? But no.\n\nWait — maybe \"ikki\" is not the recipient. \"ikki waliːg\" = \"you (pl.)\" — possibly subject?\n\nBut \"magas\" is subject — thief.\n\nSo thief gave you the dogs → so \"ikki waliːg\" = recipient, \"the dogs\" = object.\n\nBut the object is missing in the sentence. Unless \"ticcirsu\" carries an object.\n\nBut in 8, object is specified: \"kamiːg\".\n\nSo \"ticcirsu\" must take object.\n\nBut in 7, the object is not present.\n\nPossibility: the object is \"the dogs\", which appears in the verb form? No.\n\nWait — sentence 7: magas ikki waliːg ticcirsu → no object. So perhaps \"ticcirsu\" is a verb with no object? But that contradicts others.\n\nAlternatively, \"ticcirsu\" = gave, and object is missing — but in context, it must be \"the dogs\", which we get from the pattern.\n\nBut in 8: \"kamiːg\" = camels → object.\n\nIn 3: \"biticcirra\" = chicken → object.\n\nSo object must be a noun phrase in the same slot.\n\nTherefore in 7, object must be missing — but that can't be.\n\nWait — double-check original:\n\n\"magas ikki waliːg ticcirsu\" → The thief gave you (pl.) the dogs.\n\nYes — \"gave you the dogs\" — so recipient = you, object = the dogs.\n\nBut \"ticcirsu\" is only one word — no object mentioned.\n\nThus the object is missing from the sentence — but it must be inferred.\n\nTherefore, verb structure must be: [Subject] [verb] [recipient] [object] — or [Subject] [verb] [object] [to recipient]?\n\nSentence 8: \"gave the camels to the thief\" — object before recipient.\n\nSentence 3: \"give the chicken to the dogs\" — object before recipient.\n\nSentence 1: \"bought the camels for the neighbours\" — object before recipient.\n\nSentence 2: \"repaired the dress\" — object only — no recipient.\n\nSentence 4: \"stole the dresses for the young man\" — object before recipient.\n\nSentence 5: \"buying the necklaces\" — object only.\n\nSentence 6: \"found the doors for me\" — object before recipient.\n\nSo consistent pattern: object comes before recipient.\n\nOnly in 7: \"the thief gave you the dogs\" — recipient before object.\n\nThis is a contradiction.\n\nUnless \"ikki waliːg\" is not recipient.\n\n\"ikki waliːg\" — \"you (pl.)\" — could be subject?\n\nBut \"magas\" is subject — thief.\n\nSo \"magas\" = thief, \"ikki waliːg\" = you — recipient.\n\nOr is \"ticcirsu\" a verb with intransitive use?\n\nNo — other verbs have objects.\n\nAlternative: \"ticcirsu\" = gave, and it's used with recipient first because of word order? But in other cases, object comes first.\n\nBut in sentences 1,3,4,8,6: object before recipient.\n\nOnly 7 is different.\n\nUnless the object is \"the dogs\", and it's missing from the sentence.\n\nBut in the sentence: \"magas ikki waliːg ticcirsu\" → no noun.\n\nTherefore, likely a typo or misalignment.\n\nBut look at 10: sarkaːyi aygi beyyeːcciːg adeːnda → \"The cowards are giving me the necklaces.\"\n\n- \"sarkaːyi\" = cowards \n- \"aygi\" = are giving (present) \n- \"beyyeːcciːg\" = the necklaces (object) \n- \"adeːnda\" = to me (recipient)\n\nSo again: object before recipient.\n\nThus, core pattern: verb + object + to/for + recipient.\n\nNow verbs:\n\n- kanarriːg = bought (1) \n- tirt = repaired (2) \n- darbadki = give (3) \n- jahalgi = stole (4) \n- beyyeːcciːg = buying (5) \n- aygi = found (6) \n- magaski = gave (8) \n- ticcirsu = gave (7) — similar to magaski\n\nSo \"ticcirsu\" and \"magaski\" are both \"gave\".\n\nNow check for object and recipient.\n\nNow go to the questions:\n\n11. magasi argi ajomirra.\n\n- \"magasi\" — likely \"gave\" (from magas → thief, so \"magasi\" = gave) \n- \"argi\" — likely \"to\" or \"for\" (like \"tirsa\", \"allega\", etc.) \n- \"ajomirra\" — likely \"the donkey\" or \"the donkey (object)\"\n\n\"hanu\" = strike (9) → \"hanuːg\" = strike the donkey → \"hanu\" likely the verb.\n\n\"hanu\" = strike → in 9: \"hanuːg bijomri\" → \"I will strike the donkey\"\n\n\"bijomri\" = the donkey\n\nSo \"bijomri\" → the donkey\n\nSimilarly, in 11: \"ajomirra\" — could be \"the donkey\"\n\n\"argi\" — in 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = to the doors? \"elirsu\" = to?\n\n\"tirtiːg\" — likely \"to the doors\", from \"tirt\" = repair → \"tirtiːg\" = to the doors?\n\n\"tirt\" = repair → \"tirtiːg\" = to repair? No — \"tirtiːg\" could be \"to the doors\".\n\nIn sentence 2: \"tirt kadeːg allesu\" = repaired the dress.\n\nSo \"tirt\" = repaired.\n\nCould \"tirtiːg\" = to the doors?\n\nAnd \"elirsu\" = for or to?\n\nIn 6: \"eldeːnsu\" = for me → likely \"for\" or \"to\".\n\n\"elirsu\" — similar to \"eldeːnsu\" → likely \"for\" or \"to\".\n\nSo in 13: \"hanu tirtiːg elirsu\" → \"strike to the doors for?\" — doesn't make sense.\n\n\"hanu\" = strike — strike what? \"to the doors\" — strike the doors?\n\nBut in 9: \"hanuːg bijomri\" = I will strike the donkey → so \"hanu\" is verb, object \"bijomri\" = donkey.\n\nSo \"hanu\" takes object.\n\nIn 13: \"hanu tirtiːg elirsu\" — could be \"strike the doors for?\" — but \"tirtiːg\" is not object.\n\n\"tirtiːg\" = to the doors → prepositional phrase.\n\nSo \"hanu\" = strike, recipient = doors? or object = doors?\n\nBut \"hanu\" must take an object.\n\nPossibility: \"hanu\" is used with object and recipient.\n\nIn 9: \"hanuːg bijomri\" → no recipient — strikes donkey.\n\nIn 13: \"hanu tirtiːg elirsu\" → \"strike to the doors for?\" → not consistent.\n\nPossibility: \"tirtiːg\" is object — \"the doors\", \"elirsu\" = for?\n\nBut \"tirtiːg\" = has \"tirt\" and \"iːg\" → \"tirt\" = repair → \"tirtiːg\" = repaired doors?\n\nBut verb would be \"tirt\", not \"hanu\".\n\nSo no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = the doors (object), \"elirsu\" = to (recipient) → \"I strike the doors to the...\" — nonsense.\n\nSo better: \"tirtiːg\" = to the doors (direction), \"elirsu\" = for?\n\nBut \"hanu\" only takes one object.\n\nThus, likely: \"hanu\" + [object] + to/for + recipient?\n\nBut in 9, no recipient.\n\nSo hybrid: in 9, object only; in others, object + recipient.\n\nBut 13: \"hanu tirtiːg elirsu\" — \"tirtiːg\" likely object, \"elirsu\" recipient.\n\nSo \"strike the doors to the...\" — no.\n\n\"tirtiːg\" = to the doors → recipient.\n\nThen object is missing.\n\nSo \"hanu\" with only recipient — not possible.\n\nThus, likely \"tirtiːg\" is object (the doors), meaning \"strike the doors\", and \"elirsu\" = for whom?\n\nBut no person.\n\nCould \"elirsu\" = for the attack? Unlikely.\n\nAnother possibility: \"tirt\" = repair, so \"tirtiːg\" = repair the doors?\n\nBut verb is \"hanu\" → strike.\n\nSo conflict.\n\nWait — look at 14: tirti argi kamgi deːccirsa.\n\n- \"tirti\" → likely \"repair\" (from \"tirt\") \n- \"argi\" → to/for \n- \"kamgi\" → the camels? \n- \"deːccirsa\" → to the thief?\n\n\"tirti\" = repair (with object) + recipient?\n\n\"tirti argi kamgi deːccirsa\" → \"repair the camels for the thief\"? \nOr \"repair to the camels for the thief\"? No.\n\nObject should be before recipient.\n\nStructure: [verb] [object] [for/to] [recipient]\n\nSo: tirti (repair) + kamgi (camels) + argi (for/to) + deːccirsa (thief)\n\nBut deːccirsa = to the thief?\n\nYes — like \"tirsa\" = to the thief.\n\nSo \"repair the camels for the thief\" → makes sense.\n\nSimilarly, sentence 2: \"tirt kadeːg allesu\" → repaired the dress → no recipient.\n\nBut here, recipient is added.\n\nSo pattern: verb + object + for/to + recipient.\n\nNow back to 11: magasi argi ajomirra.\n\n- \"magasi\" = gave (from magas) \n- \"argi\" = for/to \n- \"ajomirra\" = the donkey (from \"bijomri\" = donkey)\n\nSo \"gave the donkey to/for\" — but what to whom?\n\nNo recipient → so likely \"gave the donkey\" — object only? But \"argi\" is present.\n\n\"argi\" = for/to — must have a recipient.\n\nBut no recipient specified.\n\nUnless \"argi\" is misread.\n\nCould \"argi\" be part of object? No.\n\n\"ajomirra\" = the donkey → object.\n\nSo \"magasi\" = gave, \"argi\" = to/for, \"ajomirra\" = object → but object already given.\n\nSo must be: gave the donkey to/for whom?\n\nMissing recipient.\n\nUnless in the verb, \"argi\" indicates direction.\n\nBut no.\n\nAnother possibility: \"magasi\" = the thief gave → subject, then \"argi\" = to, then \"ajomirra\" = to the donkey?\n\nBut \"ajomirra\" = the donkey — as in 9, \"bijomri\" = the donkey.\n\nSo \"argi ajomirra\" = to the donkey.\n\nSo \"magasi argi ajomirra\" = the thief gave to the donkey?\n\nBut gave what?\n\nStill missing object.\n\nUnless the object is implied or missing.\n\nBut all verbs require an object.\n\nIn 7: \"magas ikki waliːg ticcirsu\" = thief gave you the dogs → object implied as \"the dogs\".\n\nBut here, no object.\n\nUnless \"ajomirra\" is the object and \"argi\" is to/for.\n\nSo \"gave the donkey to/for whom?\"\n\nNo recipient.\n\nSo perhaps", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12307.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Analyze the given examples to extract patterns in Kunuz Nubian syntax.\n\nLook at Example 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \nStructure: [subject] [verb] [object] [prepositional phrase with beneficiary] \n\"ar\" = we (subject) \n\"kanarriːcciːg\" = bought (verb) \n\"kamiːg\" = the camels (object) \n\"jaːnticcirsu\" = for the neighbours (beneficiary) \n\nNote: \"for the X\" construction consistently uses a prepositional phrase with a noun (X) attached via a suffix or structure.\n\nExample 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \nSubject: \"tirt\" (the owner) \nVerb: \"kadeːg\" (repaired) \nObject: \"allesu\" (the dress) \n→ Subject-verb-object structure with no beneficiary.\n\nExample 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men (subject) \n\"will give\" = verb (biticcirra) \n\"darbadki\" = the chicken (object) \n\"biticcirra\" → verb form with suffix → \"to the dogs\" \n→ \"biticcirra\" = give to the dogs \n\nSo the structure is: [subject] [verb] [object] [for/beneficiary] \nBut for \"to\" in giving, the structure is: [verb] + [object] + [to] + [recipient] \nNote: \"darbadki\" is \"the chicken\" (object), \"biticcirra\" is not the benefit, it's the action to the recipient.\n\nThus, the verb has a suffix that indicates direction: “to X”.\n\nIn Example 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n\"man\" = he \n\"kadeːcciːg\" = stole (verb) \n\"kadeːcciːg\" = verb of stealing \n\"maːgtirsu\" = for the young man → beneficiary \n\nSo \"for\" constructions occur with a suffix \"-su\" or \"-irsu\" to indicate recipient, which is the beneficiary of the action.\n\nExample 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"ay\" = I \n\"beyyeːcciːg\" = am buying \n\"ajaːnirri\" = the necklaces (object)\n\nStandard verb with object.\n\nExample 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog (subject) \n\"aygi\" = found (verb) \n\"baːbiːg\" = the doors (object) \n\"eldeːnsu\" = for me (beneficiary)\n\nOnce again, “for me” is attached via “-su” to indicate beneficiary.\n\nExample 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n\"magas\" = thief \n\"ikki\" = you (plural) \n\"ticcirsu\" = gave to you → “ticcirsu” means “gave to (someone)” \nSo: “ticcirsu” = gave to → beneficiary is marked in the verbal suffix.\n\nExample 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n\"iːdi\" = the men \n\"magaski\" = gave (verb) \n\"kamiːg\" = camels (object) \n\"tirsa\" = to the thief → suffix “-sa” = to the thief\n\nNote: “tirsa” = to the thief \n“tir” → to, “sa” → thief\n\nIn that example, “tirsa” is the prepositional suffix “to the X”\n\nSo, verbs can have a suffix indicating direction (“to” something), and objects are directly marked.\n\nNow analyze how “for” vs “to” is used:\n\n- In Example 1: \"for the neighbours\" → \"jaːnticcirsu\" \n- In Example 6: \"for me\" → \"eldeːnsu\" \n- In Example 8: \"to the thief\" → \"tirsa\"\n\nThe root verb seems to have a directional suffix that expresses either \"to\" or \"for\" depending on context. \nBut let's check:\n\nIn Example 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" \n\"jaːnticcirsu\" → \"for the neighbours\" \nIn Example 6: \"the dog found the doors for me\" → \"eldeːnsu\"\n\n\"for X\" = beneficiary of the action → people receiving the benefit.\n\n\"to X\" = recipient of the action → direct recipient of the object.\n\nIn Example 3: \"will give the chicken to the dogs\" → \"biticcirra\" — no \"to\" in the word, but \"biticcirra\" is the verb form meaning \"give to\". \nIn Example 7: \"gave you the dogs\" → \"ticcirsu\" → \"to you\"\n\nSo pattern: \n- \"give to\" = suffix attached to verb: e.g., “ticcirsu” = give to \n- \"give for\" = e.g., \"jaːnticcirsu\" = give for \n\nBut in Example 1: \"we bought the camels for the neighbours\" → “jaːnticcirsu” \nCompare to Example 4: “he stole the dresses for the young man” → “maːgtirsu” — “for the young man” → suffix “-irsu” → “maːgtirsu”\n\nIn Example 6: “for me” → “eldeːnsu”\n\nIn Example 8: “to the thief” → “tirsa”\n\nSo the form of the suffix varies:\n\n- For giving: \n - To the X → \"tirsa\" (to the thief) \n - For the X → \"jaːnticcirsu\" (for neighbours) or \"maːgtirsu\" (for young man)\n\nBut in Example 1: “jaːnticcirsu” = for neighbours\n\nIn Example 6: “eldeːnsu” = for me\n\nSo suffixes vary by grammatical role: \n- “for” → beneficiary → headed by suffix like “-irsu” or “-su” depending on noun \n- “to” → direct recipient → headed by “-tir” or “-sa”?\n\nWait — in Example 3: “to the dogs” → in the sentence: “jahali waliːg darbadki biticcirra” \nSo verb is “biticcirra” — what is “biticcirra”? \n\"biti\" = give? \n\"ccirra\" = to?\n\nSo verb root: “biti” + “ccirra” → “biticcirra” = give to\n\nIn Example 7: “magas ikki waliːg ticcirsu” → “ticcirsu” = gave to you\n\nSo the verb has a “to” suffix attached. \n\nBut in Example 1: “kanarriːcciːg” → “bought” — no obvious “to” in the verb \n“bought for” → “jaːnticcirsu” — so “jaːnticcirsu” = bought for\n\nSo two different patterns: \n- “for” → verb + “-tir” or “-irsu” or “-su” \n- “to” → verb + “-sa” or “-tir”?\n\nWait. In Example 3: \"biticcirra\" → verb with “-ccirra” — likely “to” suffix \nIn Example 7: \"ticcirsu\" → “to” (to you) \nIn Example 8: \"tirsa\" → to the thief \n\nSo the “to” structure seems to have a base form and a suffix like “-tir” or “-sa” that triggers the object direction.\n\nBut in Example 1: “jaːnticcirsu” — “for neighbours” — no “to” suffix, but “jaːnticcirsu” contains the word “jaːnti” + “ccirsu” — possibly for.\n\nConclusion: Kunuz Nubian uses a verb that can have either a “to” suffix or a “for” suffix depending on the type of transfer.\n\nBut note: the object comes before the recipient in the clause.\n\nPattern:\n\n- [subject] + [verb] + [object] + [beneficiary clause]\n\nIn Example 3: \"The young men will give the chicken to the dogs\" \nStructure: jahali (subject) waliːg (object) darbadki (chicken) biticcirra (verb + to the dogs) \n\nBut \"biticcirra\" is the full verb form meaning \"give to the dogs\" \n\nSo verb includes the recipient in the suffix.\n\nSimilarly, in Example 1: \"we bought the camels for the neighbours\" → “kanarriːcciːg kamiːg jaːnticcirsu” \n\"kanarriːcciːg\" = bought \n\"kamiːg\" = the camels \n\"jaːnticcirsu\" = for the neighbours \n\nSo \"jaːnticcirsu\" = for the neighbours → suffix = “-ccirsu”?\n\nIn Example 6: \"the dog found the doors for me\" → “baːbiːg eldeːnsu” \n“eldeːnsu” = for me → suffix “-nsu”?\n\nIn Example 4: \"he stole the dresses for the young man\" → “maːgtirsu” → “-irsu” = for young man\n\nSo the form depends on the noun:\n\n- “young man” → “-irsu” \n- “neighbours” → “-ccirsu” \n- “me” → “-nsu” \n- “thief” → “tirsa” → for “to the thief”\n\nSo “to” and “for” have different suffixes.\n\nNow, do “to” and “for” mean exactly the same in meaning?\n\nIn Example 3: the chicken is given to the dogs — direct recipient → action goes to the dogs \nIn Example 1: camels are bought for the neighbours — the neighbours benefit → the camels are now theirs → beneficiary\n\nSo \"to\" = direct recipient of the object \n\"for\" = beneficiary (the one who gains from the action)\n\nIn English, “give the book to the teacher” vs “give the book to the teacher for his class” — but in this language, \"to\" and \"for\" are distinct.\n\nSo for translation:\n\n16. \"The neighbours are giving the necklace to the owner.\" \n→ Subject: \"the neighbours\" → from example 1: \"jaːnticcirsu\" for neighbours → but \"to the owner\" — so this is “to” → use “to the owner” suffix\n\nFrom Example 8: “the men gave the camels to the thief” → “tirsa” → “to the thief”\n\nSo “tirsa” = to the thief → so “to the owner” would be “tirsu”?\n\nCheck if suffix is “-tir” + noun?\n\n“tirsa” → “the thief” → “tir” + “sa”\n\nIn Example 3: “to the dogs” = “biticcirra” — “biti” + “ccirra” — so “ccirra”?\n\nBut “tirsa” = “tir” + “sa” → \"tir\" = to, \"sa\" = thief\n\n“biticcirra” — “biti” = give, “ccirra” = to?\n\nSo likely the base verb has a “to” suffix that is a root form + suffix that marks the object.\n\nSo for “to the owner” → what is the suffix?\n\nFrom Example 8: “tirsa” = to the thief\n\nWhat is “tir” base? Likely “to”\n\n“thief” → “sa”\n\nSo “to the [noun]” → “tir” + noun root\n\nSimilarly, in Example 6: \"for me\" → \"eldeːnsu\" → “el” + “deːnsu” → “eldeːnsu” for me\n\n“me” → “nsu”\n\nSo we can infer:\n\n- “for X” → verb + [suffix based on X] \n- “to X” → verb + “tir” + [noun root]\n\nAlso, in Example 1: “for the neighbours” → “jaːnticcirsu” → base verb “kanarriːcciːg” with “jaːnticcirsu” — likely “ja” + “nti” + “ccirsu” → “-ccirsu” for neighbours\n\nBut “neighbours” → “ja”?\n\nIs “ja” a root for neighbours?\n\nPossibly not — better to extract the word for “neighbour” → \"jaːnti\" — but in example 1: “jaːnticcirsu” = for neighbours\n\nSo “jaːnti” + “ccirsu” → “for neighbours”\n\nSimilarly, \"for the young man\" → “maːgtirsu” → “maːgti” + “rsu” → “maːgti” = young man?\n\n“maːgti” → young man?\n\n“young man” → “waliːg” in example 3 → “waliːg” → “wali”?\n\nBut “maːgti” — “ma” = young, “gti” = man?\n\nWe have to be cautious.\n\nNow for the translation:\n\n16. The neighbours are giving the necklace to the owner.\n\nSubject: \"the neighbours\" \nVerb: “are giving” — present tense, continuous? \nLook at Example 3: “will give” — future \nExample 2: “repaired” — past \nExample 1: “bought” — past\n\n“are giving” → present ongoing?\n\nIn example 8: “The men gave the camels to the thief.” — past\n\nNo present continuous.\n\nBut Example 1 is past: “we bought” — past\n\nIs there a present form?\n\nExample 5: “I am buying” → “ay beyyeːcciːg” → present continuous?\n\n“ay” = I \n“beyyeːcciːg” = am buying\n\nYes — so present progressive → \"beyyeːcciːg\"\n\nSo “are giving” → present continuous verb form?\n\nFrom Example 3: “will give” = future \nExample 5: “am buying” = present continuous\n\nSo for “giving” → base verb is likely “biti” or similar.\n\nLook at example 3: “jahali waliːg darbadki biticcirra” → “biticcirra” → verb form\n\n“biti” = give? \nBut “biticcirra” → suffix “ccirra” → likely “to”\n\nSimilarly, in Example 8: “tirsa” → to the thief\n\nSo base verb: “biti” or “tir”?\n\nIn “biticcirra” → “to the dogs”\n\nIn “tirsa” → “to the thief”\n\nSo likely the base is “tir” or “bit”?\n\nBut in example 3: “biticcirra” — “bit” + “ccirra” → to\n\nIn example 8: “tirsa” — “tir” + “sa” → to\n\nSo different roots?\n\nPossibly “biti” is “give”, and “tir” is “to” — but the verb forms are different.\n\nWait — in example 3: “give the chicken to the dogs” → “biticcirra” \nIn example 8: “give the camels to the thief” → “tirsa”\n\nSo “give” → uses different verb forms?\n\nUnlikely — probably a single verb root.\n\nAlternative: the verb has both aspects.\n\nBut perhaps the root is “bey” or “bit” — and in different constructions, suffixes vary.\n\nBut from pattern:\n\n- “to X” = verb + “tir” + root of X \n- “for X” = verb + suffix based on X\n\nWe have for sending objects:\n\nExample 3: “give the chicken to the dogs” → verb “biticcirra”\n\nExample 8: “give the camels to the thief” → “tirsa”\n\nSo both use “to” with the noun in a suffix.\n\nSo likely: verb root + “tir” + noun-root\n\nWhat is the noun root?\n\n“dogs” → “tir” + “sa” → “tirsa” — “sa” = thief?\n\n“doy” or “tir” for dogs?\n\nNo — in example 8, object is “camels” — object is “kamiːg”\n\nThe object is separate.\n\nSo verb = [subject] [verb] [object] [to X] — in example 8: \"iːdi magaski kamiːg tirsa\" → “iːdi” = men, “magaski” = gave, “kamiːg” = camels, “tirsa” = to thief\n\nSo verb = “magaski” — “gave” → base verb\n\nThen “tirsa” = to the thief\n\nSo “gave” is the base verb, and “to the thief” is marked as suffix.\n\nSimilarly, in example 3: “biticcirra” = verb + to dogs\n\nSo the verb form includes a “to” suffix that takes the noun.\n\nSo for “to the owner” — “tir” + owner root\n\nWhat is the root of “owner”?\n\nWe have “owner” in example 2: “the owner repaired” → “tirt”\n\n“tirt” = owner\n\nSo “owner” → “tirt”\n\nSo “to the owner” → “tir” + “tirt” → “tirtir”?\n\nBut in the sentence “to the thief” → “tirsa”\n\n“thief” → “sa”\n\nSo “thief” → “sa”, “owner” → “tirt”?\n\nThen “tir” + “tirt” → “tirtir", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11930.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "We analyze the given English-to-Kunuz Nubian examples to extract patterns for translating the questions in (b).\n\nStep 1: Identify common structure in examples.\n\nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu \n→ \"We bought the camels for the neighbours\" \nStructure: [subject] [past] [object] [for] [recipient] \n\"ar\" = we; \"kanarriːcciːg\" = bought; \"kamiːg\" = the camels; \"jaːnticcirsu\" = for the neighbours \n\n→ \"for\" is expressed by a relational clause with a noun (jaːnticcirsu) after the object.\n\nExample 2: tirt kadeːg allesu \n→ \"The owner repaired the dress\" \nSubject: tirt (the owner); verb: kadeːg (repaired); object: allesu (the dress)\n\nExample 3: jahali waliːg darbadki biticcirra \n→ \"The young men will give the chicken to the dogs\" \nSubject: jahali waliːg (the young men); verb: darbadki (will give); object: biticcirra (the chicken); to: dogs (implied?) \nBut \"to the dogs\" is not directly present; however, in example 1, \"for the neighbours\" uses \"jaːnticcirsu\" meaning \"for the neighbours\".\n\nExample 4: man jahalgi kadeːcciːg maːgtirsu \n→ \"He stole the dresses for the young man\" \n\"man\" = he; \"jahalgi\" = stole; \"kadeːcciːg\" = the dresses; \"maːgtirsu\" = for the young man\n\n→ So structure: [subject] [verb] [object] [for] [recipient]\n\nExample 5: ay beyyeːcciːg ajaːnirri \n→ \"I am buying the necklaces\" \n\"ay\" = I; \"beyyeːcciːg\" = am buying; \"ajaːnirri\" = the necklaces\n\nExample 6: wal aygi baːbiːg eldeːnsu \n→ \"The dog found the doors for me\" \n\"wal\" = the dog; \"aygi\" = found; \"baːbiːg\" = the doors; \"eldeːnsu\" = for me\n\n→ Pattern: [subject] [verb] [object] [for] [recipient]\n\nExample 7: magas ikki waliːg ticcirsu \n→ \"The thief gave you (pl.) the dogs\" \n\"magas\" = thief; \"ikkii\" = you (pl.); \"ticcirsu\" = gave → verb? But verb is \"ticcirsu\" or is \"ticcirsu\" the verb?\n\nWait: \"magas\" = thief; \"ikkii\" = you; \"ticcirsu\" = gave the dogs? But the verb is at end → \"ticcirsu\" = gave\n\n→ \"magas ikki waliːg ticcirsu\" → the thief gave you the dogs\n\nSo structure: [subject] [recipients] [verb] [object] \nBut note: it's not [subject] [verb] [object] [for] — rather, verb comes after object.\n\nCompare again:\n\nExample 3: jahali waliːg darbadki biticcirra \n→ young men will give the chicken → \"jahali waliːg\" (subject), \"darbadki\" (future verb), \"biticcirra\" (object), no \"to\" or \"for\" \nBut in example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \n\"jaːnticcirsu\" = for the neighbours\n\n→ So in cases with \"for\", the object is followed by \"for\" + recipient.\n\nSimilarly, example 4: man jahalgi kadeːcciːg maːgtirsu → he stole the dresses for the young man → \"maːgtirsu\" = for the young man\n\nSo: [subject] [verb] [object] [for] [recipient]\n\nExample 8: iːdi magaski kamiːg tirsa \n→ \"The men gave the camels to the thief\" \n\"iːdi\" = the men; \"magaski\" = gave; \"kamiːg\" = the camels; \"tirsu\" = to the thief?\n\nBut \"tirsu\" → appears as \"tirsu\" in example 8 → is it \"to\"?\n\nIn example 6: \"baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"for\" = a post-object phrase with recipient.\n\nSo pattern: \n[subject] [verb] [object] [for] [recipient] \nBut in example 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs — no \"for\", just gives to (you)\n\nSo when recipient is direct, it may be expressed by a recipient in the object or as a final phrase.\n\nBut note example 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me → implies \"for\" + pronoun\n\nSimilarly, example 1: \"jaːnticcirsu\" = for the neighbours → \"jaːnticcirsu\" = for (neighbours)\n\nIn example 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → no \"for\", no recipient → so only object.\n\nExample 9: ay hanuːg bijomri → I will strike the donkey → no for.\n\nSo the use of \"for\" is separate and dependent on the presence of a recipient.\n\nNow, we need to translate the following:\n\n16. The neighbours are giving the necklace to the owner.\n\n→ \"The neighbours\" = jaːnticcirsu? → in example 1, \"jaːnticcirsu\" = for the neighbours → so \"neighbours\" is \"jaːnticcirsu\"\n\nBut here they are giving → verb = give → what is the verb?\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → young men will give the chicken → \"darbadki\" = will give\n\nExample 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs → \"ticcirsu\" = gave\n\nSo \"give\" = \"darbadki\" (future) or \"ticcirsu\" (present)?\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → men gave the camels to the thief → \"magaski\" = gave → past tense\n\nSo verb \"gave\" = magaski \n\"will give\" = darbadki \n\"are giving\" = ? → continuous?\n\nBut example 3: \"will give\" → darbadki\n\nAre there present continuous forms?\n\nNo example has \"are giving\" — so perhaps the present tense is used in different form.\n\nBut in example 1: \"ar kanarriːcciːg\" → past — bought\n\n\"ay beyyeːcciːg\" → present — I am buying\n\nSo present: beyyeːcciːg → \"am buying\"\n\n\"will\" → darbadki\n\n\"past\" → kanarriːcciːg, kadeːg, ticcirsu, etc.\n\nSo \"are giving\" = ? Not directly seen.\n\nBut example 3: \"will give\" = darbadki → future\n\nExample 8: \"gave\" = magaski → past\n\nIs there a present continuous? Not found.\n\nPossibility: \"are giving\" may be expressed with a present tense verb of giving.\n\nExample 3: \"will give\" → darbadki\n\nSo perhaps \"are giving\" = darbadki? But that’s future.\n\nNo example uses \"are\" — perhaps the present tense verb is used for habitual or present, and the future is expressed with \"will\" marker.\n\nBut \"we bought\" → past; \"I am buying\" → present; \"will buy\" → future.\n\nSo for \"are giving\", likely the verb is in present tense, possibly base form + present marker?\n\nBut all present forms seem to use a marker.\n\nIn example 5: \"ay beyyeːcciːg\" → \"am buying\"\n\nSo \"be\" is used — \"be\" is in the subject?\n\n\"ay beyyeːcciːg\" → I am buying\n\n\"beyyeːcciːg\" = am buying\n\nSo present tense marker embedded.\n\nNow, \"giving\" — where is the verb?\n\nExample 3: \"darbadki\" = will give\n\nExample 7: \"ticcirsu\" = gave (past)\n\nExample 8: \"magaski\" = gave\n\nSo past: magaski \nfuture: darbadki \npresent: ? — in example 5: \"beyyeːcciːg\" = buying — so \"buying\" is the present\n\nSo verb for \"give\" = ?\n\nIs there a verb form for \"give\"?\n\nIn example 3: \"darbadki\" — will give → likely base verb is \"darbad\" or \"darbadki\"\n\nIn example 7: \"ticcirsu\" = gave → base may be \"ticcir\"\n\nBut no \"give\" in present.\n\nPossibility: the present tense of \"give\" may be \"dibr\" or something — not seen.\n\nWait: example 8: \"iːdi magaski kamiːg tirsa\" → men gave the camels to the thief → \"magaski\" = gave → past tense\n\nBut in example 3: \"darbadki\" = future — verb is \"darbadki\"\n\nSo \"give\" = a root with suffixes.\n\nWe lack \"give\" in present tense.\n\nBut perhaps \"are giving\" is expressed with the present verb form — so we must find the present verb for \"give\".\n\nBut none in data.\n\nAlternative: \"are giving\" might be formed with a present verb that means \"to give\", patterned from example 3.\n\nSince no clear form, but see:\n\nIn example 16: \"The neighbours are giving the necklace to the owner.\"\n\nWe have:\n\n- subject: the neighbours → \"jaːnticcirsu\" (as in example 1)\n\n- verb: are giving → present continuous? Not found, but possibly present tense of \"give\"\n\n- object: the necklace → \"beyyeːcciːg\" (as in \"I am buying the necklaces\") — so \"beyyeːcciːg\" = the necklaces\n\n- recipient: the owner → \"tirt\" (as in example 2: \"the owner repaired\")\n\nIn example 2: \"tirt\" = the owner\n\nSo recipient = \"tirt\"\n\nSo \"to the owner\" = \"tirsu\" + \"tirt\"? From example 8: \"to the thief\" = \"tirsa\" → \"tirsa\" = to the thief\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → men gave the camels to the thief → \"tirsa\" = to the thief\n\nIn example 6: \"eldeːnsu\" = for me — so \"for\" → might be different\n\nSo \"to\" and \"for\" — different prepositions in data?\n\nExample 6: \"found the doors for me\" → \"eldeːnsu\"\n\nExample 8: \"gave to the thief\" → \"tirsa\"\n\nSo \"to\" = \"tirsa\" → to the thief\n\n\"for\" = \"eldeːnsu\" → for me\n\nNow, in 16: \"to the owner\" → \"tirsa\" + \"tirt\"? → \"tirt\" = owner\n\nBut \"tirt\" is used as \"the owner\"\n\nSo \"to the owner\" = \"tirsa tirt\"?\n\nBut does \"tirsa\" mean \"to\" or \"for\"?\n\nIn 8: \"tirsa\" → to → so likely \"to\" = \"tirsa\"\n\nIn 6: \"eldeːnsu\" → for → so clearly \"for\" = \"eldeːnsu\"\n\nSo in 16: \"to the owner\" = \"tirsa tirt\"\n\nNow, \"the neighbours\" → \"jaːnticcirsu\" (as in example 1: \"for the neighbours\")\n\nBut is \"jaːnticcirsu\" used as subject?\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\"\n\nSo \"jaːnticcirsu\" is the recipient.\n\nBut as subject? No, it’s the recipient.\n\nBut in example 16, \"the neighbours\" is the subject → so they are giving.\n\nSo subject = \"jaːnticcirsu\"?\n\nBut only in example 1 is \"jaːnticcirsu\" used as object or recipient.\n\nIs there an example where \"the neighbours\" is the subject?\n\nNo — only as recipient.\n\nBut in example 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" is recipient.\n\nSo no subject = neighbours.\n\nBut in the target, \"the neighbours are giving\" — subject must be \"neighbours\".\n\nSo we need to find a noun for \"the neighbours\" as subject.\n\nPossibility: in example 1, the noun for \"neighbours\" is \"jaːnticcirsu\" — but used as recipient.\n\nCould it be used as subject?\n\nMaybe — no clear indication.\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\"\n\n\"aygi\" = are giving → verb\n\nSo \"sarkaːyi\" = the cowards → subject\n\n\"aygi\" = are giving (present)\n\n\"beyyeːcciːg\" = the necklaces\n\n\"adeːnda\" = to me? → \"adeːnda\" — is it \"to me\" or \"for me\"?\n\n\"adeːnda\" → in example 6: \"eldeːnsu\" = for me → so \"adeːnda\" might be \"for me\"?\n\nBut in example 10: \"giving me the necklaces\" → likely \"to me\" or \"for me\"?\n\nBut in example 10, the word is \"adeːnda\" — and in example 6, \"eldeːnsu\" = for me\n\nSo \"adeːnda\" — phonetically similar — could be for me?\n\nBut example 6: \"found the doors for me\" → \"eldeːnsu\"\n\nSo \"adeːnda\" might be \"to me\" or \"for me\"?\n\nBut in 10: \"are giving me the necklaces\" → likely \"to me\" or \"for me\"?\n\nBut no clear marker.\n\nBut in example 3: \"will give the chicken to the dogs\" → not present.\n\nBack to example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"\n\nsarkaːyi = the cowards \naygi = are giving \nbeyyeːcciːg = the necklaces \nadeːnda = to me?\n\nIf \"adeːnda\" = to me → then \"to me\" = \"adeːnda\"\n\nBut in example 6: \"for me\" = \"eldeːnsu\"\n\nSo different.\n\nPossibility: \"adeːnda\" = \"to me\"\n\n\"eldeːnsu\" = \"for me\"\n\nSo \"to\" = \"adeːnda\", \"for\" = \"eldeːnsu\"\n\nIn example 8: \"to the thief\" = \"tirsa\" → so \"to\" = \"tirsa\"\n\nContradiction — both \"tirsa\" and \"adeːnda\" used for \"to\"?\n\nIn example 8: \"to the thief\" = \"tirsa\" → so \"to\" = \"tirsa\"\n\nIn example 10: \"giving me\" → \"adeːnda\" → to me?\n\nBut \"adeːnda\" might be a different form.\n\nBut no clear semantic split.\n\nAnother idea: the recipient is expressed by a noun in a preposition.\n\nIn examples:\n\n- 1: \"for the neighbours\" → \"jaːnticcirsu\" \n- 4: \"for the young man\" → \"maːgtirsu\" \n- 2: \"the owner repaired the dress\" — no recipient \n- 6: \"for me\" → \"eldeːnsu\" \n- 10: \"to me\" → \"adeːnda\"\n\nSo \"for\" = \"eldeːnsu\" (in 6) and \"maːgtirsu\" (in 4) — for the young man\n\n\"maːgtirsu\" = for the young man\n\n\"eldeːnsu\" = for me\n\n\"tirsa\" = to the thief\n\n\"adeːnda\" = to me\n\nThen \"to\" and \"for\" are different.\n\nBut in 16: \"to the owner\" → \"to\" → so must be \"tirsa\" + owner\n\n\"owner\" = \"tirt\" (as in example 2)\n\nSo \"to the owner\" = \"tirsa tirt\"\n\nNow, verb: \"are giving\"\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\"\n\nSo \"aygi\" = are giving\n\n\"beyyeːcciːg\" = the necklaces\n\nSo the verb for \"give\" is \"aygi\"? But in example 3: \"darbadki\" = will give\n\n\"aygi\" = present (are giving)?\n\nYes — so \"aygi\" = present tense (are giving)\n\nSo \"give\" → verb = \"aygi\" (present)\n\n\"give\" is marked with \"aygi\" in present.\n\nSo for \"are giving\" → \"aygi\"\n\nSo full form for 16:\n\nsubject: the neighbours → what word?\n\nIn example 1: \"jaːnticcirsu\" = for the neighbours — so likely \"jaːnticcirsu\" is the noun for \"neighbours\"\n\nBut is it used as subject?\n\nIn example 10: \"sarkaːyi\" = the cowards → so \"sarkaːyi\" is the subject\n\nAnother noun:", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11922.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze the given sentences to identify verb patterns, case marking, and semantic roles.\n\nLook for general structure:\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = subject (we)\n- \"kanarriːcciːg\" = bought (active, past)\n- \"kamiːg\" = the camels (object)\n- \"jaːnticcirsu\" = for the neighbours (prepositional phrase, recipient)\n\nThus, verb + object + for + recipient\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = subject (the owner)\n- \"kadeːg\" = repaired (verb)\n- \"allesu\" = the dress (object)\n\nSimple transitive verb, subject + verb + object.\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = subject (young men)\n- \"waliːg\" = will (future auxiliary)\n- \"darbadki\" = give (verb)\n- \"biticcirra\" = the chicken (object)\n- \"to the dogs\" → implied → \"biticcirra\" is object, dogs are recipient\n\nStructure: subject + future + verb + object + to + recipient\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he\n- \"jahalgi\" = stole (past, active)\n- \"kadeːcciːg\" = dresses (object)\n- \"maːgtirsu\" = for the young man (prepositional phrase)\n\nPattern: subject + verb + object + for + recipient\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I (subject)\n- \"beyyeːcciːg\" = buying (present tense, continuous)\n- \"ajaːnirri\" = the necklaces (object)\n\nPresent continuous: subject + verb (present) + object\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = the dog (subject)\n- \"aygi\" = found (verb)\n- \"baːbiːg\" = doors (object)\n- \"eldeːnsu\" = for me (recipient)\n\nAgain: subject + verb + object + for + recipient\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief (subject)\n- \"ikki\" = gave (verb)\n- \"waliːg\" = you (pl.) (object)\n- \"ticcirsu\" = the dogs (object)\n\nWait: \"ikki waliːg ticcirsu\" → \"gave you the dogs\" → so object is \"you\", verb is \"ikki\" = give\n\nBut \"ticcirsu\" = \"the dogs\" → object of giving\n\nSo structure: subject + verb + object + [object]?\n\nBut how is \"you\" and \"the dogs\" both objects?\n\nActually, in this case, it's: \"gave you the dogs\" → two objects: recipient and item.\n\nNo, in 7: \"The thief gave you (pl.) the dogs.\" → so \"you\" is recipient, \"dogs\" is given.\n\nSo verb \"ikki\" = give, subject, recipient, object.\n\nBut no direct indication of prepositional \"to\" in the sentence.\n\nBut in other examples, \"to\" is marked with \"for\".\n\nCompare: example 1: \"bought the camels for the neighbours\" → \"for\" = recipient\n\nExample 4: \"stole the dresses for the young man\" → \"for\" = recipient\n\nExample 6: \"found the doors for me\" → \"for\" = recipient\n\nSo \"for\" = to recipient\n\nIn 3: \"give the chicken to the dogs\" → \"to\" = recipient\n\nIn 3, \"to\" is used directly, in others \"for\"\n\nIn 3: \"to the dogs\", in 1: \"for the neighbours\", in 4: \"for the young man\", in 6: \"for me\"\n\nSo maybe \"to\" and \"for\" are interchangeable? Or is there difference?\n\nCheck example 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\"\n\n\"to the dogs\" → preposition \"to\"\n\nBut in 1: \"we bought the camels for the neighbours\" → \"for\"\n\nWhy both?\n\nNote: \"for\" might be used with agent, \"to\" with recipient?\n\nNo, in 1: \"bought for the neighbours\" → neighbours are recipient\n\nIn 6: \"found for me\" → me is recipient\n\nIn 3: \"give to the dogs\" → recipient\n\nSo both are used to mark recipient.\n\nPossible that \"to\" and \"for\" are synonymous in this language — one might be direct, the other indirect.\n\nBut: look at 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\"\n\n\"are giving me\" → \"me\" is recipient\n\n\"adeːnda\" = necklaces — object\n\nSo verb + object + for/ to + recipient\n\nIn all cases, recipient is marked with \"for\" or \"to\".\n\nBut in 3: \"to the dogs\", in others: \"for\" → maybe shift in preposition depends on semantic role.\n\nBut perhaps the preposition is fixed: recipient is marked with \"for\" or \"to\" depending on context.\n\nBut in 3, \"to\" is used. In others, \"for\".\n\nIs there a reason?\n\nIn 3, \"the young men will give the chicken to the dogs\" — \"to\" with living entity?\n\nIn 1, \"for the neighbours\" — plural group.\n\nIn 6, \"for me\" — personal pronoun.\n\nIn 10, \"giving me\" — \"me\" as recipient.\n\nSo perhaps \"to\" is used with animals/objects, \"for\" with humans?\n\nNot clear. But in 3, \"to the dogs\" → dogs are object of giving; in 1, \"for the neighbours\" → neighbours are recipients.\n\nBut in 3, \"give the chicken to the dogs\" — dogs are the ones receiving the chicken.\n\nSo recipient is marked with \"to\".\n\nBut in 1, \"bought the camels for the neighbours\" — neighbours are recipients.\n\nSo both are receiving.\n\nPossibility: the preposition matters for transitivity.\n\nAnother idea: all recipient phrases use a preposition, and the choice may be arbitrary or context-dependent.\n\nBut overall, the pattern seems to be:\n\nSubject + [tense marker] + verb + object + [preposition + recipient]\n\nNow, for translations:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\n→ subject: the neighbours \n→ verb: are giving → tense: present continuous → what form?\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → \"beyyeːcciːg\" = buying, present continuous\n\nIn 3: \"waliːg\" = will → future\n\nIn 1: past, \"ar kanarriːcciːg\" → bought\n\nSo for present: \"beyyeːcciːg\" = buying → present tense\n\nSo \"are giving\" → likely \"beyyegi\" or \"beyyegi\" + object?\n\n\"ay beyyeːcciːg\" = I am buying\n\nSo \"beyyeːcciːg\" is the verb for \"buying\"\n\nSimilarly, \"giving\" — what is the verb?\n\nIn example 3: \"waliːg darbadki biticcirra\" → \"will give\"\n\n\"waliːg\" = will\n\n\"darbadki\" = give\n\nSo verb is \"darbadki\"\n\nIn example 7: \"ikki waliːg ticcirsu\" → \"gave\", \"ikki\" = give\n\nIn 7: \"ikki\" = past form of give\n\nSo \"ikki\" = gave (past)\n\n\"waliːg\" = will (future)\n\nThen present? Possibly \"beyyegi\" or \"dababegi\"?\n\nBut no \"giving\" present form.\n\nIn 5: \"beyyeːcciːg\" = buying → past? No, present.\n\n\"beyyeːcciːg\" = \"to buy\"\n\nSo is there a \"to give\" present form?\n\nIn example 3: \"will give\" — \"waliːg\" is auxiliary.\n\nIn example 2: \"tirt kadeːg allesu\" → \"repaired\" — past.\n\nNo present giving.\n\nBut in 5: \"I am buying\" → present continuous = \"beyyeːcciːg\"\n\nSo perhaps the present continuous is formed with \"be\" + present participle.\n\n\"beyyeːcciːg\" = buying → so \"be\" + \"yey\" part?\n\nBut \"beyye\" → \"buying\"\n\nSo \"giving\" might be \"dababegi\"? Unseen.\n\nAlternatively, look at \"tirt\" = owner, \"kadeːg\" = repaired — what is \"repaired\"?\n\nNot giving.\n\nAnother possibility: the verb is \"tir\" or something.\n\nBut in 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\"\n\n\"iːdi\" = men (subject)\n\n\"magaski\" = the camels (object)\n\n\"tirsa\" = gave → verb?\n\n\"tirsa\" = gave\n\nCompare to 7: \"ikki waliːg ticcirsu\" → \"gave you the dogs\" — \"ikki\" = gave\n\nIn 8: \"tirsa\" = gave\n\nSo verb of \"give\" is \"tir\" or \"tirsa\"?\n\nIn 8: \"tirsa\" = gave (past)\n\nIn 3: \"darbadki\" = give (with \"waliːg\" = will)\n\nSo multiple forms: present, future, past.\n\nBut no explicit present continuous \"giving\".\n\nIn 5: present continuous = \"beyyeːcciːg\" — this is \"buying\"\n\nSo \"giving\" — present continuous might be \"beyyegi\" or \"waliːg darbadki\" — but that's future.\n\nPossibility: the present continuous for \"give\" is not directly given.\n\nBut in 16: \"are giving\" → present continuous.\n\nFrom 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\nSo \"beyyeːcciːg\" = present continuous form for \"buying\"\n\nSimilarly, \"giving\" might be \"dababegi\" or \"tirbiːg\"?\n\nBut no such word.\n\nWait — in 3: \"waliːg darbadki\" = will give\n\nSo \"darbadki\" = give → past tense?\n\nIn 7: \"ikki\" = give → past\n\nSo \"ikki\" = past form of \"give\"\n\n\"tirsa\" = past form of \"give\"\n\nSo both might be past.\n\nThen what is present?\n\nIn 5: present is formed with \"beyyeːcciːg\" — which is for \"buying\"\n\nSo perhaps \"buying\" and \"giving\" are separate.\n\nBut likely, \"be\" + verb root with vowel.\n\n\"beyyeːcciːg\" = \"be\" + \"yey\" → buying\n\nSo for \"giving\" → \"beyyegi\" or \"beyyegi\"?\n\n\"be\" + \"yeg\" = giving?\n\nBut \"yeg\" not seen.\n\nIn 3: \"darbadki\" — is this past?\n\nBut with \"waliːg\" = future.\n\nSo \"waliːg\" may be future auxiliary.\n\nThen past is \"ikki\" or \"tirsa\"?\n\nIn 3: out of context: \"waliːg darbadki\" — seems future\n\nIn 7: \"ikki waliːg\" — \"ikki\" + \"waliːg\"?\n\n\"ikki waliːg\" → \"gave you\" — so \"ikki\" = gave\n\nSo \"ikki\" = past tense of \"give\"\n\n\"tirsa\" = past tense of \"give\"\n\nSo \"tirsa\" = gave\n\nSo both past forms.\n\nNo present form in examples.\n\nBut 5: \"beyyeːcciːg\" = present continuous for buying.\n\nSo present continuous is marked with \"be\" + present participle.\n\nSo \"giving\" → present participle?\n\nWhat is the root?\n\n\"buy\" → \"beyy\" → \"be\" + \"yey\" → \"beyyeːcciːg\"\n\n\"give\" → ?\n\nLook at \"darbadki\" — seems like stem.\n\nIn 3: \"waliːg darbadki\" — future + verb\n\nSo \"darbadki\" = stem of give?\n\nIn 7: \"ikki\" = past form\n\nSo \"ikki\" = past of give\n\nIn 8: \"tirsa\" = past of give\n\nSo two past forms: \"ikki\", \"tirsa\"?\n\n\"ikki\" used with \"waliːg\" — \"waliːg iki\" — no.\n\n\"ikki waliːg\" — \"ikki\" + \"waliːg\" — structure shows \"ikki\" is verb.\n\nSo possibly \"ikki\" = gave (past)\n\n\"tirsa\" = gave (past)\n\nAre they synonyms?\n\n\"tirsa\" used in 8: \"iːdi magaski kamiːg tirsa\" → men gave camels to thief\n\n\"ikki\" in 7: \"ikki waliːg ticcirsu\" → thief gave you dogs\n\nSo both are past tense of give.\n\nNow, present continuous: only \"beyyeːcciːg\" is given.\n\nSo for \"are giving\", likely \"be\" + \"give\" root in participle form.\n\nBut what is it?\n\nPossibly derived from \"darbadki\" → \"dababegi\" or \"dababegi\"?\n\nBut no form.\n\nAlternatively, in 5: \"beyyeːcciːg\" = \"buying\"\n\nSo \"buying\" = \"be\" + \"yey\" → root \"yey\"\n\nSimilarly, \"giving\" → root \"dabab\"?\n\nBut no.\n\nAnother idea: the construction may be \"be\" + verb root + object, with \"for\" or \"to\" recipient.\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\nSo \"beyyeːcciːg\" = buying → present\n\nObject: \"ajaːnirri\" → the necklaces\n\nSo for 16: \"the neighbours are giving the necklace to the owner\"\n\n→ subject: \"jaːnticcirsu\" → neighbours?\n\nFrom 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours → \"jaːnticcirsu\" = neighbours\n\nSo \"jaːnticcirsu\" = neighbours\n\n\"the necklace\" → \"beyyeːcciːg\" is for \"necklace\" — \"beyyeːcciːg\" = buying necklaces\n\nSo \"necklace\" = \"beyyeːcciːg\" — but that's buying.\n\n\"biticcirra\" = chicken in 3\n\n\"aajaːnirri\" = necklaces in 5\n\nSo \"beyyeːcciːg\" = necklaces\n\nSo \"necklace\" = singular of \"beyyeːcciːg\"? Or \"beyyeːcci\" — stem?\n\n\"beyyeːcciːg\" → likely \"be\" + \"yey\" + object\n\nSo object \"beyyeːcci\" → necklaces\n\nBut \"beyyeːcci\" as object?\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" — \"beyyeːcciːg\" = verb, \"ajaːnirri\" = object\n\nSo \"ajaːnirri\" = necklaces\n\nSo noun: \"beyyeːcci\" → necklaces\n\nSimilarly, \"ticcirsu\" = dogs\n\n\"maːgtirsu\" = young man\n\n\"biticcirra\" = chicken\n\nSo \"necklace\" → likely \"beyyeːcci\"\n\nIn 16: \"the necklace\" → \"beyyeːcci\"\n\nBut \"the\" is implied.\n\nNow, verb \"are giving\" → need to find stem for \"give\"\n\nLooking at patterns:\n\nIn example 7: \"magas ikki waliːg ticcirsu\" → thief gave you the dogs\n\n\"ikki waliːg\" → \"ikki\" = past form of give?\n\nBut \"waliːg\" = \"will\" — here \"waliːg\" appears after \"ikki\"\n\n\"ikki waliːg\" → \"gave will\" — no.\n\n\"ikki\" is verb, \"waliːg\" is future.\n\nBut 7: \"ikki waliːg ticcirsu\" → only if \"waliːg\" is part of it.\n\n\"Bear in mind: in 3: 'waliːg darbadki biticcirra' → will give the chicken to the dogs\"\n\nSo \"waliːg\" = will\n\n\"darbadki\" = give\n\nIn 7: \"ikki waliːg ticcirsu\" — \"ikki\" = gave, \"waliːg\" = will? Doesn't fit.\n\nUnless \"waliːg\" is a separate word.\n\nIn 7: \"ikki\" = gave, \"waliːg\" = is part of the object?\n\nNo — \"waliːg\" is \"you\" in plural.\n\nAh! Critical.\n\nIn example 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\"\n\n\"jali\" = young men, \"waliːg\" = you (pl.), \"darbadki\" = give\n\nSo \"waliːg\" is the object — \"you\"\n\nSimilarly, in example 4", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11829.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Analyze the source sentences to identify patterns in Kunuz Nubian syntax, especially regarding verb structure, object choice, and direction of transfer.\n\nLook at sentence 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \nStructure: [subject] [buy] [object] [for] [recipient] \n\"kanarriːcciːg\" = bought, \"kamiːg\" = the camels, \"jaːnticcirsu\" = for the neighbours \n→ The object is directly stated; \"for\" introduces a beneficiary/recipient.\n\nSentence 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n\"tirt\" = the owner, \"kadeːg\" = repaired, \"allesu\" = the dress \nNo \"for\" here — it's just an action on object. But no beneficiary is mentioned.\n\nSentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men, \"waliːg\" = will, \"darbadki\" = give, \"biticcirra\" = the chicken, \"to the dogs\" = implied or unmarked? \nWait — \"biticcirra\" is object, and \"to the dogs\" is not directly marked. But in sentence 1, \"for the neighbours\" was marked by \"jaːnticcirsu\".\n\nCompare sentence 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"ay\" = I, \"beyyeːcciːg\" = buying, \"ajaːnirri\" = the necklaces → object is marked.\n\nSentence 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog, \"aygi\" = found, \"eldeːnsu\" = the doors, \"for me\" → \"for me\" is marked as \"eldeːnsu\" → the doors are given to me? No — \"found the doors for me\" → so the doors are the object, and \"for me\" is the beneficiary.\n\nWait: \"found\" is not a transfer verb — but the structure is: [subject] [verb] [object] [for] [beneficiary].\n\nIn sentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \nIs \"to the dogs\" present? It's not explicitly a \"for\" construction — \"to the dogs\" suggests direction of movement, not a transfer of possession.\n\nBut in sentence 1: \"bought the camels for the neighbours\" — \"for\" defines the beneficiary.\n\nSentence 10: \n\"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n\"sarkaːyi\" = the cowards, \"aygi\" = are giving, \"beyyeːcciːg\" = necklaces, \"adeːnda\" = to me? But \"adeːnda\" = \"to me\"? Or is it \"for me\"?\n\nCheck: \"adeːnda\" — in context, \"giving me the necklaces\" = giving to me.\n\nBut sentence 1 has \"for the neighbours\" — \"jaːnticcirsu\" — appears to be a specific preposition for beneficiary.\n\nSo: verb + object + for + beneficiary.\n\nVerb structure: \n- \"kanarriːcciːg\" = to buy \n- \"kadeːg\" = to repair \n- \"darbadki\" = to give \n- \"baːbiːg\" = to find \n- \"beyyeːcciːg\" = to buy \n- \"aygi\" = to give \n- \"aygi\" also appears in \"wal aygi baːbiːg eldeːnsu\" → found.\n\nSo verbs are: \n- buy: kanarriːcciːg / beyyeːcciːg \n- repair: kadeːg \n- give: darbadki / aygi \n- find: baːbiːg \n\nNow consider who does what.\n\nFor transferring something from one to another: \nStructure: [subject] [verb] [object] [for] [beneficiary] \n\nIn sentence 1: we (subject), bought (verb), camels (object), for (jaːnticcirsu) = neighbours (beneficiary)\n\nIn sentence 3: young men (subject), will give (waliːg darbadki), chicken (biticcirra), to the dogs? But not explicitly \"for\".\n\nBut sentence 3 says: \"will give the chicken to the dogs\" → so it's a directional preposition, not \"for\".\n\nIn sentence 6: \"The dog found the doors for me\" → found, object = doors, for me → beneficiary.\n\nSentence 10: \"give me the necklaces\" → same: \"giving me\" — beneficiary.\n\nSo in transfer, \"for\" is used to mark recipient.\n\nThus pattern: \n[subject] [verb] [object] [for] [beneficiary]\n\nNow go to translation tasks.\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\n→ subject: the neighbours \n→ verb: giving → use \"darbadki\" (to give) \n→ object: the necklace → \"beyyeːcciːg\"? or \"beyyeːcciːg\" = necklaces — appears in multiple forms.\n\nBut in sentence 5: \"I am buying the necklaces\" → \"beyyeːcciːg\" = necklaces.\n\n\"beyyeːcciːg\" for necklaces — common noun.\n\nIn sentence 1: \"camels\" = \"kamiːg\"\n\nSo \"necklace\" → \"beyyeːcciːg\" \n\"the\" = prefix or noun marker?\n\nIn examples: \n\"ar kanarriːcciːg kamiːg\" → \"ar\" = we, \"kanarriːcciːg\" = bought, \"kamiːg\" = the camels → so \"kamiːg\" = the camels\n\nSimilarly, \"tirt kadeːg allesu\" — \"kadeːg\" = repaired, \"allesu\" = dress → so \"allesu\" = the dress\n\nSo nouns are unmarked — \"beyyeːcciːg\" → the necklaces? Possibly.\n\nBut sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"giving me the necklaces\" → \"beyyeːcciːg\" is the object, and \"adeːnda\" = to me.\n\n\"adeːnda\" = to me? \"to\" or \"for\"?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\" → which might be \"to the neighbours\"?\n\nIn sentence 6: \"found the doors for me\" → \"eldeːnsu\" = the doors, \"for me\" → so \"for\" is used.\n\nSo in giving or buying, \"for\" is used to indicate beneficiary.\n\nSo 16: \"The neighbours are giving the necklace to the owner.\"\n\n→ subject: \"kamiːg\" → but \"kamiːg\" is used in sentence 1 for \"camels\" — not for \"neighbours\"\n\nWho are \"the neighbours\"?\n\nIn sentence 1: \"We bought the camels for the neighbours.\" → \"jaːnticcirsu\" = the neighbours.\n\nSo \"jaːnticcirsu\" = the neighbours → so \"the neighbours\" = jaːnticcirsu\n\nSo subject: \"jaːnticcirsu\"\n\nBut \"jaːnticcirsu\" is plural — \"the neighbours\"\n\nNow verb: giving → in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"young men will give the chicken\" → \"waliːg\" = will, \"darbadki\" = give\n\nSo \"waliːg\" = will — future\n\n\"darbadki\" = give\n\nSo for \"are giving\", we use \"waliːg\" (will) for present future?\n\nSentence 3 uses \"waliːg\" for future.\n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving\" → uses \"aygi\", which is \"giving\" (present)\n\nWait: \n- sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving\" → \"aygi\" = present tense?\n\nBut sentence 3 uses \"waliːg\" for future. So \"waliːg\" may be future, \"aygi\" present.\n\nSentence 1: \"We bought\" → past → no future marker\n\nSentence 5: \"I am buying\" → present → \"aygi\" not used? \"aygi\" appears only in future and present?\n\nWait: sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\" → no \"waliːg\", so \"beyyeːcciːg\" is present.\n\nBut \"ay\" = I → so present.\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving\" → present.\n\nSo \"aygi\" = present tense (giving)\n\n\"waliːg\" = future (will give)\n\nSo for 16: \"are giving\" → present → use \"aygi\"\n\nSo verb: \"aygi\" + \"darbadki\" → \"aygi darbadki\"? or \"darbadki aygi\"?\n\nIn sentence 3: \"jahali waliːg darbadki biticcirra\" → \"waliːg darbadki\" → prefix verb order?\n\n\"jahali\" (subject), \"waliːg\" (future), \"darbadki\" (verb)\n\nSo subject + future + verb?\n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → subject \"sarkaːyi\", \"aygi\" (present), \"beyyeːcciːg\" (object), \"adeːnda\" (for me)\n\n\"aygi beyyeːcciːg\" = \"giving the necklaces\" — so verb + object.\n\nSo verb comes after subject.\n\nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"ar\" (we), \"kanarriːcciːg\" (verb), \"kamiːg\" (object), \"jaːnticcirsu\" (for)\n\nSo order: subject + verb + object + for + beneficiary\n\nSo for 16: \nsubject: \"jaːnticcirsu\" (the neighbours) \nverb: \"aygi darbadki\" (are giving) \nobject: \"beyyeːcciːg\" (the necklace) \nfor: beneficiary → \"tirt\" (the owner)\n\nBut \"tirt\" = owner — used in sentence 2: \"the owner repaired the dress\" → \"tirt kadeːg allesu\"\n\nSo \"tirt\" = the owner\n\nIs \"tirt\" used in transfer? In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\n\"tirsa\" = to the thief → so \"tirsa\" = to?\n\nWait — sentence 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSimilarly, sentence 1: \"for the neighbours\" → \"jaːnticcirsu\" — not \"to\"\n\nBut in sentence 8: \"tirsa\" = to the thief\n\nSo two cases: \n- \"for\" = beneficiary → in buying/buying? \n- \"to\" = direction?\n\nBut in 1: \"bought for the neighbours\" → beneficiary \nIn 8: \"gave to the thief\" → direction?\n\nBut in 10: \"giving me\" → \"adeːnda\" → appears to mean \"to me\"\n\nSo in sentence 10: \"adeːnda\" = to me\n\nSentence 6: \"found the doors for me\" → \"eldeːnsu\" = doors, \"for me\" → \"for\"\n\nBut \"for me\" and \"to me\" → possibly the same?\n\nIn sentence 10: \"adeːnda\" = to me → but in sentence 6: \"for me\" → used \"for\"?\n\nContradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" — \"for me\"\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" → \"adeːnda\" = to me?\n\nBut is \"adeːnda\" \"to me\" or \"for me\"?\n\nPossibly a single preposition \"for\" or \"to\" depending on verb?\n\nBut search for overlap.\n\nSentence 3: \"will give the chicken to the dogs\" — no \"for\", uses \"to the dogs\"? Not in text.\n\nThe text says: \"to the dogs\" — so yes, written as \"to\".\n\nBut in the sentence: \"The young men will give the chicken to the dogs\" — so \"to the dogs\"\n\nBut in the translation, it's not marked as \"for\" — so \"to\" is used.\n\nBut in sentence 1: \"bought for the neighbours\" — \"for\"\n\nIn sentence 8: \"gave to the thief\" — \"tirsa\"\n\nSo different verbs have different prepositions?\n\nBut sentence 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\"\n\n\"tirsa\" = to the thief\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"for me\"\n\nBut \"found\" isn't a transfer, so maybe \"for\" only for transfer verbs?\n\nIn sentence 1: \"bought for\" → transfer \nSentence 10: \"giving me\" → transfer → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me → used in giving\n\nSentence 6: \"found for me\" → \"baːbiːg\" — not transfer verb\n\nSo likely: for transfer verbs (buy, give), the preposition is \"to\" (adeːnda) or \"for\"? \n\nIn sentence 1: \"bought for the neighbours\" — \"jaːnticcirsu\"\n\nIn sentence 10: \"giving me\" — \"adeːnda\" = to me\n\nSo \"jaːnticcirsu\" and \"adeːnda\" are different.\n\nIn sentence 8: \"gave to the thief\" — \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"jaːnticcirsu\" = for the neighbours\n\n\"adeːnda\" = to me\n\nInconsistent?\n\nBut sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours\n\nSentence 10: \"giving me\" → \"adeːnda\" = to me\n\nSentence 8: \"gave to the thief\" → \"tirsa\" = to the thief\n\nSo different markers:\n\n- \"jaːnticcirsu\" — for recipients (neighbours) \n- \"tirsa\" — to (thief) \n- \"adeːnda\" — to (me)\n\nBut \"adeːnda\" and \"tirsa\" both mean \"to\", while \"jaːnticcirsu\" is \"for\"?\n\nBut in 10, it's \"giving me\" — so should be \"to me\", so \"adeːnda\"\n\nSimilarly, in 16: \"to the owner\" → so \"tirsa\" or \"adeːnda\"?\n\n\"the owner\" — not \"me\" → so not \"adeːnda\"\n\n\"the owner\" — \"tirt\" = owner\n\nSo what preposition?\n\nIn sentence 2: \"the owner repaired the dress\" — no preposition\n\nIn sentence 8: \"gave to the thief\" — used \"tirsa\"\n\nIn sentence 1: \"bought for the neighbours\" — used \"jaːnticcirsu\"\n\nSo why different?\n\nPossibility: \"jaːnticcirsu\" only for certain objects?\n\n\"neighbours\" is a group — possibly a specific beneficiary.\n\n\"the thief\" — \"tirsa\"\n\n\"me\" — \"adeːnda\"\n\nSo perhaps \"for\" is used when the beneficiary is not a direct recipient, or when it's a group?\n\nBut in sentence 3: \"to the dogs\" — not marked with \"for\"\n\nBut sentence 3 says: \"to the dogs\" — not a preposition listed.\n\nSo likely, in Kunuz Nubian, the preposition for transfer is \"to\" — but expressed as a specific form.\n\nLet’s compile known forms:\n\n- for the neighbours → jaːnticcirsu \n- to the thief → tirsa \n- to me → adeːnda\n\nSo \"jaːnticcirsu\" = for, \"tirsa\" = to, \"adeːnda\" = to\n\nSo no single preposition.\n\nBut in the sentence: \"the neighbours are giving the necklace to the owner\" → the owner is someone else.\n\nSo \"to the owner\" → \"tirsa\" → because \"to the thief\" uses \"tirsa\"\n\nSimilarly, in sentence 8: \"to the thief\" → \"tirsa\"\n\nSo \"tirsa\" = to + [noun]\n\n\"jaːnticcirsu\" = for + [noun]\n\nSo for \"to the owner\", use \"tirsa\"\n\nBut is \"tirsa\" general?\n\nIn sentence 6: \"the dog found the doors for me\" → uses \"for me\" → but \"for\" used?\n\n\"eldeːnsu\" = doors, \"for me\" → how is \"for me\" marked?\n\nIt's not \"tirsa\" — \"tirsa\" is for \"to the thief\"\n\nSo \"found for me\" — \"for me\" is a distinct construction.\n\nBut in sentence 10: \"giving me\" → \"ade", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + 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"ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11873.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "We analyze the Kilivila language patterns from the given examples to decode the structure of the sentences.\n\nStep 1: Identify core components and their functions.\n\n- Subject markers:\n - \"Bikota\" → \"that\"\n - \"Lekota\" → \"this\"\n - \"Bibani\" → \"one\"\n - \"Lekalimati\" → \"the old\" (may be tied to \"chief\")\n - \"Navila\" → \"how many\"\n - \"Tevila\" → \"how many\"\n - \"Am\" → question prefix (e.g., \"Amtona\" = \"which\")\n - \"Bigisi\" → \"that clever\"\n - \"Legisi\" → \"that\" or \"this\" (as in \"that woman\")\n\n- Object markers:\n - \"minasina\" → \"fish\"\n - \"mtona\" → \"man\"\n - \"gwadi\" → \"child\"\n - \"makwena\" → \"stone\"\n - \"nunumwaya\" → \"two men\"\n - \"namwaya\" → \"canoes\"\n - \"gudimanabweta\" → \"this stone\"\n\n- Verbs (with aspect):\n - \"yena\" → \"will catch\"\n - \"mtona\" → \"arrived\"\n - \"magudiwena\" → \"saw\"\n - \"lekalimati\" → \"killed\"\n - \"waga\" → \"did\"\n - \"tetala\" → \"will see\"\n - \"tau\" → \"will\"\n - \"ka’ukwa\" → \"how many\"\n\n- Numerals:\n - \"one\", \"two\" → \"nayu\", \"nunumwaya\", \"tau\", \"minasina\"\n - \"minasina\" = \"four fish\" → \"four\" is encoded in \"minasina\"\n - \"nayu\" → \"two\" in \"which man killed two pigs\" (sentence 5)\n\n- Questions:\n - \"Navila\" = how many\n - \"Am\" = which / what\n - \"Tevila\" = how many (may be linked to number of entities)\n\nStep 2: Align each structure.\n\nExample 1: \n\"one man will catch these four fish\" \n→ \"Bibani navasi yena minasina tetala tau\" \n→ \"Bibani\" = one man \n\"navasi\" = will catch \n\"minasina\" = four fish \n\"tetala tau\" = will see? No — \"tetala\" = will catch? Wait.\n\nWait: \"yena\" = catch → \"navasi\" = catch? Or \"navasi\" = is \"will catch\"?\n\nCheck sentence 1: \"Bibani navasi yena minasina tetala tau\"\n\nMaybe \"navasi\" is \"will catch\", \"yena\" is a verb?\n\nBut sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\"\n\n\"kwetala\" → will see? Yes. \"vivila\" = something; \"minawena\" = something.\n\nSo: \"kwetala\" = will see\n\nThen in sentence 1: \"navasi yena\" → \"catch\"?\n\nBut \"yena\" appears only once.\n\nSentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"Which man killed two pigs?\"\n\n\"lekalimati\" = killed \n\"nayu\" = two \n\"bunukwa\" = pigs\n\nSo: \"lekalimati\" = kill \n\"nayu\" = two \n\"bunukwa\" = pig (pl)\n\nThus, \"bunukwa\" = pig (pl), \"bunukwa\" = pig (s?) → no: two pigs → plural.\n\nSentence 4: \"Legisi waga makesiwena namwaya minana.\" \n\"Legisi\" = that \n\"waga\" = saw \n\"makesiwena\" = those canoes \n\"namwaya\" → canoes\n\nSo \"waga\" = saw \n\"makesiwena\" = saw (this form is used with object)\n\n\"makesiwena\" seems to be \"saw\" + object \n\"namwaya\" = canoes → so \"makesiwena namwaya\" = saw canoes\n\nThen sentence 1: \"Bibani navasi yena minasina tetala tau\"\n\nBreak: \n\"Bibani\" = one man \n\"navasi\" = will catch? \n\"yena\" → not found elsewhere. \n\"minasina\" → four fish \n\"tetala tau\" → \"will see\"?\n\nWait: \"tetala\" = will see? From sentence 7: \"kwetala\" = will see → likely same word.\n\nSo \"tetala\" = will see \nBut \"navasi\" is before \"yena\"\n\nPossibility: typo? Or \"navasi\" = will catch?\n\nSentence 6: \"Leyamatasi teyu tauwau nunumwaya\" → \"the old women looked after two men\"\n\n\"leyamatasi\" = old women (subject) \n\"teyu\" = looked after \n\"tauwau\" = two? Or \"tau\" = one? \n\"nunumwaya\" = two men\n\nSo \"tauwau\" = two?\n\nBut in 5: \"nayu\" = two\n\n\"nayu\" and \"tauwau\" — both used for two?\n\nSentence 13: \"Navila vivila biyamatasi tau mtona?\" \n→ \"how many women will look after this man?\"\n\n\"vivila\" = will \n\"biyamatasi\" = old women \n\"tau\" = one \n\"mtona\" = man\n\nSo \"tau\" = one\n\nBut in 6: \"teyu tauwau nunumwaya\" → \"looked after two men\"\n\nSo \"tauwau\" = two\n\nThus: \"tau\" = one, \"tauwau\" = two → so \"tau\" is not numeral for plural.\n\n\"nayu\" = two → confirmed (sentence 5)\n\n\"nayu\" = two \n\"nunumwaya\" = two men \n\"tauwau\" = two (in \"two men\")\n\nSo \"nunumwaya\" = two men → possibly \"nayu\" is separate.\n\nNow \"minasina\" = four fish → in sentence 1: \"catch these four fish\"\n\nSo \"minasina\" = four fish → so \"minasina\" = four?\n\nBut in sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\"\n\n\"minawena\" = something → so \"minasina\" = four fish, \"minawena\" = something?\n\nIs \"minasina\" for \"four\" and \"minawena\" for \"something\"?\n\nPossibly: \"minasina\" → \"four fish\", \"minawena\" → \"something\"\n\nSimilarly, in 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"Legisi\" = that \n\"dakuna\" = saw \n\"makwena\" = stone \n\"gwadi\" = child \n\"magudiwena\" = saw \n\"gudimanabweta\" = this stone\n\nSo \"makwena\" = stone → likely a noun\n\n\"magudiwena\" = saw → again \"magudiwena\" = saw\n\nSo the verb \"magudiwena\" = saw (object) → attached to object\n\nSimilarly, \"makesiwena\" = saw canoes → \"makesiwena namwaya\" → saw those canoes\n\nSo pattern: [subject] [verb] [object], with object marked by suffix.\n\nNow verbs:\n- \"yena\" → catch\n- \"mtona\" → arrived\n- \"waga\" → saw\n- \"lekalimati\" → killed\n- \"kwetala\" → will see\n- \"teyu\" → looked after\n\nSo noun phrases:\n- \"mtona\" = man\n- \"gwadi\" = child\n- \"gudimanabweta\" = this stone\n- \"nakabitam\" = clever woman? (sentence 7)\n- \"gugwadi\" = that child? (sentence 17)\n\nNow decode sentence 14: \n\"Navila vivila biyamata tomwaya mtona?\"\n\n\"Navila\" = how many \n\"vivila\" = will \n\"biyamata\" = old women? \n\"tomwaya\" = ? \n\"mtona\" = man\n\n\"biyamata\" → likely \"old women\" (from \"biyamatasi\" in sentence 13)\n\n\"tomwaya\" → not in examples \nCompare: \nIn 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\nSo \"biyamatasi\" = old women \n\"tau\" = one\n\nSo \"biyamatasi\" = old women → must be grammatical form.\n\nIn 14: \"biyamata\" → possibly same root, missing \"s\"? \"biyamata\" = old women (plural)? \n\"biyamata\" → likely grammatical form of \"biyamatasi\"\n\nBut \"biyamata\" vs \"biyamatasi\" — missing \"-si\"? Could be a contraction or different form.\n\nIn sentence 13: \"biyamatasi\" → old women\n\nSentence 14: \"biyamata\" → could be a different form?\n\nCan \"biyamata\" = old women?\n\nPossibly missing a suffix.\n\nAlternatively, could \"biyamata\" = old women (plural), and \"tomwaya\" = will look after?\n\nBut what is \"tomwaya\"?\n\n\"tomwaya\" → not in examples.\n\nCompare with \"tauwau\" = two (in sentence 6)\n\n\"nayu\" = two\n\nSo numerals: \n- \"nayu\" = two \n- \"tau\" = one \n- \"tauwau\" = two \n- \"minasina\" = four\n\nSo \"minasina\" = four\n\nIn sentence 15: \"Bikamkwamsi kweyu vivila minasina\"\n\n\"bikamkwamsi\" → could be \"which stone\"?\n\n\"Bikamkwamsi\" → from \"Am\" + \"kamkwamsi\"? \"Am\" = which\n\n\"Am\" is prefix for questions — e.g., \"Amtona\" = which man\n\nSo \"Bikamkwamsi\" → \"which stone\"?\n\n\"kamkwamsi\" = stone?\n\n\"minasina\" = four fish?\n\n\"vivila\" = will\n\nSo: \"which stone will four fish\"?\n\nUnlikely.\n\n\"Bikamkwamsi\" → possibly \"which woman\"?\n\nBut stone?\n\nIn sentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" \n→ \"the old chief killed one wild pig\"\n\n\"lekalimati\" = old chief \n\"natala\" = killed \n\"bunukwa\" = wild pig \n\"nagasisi guyau\" = one? \"guyau\" = one \n\"tokabitam\" = clever?\n\n\"tokabitam\" = clever\n\nSo \"guyau\" = one (number)\n\nSimilarly, in sentence 10: \"gudimanabweta\" = this stone\n\nSo \"gudima\" = stone?\n\n\"kamkwamsi\" → stone?\n\nSo \"kamkwamsi\" = stone\n\nSo \"Bikamkwamsi\" = which stone\n\n\"vivila minasina\" = will four fish?\n\n\"vivila\" = will → so \"which stone will four fish\"?\n\nThat doesn't make sense.\n\nAlternatively: \"kweyu\" → \"will have\" or \"will eat\"?\n\n\"vivila\" = will\n\n\"kweyu\" → is this an auxiliary?\n\nIn sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = white men? \n\"dimdim\" = white \n\"mtosiwena\" = ate?\n\n\"mtosiwena\" = ate\n\nSo \"mtosiwena\" = ate\n\nThen \"kwevila\" = how many\n\nSo \"how many white men ate?\"\n\nSo \"kwevila\" = how many (question)\n\n\"kweyu\" → might be \"will have\" or \"will eat\" derived from \"kwevila\"?\n\nIn sentence 15: \"Bikamkwamsi kweyu vivila minasina\"\n\n→ \"which stone will will four fish\"?\n\nNo — better: \"which stone will [do] something?\"\n\n\"vivila\" = will, so \"kweyu vivila\" → redundant?\n\n\"vivila\" and \"kweyu\" both mean will?\n\nPossibly \"kweyu\" = will (verb), \"vivila\" = will (same)\n\nBut in sentence 11: \"kwevila\" = how many — so in questions, \"kwevila\" = how many\n\nSimilarly, in 18: \"Legisesi ketala waga vivila minasiwena\"\n\n\"Legisesi\" = that \n\"ketala\" = will see \n\"waga\" = saw \n\"vivila\" = will \n\"minasiwena\" = something?\n\n\"ketala\" = will see → likely same as \"kwetala\"\n\nSo \"ketal\" → will see\n\nThus \"ketala\" = will see\n\nTherefore, \"vivila\" may not mean will in all cases — or it's a different form.\n\nIn 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many white men ate?\"\n\n\"kwevila\" = how many → so \"kwevila\" is number question\n\n\"vivila\" = will → in 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n\"Navila\" = how many → so \"how many women will look after this man?\"\n\nSo \"vivila\" = will \n\"biyamata\" = old women \n\"tomwaya\" = verb? \n\"mtona\" = man\n\nSo \"tomwaya\" = look after?\n\nIn sentence 6: \"leyamatasi teyu tauwau nunumwaya\"\n\n\"teyu\" = looked after\n\nSo \"teyu\" = looked after\n\nSo \"tomwaya\" = may be same as \"teyu\"?\n\nSo \"biyamata tomwaya\" = old women look after\n\nSo sentence 14: \"how many old women will look after this man?\"\n\nThus: **14. How many old women will look after this man?**\n\nNow 15: \"Bikamkwamsi kweyu vivila minasina\"\n\n\"Bikamkwamsi\" = which stone? \n\"kweyu\" = will have? or will see? \n\"vivila\" = will \n\"minasina\" = four fish\n\nBut \"which stone will have four fish\"?\n\nBut \"minasina\" = four fish → so \"which stone will have four fish\"?\n\nBut earlier, \"minasina\" = four fish, from sentence 1.\n\nBut stone doesn't have fish.\n\nMore likely: \"kweyu\" = will be? \"vivila\" = will\n\n\"kweyu vivila\" → redundant?\n\nMaybe \"kweyu\" is the verb.\n\nIn sentence 11: \"kwevila\" = how many — so \"kwevila\" is a question word\n\n\"kweyu\" → verb?\n\nSentences with \"kweyu\": only 15\n\nIn 5: \"Amtona tau lekalimati nayu bunukwa?\" → no kweyu\n\nSo possible: \"kweyu\" = will do\n\n\"vivila minasina\" = will four fish?\n\nBut again, stone having fish?\n\nAlternatively: \"minasina\" might not be \"four fish\" here.\n\nPossibly \"minasina\" = four (number), but without object?\n\nIn sentence 1: \"minasina\" = four fish\n\nBut in 15, no object.\n\nIs there a pattern where \"minasina\" can stand alone?\n\nNo clear pattern.\n\nBut in sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi\"\n\n\"Tevila\" = how many \n\"tauwau\" = two \n\"bigisesi\" = that woman? \n\"gugwadi\" = that child? \n\"gudigasisi\" = that old woman?\n\n\"gudigasisi\" → could be \"that old woman\"\n\n\"bigisesi\" → that clever woman (from sentence 7)\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\"\n\nSo \"bigisi\" = that clever woman\n\nSo \"bigisesi\" = that clever woman\n\n\"gugwadi\" = that child (from \"gwadi\")\n\n\"gudigasisi\" = that old woman? From \"gudigasisi\" → in sentence 3: \"Bikota gwadi magudiwena\" → \"that child saw\" → so \"magudiwena\" = saw → and \"gwadi\" = child\n\n\"magudiwena\" = saw → object used.\n\nIn 17: \"Tevila tauwau bigisesi gugwadi gudigasisi\"\n\nSo: how many two that clever woman that child that old woman?\n\nUngrammatical.\n\nMore likely: \"how many two\" → how many two?\n\n\"tauwau\" = two → so \"how many two\" = how many two of something?\n\nUnlikely.\n\nCould it be: \"how many [people] are there\" — but no.\n\n\"tauwau\" → could be agent?\n\nIn 16: \"Amagudina gwadi lekota?\"\n\n\"Am\" = which \n\"agudina\" = what? \n\"gwadi\" = child \n\"lekota\" = this\n\n\"Amagudina\" → which thing?\n\n\"Am\" + \"gudina\" = which?\n\n\"gudina\" = stone?\n\nFrom \"gudimanabweta\" = this stone\n\n\"gudina\" → stone?\n\n\"Amagudina\" = which stone?\n\nSo \"which stone?\" → \"which stone is this?\" → with \"gwadi lekota?\"\n\n\"gwadi lekota\" → child this?\n\nSo \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11267.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "Step-by-step analysis of the Kilivila–English correspondences to identify linguistic patterns.\n\nFirst, observe how subject, object, quantity, and tense are encoded.\n\nFrom sentence 1: \n\"ONE man will catch these FOUR fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"navasi\" = man (subject) \n- \"minasina\" = fish (object) \n- \"tetala\" = will catch \n- \"yena\" = these, determiner for quantity \n→ \"yena\" marks the object (fish), \"navasi\" the subject (man) \n→ \"tetala\" = future/persistent action\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n- \"lekota\" = this \n- \"dimdim\" = white \n- \"mtona\" = arrived \n→ \"lekota\" = demonstrative + subject \n→ \"dimdim\" is adjective (white), modifies subject \n→ so “lekota” = this white man → subject\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n- \"bikota\" = that \n- \"gwadi\" = child \n- \"magudiwena\" = will arrive \n→ \"bikota\" = demonstrative, \"gwadi\" = child (subject), \"magudiwena\" = will arrive \n→ again, subject = demonstrative + noun\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n- \"legisi\" = this \n- \"waga\" = old woman → subject \n- \"makesiwena\" = saw \n- \"namwaya\" = those → demonstrative for object \n- \"minana\" = canoes \n→ object = \"namwaya minana\" → those canoes \n→ verb = makesiwena = saw\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"amtona\" = which man? \n- \"tau\" = man \n- \"lekalimati\" = killed \n- \"nayu\" = two \n- \"bunukwa\" = pigs \n→ \"nayu\" = numeral, two \n→ \"lekalimati\" = verb = killed \n→ so 'which' + subject + verb + numeral + object\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n- \"leyamatasi\" = old women (subject) \n- \"teyu\" = looked after \n- \"tauwau\" = two men (object) \n→ \"teyu\" = verb: looked after \n→ \"tauwau\" = two men → object \n→ number: plural (women, men)\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n- \"bigisi\" = that \n- \"kwetala\" = clever \n- \"vivila\" = woman (subject) \n- \"minawena\" = something (object) \n- \"nakabitam\" = will see \n→ structure: demonstrative + adjective + subject + object + verb\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"navila\" = how many \n- \"ka’ukwa\" = dogs \n- \"lekotasi\" = arrived \n→ question: how many [X] arrived? \n→ \"navila\" = interrogative for quantity \n→ used only in questions about quantity\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n- \"amakena\" = which \n- \"waga\" = chiefs → subject \n- \"legisesi\" = that \n- \"gweguyau\" = saw \n→ \"which canoe did the chiefs see?\" → structure: which + object + did + subject + see \n→ so \"amakena\" = which (referring to canoe) \n→ object is \"legisesi gweguyau\" → that canoe (demonstrative + object) \n→ verb = \"gweguyau\" = saw \n→ so question: \"which [object] did [subject] see?\"\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"legisi\" = that \n- \"dakuna\" = beautiful \n- \"makwena\" = child (subject) \n- \"gwadi\" = child? Wait — “gwadi magudiwena” = child who saw \nWait — structure: \n\"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ likely: [demonstrative] [adjective] [subject] + [verb] + [object] \n\"makwena\" = child → subject \n\"dakuna\" = beautiful → adjective \n\"gwadi\" = that → demonstrative? \n\"magudiwena\" = saw \n\"gudimanabweta\" = stone → object \nSo: “That beautiful child saw this stone” \n→ “legisi dakuna” = that beautiful → adjectival phrase \n→ “makwena” = child (subject) \n→ “magudiwena” = saw (verb) \n→ “gudimanabweta” = stone (object)\n\nBut \"gwadi\" appears before “magudiwena”, which would suggest a subject? But there’s only one “gwadi” — likely reused from earlier.\n\nWait — cleaning: \n- \"legisi\" = that \n- \"dakuna\" = beautiful (adjective) \n- \"makwena\" = child \n- \"gwadi magudiwena\" → maybe “gwadi” = that, “magudiwena” = saw? \n→ but the object is \"gudimanabweta\" (stone)\n\nSo structure: that beautiful child (legisi dakuna makwena → subject) saw this stone (gudimanabweta)\n\nThus, the demonstration is: \ndemonstrative + adjective + noun (subject) + verb + object\n\nSentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"kwevila\" = how many \n- \"lekamkwamsi\" = things \n- \"dimdim\" = white \n- \"mtosiwena\" = ate \n→ \"kwevila\" = how many \n→ \"lekamkwamsi\" = things \n→ \"dimdim\" = white → modifies \"men\"? \nBut \"mtosiwena\" = ate\n\n\"Those white men\" — so subject is \"those white men\" \nBut the full phrase is: \"how many things did those white men eat?\" \nSo question: (how many [X]) did [subject] eat?\n\nSo far, in questions with quantity, \"navila\" or \"kwevila\" = how many \nIn questions with \"which\", \"amtona\", \"amakena\", \"bikota\", etc., \"am\" = which, \"bikota\" = that, \"legisi\" = this\n\nNow sentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n- \"lekalimati\" = killed \n- \"natala\" = one \n- \"bunukwa\" = wild pig \n- \"nagasisi\" = chief \n- \"guyau\" = clever \n- \"tokabitam\" = killed? Wait — “tokabitam” = killed again?\n\nWait: \"lekalimati\" = killed \n\"nagasisi guyau\" = clever chief? \n\"guyau\" = clever, \"nagasisi\" = chief? \nSo \"nagasisi guyau\" = clever chief \n\"lekalimati\" = killed \n\"natala\" = one \n\"bunukwa\" = wild pig \n→ killed one wild pig → subject = clever chief, object = one wild pig\n\nBut \"natala\" = one \nSo numerals: \n- \"nayu\" = two (sentence 5) \n- \"natala\" = one \n- \"teyu\" = two (sentence 6: \"two men\") \n- \"minana\" = canoes, not numeral \n- \"kwevila\" = how many → interrogative quantity \n- \"navila\" = how many (sentence 8) \n→ numerals are embedded in noun phrases: \"natala bunukwa\" = one wild pig\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"navila\" = how many \n- \"vivila\" = women \n- \"biyamatasi\" = will look after \n- \"tau\" = man \n→ so: how many women will look after this man?\n\nSo pattern: \n- Quantifier: \"navila\" = how many, used for questions about quantity \n- \"vivila\" = women → subject \n- \"biyamatasi\" = will look after \n- \"tau\" = this man → object \n\nFrom the above, we see that:\n\n- Demonstratives: \n - “lekota” = this → modifies subject in sentence 2 \n - “bikota” = that → modifies subject in sentence 3 \n - “legisi” = this → modifies object in sentence 4 (those canoes) \n - “legisi” in 10: \"legisi dakuna\" = that beautiful \n - In 16: “Amagudina gwadi lekota?” → “gwadi lekota” likely means “the one that” or “that one”? \n - Notice that \"legisi\" and \"lekota\" both can be demonstratives (this) \n - In 9: \"amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" \n \"legisesi\" = that canoe → object demonstrative\n\nSo demonstratives can be used to mark subject or object.\n\nNow analyze structure of sentences in (a):\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"navila\" = how many \n\"vivila\" = women \n\"biyamata\" = will look after? \n\"tomwaya\" = this man \n\"mtona\" = will?\n\n\"biyamata\" likely = will look after → verb \n\"tomwaya\" = this man → object \nSo: How many women will look after this man?\n\nThis matches sentence 13: \"How many women will look after this man?\" → sentence 13 is \"Navila vivila biyamatasi tau mtona?\" \nHere: \"biyamata\" → likely variant spelling of \"biyamatasi\" → verb \"will look after\" \n\"tomwaya\" → \"tau\"? \"tau\" = man, \"tomwaya\" = this man? \n\"tomwaya\" vs \"tau\" — are they equivalent?\n\nIn sentence 13: \"tau mtona\" → \"this man\" \nIn 14: \"tomwaya mtona\"? → mtona again? \"mtona\" = will?\n\nWait — \"mtona\" in 13 is with \"tau\" → \"this man\"\n\nIn 14: \"tomwaya mtona\" — could this be broken into \"tomwaya\" = this man, \"mtona\" = will?\n\nBut in 13, \"mtona\" is a verb — will\n\nIn structure: \nExpression: Navila vivila biyamata tomwaya mtona?\n\nPossible parsing: \nNavila (how many) + vivila (women) + biyamata (will look after) + tomwaya (this man) + mtona (will)?\n\nBut \"mtona\" is a verb — appears in \"mtona\" as \"arrived\" or \"will\" (see 2, 3, 13)\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nSo \"mtona\" = will → verb \nThus in 14: \"tomwaya\" = this man, \"mtona\" = will — so same meaning?\n\nBut \"tomwaya\" → is it equivalent to \"tau\"?\n\nCompare: \n- \"tau\" = man (in 13) \n- \"tomwaya\" = this man?\n\nIn 4: \"Legisi waga makesiwena namwaya minana\" → \"this old woman saw those canoes\" \n\"namwaya\" = those — object demonstrative \n\"minana\" = canoes\n\nIs \"tomwaya\" = \"this man\"? \"tau\" = man\n\n\"tomwaya\" → likely an alternate form of \"tau\" with \"m\" added? No — in 13: \"tau mtona\" — \"this man will\"\n\nIn 14: \"tomwaya mtona\" — \"this man will\"?\n\nBut \"tomwaya\" is not seen before. \nIn 10: \"gudimanabweta\" = stone \nNo \"tomwaya\"\n\nBut in 13, \"tau\" = man \nIn 14, \"tomwaya\" = this man?\n\nCould be: \"tomwaya\" = this man (like \"tau\" but with \"o\"?)\n\nPossibility: \"tomwaya\" = this man — same as \"tau\"\n\nBut \"mtona\" is repeated.\n\nSo 14 likely means: How many women will look after this man?\n\nThat matches 13.\n\nNow sentence 15: \nBikamkwamsi kweyu vivila minasina.\n\n\"Bikamkwamsi\" = that (demonstrative) \n\"kweyu\" = two? \n\"vivila\" = woman \n\"minasina\" = fish?\n\nWait — \"minasina\" = fish in sentence 1 \n\"vivila\" = woman (subject)\n\nSo \"bikamkwamsi\" = that \n\"kweyu\" = two (like \"nayu\" in sentence 5) \n\"vivila\" = woman \n\"minasina\" = fish?\n\nBut fish and woman — unrelated\n\nBut in \"kweyu\", is it \"two\"?\n\nIn sentence 5: \"nayu bunukwa\" = two pigs \nIn sentence 6: \"teyu tauwau\" = two men \nSo \"kweyu\" = two\n\nThen \"vivila minasina\" = woman and fish?\n\nBut no such phrase\n\nBut in sentence 1: one man caught four fish — \"yena minasina tetala tau\" → \"these four fish\"\n\nSo \"minasina\" = fish\n\nBut here: \"kweyu vivila minasina\" → two (women) fish? Doesn't parse\n\nPossibility: \"kweyu vivila minasina\" = two women and fish? — no\n\nOr could it be: \"kweyu\" modifies \"vivila\" → two women?\n\n\"vivila\" = woman (singular) — would require plural\n\n\"vivila\" can be plural? In sentence 6: \"leyamatasi\" = old women → plural\n\nSo \"vivila\" = woman (singular), \"vivila\" in plural = women?\n\nIn sentence 13: \"vivila biyamatasi\" → \"women will look after\"\n\nSo likely \"vivila\" can be plural.\n\nThus: \"kweyu vivila\" = two women (plurality from numeral)\n\n\"minasina\" = fish → object\n\nSo: that two women caught fish?\n\nBut \"bikamkwamsi\" = that\n\nBut \"kweyu\" = two — so \"two women\"\n\nThen \"minasina\" = fish\n\nSo the sentence: \"That two women caught fish?\" — not standard\n\nMore likely: \"That two women (will) catch fish?\"\n\nBut verb missing\n\nIn other translations, verbs are not spliced like this\n\nPossibility: \"kweyu\" only modifies noun, no verb → but no verb?\n\nCompare with sentence 1: \"navasi yena minasina tetala tau\" → subject + object + verb\n\nIs there a verb?\n\nNo verb in 15.\n\nBut sentence 12: \"lekalimati natala bunukwa nagasisi guyau tokabitam\" → two verbs?\n\n\"lekalimati\" = killed \n\"tokabitam\" = killed again? — no\n\n\"tokabitam\" = killed? \"lekalimati\" and \"tokabitam\" — same verb?\n\nPossibility: use of verb missing\n\nBut in 16: \"Amagudina gwadi lekota?\"\n\n\"amagudina\" = which one? \n\"gwadi\" = that \n\"lekota\" = this\n\nSo \"which that this\"?\n\nNo — likely: \"amagudina\" = which (as in \"which did...\") \n\"gwadi lekota\" = that this → which one?\n\nBut which one of what?\n\nIn 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\"\n\nSo structure: \"which [object] did [subject] see?\"\n\nSimilarly, 16: \"Amagudina gwadi lekota?\" → \"which [object] is that this?\" → not clear\n\nPossibility: \"amagudina\" = which \n\"gwadi lekota\" = that this → that one?\n\nBut what is the predicate?\n\nNo verb\n\nIn other cases, \"am\" or \"bi\" + object → \"which [X]\" → question\n\nIn 5: \"Amtona tau lekalimati nayu bunukwa?\" → which man killed two pigs?\n\nSo \"amtona\" = which man (subject) \n\"lekalimati\" = killed (verb) \n\"nayu bunukwa\" = two pigs (object)\n\nIn 15: \"Bikamkwamsi kweyu vivila minasina\" — no verb?\n\nCould it be that \"vivila\" is the subject and \"minasina\" is object?\n\nBut no verb.\n\nBut in 4: \"makesiwena\" = saw — verb\n\nIn ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11990.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze patterns in English-Kilivila pairs to identify core linguistic constructions.\n\nLook for consistent roles of words and how pronouns, numerals, and aspect are structured.\n\nExample 1: \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\"\n- \"One man\" = \"Bibani navasi\" → \"Bibani\" = one, \"navasi\" = man\n- \"will catch\" = \"tetala tau\" → \"tetala\" = catch, \"tau\" = future (will)\n- \"these four fish\" = \"yena minasina\" → \"yena\" = these, \"minasina\" = fish\n\nSo: \n\"one man\" → \"Bibani navasi\" \n\"will catch\" → \"tetala tau\" \n\"these four fish\" → \"yena minasina\" \n\"minasina\" = fish (plural), \"yena\" = these (demonstrative)\n\nExample 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\"\n- \"This\" = \"lekota\"\n- \"white\" = \"dimdim\"\n- \"man\" = \"mtona\"\n- \"arrived\" = \"mtona\" (same form?) → wait, \"mtona\" appears twice?\n\nWait: \"Lekota dimdim mtona\" → \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man, \"mtona\" = arrived?\n\nUnlikely. But \"mtona\" is used both for man and arrived? That can't be.\n\nAlternative: perhaps \"mtona\" is only for man. Then \"arrived\" is missing.\n\nWait: in 1, \"will catch\" is \"tetala tau\", so \"tau\" = future.\n\nIn 2: \"arrived\" — might be \"mtona\" = arrived?\n\nBut \"mtona\" is used for man in 2. So must be ambiguous.\n\nBut 3: \"That child will arrive\" → \"Bikota gwadi magudiwena.\"\n\n\"bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive?\n\nYes: \"magudiwena\" appears in 3, 10, 13, etc. → has internal structure: \"magudi\" (arrive) + \"wena\" (future)\n\nIn 1: \"tetala tau\" → \"tetala\" (catch), \"tau\" (future)\n\nIn 3: \"magudiwena\" → \"magudi\" (arrive) + \"wena\" → future\n\nIn 4: \"saw\" → \"waga makesiwena\" → \"makesiwena\" = saw, future?\n\nIn 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n\"Amtona\" = which man? \n\"tau\" = killed \n\"lekalimati\" = man (subject?) \n\"nayu\" = two \n\"bunukwa\" = pigs\n\n\"tau\" = kill → verb\n\nIn 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya.\"\n\n\"leyamatasi\" = old women \n\"teyu\" = looked after \n\"tauwau\" = two men? \n\"nunumwaya\" = men\n\n\"tauwau\" = two? or \"tauwau\" = looked after?\n\n\"teyu\" = look after → verb \n\"tauwau\" → possible adjective, or noun?\n\nIn 7: \"That clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam.\"\n\n\"bigisi\" = that \n\"kwetala\" = clever \n\"vivila\" = woman \n\"minawena\" = will see? \n\"nakabitam\" = something\n\n\"minawena\" = see + future? matches \"magudiwena\" → likely: base verb + wena → future\n\nIn 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\n\"navila\" = how many \n\"ka’ukwa\" = dogs \n\"lekotasi\" = arrived?\n\n\"lekota\" = this, so \"lekotasi\" = arrived? → verb \"leki\" + \"tasi\" = arrived?\n\nBut in 4: \"saw\" → \"waga makesiwena\"\n\nIn 8: \"arrived\" → offered as \"lekotasi\"\n\nIn 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n\"Amakena\" = which canoe? \n\"waga\" = saw \n\"legisesi\" = the chiefs? \n\"gweguyau\" = canoe?\n\nWait: \"gweguyau\" → likely \"canoe\"\n\nBack to verb structure:\n\n- Action verbs: \"tetala\" (catch), \"magudi\" (arrive), \"makesi\" (saw), \"leki\" (arrive?), \"gweguyau\" (canoe)\n\nBut \"makesiwena\" → saw + future \n\"magudiwena\" → arrive + future\n\nSo: verb + wena → future\n\nAlso, in 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"kwevila\" = how many \n\"lekamkwamsi\" = those white men \n\"mtosiwena\" = ate + future?\n\n\"mtosi\" → eat, \"wena\" → future → yes\n\nSo verb base + wena = future\n\nThus: future = verb + wena\n\nPresent/future is marked with wena.\n\n\"will see\" = \"minawena\", \"will arrive\" = \"magudiwena\", \"will eat\" = \"mtosiwena\"\n\nPast? Missing.\n\nIn 4: \"saw\" → \"waga makesiwena\" → past? But \"wena\" is future.\n\nContradiction.\n\nWait — not all are future.\n\nBut in 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\" → wena → future\n\nIn 4: \"This old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana.\"\n\n\"makesiwena\" = saw? → wena = future?\n\nBut \"saw\" is past.\n\nSo inconsistency.\n\nUnless \"wena\" marks future, and \"without wena\" is past?\n\nBut in 4: \"makesiwena\" → wena → future?\n\nBut saw is past.\n\nMust be other pattern.\n\nLook at \"waga\" → \"saw\" → in 4, and in 10: \"saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n\n\"gudimanabweta\" → stone?\n\n\"makwena\" → \"made\" → past? \"makwena\" = materialized or visited?\n\nBut \"waga makesiwena\" = saw + future → but \"saw\" is past.\n\nWait — perhaps the future marker is not wena, or it's not always present.\n\nAnother idea: perhaps the verb is in a non-future form, and the future is at the end.\n\nExample: \"that clever woman will see\" → \"Bigisi kwetala vivila minawena nakabitam.\"\n\n\"minawena\" = will see\n\n\"nakabitam\" = something\n\nSo \"minawena\" = will see\n\nSimilarly, \"magudiwena\" = will arrive\n\n\"mtosiwena\" = will eat\n\n\"tetala tau\" = will catch (with tau)\n\n\"tau\" is used in some cases as future, but not in others.\n\n\"navasi yena minasina tetala tau\" → \"tetala tau\" = will catch\n\nBut in 2: \"This white man arrived\" → \"Lekota dimdim mtona\"\n\nNo \"wena\" → so arrival is without future marker?\n\nBut in 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\" → has wena\n\nIn 2: \"This white man arrived\" → no wena → so present or past?\n\nIn 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\n\"vivila\" = woman, \"biyamatasi\" = look after, \"tau\" = will, \"mtona\" = man\n\n\"tau\" = will → future marker\n\nSo \"tau\" = future, \"wena\" = future? Contradiction.\n\nBut in 1: \"tetala tau\" → \"tetala\" = catch, \"tau\" = future?\n\nIn 2: \"mtona\" — both man and arrived, and no future marker → is \"mtona\" = arrived?\n\nIn 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\nNo wena → \"waga\" = saw, so did\n\nIn 10: \"That beautiful child saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n\n\"makwena\" → saw? → but \"makwena\" not matching \"waga makesiwena\"\n\n\"makwena\" → didn't have \"waga\"?\n\n\"Legisi dakuna makwena\" → \"dakuna\" = beautiful? \"makwena\" = saw?\n\nBut \"waga makesiwena\" = saw → now \"makwena\" = saw? then \"wena\" is not exclusive.\n\nBut in 4: \"waga makesiwena\" = saw\n\nIn 10: \"makwena\" → saw → so \"makwena\" = saw\n\nThen \"makesiwena\" = same?\n\nBut \"waga\" and \"makwena\" both for saw?\n\nIn 10: \"gudimanabweta\" = stone\n\nSo \"saw\" = makwena or makesiwena?\n\nIn 4: \"waga makesiwena\" → present?\n\nBut 10: \"makwena\" → without wena = saw?\n\nInconsistent.\n\nAlternative: \"wena\" is not a future marker.\n\nPerhaps \"wena\" is a kind of internal marker for \"will\" or \"something\" — not future.\n\nBut in 1: \"tetala tau\" → catch, future → \"tau\"\n\nIn 3: \"magudiwena\" → arrive will → \"wena\"\n\nSo possible: future marker is \"wena\" in some verbs, \"tau\" in others?\n\nBut \"tau\" is used in 1, 13, 5, 6, etc.\n\n5: \"Amtona tau lekalimati nayu bunukwa?\" → which man killed two pigs?\n\n\"tau\" = killed\n\nSo \"tau\" = killed (verb) — not future\n\nSo \"tau\" is a past or present verb?\n\nBut \"will\" is missing.\n\nOnly when \"wena\" appears, future?\n\n1: \"tetala tau\" → \"tetala\" = catch, \"tau\" = future? or \"tau\" = verb root?\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after?\n\n\"tau\" = will\n\nSo \"tau\" = future\n\nIn 4: \"waga makesiwena\" → saw — not future?\n\nIn 10: \"makwena\" → saw — is that future?\n\nWait — in 1: \"will catch\" → \"tetala tau\" — \"tau\" = future\n\nIn 13: \"will look after\" → \"biyamatasi tau\" → \"tau\" = future\n\nIn 3: \"will arrive\" → \"magudiwena\" → \"wena\" = future\n\nIn 5: \"killed\" → \"tau\" — not future?\n\n\"Amtona tau lekalimati...\" → past tense\n\nSo \"tau\" = past tense verb? \"killed\"\n\nBut in 1 and 13, \"tau\" is future?\n\nIn 1: \"will catch\" → \"tetala tau\" — future\n\nIn 13: \"will look after\" → \"biyamatasi tau\" — future\n\nIn 5: \"killed\" → \"tau\" — past\n\nSo contradiction.\n\nUnless the tense depends on verb.\n\nSo verb root + future marker → future\n\n- \"tetala\" + \"tau\" → \"tetala tau\" → catch (future)?\n- \"magudi\" + \"wena\" → arrive (future)\n- \"makesi\" + \"wena\" → saw? (future)\n- \"leki\" + \"tasi\" → arrived (past)\n- \"mtosi\" + \"wena\" → will eat\n\nSo far, \"wena\" is used in future for some verbs, and \"tau\" is used in others.\n\nBut in 13: \"will look after\" → \"biyamatasi tau\" → \"tau\" = future\n\nIn 4: \"saw\" → \"waga makesiwena\" → \"wena\" = future?\n\nBut \"saw\" is past.\n\nSo not matching.\n\nUnless \"makesiwena\" is not past.\n\nAnother possibility: perhaps all verbs with \"wena\" are future, all verbs without are past.\n\nIn 2: \"arrived\" → \"lekota dimdim mtona\" — no wena → past\n\nIn 3: \"will arrive\" → \"magudiwena\" — has wena → future\n\nIn 4: \"saw\" → \"waga makesiwena\" — has wena → future? but saw is past\n\nContradiction.\n\nUnless \"saw\" is future? Unlikely.\n\nPerhaps \"waga\" is subject, \"makesiwena\" is verb.\n\nBut in 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" — \"makwena\" = saw?\n\n\"makwena\" = saw, but no \"waga\"?\n\n\"makwena\" appears without \"waga\"?\n\nOnly in 4, \"waga makesiwena\"\n\nIn 10: \"makwena\" = saw\n\nSo \"makwena\" = saw\n\nThen \"makesiwena\" = saw + future?\n\nBut in 4, \"waga makesiwena\" = saw — so if \"makesiwena\" = saw, then it's the form.\n\nIn 10: \"makwena\" only → so \"makwena\" = saw?\n\nThen in 4, \"makesiwena\" = saw?\n\nSo both are saw.\n\nSo \"makesiwena\" and \"makwena\" are both forms for \"saw\" — one with \"wena\", one without?\n\nThat suggests \"wena\" is not a future marker.\n\nBut in 3: \"will arrive\" → \"magudiwena\" → has wena\n\nIn 1: \"will catch\" → \"tetala tau\" → has tau, not wena\n\nSo different verbs have different markers.\n\nPossibility: future marker is internal and verb-dependent.\n\nList verb roots with their future markers:\n\n- catch: tetala + tau → future\n- arrive: magudi + wena → future\n- see: makesi + wena → future\n- kill: tau → past (5)\n- look after: biyamatasi + tau → future (13)\n- eat: mtona? no — 11: \"mtosiwena\" → eat + wena\n\nIn 6: \"looked after\" → \"teyu tauwau\" → \"teyu\" = looked after, \"tauwau\" = two men\n\nSo \"teyu\" = verb of look after\n\nNo future marker → past?\n\nIn 13: \"will look after\" → \"biyamatasi tau\" → future\n\nSo when future tense, marker is \"tau\" or \"wena\" depending on verb.\n\nBut \"wena\" is used in arrive and see, \"tau\" in catch and look after.\n\nSo no consistent marker.\n\nInstead, the object or subject structure may be key.\n\nTry subject-verb-object pattern.\n\nExample 1: \"one man will catch these four fish\"\n→ \"Bibani navasi yena minasina tetala tau\"\n\nSubject: \"Bibani navasi\" = one man \nVerb: \"tetala tau\" = will catch \nObject: \"yena minasina\" = these four fish\n\n\"yena\" = these, \"minasina\" = fish → \"minasina\" = plural fish\n\n\"tau\" = future\n\nExample 2: \"This white man arrived\"\n→ \"Lekota dimdim mtona\"\n\nSubject: \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man → \"lekota dimdim mtona\" = this white man \nVerb: \"mtona\" — but same word used for man and arrived?\n\nPerhaps \"mtona\" is arriving? But then \"mtona\" = verb of arrive?\n\nIn 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\"\n\n\"bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive\n\nSo \"magudi\" = arrive, \"wena\" = future\n\nIn 2: no future marker → so past?\n\nIn 4: \"saw\" → \"waga makesiwena\" → has wena → future?\n\nBut \"saw\" is past.\n\nConflict.\n\nUnless \"wena\" means \"will\" only for certain verbs.\n\nBut in 13: \"will look after\" → \"tau\" → future\n\nIn 1: \"will catch\" → \"tau\" → future\n\nIn 5: \"killed\" → \"tau\" → past\n\nSo \"tau\" is used for both past and future, depending on verb?\n\nThat suggests the tense is verb-specific.\n\nIn 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\n\"leyamatasi\" = old women \n\"teyu\" = looked after \n\"tauwau\" = two men? \n\"nunumwaya\" = men\n\n\"teyu\" = looked after — past \n\"tauwau\" = two men → is \"tau\" = number?\n\nIn 5: \"nayu\" = two → \"nayu\" = two\n\nIn 1: \"minasina\" → fish — plural\n\nIn 4: \"namwaya minana\" → \"namwaya\" = canoes, \"minana\" = plural?\n\nSo numer", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11475.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Identify core linguistic patterns from the given English-Kilivila pairs.\n\nPattern: Kilivila often uses markers for:\n- Subject (e.g., *Bikota*, *Lekota*, *Navila*) → refer to \"that\", \"this\", \"which\"\n- Object (e.g., *minasina*, *mtona*, *gwadi*, *nayu*) → refer to \"fish\", \"man\", \"child\", \"pigs\"\n- Quantifiers: *one*, *two*, *many*, *how many* → often signaled by *navila*, *kwevila*, *am*, *tevila*\n- Verbs: *will*, *saw*, *arrived*, *killed*, *looked after*, *see* → verb form depends on subject and aspect\n\nStep 2: Analyze verb structure and argument order.\n\nLook at sentence 1:\n- English: \"One man will catch these four fish.\"\n- Kilivila: \"Bibani navasi yena minasina tetala tau.\"\n- \"navasi\" = man (subject), \"yena\" = these, \"minasina\" = fish, \"tetala tau\" = will catch\n\n→ \"teta\" (catch) + \"tau\" (will) → \"will catch\"\n→ \"yena\" = \"these\", modifying \"minasina\" = fish\n\nSentence 2:\n- \"This white man arrived.\"\n- \"Lekota dimdim mtona.\"\n- \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man → “this white man” → subject\n→ \"mtona\" = man → object of goal?\n\nWait: “arrived” is not a transitive verb → should not take object → so \"mtona\" is subject, \"dimdim\" is adjective.\n\nSo: \"lekota dimdim mtona\" = \"this white man\" — subject, adjective after\n\nSentence 3:\n- \"That child will arrive.\"\n- \"Bikota gwadi magudiwena.\"\n- \"bikota\" = that, \"gwadi\" = child, \"magudiwena\" = will arrive\n\n→ \"gwadi\" = child = subject, \"magudiwena\" = will arrive → verb phrase\n\nSentence 4:\n- \"This old woman saw those canoes.\"\n- \"Legisi waga makesiwena namwaya minana.\"\n- \"legisi\" = this, \"waga\" = old, \"makesiwena\" = saw, \"namwaya\" = those, \"minana\" = canoes\n\n→ \"makesiwena\" = saw → transitive verb → takes object \"namwaya minana\" → those canoes\n\nSo verb + object structure: verb is transitive when it takes a noun phrase (e.g., saw canoes)\n\nSentence 5:\n- \"Which man killed two pigs?\"\n- \"Amtona tau lekalimati nayu bunukwa?\"\n- \"amtona\" = which, \"tau\" = man, \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\n→ \"which man killed two pigs\" → the order is: question word + subject + verb + numeral + object\n\n→ \"amtona\" = \"which\", \"tau\" = man (subject), \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\nSo \"amtona tau\" → which man\n\nSentence 6:\n- \"The old women looked after two men.\"\n- \"Leyamatasi teyu tauwau nunumwaya.\"\n- \"leyamatasi\" = the old women → subject, \"teyu\" = looked after, \"tauwau\" = two, \"nunumwaya\" = men\n\n→ \"teyu\" = looked after → transitive verb → object \"tauwau nunumwaya\" → two men\n\nSentence 7:\n- \"That clever woman will see something.\"\n- \"Bigisi kwetala vivila minawena nakabitam.\"\n- \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman, \"minawena\" = will see, \"nakabitam\" = something\n\n→ \"vivila\" = woman, \"minawena\" = will see, \"nakabitam\" = something\n\n→ \"minawena\" = will see → transitive? \"nakabitam\" = something → object\n\nSo: subject = woman, verb = will see, object = something\n\nSentence 8:\n- \"How many dogs arrived?\"\n- \"Navila ka’ukwa lekotasi?\"\n- \"navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived?\n\nWait: \"lekotasi\" = arrived? Yes, in sentence 2, \"mtona\" = man, \"lekota\" = this → \"lekota\" is a form of “this” and \"lekota\" → \"arrived\"?\n\nLook at sentence 2: \"Lekota dimdim mtona.\" — this white man arrived. So \"lekota\" is not the verb — “mtona” is the subject.\n\nSo: \"lekotasi\" = arrived → verb\n\nSo: \"navila ka’ukwa lekotasi?\" = How many dogs arrived?\n\n→ \"navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived\n\n→ quantifier + noun + verb → questions about number\n\nSentence 9:\n- \"Which canoe did the chiefs see?\"\n- \"Amakena waga legisesi gweguyau?\"\n- \"amakena\" = which, \"waga\" = chief, \"legisesi\" = saw, \"gweguyau\" = canoe?\n\n→ \"gweguyau\" = canoe → object\n\n→ verb is \"legisesi\" → saw → transitive → object after\n\nSo: which canoe did the chiefs see?\n\nStructure: question word + subject + verb + object\n\nSo → \"amakena waga legisesi gweguyau?\" = which canoe did the chiefs see?\n\nYes.\n\nSentence 10:\n- \"That beautiful child saw this stone.\"\n- \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n- \"legisi\" = that, \"dakuna\" = beautiful, \"makwena\" = child, \"gwadi\" = this, \"magudiwena\" = saw, \"gudimanabweta\" = stone?\n\nWait — “gudimanabweta” = stone? Likely.\n\n\"gwadi magudiwena\" → \"this saw\"? No.\n\n\"gwadi\" = this, \"magudiwena\" = saw — so “this saw”?\n\nBut subject is child.\n\n→ \"legisi\" = that, \"dakuna\" = beautiful, \"makwena\" = child → subject\n\n\"gwadi\" = this — likely modifies \"gudimanabweta\" = stone → object\n\n\"magudiwena\" = saw → verb\n\nSo: “that beautiful child saw this stone”\n\nStructure: subject (that beautiful child) + verb (saw) + object (this stone)\n\nSo verb comes after subject, object comes after verb — standard\n\nSentence 11:\n- \"How many things did those white men eat?\"\n- \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n- \"kwevila\" = how many, \"lekamkwamsi\" = things, \"dimdim\" = white, \"mtosiwena\" = ate?\n\n\"mtosiwena\" = ate → verb\n\n→ question: how many things did those white men eat?\n\n→ structure: kwevila (how many) + object (lekamkwamsi) + adjective (dimdim) + verb (mtosiwena)\n\nBut verb is at end → \"did those white men eat\"?\n\nSo verb comes last → passive or inverse order?\n\nCheck sentence 2: \"this white man arrived\" → \"lekota dimdim mtona\" → subject + adjective → verb not shown → no verb in that phrase\n\nSentence 10: \"that beautiful child saw this stone\" → subject + adjective + verb + object\n\nBut here: \"kwevila lekamkwamsi dimdim mtosiwena?\"\n\n→ \"lekamkwamsi\" = things (object), \"dimdim\" = white (adjective), \"mtosiwena\" = ate (verb)\n\nSo verb at end — likely: \"how many things did those white men eat?\"\n\nBut \"lekamkwamsi\" = things → plural noun\n\n\"dimdim\" = white → adjective modifying subjects?\n\n\"mtosiwena\" = ate → verb\n\nBut subject is missing?\n\nIn sentence 10: subject was \"legisi dakuna makwena\" → that beautiful child\n\nIn sentence 11: no subject? Only \"kwevila lekamkwamsi dimdim mtosiwena?\"\n\nBut \"dimdim\" = white → likely describes \"men\"\n\nSo \"those white men\" — we infer from context.\n\nThus: \"how many things did those white men eat?\"\n\n→ verb at end, noun at start, adjective before verb → supports this.\n\nSentence 12:\n- \"The clever chief killed one wild pig.\"\n- \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n- \"lekalimati\" = killed, \"natala\" = one, \"bunukwa\" = wild pig, \"nagasisi\" = chief, \"guyau\" = clever\n\nSo: \"guyau\" = clever → describes \"nagasisi\" (chief)\n\n\"natala\" = one → numeral → before object?\n\n\"bunukwa\" = wild pig\n\nSo: \"the clever chief killed one wild pig\"\n\nOrder: verb (lekalimati) + numeral (natala) + object (bunukwa) + modifier (guyau) on subject?\n\nBut \"guyau\" = clever → modifies \"nagasisi\" = chief\n\nSo: chief (nagasisi) = subject, has adjective \"guyau\"\n\n\"lekalimati\" = killed → verb\n\n\"natala\" = one → modifies object → \"one wild pig\"\n\nSo object: \"natala bunukwa\" → one wild pig\n\nThen subject: \"nagasisi guyau\" → clever chief\n\nSo structure: verb + numeral + object (object with number) + subject (with modifier)\n\nWait — not standard. Let’s reverse.\n\nBut in sentence 5: \"amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → \"amtona tau\" = which man, \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\nSo: subject + verb + numeral + object\n\nSame structure.\n\nSentence 13:\n- \"How many women will look after this man?\"\n- \"Navila vivila biyamatasi tau mtona?\"\n- \"navila\" = how many, \"vivila\" = women, \"biyamatasi\" = will look after, \"tau\" = this, \"mtona\" = man\n\nSo: \"how many women will look after this man?\"\n\n→ \"navila\" = how many, \"vivila\" = women, \"biyamatasi\" = look after (verb), \"tau mtona\" = this man (object)\n\nSo verb is \"biyamatasi\" → transitive → takes object\n\nHence, verb comes after subject, before object.\n\nSo general pattern of transitive verbs:\n- Subject → adjective (if any) → verb → object\n\nQuestions with \"how many\" start with \"navila\" or \"kwevila\"\n\n\"navila\" = how many → quantifier\n\n\"vivila\" = women → plural noun\n\n\"biyamatasi\" = will look after → verb\n\n\"tau mtona\" = this man → object\n\nNow proceed to sentences 14–18.\n\n14. Navila vivila biyamata tomwaya mtona?\n→ \"navila\" = how many, \"vivila\" = women, \"biyamata\" = look after, \"tomwaya\" = this, \"mtona\" = man?\n\nWait — \"mtona\" = man → object\n\n\"biyamata\" = look after → verb\n\nSo → \"how many women will look after this man?\"\n\nCompare to 13: \"Navila vivila biyamatasi tau mtona?\" → same structure → \"how many women will look after this man?\"\n\n\"biyamatasi\" vs \"biyamata\" — likely just a form variation?\n\n\"biyamata\" → might be present tense of \"look after\"? \"biyamatasi\" in 13 was \"will look after\"\n\nBut in 13: \"biyamatasi\" → future tense? Yes, from \"will\"\n\nIn 13: \"will look after\"\n\nIn 14: \"biyamata\" — lacks \"si\"? Possibly a present tense?\n\nBut sentence 13: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\" — matches\n\nSo 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n→ \"biyamata\" — is it present or future?\n\nCompare with 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" → \"minawena\" = will see\n\n\"minawena\" = will see → future\n\nSimilarly, in 13, \"biyamatasi\" = will look after → future\n\nBut \"biyamata\" → missing \"si\"\n\nIs it a tense marker?\n\nCheck for any other \"biyama\" forms.\n\nSentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\"\n\nNo \"biyama\"\n\nSentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" → \"clever chief killed one wild pig\"\n\nNo \"biyama\"\n\n\"biyamatasi\" in 13 — future\n\n\"biyamata\" — might be present?\n\nBut sentence 14 has \"navila\" — question about number\n\nSo likely: \"how many women look after this man?\"\n\nBut in 13: \"will\" — future\n\nSo is \"biyamatasi\" future, \"biyamata\" present?\n\nBut in 13: \"will look after\" → \"biyamatasi\"\n\nIn 14: \"biyamata\" → without \"si\"\n\nPossibly a misfeature?\n\nBut the pattern of tense in such verbs: \"will\" marked by \"si\"?\n\nLet’s check if any present verb.\n\nSentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"will see\" → \"minawena\"\n\nNo present, all seem future.\n\nBut 14 — possible that \"biyamata\" is a past or present tense?\n\nBut in translations, 13 uses \"will\", so likely tense is future.\n\nPossibly translation error — or \"biyamata\" is a typo of \"biyamatasi\"?\n\nBut the word is given as \"biyamata\"\n\nCheck sentence 4: \"makesiwena\" = saw → past\n\nSo past → \"makesiwena\"\n\nFuture → \"minawena\", \"biyamatasi\", \"biyamata\"?\n\nNo consistent pattern.\n\nAlternatively: perhaps \"biyama\" is the root, \"tai\" or \"si\" indicates future.\n\n\"biyamatasi\" — \"tasi\" — future?\n\n\"biyamata\" — without future marker?\n\nBut in question 14: no future marker.\n\nSentence 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n→ \"how many women look after this man?\"\n\nBut in 13: \"will look after\" → future\n\nSo unless \"biyamata\" is future, which is doubtful.\n\nBut observe: sentence 13 is \"how many women will look after this man?\"\n\nSentence 14: \"how many women look after this man?\"\n\nIf tense is missing, could be present.\n\nBut the problem says: one of these has two possible translations.\n\nSo 14 may be ambiguous.\n\nBut let's go through others.\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n→ \"bikamkwamsi\" = which, \"kweyu\" = two, \"vivila\" = woman, \"minasina\" = fish?\n\nWait: \"vivila\" = woman → but \"minasina\" = fish?\n\n\"minasina\" = fish → object\n\nSo \"which two women these fish\"?\n\nNo — \"bikamkwamsi\" = which, \"kweyu\" = two, \"vivila\" = woman → so \"which two women\"?\n\nThen \"minasina\" → fish?\n\nBut fish is not related to women.\n\nPossibly: \"which two women will catch these fish\"?\n\nBut \"vivila minasina\" — no verb.\n\nNo verb?\n\nBut in earlier sentences, verbs are always present.\n\nUnless \"vivila\" is a verb?\n\nNo — in sentence 13: \"biyamatasi\" = will look after → verb\n\nIn sentence 7: \"minawena\" = will see → verb\n\nSo \"vivila\" as verb? Unlikely.\n\n\"minasina\" = fish — noun\n\nSo structure: which two women fish?\n\nNo — ungrammatical.\n\n\"bikamkwamsi\" = which, \"kweyu\" = two, \"vivila\" = women, \"minasina\" = fish?\n\nSo \"which two women (are) these fish?\" → nonsense.\n\nPossibly: \"which two fish will these women catch?\"\n\nBut we have \"bikamkwamsi kweyu vivila minasina\"\n\nIf the verb is missing, perhaps it's \"will catch\" or \"are\"?\n\nLook at sentence 1: \"one man will catch these four fish\"\n\n\"bibi navasi yena minasina tetala tau\" → \"will catch\"\n\nSo verb \"tetala\" = catch\n\nIs \"vivila\" a verb?\n\nSearch: in sentence 2: \"lekota dimdim mtona\" — no verb\n\nSentence 3: \"bikota gwadi magudiwena\" — \"magudiwena\" = will arrive\n\nNo \"vivila\"\n\nSentence 4: \"makesiwena\" = saw", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12306.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 0, + "output": "Step 1: Identify key linguistic patterns from the given examples.\n\nIn Kilivila, questions of the form \"How many X did Y do?\" use the structure:\n- \"Navila\" = \"how many\"\n- followed by noun (X), then \"lekota/lengota\" = \"did\" or \"see/look at\" depending on verb\n- subject of action is typically in a form that matches the verb's role\n\nExample 1: \"One man will catch these four fish\" → \"Bibani navasi yena minasina tetala tau.\"\n→ \"navasi\" = catch, \"yena\" = these, \"tetala\" = four, \"tau\" = fish\n→ So \"navasi\" is the verb, \"yena\" marks object, \"tetala\" is numeral, \"tau\" is noun.\n\nExample 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n→ \"navila\" = how many, \"ka’ukwa\" = dogs, \"lekotasi\" = arrived\n→ \"lekota\" + \"-si\" = arrived (past), so \"lekotasi\" is past tense of arrive.\n\nExample 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n→ \"Navila\" = how many, \"vivila\" = look after, \"biyamatasi\" = women, \"tau\" = this, \"mtona\" = man\n→ \"biyamatasi\" = women (plural), \"vivila\" = verb, \"mtona\" = target object\n\nPattern: \n- \"Navila\" = \"how many\" \n- noun of thing counted \n- verb (e.g., lekota = arrive, makwena = see, vivila = look after) \n- subject is usually in noun form (e.g., \"biyamatasi\" = women) \n- \"tau\" = this, \"yena\" = those, \"mtona\" = man, etc. \n- numerals are explicit (e.g., \"tetala\" = four)\n\nStep 2: Analyze object markers\n\nIn example 1: \"catch these four fish\" → \"minasina tetala tau\" → \"minasina\" = fish, \"tetala\" = four, \"tau\" = these \nIn example 4: \"saw those canoes\" → \"waga makesiwena namwaya minana\" → \"waga\" = saw, \"makesiwena\" = those canoes? \nWait — \"makesiwena\" → likely \"makesi\" = canoe, \"wena\" = those → \"makesiwena\" = those canoes \n\"namwaya\" = those? → \"minana\" = those? \nNote: In 10: \"saw this stone\" → \"gwadi magudiwena gudimanabweta\" → \"magudiwena\" = this stone? \n\"magudiwena\" = this child? or this stone?\n\nActually, in 10: \"That beautiful child saw this stone\" \n→ \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"makwena\" = this stone? → \"makwena\" = this, \"gwadi\" = beautiful, \"magudiwena\" = child? \nWait, \"gwadi\" is likely adjective → \"gwadi\" = beautiful, \"magudiwena\" = child (magudi = child, wena = this) \n\"gudimanabweta\" = stone\n\nSo: \"makwena\" = this (referring to stone), not noun phrase.\n\nSo: verb \"makesiwena\" = saw canoes, \"makwena\" = these/those → object?\n\nWait, example 4: \"That child saw those canoes\" → \"Bikota gwadi magudiwena. Legisi waga makesiwena namwaya minana.\" \n→ \"waga\" = saw, \"makesiwena\" = those canoes → \"makesi\" = canoe, \"wena\" = those \n→ \"namwaya\" = those → \"minana\" = those? Inconsistent.\n\nBut in 4: \"namwaya minana\" → both used as objects? Probably \"namwaya\" = those canoes → \"minana\" is redundant?\n\nIn 10: \"gudimanabweta\" = stone. \"gwadi magudiwena\" = this child → \"magudiwena\" = this child\n\nIn 10: \"saw this stone\" → \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"dakuna\" = saw? Not matching earlier.\n\nWait — \"Legisi\" = that → \"dakuna\" → actual verb?\n\nExample 4: \"Legisi waga makesiwena namwaya minana\" \n→ \"Legisi\" = that, \"waga\" = saw, \"makesiwena\" = those canoes → so object is \"makesiwena\"\n\nSo: object of verb is constructed as [noun + wena], where wena = those/this/these \n\"makesiwena\" = canoes (makesi) + wena (those)\n\n\"makwena\" = stone (makwa) + wena = this stone\n\nSo: nouns are base form + wena (for definite), or yena (these, those), or tau (this)\n\nSo:\n- \"wena\" = those?\n- \"yena\" = these?\n- \"tau\" = this?\n\nCheck:\n1: \"minasina tetala tau\" → \"these four fish\" → \"tau\" at end → so \"tau\" marks \"these\"\n4: \"namwaya minana\" → \"those canoes\"? \"minana\" = those?\n\nIn 1: fish → \"tetala tau\" → \"four fish\" → \"tau\" = these\nIn 4: canoes → \"namwaya minana\" → \"those canoes\" → \"minana\" = those?\nIn 10: \"gwadi magudiwena gudimanabweta\" → \"this child\" → \"magudiwena\" → \"this child\"\n\nSo: \n- wena = this \n- yena = these \n- minana = those? \nBut in 4: \"namwaya minana\" → \"nam\" = ? → perhaps \"nam\" = those?\n\nIn example 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"tau\" = this? \"nayu\" = two? → \"bunukwa\" = pigs → \"nayu\" = two → scalar number\n\nSo \"nayu\" = two → used in numerals\n\nExample 12: \"The clever chief killed one wild pig\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"nata\" = one? → \"natala\" → possibly \"nata\" + \"la\"? \n\"nayu\" = two, \"nata\" = one?\n\nExample 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"leka\" + \"mkwamsi\" = men, \"dimdim\" = white, \"mtosiwena\" = things? \n\"mtosiwena\" = things (mto = thing, si? wena = those)\n\n\"mtosiwena\" = those things → object\n\nSo object expressions: [noun] + [specifier] → wena = this, yena = these, minana = those?\n\nBut in 19: \"How many canoes did those old women see?\" \n→ need to mirror structure of example 4 or 8 or 13.\n\nExample 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many \n→ \"vivila\" = look after \n→ \"biyamatasi\" = old women (biya = old, matasi = women) \n→ \"tau\" = this \n→ \"mtona\" = man\n\nSo pattern: \n\"Navila [verb] [subject] [specifier] [object]\" \nBut in 13, object is \"mtona\" (this man)\n\nIn example 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → only objects via verb → no object head, but \"ka’ukwa\" = dogs → subject of arrival\n\nSo \"navila X lekotasi\" → X = number of dogs → \"how many dogs arrived?\"\n\nSo for questions: \n\"how many X did Y do?\" → \"navila X lekotasi\" (if arrival), or \"navila X verb Y\" → if action\n\nFor 19: \"How many canoes did those old women see?\" \nMatch to example 4: \"That child saw those canoes\" → \"Legisi waga makesiwena namwaya minana\"\n\nSo:\n- \"waga\" = saw (verb)\n- \"makesiwena\" = those canoes → \"makesi\" = canoes, \"wena\" = those\n- \"namwaya minana\" → redundant? Or \"namwaya\" = those, \"minana\" = those → likely both \"namwaya\" = those canoes?\n\nIn 4: \"Legisi waga makesiwena namwaya minana\" → \"namwaya\" and \"minana\" both? Possibly \"namwaya\" = those (in genitive? or object)\n\nPossibly only one object: \"makesiwena\" = those canoes → \"wena\" = those\n\nBut in 10: \"saw this stone\" → \"gwadi magudiwena gudimanabweta\" → \"magudiwena\" = this child, \"gudimanabweta\" = stone\n\nSo verb structure: [adjective] [subject] [verb] [object]\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → subject \"legisi\" (that), verb \"waga\" (saw), object \"makesiwena namwaya minana\"? Or is \"makesiwena\" the object?\n\nPossibly \"makesiwena\" is the object, and \"namwaya\" is redundant or part of it.\n\nBut \"makesiwena\" = canoes + wena → so likely only one object.\n\nThus, for \"How many canoes did those old women see?\" \n→ \"Navila\" (how many) \n→ \"makesi\" (canoe), \"wena\" (those)? \n→ subject: \"old women\" → from example 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\n\"Leyamatasi\" = old women, \"teyu\" = looked after, \"tauwau\" = two, \"nunumwaya\" = men\n\nSo: \"leyamatasi\" = old women → \"biyamatasi\" = women? \"biya\" = old?\n\n\"biyamatasi\" = old women → in 13: \"biyamatasi\" = women\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → how many women will look after this man?\n\nSo:\n- \"biyamatasi\" = old women (postpositive attributive)\n\nSo for 19: subject = \"old women\" → \"biyamatasi\"\n\nVerb: \"see\" → from example 4: \"waga\" = saw → \"waga\" is likely \"see\"\n\nExample 10: \"saw this stone\" → \"dakuna\" → wait, what is the verb?\n\nActually, example 4: \"waga\" = saw \nExample 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"dakuna\" = saw? \nYes → \"dakuna\" alternates with \"waga\"? \nNo — 4: \"waga\", 10: \"dakuna\" → different verbs?\n\nPossibility: alternate forms.\n\nBut in 3: \"That child will arrive\" → \"Bikota gwadi magudiwena.\" → no verb.\n\nIn 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"teyu\" = looked after\n\nSo \"vivila\" = look after → \"teyu\" = look after \n\n\"teyu\" and \"waga\" — different verbs.\n\n\"see\" = waga or dakuna? \n\"look after\" = teyu or vivila?\n\nExample 13: \"will look after\" → \"vivila\" \nSo \"look after\" = vivila \n\"see\" = waga or dakuna?\n\nIn 10: \"saw\" → \"dakuna\" \nIn 4: \"saw\" → \"waga\" \nInconsistency?\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → \"waga\" = saw \nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"dakuna\" = saw \nPossibly \"waga\" and \"dakuna\" are both forms for \"see\", with different contexts.\n\nPerhaps \"waga\" = see, \"dakuna\" = see (same root)?\n\nMaybe different pronunciations or context-dependent.\n\nBut for consistency: \"see\" = waga or dakuna → use whichever appears in object construction.\n\nIn 19: \"see\" → use \"waga\" as base\n\nSo: \"Navila makesi wena biyamatasi?\" — but need to place \"those\" and \"old women\"\n\nPattern in example 4: \"Legisi waga makesiwena namwaya minana\"\n\nStructure: \n- Subject: \"Legisi\" = that \n- Verb: \"waga\" = saw \n- Object: \"makesiwena namwaya minana\" → canoes + those?\n\nBut \"makesi\" is canoes, \"wena\" = those? \n\"namwaya\" = those — possibly redundant?\n\nIn 10: \"dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"makwena\" = this stone → \"wena\" = this \n\"gwadi\" = beautiful → adjective \n\"magudiwena\" = this child → subject of \"saw\"? \n\"gwadi magudiwena\" = this child → noun phrase\n\nSo: “saw this stone” → “dakuna makwena gwadi magudiwena gudimanabweta” \n→ \"makwena\" = this stone? → \"makwena\" = this + stone\n\nSo potential: \n- [adjective] + [noun] + [wena] = this / those / these \n- \"wena\" = this \n- \"yena\" = these \n- \"minana\" = those? \n\nBut in 4: “makesiwena namwaya minana” → both?\n\nPossibly \"makesiwena\" = canoe with wena → \"wena\" = these/that, \"namwaya\" = those → over-embedded?\n\nAlternative: verb object is [noun] + [wena], and \"wena\" = those.\n\nIn 4: \"makesiwena\" = those canoes \nIn 10: \"makwena\" = this stone → \"makwena\" = stone + wena (this)\n\nSo for 19: \"How many canoes did those old women see?\" \n→ \"Navila makesi wena biyamatasi?\" → \"wena\" = those → \"makesi\" = canoes → \"biyamatasi\" = old women\n\nBut \"navila\" is \"how many\", so it should be followed by object and verb.\n\nStructure: \"Navila [object] [verb] [subject]?\"\n\nBut 13: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\" \n→ \"vivila\" = verb (look after), \"biyamatasi\" = subject, \"tau\" = this, \"mtona\" = man\n\nSo verb comes before subject? No — \"vivila biyamatasi\" → verb then subject?\n\nNo, in 13: \"vivila biyamatasi\" = look after [women]? \n\"vivila\" = verb, \"biyamatasi\" = subject → subject after verb.\n\nIn 1: \"Bibani navasi yena minasina tetala tau\" → \"navasi\" = catch, \"yena\" = these, \"minasina tetala tau\" = fish\n\n\"navasi\" verb, object \"yena minasina tetala tau\"\n\nIn 4: \"waga makesiwena namwaya minana\" → \"waga\" = saw, object = makesiwena namwaya minana\n\nSo verb then object.\n\nSo pattern: [verb] [object] → object = [noun + specifier]\n\nSo for 19: \"Navila makesi wena biyamatasi?\" → how many canoes? did old women see?\n\nBut this places \"biyamatasi\" after verb — is it object or subject?\n\nSubject should be agent (old women), object is canoes.\n\nIn 4: subject is \"that child\", verb \"saw\", object \"those canoes\"\n\nSo agent (subject) comes before verb (in English), but in Kilivila, verb comes first?\n\nIn 4: \"Legisi waga makesiwena namwaya minana\" → subject \"legisi\", verb \"waga\", object \"makesiwena...\"\n\nSo: subject → verb → object\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → subject → verb → object\n\nIn 13: \"Navila vivila biyamatasi tau mtona?\" → no subject → implies \"how many\" with verb and object\n\nBut 13 is \"how many women will look after this man\" → implies agent is women, object is man\n\nSo: \"Navila vivila biyamatasi tau mtona\" → \"how many [women] will look after [this man]\"\n\n→ So structure: \"Navila [verb] [subject] [specifier] [object]\"\n\nSo verb, then subject,", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11556.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 1, + "output": "First, analyze the given English-Kilivila pairs to extract linguistic patterns in syntax, word order, and semantic mapping.\n\nKey observations from examples:\n\n1. Question forms: \n - \"How many X did Y see?\" → \"Navila x lekotasi?\" (e.g., 8: How many dogs arrived? → Navila ka’ukwa lekotasi?) \n → \"Navila\" = how many; followed by a noun; \"lekotasi\" = arrived (past) → so \"Navila X lekotasi?\" = How many X?\n\n - \"Which X did Y see?\" → \"Amakena waga X gweguyau?\" (9: Which canoe did the chiefs see?) \n → \"Amakena waga\" = which (of); \"gweguyau\" = saw → structure: \"Amakena waga [NP] gweguyau?\"\n\n2. Subject-verb-object order: \n - English: “This white man arrived.” → Lekota dimdim mtona \n → “Lekota” (this) + “dimdim” (white) + “mtona” (arrived) → subject → adjective → verb \n → This syntax appears to be subject (demonstrative), then adjective, then verb.\n\n3. Future tense: \n - “One man will catch these four fish.” → Bibani navasi yena minasina tetala tau. \n → “will” is marked by \"tau\" at the end → \"tetala tau\" = will catch \n → Note: \"tetala\" = catch; \"tau\" = future. \n → Future: verb + \"tau\"\n\n4. \"See\" constructions: \n - \"That child will arrive.\" → Bikota gwadi magudiwena → \"gwadi\" = child; \"magudiwena\" = will arrive? \n → \"magudiwena\" = will arrive → thus \"magudiwena\" = future of arrive. \n → \"See\" verbs: \"makesiwena\" in (4) → \"saw\" → “makesiwena” is past tense of \"see\"\n\n - (4): “That child will arrive” → “Bikota gwadi magudiwena” → subject + noun + future verb \n → But (10): “That beautiful child saw this stone” → Legisi dakuna makwena gwadi magudiwena gudimanabweta \n → \"Legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = this; \"magudiwena\" = saw; \"gudimanabweta\" = stone \n → Structure: [demonstrative] [adjective] [noun] [demonstrative] [verb] [object] \n → So seeing: [subject] [adj] [noun] [adj] [demonstrative] [verb] [object] \n → But \"makesiwena\" appears in (4) = saw → “waga makesiwena” → \"waga\" = those; \"makesiwena\" = saw\n\n → Confirm: (4) “This old woman saw those canoes.” → Legisi waga makesiwena namwaya minana \n → \"Legisi\" = this; \"waga\" = those; \"makesiwena\" = saw; \"namwaya\" = canoes; \"minana\" = plural? \n → \"namwaya\" = canoes → plural, so \"namwaya\" = canoes (pl) \n → \"makesiwena\" = saw (past) → so \"waga makesiwena\" = saw those\n\n → So past observation: [demonstrative] [object dim. or group] [verb] [object noun]\n\n5. Numerals: \n - “four” → \"yena\" in (1): \"One man will catch these four fish\" → “yena minasina” → “yena” = four \n → “yena” = four → pluralize: \"minasina\" = fish → “yena minasina” = four fish \n → In (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → \"ka’ukwa\" = dogs \n → (11): \"How many things did those white men eat?\" → “Kwevila lekamkwamsi dimdim mtosiwena?” \n → “lekamkwamsi” = those white men; “mtosiwena” = ate → so “mtosiwena” = past of eat \n → “kwevila” = how many → applies to the count of things\n\n → So “how many X” → “Navila X lekotasi” for past events → but (11): “Kwevila lekamkwamsi dimdim mtosiwena?” \n → unlike (8): “Navila ka’ukwa lekotasi?” → here it’s “Kwevila” + agent + verb \n → So “kwevila” = how many → so pattern: “how many X did Y do?” → “Kwevila Y did_verb?” \n → Actually, (8): How many dogs arrived? → Navila ka’ukwa lekotasi? → lekotasi = arrived → so \"Navila X lekotasi\" = how many X arrived \n → But (11): “How many things did those white men eat?” → Kwevila lekamkwamsi dimdim mtosiwena? \n → This has \"Kwevila\" (how many) then agent, then verb → so the structure is: “how many X did Y do?” → Kwevila [agent] [adj] [verb]\n\n → So for questions like “how many X did Y do?” → Kwevila [agent] [adj] [verb]\n\n → Conversely, “how many X did Y see?” → “Navila X lekotasi” → if X is object, and lekotasi = saw? \n → (10): “That beautiful child saw this stone” → Legisi dakuna makwena gwadi magudiwena gudimanabweta → shows that verb is \"magudiwena\" = saw \n → But no direct “how many X did Y see” in data? \n → (19): How many canoes did those old women see? → target \n → So pattern: “how many X did Y see?” → “Navila X lekotasi” → but “lekotasi” = arrived? \n → Not matching → need to find the saw word.\n\n → In (4): \"This old woman saw those canoes\" → “Legisi waga makesiwena namwaya minana” \n → “makesiwena” = saw → so \"waga makesiwena\" = saw those → so “X makesiwena Y” = X saw Y\n\n → So in question: “How many canoes did those old women see?” \n → Subject: “those old women” → “waga” + “old” + “women” \n → “waga” = those \n → Old → “legisi” or “gweguyau”? \n → \"legisi\" = this, “gweguyau” = saw \n → “wagi” or “waga” = those \n → In (4): “Legisi” = this; “waga” = those \n → So “those old women” → “waga lugi” or “waga legis”?\n\n → (3): “That child will arrive” → “Bikota gwadi magudiwena” → “gwadi” = that; “magudiwena” = will arrive \n → (2): “This white man arrived” → “Lekota dimdim mtona” → “leko” = this; “dimdim” = white; “mtona” = arrived\n\n → “This” → lekota; “that” → bikota; “this old woman” → “legisi” or “legota”? \n (4): “This old woman saw those canoes” → “Legisi waga makesiwena namwaya minana”\n\n → So “this” → “legisi” in (4); “that” → “bikota” in (3); “this white man” → “lekota dimdim mtona”\n\n → So demonstratives: \n “this” → lekota, legisi \n “that” → bikota \n “these” → waga (in 4: “waga” = those)\n\n → “waga” = those → plural\n\n → So for “those old women” → “waga” + “old” + “women” → “waga legisi”?\n\n → But “legisi” = this → so different from \"old women\"\n\n → What word for “old”?\n\n → (3): “That child will arrive” → “Bikota gwadi magudiwena” \n → (4): “This old woman saw those canoes” → “Legisi waga makesiwena namwaya minana” \n → “waga” = those → object \n → “namwaya” = canoes \n → In (12): “The clever chief killed one wild pig” → “Lekalimati natala bunukwa nagasisi guyau tokabitam” \n → “lekalimati” = the clever chief → “natala” = one → “bunukwa” = wild pig → “nagasisi” = killed → “guyau” = wild? → “tokabitam” = one?\n\n → “natala” = one → used in (12) for “one wild pig”\n\n → (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n → “vivila” = women; “biyamatasi” = look after; “tau” = future → “tau mtona” = will look after \n → So future: verb + “tau”\n\n → So structure for future: [subject] [verb] + “tau”\n\n → Past: verb without “tau” → e.g., “makesiwena” = saw → past\n\n → Future: e.g., “tetala tau” = will catch\n\n → So for 20: “These four white men will look after this clever child” \n → These white men → “waga” + “white” → “waga dimdim” → “waga dimdim” = these white men \n → will look after → “biyamatasi tau” → “biyamatasi” = look after \n → this clever child → “gwadi” + “clever” → “gwadi kweguyau”? \n → “kweguyau” = clever? → in (12): “lekalimati natala bunukwa nagasisi guyau tokabitam” → “guyau” = wild? \n → “guyau” = wild → not clever\n\n → (7): “That clever woman will see something” → “Bigisi kwetala vivila minawena nakabitam” \n → “Bigisi” = that; “kwetala” = clever; “vivila” = woman; “minawena” = something; “nakabitam” = will see? \n → “nakabitam” = will see → past of see? \n → “makesiwena” = saw; “nakabitam” = will see → so “nakabitam” = future of see\n\n → So see: “makesiwena” = saw; “nakabitam” = will see\n\n → So future of “see” = “nakabitam”\n\n → So “will look after” → “biyamatasi tau” → so “biyamatasi” + “tau”\n\n → So 20: \n These four white men → “waga dimdim” → “waga dimdim” = these white men \n will look after → “biyamatasi tau” \n this clever child → “gwadi kwetala” → “gwadi” = this; “kwetala” = clever → but in (7): “kwetala” = clever woman \n so “gwadi kwetala” = this clever woman → correct \n → So: “waga dimdim biyamatasi tau gwadi kwetala”\n\n But is that the full structure?\n\n → Check example (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n → So “Navila vivila biyamatasi tau mtona” = how many women will look after this man? \n → So the marker is “Navila” for how many → then subject (women), verb (biyamatasi), future (tau), object (this man) \n → Object: “mtona” = this man → so “mtona” = this [man]\n\n → So in 20: \n Subject: “These four white men” → “waga dimdim” — is “four” included? \n → In (1): “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau” \n → “yena” = four → so “yena” = four \n → So “these four white men” → “waga dimdim yena”? → but “yena” is numeral \n → But in (5): “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?” \n → “nayu” = two → so “nayu” = two \n → “nayu” = two → “yena” = four → digits needed\n\n → So “four” → “yena” (as in 1)\n\n → So “these four white men” → “waga dimdim yena”?\n\n → But (1): “yena minasina” = four fish → yena is attached to fish → so “waga dimdim yena” = these white men, plural with number? \n → But in (12): “one wild pig” → “natala bunukwa” → “natala” = one → “bunukwa” = pig \n → So numerals like “one”, “two” are separate adjectives or modifiers\n\n → So “these four white men” → “waga dimdim yena” — possible? \n → But in (1): “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau” \n → This is “one man” → “Bibani navasi” → “Bibani” = one → “navasi” = man → so “Bibani” = one → so “Bibani navasi” = one man\n\n → So numeral is separate → e.g., “one” = Bibani \n → “two” = nayu \n → “four” = yena\n\n → So “four white men” → “yena dimdim” → “yena” = four; “dimdim” = white → “yena dimdim” = four white men\n\n → “these four white men” → “waga yena dimdim” → “waga” = these; “yena” = four; “dimdim” = white → so “waga yena dimdim” = these four white men\n\n → Then they will look after → “biyamatasi tau” \n → This clever child → “gwadi kwetala” → this clever child\n\n → So whole: “waga yena dimdim biyamatasi tau gwadi kwetala”\n\n → Word order: subject → verb → object → so subject + verb + object\n\n → In (13): “Navila vivila biyamatasi tau mtona?” → how many women will look after this man? \n → verb comes before object? “biyamatasi tau” = will look after → then object “mtona” = this man\n\n → So verb + object → not subject–verb–object as in English\n\n → But in (2): “This white man arrived” → “lekota dimdim mtona” → subject → adjective → verb\n\n → Order in surface form may not follow direct English mapping.\n\n → For 20: likely: “waga yena dimdim biyamatasi tau gwadi kwetala”\n\n → But is \"biyamatasi\" the correct word for \"look after\"?\n\n → (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” → yes → “biyamatasi” = look after\n\n → So correct.\n\n6. 21: “How many children will eat these pigs?” \n → How many children → “Navila” + “children” \n → will eat → “mtosiwena” = eat → future: “mtosiwena tau” \n → these pigs → “yena” = four? → no, pigs → “bunukwa” in (12): “bunukwa” = wild pig → so “bunukwa” = pig \n → “these” → “waga” \n → so “waga bunukwa” = these pigs \n → So full: “Navila vivila mtsosiwena tau waga bunukwa” → how many children will eat these pigs?\n\n → But structure in (11): “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?” \n → “Kwevila” = how many → then agent → verb → so “how many X did Y do?” → “Kwevila Y did_verb?” \n → So “how many children will eat these pigs?” → “Navila vivila mtsosiwena tau waga bunukwa” \n → Is “Navila” used here? \n → In (8): “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” → so “Navila X lekotasi” = how many X? \n → But (11): “How many things did those white", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11752.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 2, + "output": "Step 1: Analyze the pattern of questions and translations to determine structure.\n\nIn the given examples, questions starting with \"How many X did Y see?\" follow a pattern: \n- “How many [object] did [subject] see?” → “Navila [object] [subject] waga [verb]?” \nFor instance:\n\n- (8) “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” \n → “Navila” = how many; “ka’ukwa” = dogs; “lekotasi” = arrived.\n\n- (4) “This old woman saw those canoes.” → “Legisi waga makesiwena namwaya minana.” \n → “Legisi” = this old woman; “waga” = saw; “namwaya” = those canoes.\n\nBut in (19): “How many canoes did those old women see?” \n→ Should be: “Navila namwaya [subject] waga makesiwena?”\n\nIn (4), “Legisi” = “this old woman” (singular), “namwaya” = “those canoes” (plural). \nNow observe: \n- “those old women” → plural; reconstruction: “lekotasi” = arrived (from 2), “legisi” = old woman → plural form?\n\nFrom (3): “That child will arrive” → “Bikota gwadi magudiwena” \n→ “Bikota” = that; “gwadi” = child; “magudiwena” = will arrive.\n\n(12): “The clever chief killed one wild pig.” → “Lekalimati natala bunukwa nagasisi guyau tokabitam.” \n→ “lekalimati” = clever chief; “natala” = one; “bunukwa” = wild pig; “nagasisi” = killed.\n\nSo, numerals: \n- “one” = natala \n- “two” = nayu (from 5: “Which man killed two pigs?” → “nayu bunukwa”)\n\n(5): “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?” \n→ “Amtona” = which; “tau” = man; “lekalimati” = killed (a verb stem); “nayu” = two; “bunukwa” = pigs.\n\nSo: “which + subject + verb + numeral + object” — forms “Amtona tau lekalimati nayu bunukwa?”\n\nNow re-express (19): “How many canoes did those old women see?” \n→ Similar to (8): “How many [X] did [Y] see?” \nIn (8): “Navila ka’ukwa lekotasi?” → “Navila” + [object] + [subject] + verb (of seeing)? \nBut (8) is “arrived”, not “saw”.\n\n(4): “This old woman saw those canoes” → “Legisi waga makesiwena namwaya minana” \n→ Subject: “Legisi” → old woman; verb: “waga makesiwena” → saw; object: “namwaya minana” → those canoes.\n\nSo: “subject + waga + verb + object”?\n\nBut in (19), “how many canoes did those old women see?” \n→ This is “how many [object] did [subject] see?” \nSo: “Navila namwaya [subject] waga makesiwena?”\n\n→ “Namwaya” = canoes (plural); “those old women” → plural “lekotasi”?\n\nFrom (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n→ “Navila” = how many; “vivila” = women; “biyamatasi” = will look after; “tau” = this man.\n\nSo “Navila [subject] [verb] [object]”?\n\nBut in (13): “Navila vivila biyamatasi tau mtona” → “how many women will look after this man?”\n\nSo pattern is: “Navila [subject] [verb] [object]”\n\nBut in (4): “Legisi waga makesiwena namwaya minana” – this is not “Navila” structure.\n\nWait: sentence (8): “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” \n→ “Navila” + [object] + [subject] + “lekotasi” (arrived)\n\nSo for questions with arrival: “Navila [object] [subject] [verb]?”\n\nBut in (19): “see” is the verb — not “arrived”\n\nSo use (4): “Legisi” = subject; “waga” = saw; “namwaya” = object.\n\nSo for “how many canoes did those old women see?” \n→ “Navila namwaya [subject] waga makesiwena?”\n\nIn (13): “Navila vivila biyamatasi tau mtona” → “how many women will look after this man?” \n→ subjects: “vivila” (women); verb: “biyamatasi” (look after); object: “tau mtona” (this man)\n\nSo: “Navila [subject] [verb] [object]”\n\nBut in (4), the verb form is “makesiwena” — “see” — and “waga is the verb prefix”?\n\nWait, (4): “Legisi waga makesiwena namwaya minana” → “old woman saw canoes”\n\nSo “waga” is the verb stem (to see), “makesiwena” may be derived from “waga” + aspect?\n\nBut also: (10): “That beautiful child saw this stone” → “Legisi dakuna makwena gwadi magudiwena gudimanabweta”\n\nWait: “Legisi” = that beautiful child; “dakuna” = saw? But “dakuna” is used, not “waga”?\n\n(10): “Legisi dakuna makwena gwadi magudiwena gudimanabweta”\n\n→ “dakuna” = saw? But “waga” is not used.\n\n(4): “waga makesiwena” → “saw”\n\n(10): “dakuna” → saw?\n\nSo different verbs for see?\n\nPossibility: “waga” and “dakuna” both mean “to see”? Or “waga” is for direct object, “dakuna” otherwise?\n\nBut (10): “saw this stone” → “dakuna makwena gwadi magudiwena gudimanabweta”\n\n“makwena” = this stone? “gwadi” = child? “magudiwena” = saw?\n\nActually, “gwadi magudiwena” — “that child saw”?\n\n“Legisi” = that beautiful child → “Legisi dakuna makwena gwadi magudiwena gudimanabweta”\n\n→ “dakuna” + “makwena” → “saw this stone” — “makwena” = this stone; “gwadi” = child; “magudiwena” = saw?\n\nWait, the structure seems off.\n\nBreak down (10): \n“Legisi dakuna makwena gwadi magudiwena gudimanabweta”\n\nLikely: “Legisi” = this beautiful child; “dakuna” = saw; “makwena” = this stone; “gwadi” = child? That’s redundant.\n\nAlternative: perhaps only one noun is required.\n\n“makwena” = this stone? “gwadi” = child → might be separate.\n\nBut “magudiwena” = saw?\n\nSo maybe “dakuna” and “waga” are not the same?\n\nBut in (4): “waga makesiwena” → “saw”\n\nIn (10): “dakuna makwena” → “saw this stone”\n\nSo “dakuna” might be “saw”, “makwena” = this stone.\n\nBut in (4): “makesiwena” = saw, “namwaya” = canoes.\n\nSo maybe “waga” and “dakuna” are both seen verbs?\n\nPattern for “see”: object comes after verb? “waga makesiwena namwaya” → sees canoes → object after.\n\nIn (10): “dakuna makwena gwadi magudiwena gudimanabweta”\n\n→ “dakuna” + “makwena” → “saw this stone”?\n\nBut “gwadi” is “that child”, which is already the subject?\n\nPossibility: the subject is repeated?\n\n(10): “da” + “kuna” → saw; “makwena” → this stone → object.\n\nSo “dakuna” = saw (verb), “makwena” = this stone.\n\nBut in (4): “waga makesiwena” = saw canoes.\n\nSo identical structure: verb + object.\n\nIn (4): “waga makesiwena namwaya minana” → “saw canoes” → “makesiwena” is the verb form.\n\nSo in (19): “how many canoes did those old women see?” → “Navila namwaya lekotasi waga makesiwena?”\n\nBut we need to verify plural: “old women” → two women → plural.\n\nIn (13): “how many women will look after” → “Navila vivila biyamatasi tau mtona”\n\n→ “vivila” = women, plural.\n\nIn (2): “This white man arrived” → “Lekota dimdim mtona” → “lekota” = this; “dimdim” = white; “mtona” = man.\n\nIn (3): “That child will arrive” → “Bikota gwadi magudiwena” → “gwadi” = child.\n\nSo “gwadi” = child → singular.\n\nNo plural form.\n\nBut “women” → “vivila” in (13) → plural.\n\nSimilarly, “canoes” → “namwaya” → used in (4) for “those canoes”.\n\nSo “namwaya” = canoes → plural.\n\n“old women” → “lekotasi” → from (4), “legisi” = old woman (singular), so plural could be “lekotasi”?\n\nIn (3): “Bikota gwadi” → that child → singular.\n\nIn (4): “Legisi” → this old woman.\n\nIn (13): “vivila” → women, plural.\n\nSo likely “lekotasi” = old women (plural).\n\nThus (19): “Navila namwaya lekotasi waga makesiwena?”\n\nIs that correct?\n\nBut the sentence is: “how many canoes did those old women see?”\n\nStandard format in poetic structure: “how many [object] did [subject] see?”\n\nSo yes: “Navila namwaya lekotasi waga makesiwena”\n\nWait — check verb: in (4): “waga makesiwena” → saw.\n\nSo correct.\n\nNow (20): “These four white men will look after this clever child.”\n\n“These four white men” → plural subject.\n\n“will look after” → future tense.\n\nLook at (13): “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona”\n\n→ “Navila” = how many; “vivila” = women; “biyamatasi” = will look after; “tau mtona” = this man.\n\nSo structure: “Navila [subject] [verb] [object]”\n\nIn (13): the verb is “biyamatasi” → will look after.\n\nIn (12): “The clever chief killed one wild pig” → “Lekalimati natala bunukwa nagasisi guyau tokabitam”\n\n→ “lekalimati” = chief; “natala” = one; “bunukwa” = wild pig; “nagasisi” = killed; “guyau tokabitam” = wild pig? Wait — “guyau” = wild? “tokabitam” = pig?\n\nPossibility: “guyau” = wild; “tokabitam” = pig → “wild pig”\n\nBut “bunukwa” = wild pig?\n\nSo “bunukwa” = wild pig?\n\nIn (5): “Which man killed two pigs?” → “Amtona tau lekalimati nayu bunukwa?”\n\n“Amtona” = which; “tau” = man; “lekalimati” = killed; “nayu” = two; “bunukwa” = pigs.\n\nSo “bunukwa” = pigs (plural)\n\n(12): “one wild pig” → “natala bunukwa” → “bunukwa” = wild pig?\n\nBut “wild pig” is one — so “bunukwa” = pig, possibly with “nagasisi guyau” = killed (wild) pig?\n\nBut in (12): “nagasisi guyau tokabitam” → “killed wild pig” — but “tokabitam” = pig?\n\nPossibility “tokabitam” = pig; “guyau” = wild.\n\nBut “bunukwa” = pig?\n\nSo “bunukwa” = pig — used as object.\n\nThus in (20): “These four white men will look after this clever child.”\n\n→ “These four” → numeral “four”\n\nFrom (1): “One man” → “navasi” = one? Or “navasi” = man?\n\n(1): “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau”\n\n→ “navasi” = man; “yena” = will catch; “minasina” = these four; “tetala” = fish; “tau” = man?\n\nWait — “minasina” = these four? Possibly “minasina” = these four fish?\n\n“tetala” = fish → “minasina tetala” = these four fish?\n\nSo “minasina” = these four → noun phrase?\n\nIn (1): “minasina” = these four fish → so numerals are embedded in object?\n\nBut in (5): “two pigs” → “nayu bunukwa”\n\nIn (12): “one wild pig” → “natala bunukwa”\n\nSo numerals: \n- one → natala \n- two → nayu \n\nSo four → ? Not directly given.\n\nIn (1): “these four fish” → “minasina tetala tau”\n\n→ “minasina” = four? → likely, “minasina” = four (number)\n\nNow (8): “How many dogs arrived?” → “Navila ka’ukwa lekotasi?”\n\n→ No numeral used → just “how many”\n\nIn (20): “These four white men” → so numeral required.\n\n“four” → object or subject?\n\nIn (1): “one man” → subject = “navasi” → singular man\n\nSo “white men” → plural → “dimdim mtona” in (2) → “white man” → “dimdim mtona”\n\nSo “white men” → “dimdim” = white; “mtona” = man → plural “mtona” — likely “mtona” is generic, plural form?\n\nIn (2): “This white man arrived” → “Lekota dimdim mtona” → “mtona” = man.\n\nSo “mtona” = man → plural form likely.\n\nSo “white men” → “dimdim mtona”\n\n“four” → “minasina” → as in “minasina tetala” → these four fish.\n\nSo “These four” → “minasina”\n\nBut is it “minasina” directly?\n\n(1): “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau”\n\nSo “minasina tetala” → these four fish → \"minasina\" = four\n\nSo for “these four white men” → “minasina dimdim mtona”\n\nNow verb: “will look after”\n\nFrom (13): “will look after” → “biyamatasi”\n\nSo structure: “subject + biyamatasi + object”\n\nIn (13): “Navila vivila biyamatasi tau mtona” → “how many women will look after this man?”\n\nSo for (20): “minasina dimdim mtona biyamatasi gwadi magudiwena”\n\n“this clever child” → “gwadi magudiwena” → “that child” → “gwadi” = child; “magudiwena” = will?\n\nBut in (3): “Bikota gwadi magudiwena” → “that child will arrive” → so “magudiwena” = will arrive?\n\nIn (13): “biyamatasi” = will look after.\n\nSo “magudiwena” = will see or arrive?\n\nIn (3): “will arrive” → “magudiwena”\n\nSo “magudiwena” = will arrive, not “will look after”.\n\n“biyamatasi” = will look after.\n\nSo for “this clever child” → not just “gwadi”, but “clever child” → “bigusi” or “lekalimati”?\n\nIn (12): “clever chief” → “lekalimati”\n\nIn (10): “beautiful child” → “dakuna makwena gwadi magudiwena gudimanabweta”\n\nLater: “dakuna” → saw; “gwadi” = child; “magudiwena” = will?\n\nSo “gwadi” = child → “clever child” → “lekalimati gwadi”?\n\nIn (12): “lekalimati” = clever chief.\n\nSo likely “lekalimati” = clever → applies to woman or child?\n\nIn (20): “this clever child” → “gwadi lekalimati”?\n\nBut in (3): “that child” = “gwadi”\n\nSo “that clever child” = “gwadi lekalimati”?\n\nPossibly.\n\nSo “this clever child” → “gwadi lekalimati”\n\nThus (20): “minasina dimdim mtona biyamatasi gwadi lekalimati”\n\nNow (21): “How many children will eat these pigs?”\n\nStructure: from (13): “Navila [subject", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11638.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "anti_nearmiss", + "sample_index": 3, + "output": "Step 1: Identify the grammatical structures from the provided examples to detect patterns in subject, object, tense, number, and question form.\n\nExample 1: \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"Bibani\" (one man) → subject \n- \"navasi\" (will catch) → future verb \n- \"yena\" (these) → demonstrative for object \n- \"minasina\" (four fish) → object \n→ Pattern: Subject + future verb + demonstrative + object (with numeral)\n\nExample 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\" \n- \"Lekota\" (this) → demonstrative \n- \"dimdim\" (white) → adjective \n- \"mtona\" (arrived) → verb \n→ Subject is marked by demonstrative; no explicit number; verb is past.\n\nExample 3: \"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n- \"Bikota\" (that) → demonstrative \n- \"gwadi\" (child) → noun \n- \"magudiwena\" (will arrive) → future verb \n→ Demonstrative + noun + future verb\n\nExample 4: \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n- \"Legisi\" (this) → demonstrative \n- \"waga\" (old woman) → subject \n- \"makesiwena\" (saw) → past verb \n- \"namwaya\" (those) → demonstrative \n- \"minana\" (canoes) → object \n→ Subject demonstrative + noun + past verb + demonstrative + object\n\nExample 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"Amtona\" (which) → interrogative \n- \"tau\" (man) → subject \n- \"lekalimati\" (killed) → verb \n- \"nayu\" (two) → numeral \n- \"bunukwa\" (pigs) → object \n→ Interrogative + subject + verb + numeral + object\n\nExample 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n- \"Leyamatasi\" (old women) → subject \n- \"teyu\" (looked after) → verb \n- \"tauwau\" (two) → numeral \n- \"nunumwaya\" (men) → object \n→ Subject + verb + numeral + object\n\nExample 7: \"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n- \"Bigisi\" (that) → demonstrative \n- \"kwetala\" (clever woman) → subject \n- \"vivila\" (will see) → future verb \n- \"minawena\" (something) → object \n→ Demonstrative + subject + future verb + indefinite object\n\nExample 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" (how many) → interrogative \n- \"ka’ukwa\" (dogs) → object \n- \"lekotasi\" (arrived) → verb \n→ \"How many\" + object + verb → suspect order reversal\n\nExample 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n- \"Amakena\" (which) → interrogative \n- \"waga\" (the chiefs) → subject \n- \"legisesi\" (saw) → verb \n- \"gweguyau\" (canoe) → object \n→ Interrogative + subject + verb + object\n\nExample 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"Legisi\" (that) → demonstrative \n- \"dakuna\" (beautiful child) → noun phrase \n- \"makwena\" (saw) → verb \n- \"gwadi\" (this) → demonstrative \n- \"magudiwena\" (stone) → object \n→ Demonstrative + noun + verb + demonstrative + object \n→ Subject–verb–object with demonstratives on both ends\n\nExample 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" (how many) → interrogative \n- \"lekamkwamsi\" (things) → object \n- \"dimdim\" (white) → adjective \n- \"mtosiwena\" (ate) → verb \n→ \"How many\" + object + verb \n→ key pattern: questions begin with \"how many\" or \"which\", then object, then verb\n\nExample 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n- \"Lekalimati\" (the clever chief) → subject \n- \"natala\" (killed) → verb \n- \"bunukwa\" (one wild pig) → object \n→ Subject + verb + object (with descriptive adjective + numeral)\n\nExample 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"Navila\" (how many) → interrogative \n- \"vivila\" (will look after) → future verb \n- \"biyamatasi\" (women) → object \n- \"tau\" (this) → demonstrative \n- \"mtona\" (man) → object of “look after” \n→ \"how many\" + verb + noun + demonstrative + noun \n→ Reversal: object comes before subject? Not exactly.\n\nWait: “Navila vivila biyamatasi tau mtona” \n- “Navila” — how many \n- “vivila” — will look after \n- “biyamatasi” — women (subject of “look after”) \n- “tau” — this \n- “mtona” — man (object)\n\nSo structure: how many + future verb + subject + demonstrative + object \n→ This contradicts prior.\n\nBut earlier: \"How many men will look after this child?\" → likely would be \"Navila vivila tau gwadi magudiwena?\"\n\nCompare with 13: \"how many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona\"\n\nSo: how many + future verb + [subject] + demonstrative + object\n\n→ But in 13, \"biyamatasi\" is subject of verb \"vivila\" (will look after), and \"tau mtona\" is object\n\nSo pattern: \n(1) For questions with \"how many\", structure is: \n\"Navila\" (how many) + [verb] + [subject] + demonstrative + object \n(2) For questions with \"which\", structure is: \n\"Amtona\" or \"Amakena\" + [subject] + [verb] + [object] \n(3) For declarative, structure is: \n[demonstrative] + [noun or subject] + [verb] + [demonstrative] + [object] \n(4) Number is often included explicitly (e.g., \"tau\", \"nayu\", \"minana\")\n\nNow examine question 19: \"How many canoes did those old women see?\"\n\n→ This is a question with \"how many\", so starts with \"Navila\" \n→ Object: \"canoes\" → needs demonstrative? \n→ Subject: \"those old women\" → \"legisi\" (that/those) or \"leyamatasi\" (old women)? \n→ Verb: \"see\" → \"makesiwena\" (saw), \"vivila\" (will see)\n\nFrom example 4: \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana\" \n→ \"legisi\" (this) + \"waga\" (old woman) + \"makesiwena\" (saw) + \"namwaya\" (those) + \"minana\" (canoes)\n\nSo: Demonstrative + subject + verb + demonstrative + object\n\nBut in questions, we see: \nExample 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" (how many) + object (dogs) + verb (arrived)\n\nExample 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"Kwevila\" (how many) + object (things) + verb (ate)\n\nWait — \"lekamkwamsi\" is \"things\", but it's marked as object, not subject. \n\"dimdim\" is white men → adjective \n\"mtosiwena\" is ate → verb\n\nBut order: how many + object + verb \n→ Structure of questions with how many: how many + object + verb \n→ Verb is in root form? \n→ In 11: \"lekamkwamsi dimdim mtosiwena?\" → object + adjective + verb\n\nSo pattern for \"How many X did Y?\" → \"Navila X [adjective] verb?\" \nBut in 8: \"Navila ka’ukwa lekotasi?\" → how many dogs arrived? \n→ ka’ukwa (dogs) + lekotasi (arrived)\n\nNo adjective. \nIn 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → things (object) + white (adj) + ate (verb)\n\nSo perhaps: \"How many X [mod] verb?\" with X = object\n\nThus, for \"How many canoes did those old women see?\" → \n\"Navila\" + \"namwaya\" (those) + \"minana\" (canoes) + \"makesiwena\" (saw)? \nBut \"makesiwena\" is past → but \"did see\" = past\n\nBut in example 4: \"saw\" → \"makesiwena\"\n\nSo verb is \"makesiwena\" → past\n\nBut in declaratives, object is after verb.\n\nIn question, only possible structure: how many + object + verb?\n\nBut in 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"Navila\" + \"vivila\" (will look after) + \"biyamatasi\" (women) + \"tau\" (this) + \"mtona\" (man)\n\nHere, subject (women) is after verb, and object (man) is after demonstrative.\n\nSo structure is: \"how many\" + future verb + subject + demonstrative + object\n\nBut in 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"Kwevila\" + \"lekamkwamsi\" (things) + \"dimdim\" (white) + \"mtosiwena\" (ate)\n\nNo subject. So when it’s \"how many X did Y\", it may be different.\n\nWait, the question is \"how many canoes did those old women see?\" \n→ Object: canoes \n→ Subject: those old women (who saw them)\n\nSo this is \"how many X did Y see?\"\n\nThis matches example 4 and 12, which have \"X did Y see?\"\n\nBut example 4: \"this old woman saw those canoes\" → \"legisi waga makesiwena namwaya minana\"\n\nSo: subject + verb + demonstrative + object\n\nIn question form, is the subject present?\n\nIn 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"Amakena\" (which) + \"waga\" (chiefs) + \"legisesi\" (saw) + \"gweguyau\" (canoe)\n\n→ Subject + verb + object → so the object is directly after verb\n\nSo in \"how many X did Y see?\", the structure is: \n\"Navila\" (how many) + [object] + \"makesiwena\" (saw) + [subject]? \nBut no subject in 8.\n\nBut in 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"Kwevila\" + \"lekamkwamsi\" (things) + \"dimdim\" (white) + \"mtosiwena\" (ate)\n\nNo subject. \"those white men\" is omitted? But the sentence is \"how many things did those white men eat?\" \nSo subject should be included.\n\nBut the translation is \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"lekamkwamsi\" is \"things\" → so object \n→ \"dimdim\" is white → adjective \n→ \"mtosiwena\" is ate → verb \n→ missing subject? \n\nWait — how can \"how many X did Y eat\" be translated without Y?\n\nExample 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibility: the object is \"things\", and the verb is \"ate\", and the subject is encoded in \"dimdim\"? No — \"dimdim\" is white, not men.\n\nUnless \"dimdim\" is modifying the subject? \nBut \"lekamkwamsi dimdim\" — things white? = white things?\n\nThat doesn’t make sense.\n\nBut \"dimdim\" is used in \"dimdim mtona\" (white man) → so \"dimdim\" = white, adjective.\n\nThus, \"lekamkwamsi dimdim\" = white things → white things?\n\nBut \"those white men\" — men are the subject, not things.\n\nThus, the translation must have a mistake in parsing.\n\nWait — \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossible: \"Kwevila\" (how many) + \"lekamkwamsi\" (things) + \"dimdim\" (white) + \"mtosiwena\" (ate)\n\nBut what about \"those white men\"?\n\nPossibility: the subject is not explicitly stated? But that would be strange.\n\nCompare to example 4: \"This old woman saw those canoes\" → \"legisi waga makesiwena namwaya minana\"\n\n→ Subject is \"legisi waga\", then verb, then demonstrative + noun.\n\nIn 11: perhaps it is \"how many things did the white men eat?\" — so subject is \"white men\"\n\nSo is \"dimdim\" referring to men?\n\n\"dimdim\" alone = white\n\n\"dimdim mtona\" = white man\n\nSo \"dimdim mtosiwena\" = white ate?\n\nBut \"mtosiwena\" is \"ate\", not \"white ate\"\n\nThus, likely, \"dimdim\" modifies the subject of \"ate\", and \"lekamkwamsi\" is the object.\n\nSo: \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n→ subject is implied or encoded in \"dimdim\"?\n\nNo — no \"those\" or \"men\" directly.\n\nAlternative: \"Kwevila\" is how many, then object, then verb — no subject.\n\nBut all questions with \"how many\" seem to have the object as noun phrase and verb.\n\nIn 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona\"\n\n→ \"Navila\" + \"vivila\" (will look after) + \"biyamatasi\" (women) + \"tau\" (this) + \"mtona\" (man)\n\nSo verb + subject + demonstrative + object\n\nThus, when the verb is a transitive verb with a subject, the structure is: \nhow many + future verb + subject + demonstrative + object\n\nWhen the verb is intransitive (e.g. \"arrived\", \"saw\"), or when asking about number of object, it may be: \nhow many + object + verb\n\nBut 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"ka’ukwa\" = dogs (object) + \"lekotasi\" = arrived (verb)\n\n→ So structure: how many + object + verb\n\nIn 11: \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"lekamkwamsi\" = things (object) + \"dimdim\" = white? → but white of what? \n→ unless \"dimdim\" modifies men, but men aren't mentioned\n\nBut in the translation, \"dimdim\" is adjacent to verb, so likely modifies the verb's subject.\n\nWait — \"mtosiwena\" = ate → \"dimdim mtosiwena\" = white ate?\n\nBut \"white ate\" doesn't make sense in context.\n\nUnless \"dimdim\" is modifying the subject of the verb.\n\nBut the subject is \"those white men\" — so \"dimdim\" should be with \"mtona\" or \"waga\"\n\nBut in example 2: \"This white man arrived\" → \"Lekota dimdim mtona\" \n→ \"dimdim\" + \"mtona\" → white man\n\nSo \"dimdim mtona\" = white man\n\nThus, \"dimdim mtosiwena\" = white ate? No — \"mtosiwena\" is \"ate\"\n\nSo \"dimdim mtosiwena\" = white ate?\n\nBut \"how many things did those white men eat?\" — so the subject is \"those white men\"\n\nSo perhaps the translation has a construction where the subject is not explicitly formed.\n\nBut in 13, the subject is directly provided: \"biyamatasi\" (women)\n\nSo in 11, if the subject is not explicitly formed, how?\n\nPerhaps the pattern is:\n\n- For \"how many X did Y do?\" → \"Navila X [adjective] verb?\" (if Y is defined by adjective) \n- For \"how many X will Y do?\" → \"Navila verb Y [demonstrative] object?\" — no\n\nBut in 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12732.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nPrivate error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private error checks. Do not rely on a word that merely looks familiar; prove its role from the examples. Watch especially for subject/object reversal, singular vs plural, omitted numerals such as 'one' or 'two', tense/aspect errors, copied forms assigned to the wrong target, and number-system pieces composed in the wrong order.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "redacted_solution_hint_mask1", + "sample_index": 0, + "output": "We are to determine the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, based on the given patterns and examples.\n\nFirst, consider \"to exhaust\". From the list, we see:\n\n- a‘öf fau → year’s end \nThis is interpreted as a compound: “a‘öf” (to exhaust) + “fau” (year) = “year’s end”\n\nSo, \"a‘öf\" must be a verb meaning \"to exhaust\", and it combines with \"fau\" via the rule:\n\nWhen forming a compound word (V + N), the first word undergoes a specific reduction pattern depending on its final syllable.\n\nThe rule provided is:\n\n- VCV → V C \n- VCu → V C \n- VCi → ¨V C \n- VCa → V a C \n\nNote: In \"a‘öf\", we have: a (initial), ‘ö (vowel), f (consonant). So it’s a ‘öf → which is V C (V = ‘ö, C = f)\n\nBut the compound is a‘öf fau → “to exhaust + year = year’s end”\n\nSo the verb \"to exhaust\" is a‘öf.\n\nBut the question says we cannot translate “to exhaust” with certainty, and the hints say the possible forms are:\na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nThis suggests that \"to exhaust\" is a verb whose form might vary due to vowel length or other phonological rules, and the compound formation must preserve the structure.\n\nWe are to find the **theoretically possible** forms — not necessarily the actual one, but ones that could arise under the grammatical rules given.\n\nLook at the rules:\n\n- When forming compounds (V + N), the prefix (or base) undergoes phonological changes:\n - VCV → V C \n - VCu → V C \n - VCi → ¨V C \n - VCa → V a C \n\nAlso, when a noun or verb is doubled: e.g., ‘ele + ‘ele → ‘el‘ele\n\nThis suggests that some forms result from assimilation or reduction due to the second element.\n\nNow, we are told that the compound “a‘öf fau” exists, and it means “year’s end”.\n\nSo “a‘öf” is a possible form for “to exhaust”.\n\nBut the possible forms listed in the hint are:\na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nThese differ in:\n- vowel quality: o vs ö\n- length or vowel type: i, u, ö, f, ü\n\nWe must see what could generate such forms under the rules.\n\nNote: In Rotuman, vowels are:\n- ‘a’ = open o \n- ‘ä’ ≈ a in crack \n- ‘ö’ ≈ French eu or German ö \n- ‘ü’ ≈ French u or German ü\n\nAlso, vowel length is marked with ¯.\n\nNow, the compound formation: V + N → the first element may change based on its ending.\n\nIn “a‘öf fau”, the first word is “a‘öf” — this is V C (a‘öf → V = ‘ö, C = f)\n\nBut “a‘öf” is a verb. Could “a‘öf” be derived from a longer form?\n\nThe rules show changes like:\n\n- VCV → V C \nThis could mean, if the verb ends in a VCV syllable, it reduces to VC.\n\nSo perhaps the full verb meant to be something like “a‘öfû” (with a VCV or VCu ending), which becomes “a‘öf”.\n\nSimilarly, if it ends in VCa → V a C → meaning a ‘a’ becomes attached.\n\nBut here, “a‘öf” ends with f → so it could be from a longer base.\n\nNow, what about \"word\"?\n\nWe are to find a theoretically possible form.\n\nWe have no direct example of “word”.\n\nBut look at the compound patterns:\n\nAll compounds follow:\n- N1 + N2 → modifies N1\n- V + O → verb + object → compound meaning\n- N + A → noun + adjective → meaning “one who has A N”\n\nNo direct word for “word” appears.\n\nBut we have:\n- “uku” is not in list\n- “kia” = neck\n- “puli” = glue\n- “pala” = pierce\n- “nu’suar tiro” = window\n- “nu‘sura” = door\n\nNo clear standalone term for “word”.\n\nBut perhaps “word” could form a compound with something.\n\nWe see “pogi” = night \n“pala” = pierce \n“ka.lu” = bracelet; to encircle \n“pa” or “pu”-something?\n\nWait — in the (c) section: \n“curly hair — leav pirpiri” → so leav + pirpiri = curly hair\n\n“Sticky — pulpulu” → pul + pulu → \"pulu\"? \n\"pulu\" = glue → so could \"pulu\" mean sticky?\n\nBut “pulu” appears in: \"pulu — glue\"\n\nSo sticky = pulpulu → possibly used as a compound: \"pulu + pulu\"?\n\nBut \"pulu\" is a noun and adjective.\n\nCould “word” be derived from a compound like “word + thing”?\n\nBut no such compound.\n\nAlternatively, could \"word\" be formed from a noun that combines with an adjective?\n\nBut we see no case.\n\nBut look: the compound rule applies to nouns and verbs.\n\nSo base + base → compound.\n\nFor example: ‘ele + ‘ele → ‘el‘ele = shallow\n\nSimilarly, \"a‘öf\" + \"fau\" → “year’s end”\n\nWe are told that “to exhaust” is formed from a base that undergoes reduction.\n\nThe reduction rules are:\n\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC\n\nSo, if the original verb had the form VCV, it becomes VC.\n\nIn “a‘öf”, we have VCV (a‘öf) → a‘öf → only if it ends in a vowel + consonant.\n\na‘öf: a (vowel), ‘ö (vowel), f (consonant) → VCV → reduces to VC → a‘öf\n\nSo the original form could be something like a‘öfû, a‘öfu, a‘öfö, etc., where the final vowel is long or reduced.\n\nThus, possible forms are those that can reduce to a‘öf via the rule.\n\nSo a‘öf can be derived from:\n\n- a‘öfû → VCV with u → becomes a‘öf (VC)\n- a‘öfu → VCV with u → becomes a‘öf \n- a‘öfö → VCV with ö → becomes a‘öf \n- a‘ofi → o is open o, which is not ö → could it reduce?\n\nNote: the reduction rule allows VCV → VC, regardless of vowel.\n\nBut the vowel might be preserved in the original, and just shortened in form.\n\nThus, any form ending in VC with vowel ‘ö’, ‘u’, or ‘o’ may reduce to VC.\n\nBut the question lists: a‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nAmong these:\n\n- a‘öfö → ends in fö → VCV → reduces to VC (a‘öf) → valid \n- a‘öfu → reduces to a‘öf → valid \n- a‘öfü → VCV or VCu → reduction to VC? \n - VCV → VC → yes, possible \n- a‘ofü → o instead of ö → o is a different vowel → possible if o is allowed \n- a‘ofi → ends in fi → VCa → VCa → becomes VaC → so becomes a‘ofi → which would be a‘o f i → but this would reduce to a‘o f i → which is not a‘öf\n\nWait: the rule says: VCa → VaC\n\nSo if a form ends in VCa, it becomes VaC.\n\nSo “a‘ofi” ends in “o f i” → i is not a, so not VCa.\n\nVaC means: V a C → so vowel, then a, then consonant.\n\nSo “a‘ofi” does not follow the reduction rule to become a‘öf.\n\nBut a‘öf is just VC (vowel-consonant), not V a C.\n\nSo only forms that reduce to VC are valid.\n\nWhich forms will reduce to a‘öf (which is VC)?\n\n- a‘öfö → VCV → reduces to VC → becomes a‘öf → valid \n- a‘öfu → VCV → reduces to VC → becomes a‘öf → valid \n- a‘öfü → VCV → reduces to VC → becomes a‘öf → valid \n- a‘ofü → VCV → reduces to VC → becomes a‘of → not a‘öf → different vowel \n- a‘ofi → not VCV → ends in i → which would require special rule? \n VCa → VaC → only when final vowel is a → i is not a → so not applicable\n\nTherefore, only forms with final vowel in VCV or VCu (i.e. not ending in i) will reduce.\n\nThe forms that reduce to a‘öf are:\n\n- a‘öfö \n- a‘öfu \n- a‘öfü \n\nWhy not a‘ofü? Because it has 'o' instead of 'ö', and the rule reduces to the vowel sound, so the mapping is phonetic.\n\nBut the reduction pattern depends on vowel identity: ö is different from o.\n\nAnd the compound a‘öf fau must use 'ö' — not 'o'.\n\nSo only forms with ‘ö’ will reduce correctly to ‘öf’.\n\nTherefore, the theoretically possible forms for “to exhaust” are those that can reduce to a‘öf via the rules.\n\nHence, valid ones are:\n\n- a‘öfö \n- a‘öfu \n- a‘öfü\n\nThe hint says: a‘öfö, a‘öfu, a‘öfü, a‘öfi, a‘ofi, a‘ofü\n\nBut only those that reduce to a‘öf (with ‘ö’ at start) are valid.\n\nNow, a‘öfi → ends in i → not VCV → VCi → which becomes ¨VC → with length sign.\n\nSo a‘öfi → becomes a‘öfi → but with ¨V C → would be a‘öfi → with a glottal stop or lengthened vowel?\n\nBut the reduced form is not a‘öf.\n\nTherefore, only the forms ending in f (consonant) and with root VCV or VCu are valid.\n\nThus, forms that reduce to a‘öf are:\n\n- a‘öfö \n- a‘öfu \n- a‘öfü\n\nNow for “word”.\n\nWe have no direct example.\n\nBut look at the compound rule: compounds form when two nouns or verbs combine.\n\nWe can suppose that “word” may be formed via a similar pattern.\n\nBut what could “word” be?\n\nWe see:\n\n- \"to cut\" = \"olo\" \n- \"to be near\" = \"ele\" \n- \"to use sign language\" = \"fäeag ‘u‘u\" → compound: “fäeag” + “u‘u”\n\nSo “fäeag” = to use, “u‘u” = hand/arm → “to use hand” = to use sign language.\n\nThus, the compound is V + N = to use hand.\n\nSo “word” could be formed as a compound: e.g., “word + something”\n\nBut we don’t see any compound with “word”.\n\nAlternatively, could “word” be a noun that combines with an adjective?\n\nLike “a word” or “a word is deep”?\n\nBut not apparent.\n\nAnother hypothesis: the vowel reduction rules may suggest that some words derive from longer forms.\n\nFor instance, “word” might be a shortened form of something like “wōr” or “wöf”, but not in the data.\n\nBut in Rotuman, words often have internal modifications.\n\nCould “word” be derived from “luka” or “pulu”?\n\nWait — in (c): \"to flash\" = \"rima\", \"rū huga\" = stomach ache, \"huli\" = to turn over.\n\nNo.\n\nAlternatively, consider that “to exhaust” has multiple forms due to reduction from VCV → VC.\n\nSimilarly, “word” may have multiple forms due to the same rule.\n\nBut what is the base?\n\nWe have no compound like “word + X”.\n\nBut suppose that “word” could be formed as “a wo” → like “a‘wo”?\n\nBut a‘wo? Not in list.\n\nAlternatively, look at the only verb compounds: \na‘öf fau → to exhaust + year → year’s end \nhül ha.fu → to blow (of hurricane) → “to turn over + rock”\n\nSo in both, the verb is reduced.\n\nThus, “to exhaust” is a verb that reduces to a‘öf from a longer form ending in VCV.\n\nSimilarly, a word like “word” might be a noun that could reduce when combined.\n\nBut we don’t have such a compound.\n\nSo the only possible way to assign a “theoretically possible” translation is to assume that “word” could have a form that, under the reduction rules, could form a compound.\n\nBut we lack evidence.\n\nHowever, the problem says: “you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty” — but we must give the theoretically possible forms.\n\nSo the possible form for “to exhaust” is any form that can reduce to a‘öf via the rules.\n\nFrom the list in the hint: a‘öfö, a‘öfu, a‘öfü\n\nAnd a‘ofi, a‘öfi, a‘ofü — but only forms that lead to a‘öf are valid.\n\nSo a‘öfö, a‘öfu, a‘öfü are valid.\n\nNow for “word” — is there any similar pattern?\n\nWe have no direct example, so we must infer based on structure.\n\nIs there a word like “a‘uo” or “a‘wö”?\n\nPerhaps “word” is a noun composed of two parts.\n\nFor example, in “is susu” = sharp-pointed, “is” = sharp, “susu” = nipple.\n\nSo “is” + “susu” → sharp-pointed.\n\nSimilarly, could “word” be something like “a‘wo” + another?\n\nBut no such phrase.\n\nWait — in the list: “pala” = pierce — “pala” could be a verb.\n\n“pala” + ? = something?\n\nNo.\n\nAnother idea: the word “word” may be a noun that is formed via the rule of noun + noun.\n\nFor example: “a word” might be “a sa” or “a sō”?\n\nBut we don’t have such examples.\n\nBut in (d), the hint gives only the form for “to exhaust” — and says “a‘öf” is the actual verb, but “the theoretically possible translations” include variations that reduce to it.\n\nSimilarly, for “word”, what could be a possible form?\n\nBut without examples, is there any indication?\n\nLook back at (c): “curly hair — leav pirpiri” → leav (hair) + pirpiri → curly\n\nIn that, “leav” is a noun, “pirpiri” may be an adjective or verb? “piri” = to curl → so “piri” + “piri” = pirpiri → doubled?\n\nThe rule says: when forming adjective by doubling noun or verb: e.g., ‘ele + ‘ele → ‘el‘ele\n\nSo “piri” doubled → “pirpiri”\n\nSo “piri” = to curl → “pirpiri” = curly?\n\nPerhaps.\n\nSimilarly, “pulu” → “pulpulu” = sticky → doubled?\n\n“pulu” + “pulu” → “pulpulu” → sticky\n\nSo “pulu” doubled → becomes “pulpulu” → sticky\n\nThus, some adjectives are formed by doubling.\n\nSo “word” might be formed by doubling?\n\nBut “word” is not an adjective.\n\nBut perhaps a noun that could be doubled.\n\nFor instance, “a ‘wo” → double → “’wōwō”?\n\nBut not obvious.\n\nPerhaps, the word “word” could be derived from a root that was reduced.\n\nBut we have no example.\n\nAlternatively, could “word” be “a‘wo” or “a‘wö”?\n\nSince vowel reduction is common, and forms like a‘öf are from VCV → VC, then similarly, “word” might have a form like a‘wo?\n\nBut there is no evidence.\n\nBut note: in the list, \"pala\" = pierce; “pala” could be used in compound.\n\nBut not with “word”.\n\nAnother idea: “to exhaust” is a verb; “word” is a noun.\n\nIn compounds, we have:\n- V + O → verb + object\n- N + A → noun + adjective\n- N1 N2 → modifier + modified\n\nSo “word” could be a noun.\n\nBut if it forms a compound with an adjective, it would reduce?\n\nFor instance, “a big word” → but no example.\n\nWe lack support.\n\nBut the only possible inference is that since “to exhaust” has multiple forms due to VCV → VC, similarly, a word might have a form that undergoes reduction.\n\nBut we have no stem.\n\nTherefore, the only theoretically possible form for “word” is one that could reduce via the rules.\n\nWhat forms could reduce to “wo”?\n\nFor example:\n\n- wö → may become wo? \n- wöf → wöf → VCV → VC → wöf → reduces to wöf → but that's not a word\n\nBut if we assume a base like “wö” (as in “wö”) → VCV? Ends in vowel+consonant? wö → not with consonant.\n\nUnless it is “wöv” → reduces to “wöv” → no.\n\nPerhaps “word” is not a finite form.\n\nBut the only word that appears in rules is verbs and nouns formed by reduction.\n\nGiven that no example exists, and the problem says we cannot translate with certainty, the only possible answer is based on the pattern of reduction.\n\nThus, the theoretically possible form for “word” would be a variant that could undergo reduction, like a base ending in VCV or VCu.\n\nBut without a stem", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13219.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "redacted_solution_hint_mask1", + "sample_index": 1, + "output": "We are asked to determine the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, based on the given linguistic rules and examples.\n\nFirst, consider the compound formation rule given:\n\nWhen two words form a phrase:\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC \n\nAlso, when an adjective is formed by doubling a noun or verb: \ne.g., ‘ele + ‘ele → ‘el‘ele (‘to be near’ × 2 = ‘shallow’)\n\nMoreover, the word order is:\n- N1 N2 (N1 modified, N2 modifier)\n- N A (means \"one who has A N\")\n- V O (verb + object → compound noun or verb)\n\nNow, look at the provided example for \"to exhaust\":\n- a‘öf fau → year’s end \nThis is interpreted as: *to exhaust* + *year* → *year’s end*\n\nTherefore, \"to exhaust\" is the verb component, and \"fau\" is the object (year). \nThe compound is formed via verb + object: V O → compound noun or verb.\n\nGiven the formation pattern:\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC \n\nThe form \"a‘öf\" is a candidate for \"to exhaust\". \nLooking at the pattern:\n\n\"a‘öf\" has the structure: a (consonant?) + ‘öf (VC). \nBut note: 'a' is a consonant, and ‘öf’ is VC → so 'a’ + ‘öf’ → a‘öf\n\nNow, \"a‘öf\" → a consonant + vowel + consonant (a‘öf) \nIn the compound \"a‘öf fau\", \"a‘öf\" is the verb, and \"fau\" is the noun.\n\nFrom the rule: VCV → VC — here, if the original had VCV, it shortens to VC.\n\nBut \"a‘öf\" does not appear as a root in the list. However, we are told that the only direct translation we can derive is for \"to exhaust\", and it is given as:\n\na‘öf (or a‘öfö, a‘öfu, a‘öfü, a‘ofü)\n\nSo the base form \"a‘öf\" is plausible as \"to exhaust\".\n\nThe pattern suggests that \"to exhaust\" is a verb, and its form has undergone reduction.\n\nNow, what form would a verb like \"to exhaust\" have from a base? \nIf the base is VCV, it becomes VC. \nCould \"to exhaust\" be derived from a root like *a‘öf* that comes from an original root like *a‘öfö*?\n\nGiven that *a‘öf* is already shortened (VC → VC), and the examples show compounds like *a‘öf fau*, it suggests that *a‘öf* is the reduced form.\n\nBut the problem says: \"you cannot translate 'word' and 'to exhaust' into Rotuman with certainty\", so we need the *theoretically possible* forms.\n\nSo for \"to exhaust\", we are told: \na‘öf (or a‘öfö, a‘öfu, a‘öfü, a‘ofü)\n\nThis list includes variations due to the morphophonological rules.\n\nWhere does the variation come from?\n\nRule: \n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC\n\nNow, \"a‘öf\" comes from a root with VCV → VC.\n\nBut if the original root were *a‘öfö*, that would be VCVV → but VCV → VC\n\nSo *a‘öfö* → VCVV → ? \nBreaking down: \na’öfö → consonant (a), vowel (ö), consonant (f), vowel (ö) → VCV\n\nBut the rule applies to *VCV* → *VC*\n\nSo *a‘öfö* → *a‘öf* (VC → VC)\n\nSimilarly, *a‘öfu* → *a‘öf* (since u → u, but VCu → VC)\n\nSo if original root is *a‘öfu*, which is VCu, then it becomes *a‘öf*\n\nSame with *a‘öfü* → VCu → VC, becomes *a‘öf*\n\na‘ofü — similar, with initial consonant cluster? a‘ofü → still becomes a’öf?\n\nBut note: the original root might be something like *a’öf* (VCC) → but a’öf has VCV → so under rule, → VC → a‘öf\n\nSo the original word may have been longer, and the VCV → VC rule reduced it.\n\nThus, \"to exhaust\" could have originally been derived from roots like:\n- a‘öfö \n- a‘öfu \n- a‘öfü \n- a‘ofü \n- a‘öf \n\nAll of which reduce to a‘öf under the rules.\n\nSo the *theoretically possible* forms of \"to exhaust\" are: \na‘öf, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nBut we are told in the prompt that \"a‘öf (or a‘öfö, a‘öfu, a‘öfü, a‘ofü)\" are the possibilities.\n\nSo that matches.\n\nNow, for \"word\".\n\nWe are to derive the *theoretically possible* form of \"word\".\n\nWe have no direct example like “word” → X.\n\nBut we have examples of compound formation.\n\nWhat compounds involve \"word\"?\n\nWe know that the word order is:\n- V O → compound noun or verb\n- N1 N2 → noun modification\n- N A → \"one who has A N\"\n\n\"word\" could be a noun.\n\nIf \"word\" is a noun, it might appear in a compound like:\nX + word → something\n\nBut we are not told any such compound.\n\nCould \"word\" be formed by doubling a root?\n\nWe are told that the doubling of noun/verb gives adjective.\n\nFor example: \n‘ele + ‘ele → ‘el‘ele (shallow)\n\nSo if we had a root for \"word\", doubling it could give a related adjective.\n\nBut we are not given any such compound.\n\nCould \"word\" be part of a compound like \"to say word\" or \"word of year\"? Not directly.\n\nIs there any compound involving \"word\"?\n\nNo, but maybe we can infer from the pattern of vowel reduction.\n\nIn the example: \na‘öf fau → year’s end (a‘öf = to exhaust, fau = year)\n\nAlso: hül ha.fu → to blow (hül = to turn over, ha.fu = rock)\n\nSo verb + noun → compound noun or verb.\n\nSo if \"word\" were a noun, it might be used as an object.\n\nBut no example shows it.\n\nPerhaps \"word\" is derived from a root that undergoes VCV → VC or other reductions.\n\nBut we have no candidates.\n\nCould \"word\" be a noun derived from a root such as *\"wurd\"*?\n\nIn Rotuman, no root for \"word\" is given.\n\nBut we might consider the possibility that \"word\" corresponds to a root that was originally VCV, and underwent reduction.\n\nBut what root?\n\nWe might try to look for a root that could become \"word\".\n\nBut we don’t have any.\n\nAlternatively, perhaps \"word\" is a suppressed noun, and its form is reconstructed via analogy.\n\nBut there is a clue: in the part (c), we have:\n- \"to cut copra\" = ‘ol niu \n- \"curly hair\" = leav pirpiri \n- \"sticky\" = pulpulu \n- \"rubbish\" = mofa\n\nBut no \"word\".\n\nWait — in (c), \"to flash\" = rima.\n\nNo.\n\nAlternatively, consider that the VCV → VC rule applies to forming compounds.\n\nSuppose there is a root like *wöd* → VCV → *wöd* → *wöd*? But that would just be VCV, not reduced.\n\nOr *wödu* → VCu → VC → *wöd*\n\nSo possible reduced form: wöd\n\nOr *wöda* → VCa → VaC → *wöda* → *wöda*? VCa → VaC → so *wöda* → *wöda* (same?)\n\nBut *wöda* → VaC → might become *wöda* → still VCa → so becomes *wöda* (same)\n\nBut not helpful.\n\nNow, note that the only example of a word reducible is *a‘öf*.\n\nSo perhaps \"word\" has a possible form derived similarly.\n\nBut we don’t have data.\n\nThe question is: what are the *theoretically possible* forms?\n\nSo based on the morphophonological rules, form of a root can be reduced as:\n\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC\n\nSo if \"word\" were a root that originally had VCV, it could reduce to VC.\n\nSuppose the root was *wöd*, which is VCV → reduces to *wöd* (VC)\n\nIf it was *wödu*, VCu → VC → *wöd*\n\nIf it was *wödi*, VCi → ¨VC → *wödi* → *wö¨di*\n\nIf it was *wöda*, VCa → VaC → *wöda* → *wöda*\n\nSo possible forms: wöd, wödu, wödi, wöda, wö¨di\n\nBut do we have any reason to believe these forms?\n\nWe have no evidence.\n\nBut the question says: \"what would the theoretically possible translations\" — meaning based on the rules, what forms could emerge?\n\nSince there is no direct evidence, the only way to assign a plausible form is via the morphophonological rules.\n\nBut it's not constrained.\n\nHowever, in the example for \"to exhaust\", we are given multiple variants: a‘öf, a‘öfö, a‘öfu, a‘öfü, a‘ofü — all of which reduce to a‘öf under the rules.\n\nSimilarly, for \"word\", if the root were *wöd*, then *wöd* is the reduced form.\n\nIf original root had a vowel change, other forms might be possible.\n\nBut do we have any root for \"word\"? No.\n\nSo can we reconstruct it?\n\nLooking back at the language, Rotuman uses a limited set of phonemes.\n\nAlso, in the list, we have:\n- a‘öf — to exhaust \n- fau — year \n- pala — pierce \n- pogi — night \n- maf — glass \n- niu — copra \n- nu‘suar — door \n- puhra.ki — to boil\n\nNo occurrence of a word that looks like \"word\".\n\nBut note: in compound formation, a noun can be reduced.\n\nBut no.\n\nAnother idea: could \"word\" be a compound itself?\n\nFor example, a noun formed like N1 N2?\n\nWe have: huag ‘el‘ele → impatient \n‘el‘ele = shallow (from ‘ele + ‘ele)\n\nSo compound of noun + noun.\n\nBut no \"word\" in such.\n\nIs there a word that sounds like \"word\"?\n\nIn Rotuman, do we have a word that might be derived from a root like *wöd*?\n\nWe don’t have evidence.\n\nBut the problem says: \"theoretically possible\" — so we can derive based on morphological rules.\n\nSo any form that arises from VCV → VC, VCu → VC, etc., is possible.\n\nSo for \"word\", if the original root is VCV, it becomes VC → so reduced form is word with VCV → VC.\n\nSo possible forms: \n- wöd (from wöd → wöd) \n- wödu → wöd \n- wöda → wöda (via VCa → VaC)\n\nBut wöda is VCa → VaC: so VCa → VaC, so becomes *wöda* (which is V a C)\n\nBut “wöda” ends in C, so it's not reduced.\n\nBut \"word\" itself — if it were pronounced *wöd*, it would be reduced.\n\nBut we have no clue.\n\nBut note: in the provided example, “to exhaust” is given in a list of possibilities.\n\nFor \"word\", no such list is given — we have to infer.\n\nBut perhaps the only possible form arises from the same rules.\n\nBut no example.\n\nAnother possibility: maybe “word” is missing from the data, but we can deduce its form based on similarity.\n\nBut there's no compound involving it.\n\nConclusion: \nSince we cannot translate \"word\" with certainty, the theoretically possible translations are those that could result from the application of the morphophonological rules (VCV → VC, etc.) to a root meaning \"word\".\n\nTherefore, plausible forms are derived from roots with VCV, VCu, VCi, VCa.\n\nFor example:\n- wöd (from a VCV root)\n- wödu (from VCu → VC → wöd)\n- wödi (from VCi → ¨VC → wö¨di)\n- wöda (from VCa → VaC → wöda)\n\nBut we don’t know the root.\n\nSo the simplest theoretically possible form — and the only one shown in the \"to exhaust\" case — is a short VCV → VC form.\n\nThus, the most plausible theoretically possible form of \"word\" is **wöd** — as a reduced form.\n\nAlternatively, could it be formed from a \"to be\" or other verb?\n\nUnlikely.\n\nIn the absence of data, and consistent with the rules, a reduced VCV form is most plausible.\n\nThus:\n\nd.1 / word: wöd \nd.2 / to exhaust: a‘öf, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nBut note: for \"to exhaust\", the prompt says: \"a‘öf (or a‘öfö, a‘öfu, a‘öfü, a‘ofü)\" — so list should include those.\n\nFor \"word\", nothing is given — only the rule.\n\nSo based on rules, possible forms are those with VCV → VC, etc.\n\nSo only minimal form — likely wöd.\n\nBut is there a word like \"word\" in the data?\n\nNo.\n\nBut in the compound \"a‘öf fau\", \"a‘öf\" is reduced.\n\nSimilarly, if \"word\" were a root, reduced form would be VC.\n\nSo the form is **wöd**.\n\nFinal answer:\n\n\\boxed{d.1: wöd; d.2: a‘öf, a‘öfö, a‘öfu, a‘öfü, a‘ofü}", + "generated_tokens": 3270, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: wöd; d.2: a‘öf, a‘öfö, a‘öfu, a‘öfü, a‘ofü", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 10372.0, + "ioling_final_answer_chars": 47.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "redacted_solution_hint_mask1", + "sample_index": 2, + "output": "We are given a list of Rotuman words and their translations, along with a set of rules for compound word formation. The question asks for the *theoretically possible* translations of \"word\" and \"to exhaust\" into Rotuman, noting that these cannot be determined with certainty from the given data.\n\nWe are to use the provided linguistic rules to deduce plausible forms.\n\n---\n\n### Step 1: Understand the compound formation rules\n\nThe problem gives rules for how a first word changes when combined with another in compound constructions:\n\n- **VCV → VC** \n- **VCu → VC** \n- **VCi → ¨VC** (lengthened vowel) \n- **VCa → VaC** (vowel shift to consonant)\n\nAlso, when forming adjectives by doubling a noun or verb:\n- e.g., ‘ele + ‘ele → ‘el‘ele (shallow; \"to be near\" × 2 = shallow)\n\nAdditionally, compound word formation follows these patterns:\n- **N1 N2** (N1 modified by N2)\n- **N A** (one who has property A)\n- **V O** (verb + object → can be noun or verb)\n\n---\n\n### Step 2: Analyze \"to exhaust\"\n\nWe are told:\n> to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü)\n\nThis suggests multiple plausible forms:\n- a‘öf fau → year’s end (literally: \"to exhaust + year\" = year’s end)\n\nSo, in the compound **V O**, \"a‘öf\" is a verb meaning \"to exhaust\", and \"fau\" (year) is the object.\n\nHence, **a‘öf** is the likely root for \"to exhaust\".\n\nNow, what forms are possible?\n\nGiven the rules, we look at the formation of \"a‘öf fau\".\n\n\"fa\" is a vowel. \"fau\" is a simple word — likely derived from a base.\n\nBut note: the rule applies to the **first** word when combining.\n\nWe see that \"a‘öf\" is likely formed by some base.\n\nBut we don’t have evidence of \"word\" being formed from any base.\n\nHowever, we can *reverse-engineer* \"to exhaust\" from the example:\n\n- a‘öf + fau → year’s end → so \"a‘öf\" means \"to exhaust\"\n\nAre other versions valid?\n\nYes, the problem lists:\n- a‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nThese vary in vowel sequences and glottal stops. Why?\n\nPossibility: vowel shaping rules apply.\n\nLet’s consider the structure of \"a‘öf\".\n\n“a” is a vowel, “ö” is a vowel (like French “eu”), “f” is a consonant.\n\nIs “a‘öf” a root? Is it derived from a base?\n\nWe don’t have a direct match.\n\nBut we see that \"a‘öf fau\" is a compound.\n\nAccording to the rules, one word undergoes change when combined with another.\n\nIn “a‘öf fau”, “a‘öf” is likely a verb stem, and it combines with \"fau\".\n\nBut the rules specify changes only when the first word undergoes transformation:\n\n- VCV → VC \n → if the first word has VCV, it becomes VC\n\nBut \"a‘öf\" is VCV: \n- a (V), ‘ (glottal), ö (V), f (C) → a‘öf → VCV? \nWait: a‘öf → a (V), ‘ (C), ö (V), f (C)\n\nSo structure: V C V C → not VCV → not applicable.\n\nWait — the rule says VCV → VC. So if the first word is VCV, it becomes VC.\n\nFor example: \"ele\" + \"ele\" → \"el‘ele\" → note: “ele” has VCV (e-l-e)? No: “ele” is e-l-e — V-C-V → yes, V-C-V → becomes V-C → el‘e?\n\nBut we have \"el‘ele\" → so the double “ele” results in “el‘ele” — which is V-C + V-C? Wait.\n\nActually, in \"ele + ele\" → \"el‘ele\" → so \"ele\" (V-C-V) → \"el‘e\" → not clear.\n\nBut the rule says:\n- VCV → VC \n e.g., V-C-V → V-C (one consonant removed)\n\nBut \"ele\" is e-l-e → V-C-V → becomes e-l → “el” — but we get “el‘ele”\n\nWait — perhaps V-C-V → V-C (shortened), and the second “ele” is not reduced?\n\nActually, the example: ‘ele + ‘ele → ‘el‘ele \nSo “ele” + “ele” → “el‘ele” → so first “ele” becomes “el‘” (V-C + glottal stop) — not exactly VCV→VC.\n\nWait — the rule says VCV → VC, so V-C-V → V-C → but “el‘” → e-l’ → could be e-l with glottal.\n\nBut in \"el‘ele\", it's el’ + ele — so the “ele” is preserved?\n\nPossibly, the rule applies when forming compounds: the first word undergoes modification, and the second is unchanged.\n\nIn “a‘öf fau”, \"a‘öf\" is the verb, combining with \"fau\".\n\nBut \"a‘öf\" is not a VCV word. \"a‘öf\" = a (V), ‘ (glottal), ö (V), f (C) → V-C-V-C? Not VCV.\n\nSo maybe the rule does not apply to \"a‘öf\".\n\nBut the key is in the phrase: \"to exhaust\" = a‘öf + year → \"year’s end\"\n\nSo \"to exhaust\" must be the root of \"a‘öf\".\n\nWe are told that the possible forms are: \na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nSo variations of \"a‘öf\" with different vowels and glottals.\n\nTherefore, any of these could be valid roots, depending on vowel length, glottal, or consonant shifts via phonological rules.\n\nBut do any of these follow the rules?\n\nFor example, could “a‘ofi” arise from a base?\n\nWe don’t have direct path.\n\nBut possibility: “a‘öf” comes from a root with vowel changes or glottal insertion.\n\nNote that in compound words, the first word may undergo vowel shortening or deletion.\n\nBut we are not given a base for \"to exhaust\".\n\nSo what are the possible forms?\n\nFrom the problem, it is already partially given: \n\"to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü)\"\n\nSo the *possible* forms are: \na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nNote: “a‘öf” is not listed — only variants with different vowel sequences.\n\nSo these are plausible derivations based on vowel variation.\n\nNow, is there any pattern we can extract for \"word\"?\n\n---\n\n### Step 3: Analyze \"word\"\n\nWe need to find the theoretically *possible* translation of \"word\".\n\nWe have no direct word for \"word\".\n\nBut we have:\n- rotuman words: “pala” = pierce, “pogi” = night, “nu‘suar” = window, “nu‘sura” = door\n\nNo obvious word matching \"word\".\n\nWe see compounds like:\n- “huli” = to turn over \n- “huli” + “huli” = ? \n\nBut no example of “word” or its compound.\n\nIs \"word\" likely to appear in a compound?\n\nLook for bases that could compound with a noun.\n\nFor instance, from (b): \n- \"huag lala\" = patient \n→ “huag” (heart) + “lala” (deep) → patient\n\n- \"ha.f puhra.ki\" = volcanic rock → “ha.f” (rocky) + “puhra.ki” (to boil) → volcanic rock\n\n- \"maf tiro\" = spectacles → “maf” (glass) + “tiro” (glass/stuff)\n\nSo “tiro” could be a noun meaning “glass”, “glassy” or “glass-like”\n\nCould “word” be a compound? Possibly.\n\nFor instance, if “word” is a noun, maybe something like:\n\n- “pala word”? \n- or “word” formed from a base + a noun?\n\nLook for verb + noun → compound.\n\nWe see:\n- \"a‘öf fau\" = year’s end → verb + noun\n\nSo verb + noun compounds are common.\n\nSo perhaps \"to word\" or \"word\" as a noun?\n\nBut we don’t have examples.\n\nIs there a base that could become a noun when doubled?\n\nWe have:\n- 'ele + 'ele → 'el‘ele (shallow)\n\nSo, doubling a noun or verb → adjective.\n\nSo, if we think of “word” as a noun, could it be formed as \"word + word\" → adjective?\n\nPossibly.\n\nBut what existing form could generate \"word\"?\n\nWe see:\n- “ma.titi” = coldness\n- “ma.tit mamasa” = ice → coldness + solid\n\nSo compound of noun + noun → adjective.\n\nCould \"word + word\" → something like \"wordness\"?\n\nBut we don’t have such word.\n\nWe don’t have a base like \"w\" or \"wa\".\n\nBut could “word” be derived from a base like “pala” (pierce) or “tiro” (glass)? Unlikely.\n\nAnother possibility: the word \"word\" might be formed from a verb meaning \"to speak\" or \"to utter\".\n\nBut we don’t have such a verb.\n\nCould “word” be a verb meaning “to speak”?\n\nIf so, it could form compounds like:\n- “to word” + object → verb + object\n\nBut no such compound is given.\n\nAlternatively, could it be formed from a noun?\n\nWe see that nouns can become adjectives via doubling.\n\nFor example:\n- 'ele → 'el‘ele (shallow)\n\nSo, if a word like “word” were doubled, it would become an adjective like “wordy” or “wordiness”.\n\nBut no such form is in the list.\n\nSo is “word” likely to appear in a compound?\n\nWe have no anchor.\n\nThus, we cannot determine a specific form.\n\nHowever, the problem says: \"What would the theoretically possible translations of these words into Rotuman be?\"\n\nSo, for \"to exhaust\", we already have a list of possible forms.\n\nFor \"word\", we must infer a plausible root or form.\n\nCould \"word\" be formed from a known base?\n\nIs “tiro” used elsewhere?\n\n\"maf tiro\" = spectacles → \"maf\" (glass) + \"tiro\" (glass)\n\nSo “tiro” is a noun.\n\nCould “word” be similar?\n\nNo.\n\nIs there a word like “pala” or “piri”?\n\n“piri” = to curl\n\n“piri” + “piri” = ? → not given.\n\nNo doubling for verbs.\n\nBut note: the pattern for forming adjectives by doubling.\n\nSo if we had a root for “word” — say “wā” — then “wā + wā” → “wāwā” → wordy?\n\nBut nothing in the list suggests a “wā”-like base.\n\nAlternatively, could “word” be derived from “pala” (to pierce), or from “nu” (copra)?\n\nUnlikely.\n\nCould it be related to “to speak”?\n\nWe have no verb for \"to speak\".\n\nCould “word” be encoded via a compound?\n\nFor instance, in English, “a word” might be “a spoken thing”.\n\nBut in Rotuman, we have no evidence.\n\nBut look at \"pogi\" = night.\n\n\"nu‘suar tiro\" = window \n\"nu‘sura\" = door\n\nCould there be a compound like “word” + “door”?\n\nNo data.\n\nSo from the data, we cannot determine a definitive form.\n\nBut the problem says: “theoretically possible translations”\n\nSo we must infer what forms are *possible* based on the rules.\n\nSo what if “word” were a noun? Could it be formed via VCV → VC?\n\nSuppose a base is “wāk” → V-C-V → becomes “wā” → V-C?\n\nBut do we have such a base?\n\nNo.\n\nWe have:\n- “huli” = to turn over → could become “hulihuli” → “hulihuli”?\n\nBut no example.\n\nThe pattern in doubling:\n- 'ele + 'ele → 'el‘ele → so first element is altered, second preserved?\n\nWait: 'ele + 'ele → 'el‘ele → “el‘” + “ele”?\n\nSo first element is shortened: ele → el‘ → because V-C-V → V-C → with glottal?\n\nRule says:\n- VCV → VC\n\nSo ele (e-l-e) = V-C-V → becomes e-l → el → but we have el‘ele — so el‘ + ele\n\nPossibly, the first word becomes V-C with glottal stop, followed by the second word.\n\nSo V-C-V → V-C → with glottal?\n\nNow, could “word” be formed from such a base?\n\nBut we have no base.\n\nSo, without evidence of a base for “word”, the only possible form would be a guess based on phonology.\n\nBut the problem is about *theoretically possible* translations.\n\nSo, possible forms for \"word\" might be:\n\n- A noun formed via doubling a base, e.g., if a root like “wā” exists, then “wāwā” → wordy\n\nBut no such root is present.\n\nAlternatively, could \"word\" be a compound like \"to say + something\"?\n\nWe lack the verb.\n\nAnother possibility: look for a base that can form a noun when doubled.\n\nBut only “ele” is given as such.\n\nSo the only pattern is that doubling a word forms an adjective.\n\nTherefore, \"word\" as a noun may not be directly formable.\n\nBut could it be a verb?\n\nWe have no verb for \"to speak\".\n\nThus, from the data, we cannot determine a translation for “word”.\n\nBut the question is: *what would the theoretically possible translations be?*\n\nSo, could “word” appear as a compound?\n\nFor example, \"to word\" = to speak?\n\nBut we don’t have such.\n\nAlternatively, in compound form: “word + something”.\n\nBut no data.\n\nHence, the only possible form we might deduce is from phonological rules.\n\nPossibility: if \"word\" is a noun, it might appear as a base that undergoes VCV → VC when doubled.\n\nSo, if we imagine a base like “woa” → V-C-V → becomes “wo” → “wo” + “wo” → “wo wo”?\n\nBut no such word is in the list.\n\nThus, we have no grounding.\n\nBut note: in the compound “a‘öf fau”, the verb \"to exhaust\" is the first element.\n\nSimilarly, we might infer that \"word\" as a verb would be expressed by a stem that can be combined with an object.\n\nSo perhaps the \"theoretically possible\" form would be a stem created via the same phonological rules.\n\nBut no such stem is present.\n\nStill, the question is not to find a known word, but what could be plausible.\n\nAlso, from the problem, in part (d), we are told that \"to exhaust\" has several options.\n\nSo for \"word\", since no example or rule creates it, what could be the *theoretically possible* form?\n\nPossibility: a base with a vowel and consonant structure, following VCV → VC or similar.\n\nBut we see no such evidence.\n\nHowever, note the compound \"pala\" = pierce → “pala” = V-C → “pala”\n\nIs there a word like “pala”?\n\nIn \"nu‘suar tiro\" — “tiro” is a noun, “nu” is a base.\n\nCould “word” be formed from a base like “wā”?\n\nBut again, no.\n\nAlternatively, could “word” be a common noun, and appear as a root?\n\nWe have no examples.\n\nBut from the absence, and the rules, the only reasonable conclusion is that \"word\" might be formed from a base that undergoes VCV → VC or VCa → VaC, etc.\n\nBut no such base is known.\n\nTherefore, we cannot provide a definite form.\n\nBut the problem says \"theoretically possible\", so we must provide a plausible candidate.\n\nGiven that all compound forms are built from known roots, and no “word” root exists, the only possible form is a stem that follows the same pattern.\n\nBut again, no example.\n\nStill, the model for \"to exhaust\" shows multiple possibilities based on vowel variants.\n\nSimilarly, for “word”, if a root existed, it could vary.\n\nBut there is no indication.\n\nSo, is there any word that might stand in for \"word\"?\n\nLook at \"huli\" — to turn over → could be “to word”?\n\nUnlikely.\n\n\"pala\" = pierce — like \"to strike\"?\n\nNo.\n\n\"huli\" — turn over → \"turn over\" = huli?\n\nSo, is there a compound like \"turn over word\"? Not stated.\n\nSo, we conclude: **the theoretically possible form for \"word\" cannot be determined from the data, but if it were formed via a VCV stem, it might become a VC stem.**\n\nBut then what would be the actual form?\n\nWe see no base.\n\nThus, we must assume that a possible form could be something like “wā” or “wāwā”, but not present.\n\nAlternatively, perhaps from the root \"pala\", something like \"pawala\" or \"palā\"?\n\nBut no evidence.\n\nWait — the example with “ele + ele” → “el‘ele” — so doubling a V-C-V → V-C + V-C → with glottal?\n\nSo “el‘ele” = el’ + ele\n\nSo a V-C-V base → becomes V-C + V-C, with glottal in between.\n\nThus, for \"word\", if \"woa\" were a base, “woa + woa” → “woa woa” or “wo‘a woa”?\n\nBut still not known.\n\nSo we cannot provide a specific form.\n\nBut the question is asking for *the theoretically possible* forms.\n\nThus, the most reasonable answer is that:\n\n- For \"to exhaust\": the possible forms are listed as a‘o", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13792.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "redacted_solution_hint_mask1", + "sample_index": 3, + "output": "We are given a series of Rotuman compound words and their English meanings, and we are to infer the theoretically possible translations of two English words: **\"word\"** and **\"to exhaust\"**.\n\nWe are told that when two words form a compound, the first word undergoes specific phonological changes depending on its ending:\n\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC \n\nAdditionally, when forming adjectives by doubling a noun or verb (e.g., N + N → N-modified), the same rules apply, and the structure is often noun + modifier (N1 N2), or N A (with \"one who has A N\"), or V O (verb + object → noun or verb).\n\nLet’s analyze what we know about \"to exhaust\".\n\nWe are given:\n- a‘öf fau — year’s end\n\nThis suggests that **a‘öf** + **fau** → year’s end.\n\nThe structure here is V + N → noun phrase meaning a time-related concept.\n\n\"to exhaust\" is the verb meaning \"to use up\", \"to deplete\", like \"to use up a year\".\n\nSo, **a‘öf fau** = year’s end → suggests that a‘öf means \"to exhaust\" (since year’s end is after year is exhausted).\n\nNow, we are told in the guidance that **to exhaust** has possible forms: \na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü.\n\nThese are all variations of “a‘öf” with different vowel or consonant patterns.\n\nWe also see the pattern of change in compounds:\n\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC \n\nNow, look at **a‘öf fau** — the root is **a‘öf**, then **fau**.\n\n\"faú\" is a noun (year). So the verb “to exhaust” (a‘öf) is combined with a noun to make a noun phrase: “to exhaust a year” → year’s end.\n\nNow, is there a pattern where a verb + noun → noun meaning \"end of X\"?\n\nYes, e.g., \"to cut\" (olo) leads to “to cut a year” → possibly “to cut off”? But not directly listed.\n\nAnother clue: similar compound structures appear in (c): \n\"ha.f puhra.ki — volcanic rock\" → so \"ha.f\" (to boil) + \"puhra.ki\" → volcanic rock.\n\nSo rule: verb (V) + object (O) → compound meaning, possibly a noun or verb.\n\nSimilarly, “hül ha.fu” = to blow (of a hurricane) → “to turn over” + “rock” → to blow.\n\nNote: \"ha.fu\" = rocky; \"hül\" = to turn over.\n\nSo, **hül ha.fu** = \"to turn over rock\" → to blow (of a hurricane).\n\nSo the pattern is: \n- verb + noun → new word (can be a verb or noun)\n\nThus, “to exhaust” + “year” → “year’s end” → compound: verb + noun.\n\nThe root verb is thus **a‘öf**, with the pattern following the VCV → VC rule.\n\nBut the compound is a‘öf fau — so the verb is **a‘öf**.\n\nNow, the possible forms given are:\na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nWe must determine which of these could be the actual root.\n\nWe are told that in a compound, the first word undergoes transformation:\n\n- VCV → VC \n- VCu → VC \n- VCi → ¨VC \n- VCa → VaC \n\nNow, **a‘öf** — let’s break it down.\n\na‘öf: \n- a (V), ‘ö (V), f (C) → so VVC → which is not directly covered.\n\nBut the rule says only for VCV, VCu, etc.\n\nBut notice: \"a‘öf\" is likely a verb root.\n\nWhat if we consider that the base form of \"to exhaust\" could be a verb that has a specific pattern, and due to compounding, it is reduced to VC.\n\nBut the example compound is a‘öf fau — so a‘öf is used as a verb in compound.\n\nNow, in the guidance, it says: \na‘öf fau — year’s end \n→ supports that **a‘öf** is \"to exhaust\"\n\nSo the theoretically possible forms of “to exhaust” are those that conform to the phonological rules and that could be derived into “a‘öf” via compounding.\n\nBut we are told that “you cannot translate” “word” and “to exhaust” with certainty — so what are the possible forms?\n\nFor “to exhaust”, the guidance already lists possible forms: \na‘ofi (a‘ofī), a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nWe are asked to give the **theoretically possible** forms — likely derived from the rules and patterns used.\n\nNow, consider the pattern of compounding: \nThe first word undergoes a reduction: for example, VCV → VC.\n\nBut **a‘öf** ends in **f**, which is a consonant.\n\nWe must check if “a‘öf” follows any of the rules.\n\n\"ö\" is a vowel, \"f\" is a consonant → so VVC → not VCV.\n\nBut it starts with “a”, then “ö”, then “f”.\n\nSo “a’öf” is not VCV, not VCu (u), not VCi (i), not VCa (a).\n\nSo why is it allowed?\n\nPerhaps the form “a‘öf” is itself the root and undergoes compounding.\n\nBut the rules apply only in the formation of compounds, and the compound is a‘öf fau.\n\nSo the verb \"to exhaust\" is a‘öf.\n\nBut we are to list **theoretically possible** forms.\n\nThe guidance lists several: \na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nThese are all forms that could arise from vowel alternations or changes in the vowel sequence.\n\nWe are to find which forms are possible under the compounding rules.\n\nBut the key is: in the compound, the first word is reduced.\n\nFor example, if a verb has a root like VCV, it becomes VC.\n\nBut \"a‘öf\" is not VCV → it’s VVC.\n\nSo why is it a valid verb?\n\nPossibly, the root is not VCV but a different form.\n\nAlternatively, maybe the word “to exhaust” has multiple possible forms due to vowel variations.\n\nLooking at the vowel shifts:\n\n- a is open o \n- ä is like crack \n- ö is French eu \n- ü is French u \n\nThe original “word” has no direct example.\n\nFor “word” — no compound is given.\n\nBut we can infer via analogy.\n\nIs there any noun meaning “word” or “something spoken”?\n\nWe have:\n- “pala” — pierce \n- “pogi” — night \n- “puli” — glue? (pulu) \n- “ka.lu” — bracelet; to encircle \n- “riamrima” — shiny \n- “rū huga” — stomach ache \n- “to‘a” — hero \n- “niu” — copra \n- “nu‘suar tiro” — window \n- “nu‘sura” — door \n\nWe have a compound: \"maf tiro — spectacles\" → maf + tiro → spectacles\n\n\"maf\" = to cut, \"tiro\" = glass → \"to cut glass\" → spectacles?\n\n\"nu‘suar tiro\" = window → so \"nu’suar\" + \"tiro\" → window\n\n\"nu‘sura\" = door\n\nSo the pattern: noun + noun → compound meaning.\n\nAlso: \"to cut copra\" = “ol niu” → “olo” is to cut, “niu” is copra → so olo niu = to cut copra.\n\nSo verb + noun → action on object.\n\nBack to “to exhaust”.\n\nWe have: a‘öf fau → year’s end → so “to exhaust a year” = year’s end\n\nSo the verb “to exhaust” is a‘öf.\n\nBut what about possible forms?\n\nThe guidance says: a‘öf fau → indicates that the form is a‘öf.\n\nNow, could there be a base form such as a‘ofi (a'ofi), which would be a VVC with o?\n\nCompare to a‘öf — vowel ö.\n\nCould vowel change be phonemic?\n\nYes — in many languages, vowels may alternate.\n\nIn the compounding rules, we see VCV → VC, etc.\n\nBut a‘öf is VVC → ends with f.\n\nCould “a‘öf” be derived from a base like a‘ofi?\n\na‘ofi — a’ofi → VVC → same as a‘öf?\n\nOnly if vowels can alternate.\n\nThe rule says: VCa → VaC → e.g., VCa → VaC.\n\nBut a‘öf has no “a” at the end.\n\nWe are to list the **theoretically possible** forms.\n\nThe guidance lists: a‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nThese are all forms with variation in vowel and consonant (like diphthongs or length).\n\nBut under the compounding rules, when forming a compound, the first word undergoes reduction:\n\nAll of these are consistent with being roots that can combine with a noun, such as “fau”.\n\nFor example:\n\n- a‘ofi fau → to exhaust (year) → year’s end?\n- a‘öfi fau → same?\n- a‘öfö → possible, but “öfö” might be redundant?\n\nBut the compound is given as “a‘öf fau”.\n\nSo the actual form is “a‘öf”.\n\nBut the problem says: “what would the theoretically possible translations be?”\n\nSo it is not asking for the actual form, but the possible forms consistent with the rules and the data.\n\nWe see that under vowel variation, forms like a‘ofi (o instead of ö), a‘öfi (with i at end), etc., are possible if the vowel is variant.\n\nBut the rule does not allow VCa → VaC for all cases — only specific ones.\n\nThe only rule involving vowel change is: \n- VCa → VaC \n\nSo if a word ends in \"a\", it becomes \"VaC\".\n\nBut all listed forms end in f, u, or o — not a.\n\nSo VCa → VaC is not triggered.\n\nTherefore, only the forms that conform to the standard consonants and vowel types are acceptable.\n\na‘öf → vowel ö, consonant f → acceptable.\n\na‘ofi → vowel o, ends in i → ends in vowel → not in VCa → so not subject to that rule.\n\nBut is there a rule for VCV → VC?\n\na‘öf is VVC — not VCV.\n\nSo only if the root had VCV would it reduce to VC.\n\nBut “a‘öf” is not VCV.\n\nSo it cannot reduce via that rule.\n\nBut in the compound, the first word is used as-is.\n\nSo the form “a‘öf” is acceptable.\n\nOther forms listed (a‘öfu, a‘öfü, etc.) — could these be legitimate?\n\nFor instance, “a‘öfu” — ends in “u” → not “f”.\n\nCould “a‘öfu” be a valid form?\n\nIf it follows the rule VCu → VC, then it would become VC.\n\nSo “a‘öfu” → if it were the root, it would reduce to “a‘öf” (VC), which then combines with \"fau\".\n\nThen a‘öfu → a‘öf → a‘öf fau.\n\nSimilarly, a‘öfö → would be a VVC → might not trigger rule.\n\nThe rule VCu → VC applies when the word ends in “u”.\n\nSo if the verb root ends in “u”, it reduces to “VC”.\n\nTherefore, a root ending in “u” becomes “VC”.\n\nSo forms ending in “u” (like a‘öfu) would reduce to a‘öf (by VCu → VC).\n\nSimilarly, a‘öfö — ends in “ö” → not u → no reduction.\n\nSo possible former roots that reduce to a‘öf are:\n\n- a‘öfu → VCu → VC → a‘öf \n- a‘öfö → VC (if it ends in ö, no rule) \n- a‘ofü → VC (ends in ü? invariant?) \n\nBut “a‘öf” is the reduced form.\n\nSo the original forms that would reduce to “a‘öf” are:\n\nAny root that ends in u or f or ö, and if it ends in u → reduces to VC.\n\nSo:\n\n- a‘öfu → VCu → VC → a‘öf → gives “a‘öf fau”\n- a‘öfö → may be direct\n- a‘öf → direct\n- a‘ofi → no rule — different vowel\n- a‘öfi → ends in i — not u, not covered\n\nBut the guidance says: a‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nNow, which of these are plausible?\n\nWe have no direct example, but the compounding rule allows VCu → VC.\n\nSo any root ending in “u” reduces to VC.\n\nSo a‘öfu → reduces to a‘öf → valid.\n\nSimilarly, a‘öfö ends in “ö” — no rule → so it stays.\n\nBut is “a‘öfö” possible?\n\nNo direct rule — unless ö is considered like u.\n\nBut the vowel types are distinct.\n\nSo only roots that end in u (VCu → VC) are likely to reduce to a‘öf.\n\nTherefore, the only forms that could reduce to \"a‘öf\" are those ending in \"u\".\n\nBut a‘öfu ends in u → reduces to a‘öf.\n\na‘öfü — ends in ü → not u → may not reduce.\n\na‘öfö — ends in ö → not u.\n\nSo only a‘öfu → VCu → VC → a‘öf.\n\na‘ofü — ends in ü → no rule.\n\na‘ofi — o instead of ö → vowel variation → plausible if vowel alternation exists.\n\nSimilarly, a‘öfi — ends in i → no rule.\n\nBut the rule VCi → ¨VC — only applies to VCi → becomes ¨VC, not VC.\n\nSo roots ending in i become ¨VC.\n\nSo cannot reduce to a‘öf directly.\n\nSo the only plausible form that reduces to a‘öf is a‘öfu via VCu → VC.\n\nBut the given list includes multiple.\n\nPerhaps the vowel is variable — so “ö” and “o” are phonemic variations.\n\nThus, \"a‘ofi\" (o) and \"a‘öfi\" (ö) could both be forms.\n\nThe root may have vowel alternation.\n\nThus, the theoretically possible forms of \"to exhaust\" are all listed — because the verb may have variable vowel values, and variation in ending (e.g., u, i, o) may exist.\n\nBut the key point is that the compound is “a‘öf fau”, so the reduced form is a‘öf.\n\nThus, the original root could have been:\n\n- a‘öf → direct \n- a‘öfu → VCu → VC \n- a‘öfö → no rule → possible \n- a‘ofi → vowel change \n- a‘öfi → vowel change \n- a‘ofü → similar\n\nBut to be theoretically possible, all these could represent different phonological forms of the same root.\n\nTherefore, the possible forms are those listed.\n\nSo for “to exhaust” → a‘öf is the result, but the input form could be any of these.\n\nTherefore, the theoretically possible translations are: \na‘ofi, a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü\n\nNow, for “word”.\n\nIs there a compound involving “word”?\n\nWe have a compound: \"pogi — night\" → standalone.\n\nNo compound involving a noun like “word”.\n\nBut consider: the structure V + O → compound.\n\nCould \"word\" be formed as a verb or noun?\n\nWe have: “pala — pierce” = to pierce.\n\n“to cut” = olo.\n\nWe have “pogi” — night.\n\nNo compound involving a word.\n\nBut perhaps “word” is a noun that can be formed by noun + noun?\n\nFor example, “door” is nu‘sura.\n\n“window” is nu‘suar tiro.\n\nCould “word” be formed from a noun like “to speak” or “to say”?\n\nWe do not have such a word.\n\nBut note: “word” might be derived from a verb meaning “to say”.\n\nIs there a verb meaning “to say”?\n\nWe have:\n\n- “a‘öf” → to exhaust \n- “olo” → to cut \n- “pala” → to pierce \n- “puhra.ki” → to boil \n- “huli” → to turn over \n- “huni” → lower end \n- “mamasa” → solid \n- “ma.tit” → coldness \n- “ka.lu” → to encircle \n\nNo “to say” or “to speak”.\n\nCould “word” be a noun meaning “something said”?\n\nNo direct compound.\n\nBut the compounding rule: N1 N2 → N1 modified by N2.\n\nCould “word” be formed from something like “a word”?\n\nFor example, “to be near” (‘el‘ele) → shallow from ‘ele + ‘ele.\n\nSimilarly, “a word” might be “a point” — but not found.\n\n“is ‘ā” = sharp-pointed → “is” + “ā” → sharp-pointed?\n\n“is” is a verb meaning “to be sharp”?\n\n“is” → sharp-pointed, “is susu” = nipple.\n\nCould “word” be related to “point”?\n\n“is ‘ā” = sharp-pointed.\n\n“word” → perhaps “a word” = a sharp point?\n\nNot clear.\n\nBut consider: noun + noun → compound.\n\nWe have “mamasa” — solid\n\n“ma.tit” — coldness\n\n“ma.tit mamasa” = ice →", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12979.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. When two words constitute a phrase, the form of the first word undergoes\nthe following change:\n -VCV →-VC\n -VCu →-VC (V: vowel, C: consonant).\n -VCi →-¨VC\n -VCa →-VaC\n The same thing happens when an adjective is formed by doubling a noun or a verb: ‘ele\n+ ‘ele →‘el‘ele ‘to be near × 2 = shallow’. The word order is\n • N1 N2 (N1: modified, N2: modifier);\n • N A (also with the meaning ‘one who has A N’: huag ‘el‘ele ‘heart + shallow = impatient’);\n • V O (the resulting compound word can be a noun or a verb: a‘öf fau ‘to exhaust +\n year = year’s end’, hül ha.fu ‘to turn over + rock = to blow (of a hurricane)’).\n\n (a) ‘u‘u — arm/hand, isu — nose, kia — neck, leva — hair, mafa — eye, susu —\n breast, huga — heart.\n\n (b) tiro — glass (stuff),\n poga — hole,\n huag lala — patient,\n ha.f puhra.ki — volcanic rock,\n maf pogi = maf pala — blind.\n\n (c) round — ka.lka. lu; to cut copra — ‘ol niu; curly hair — leav pirpiri; sticky — pulpulu;\n to flash — rima; rubbish — mofa.\n (d) • word: [TARGET ANSWER REDACTED].\n • to exhaust: a‘ofi(or a‘öfi, a‘öfö, a‘öfu, a‘öfü, a‘ofü).", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "redacted_solution_hint_mask1", + "sample_index": 0, + "output": "Step 1: Identify root and suffix patterns from given examples.\n\nRoots and their suffixes:\n\n- aq”ipsa → \"the cave too\" → root \"aq\" + suffix \"ipsa\" → \"too\"\n- aq”na → \"in the cave\" → root \"aq\" + suffix \"na\"\n- qucxap”a → \"through the lake\" → root \"qucx\" + \"ap”a\"\n- qucxst”psa → \"from our1+2 lake too\" → root \"qucx\" + \"st”psa\" → \"from our1+2 lake too\"\n- chushp”a → \"his corner\" → root \"chush\" + \"p”a\" → \"his\"\n- marka → \"the town\"\n- markp”t”a → \"from his town\" → root \"mark\" + \"p”t”a\" → \"from his town\"\n- ishinhna → \"in my bed\" → root \"ishin\" + \"hna\"\n- ishmana → \"your bed\" → root \"ish\" + \"mana\" → wait, given as \"ishma\" → \"your bed\"\n- utamt”a → \"from your house\" → root \"utam\" + \"t”a\"\n- utnha → \"my house\"\n- p”ak”u → \"the pot\"\n- p”ak”unhpsa → \"my pot too\" → root \"p”ak”u\" + \"nhpsa\" → \"too\"\n- yaputxi → \"is it the field?\" → root \"yap\" + \"utxi\"\n- yapsanpsa → \"in our1+2 field too\" → root \"yap\" + \"sanpsa\" → \"in our1+2 field too\"\n\nStep 2: Analyze suffix behavior (provided in rule card):\n\nPossessor suffixes:\n- -p”a → used as possessive (e.g., his, your, our)\n- -sa → possessive (e.g., \"our1+2\" in qucxst”psa, yapsanpsa)\n- -t”a → from (e.g., \"from his town\", markp”t”a)\n\nCase suffixes:\n- -p”a → neutral or default\n- -na → in the [place]\n- -txi → is it? (question form)\n- -psa → too (additive)\n\nOral suffixes:\n- Always consume preceding vowel\n- Only consume if the vowel belongs to another suffix\n\nNasal suffixes:\n- Consume vowel if suffix keeps its own (e.g., -nha, -ma), otherwise leave it\n\nNow examine derivation of the target forms:\n\n1. utnhantxi\n\nRoot: utn → \"my house\" → utnha → so root is \"utn\"\n\n- utnha = my house\n- utnhantxi → likely \"in my house too\" or \"is it in my house?\"\n\nBut utnhantxi has -txi → question form → “is it…” → “is it in my house?”\n\nAlso, the suffix -txi appears in:\n- ishinhna → in my bed\n- yaputxi → is it the field?\n\nSo -txi = question → “is it...?”\n\nNow, suffix after \"utn\" = -hantxi? But structure: utnha → \"my house\"\n\nIn utnha: -ha → so is -ha a nasal suffix? Yes — \"nha\" is listed among nasal suffixes.\n\n- Nasal suffixes: -nha, -ma → consume vowel if they keep theirs.\n\nIn utnha → \"my house\" → \"utn\" + \"ha\" → \"ha\" is nasal suffix → consumes the preceding vowel?\n\nBut \"utn\" ends in \"n\" → vowel before \"n\"? No. \"utn\" has no vowel before the nasal.\n\nActually, structure must be: root + suffix.\n\nRoot: utn → root word?\n\nBut others like:\n- utnha = my house → root utn + nasal -ha\n- utamt”a = from your house → root utam + -t”a → case suffix\n\nSo nasal suffixes: -nha, -ma → used with root to form possessive or place?\n\nBut must be formed with elision rules.\n\nNow observe:\n\n- in my bed → ishinhna\n- in your bed → ishma → root ish + ma → ishma → so \"ma\" is nasal suffix\n\n- in my house → utnha → \"utn\" + \"ha\"\n\nSo the pattern is:\n- -nha → in my house → \"in my house\"\n- -t”a → from someone’s place\n\nAlso: -txi → is it?\n\n- yaputxi → is it the field?\n- markstxi → is it our1+2 town?\n\nSo from marking rules:\n\nNow, utnhantxi → utn + hantxi?\n\nBut nasal suffixes: -nha — so if \"ha\" is shared with nasal, then if nasal suffix takes vowel, vowel before it is consumed.\n\nBut here: utn → if we have utn + na → would be \"in the cave\"? No.\n\nNote that in aq”na → \"in the cave\" → root aq + na\n\nSo -na → in the [place]\n\nSimilarly, ishinhna → in my bed → root ishin + hna → so -hna = \"in the bed\"\n\nSo -na and -hna are case suffixes of location.\n\nNow, rule on nasal suffixes:\n\n\"consume the vowel if they keep theirs, but leave it if they give up theirs\"\n\nSo if nasal suffix takes the vowel, and uses it (e.g., keeps its own), it consumes the following vowel.\n\nIn this problem:\n\n- aq”na → \"in the cave\" → root aq + na → \"na\" attaches → when does vowel get consumed?\n\nIn chushp”a → \"his corner\" → root chush + p”a → possessive\n\nRoot chush → corner → chushp”a = his corner\n\np”a → possessive suffix → ruled as \"possessor\" — consumes vowel before it?\n\nBut in chushp”a, \"chush\" ends with \"sh\", so no vowel → no vowel to consume → okay.\n\nSimilarly, marka → \"the town\" → no suffix → root\n\nmarkp”t”a → from his town → root mark + p”t”a → p”t”a → \"from his\"\n\nBut the \"p”a\" is in \"p”a\" → so if a vowel is before it, and it's a possessive, it consumes it?\n\nNow, from the examples:\n\n- p”ak”u → \"the pot\" → root p”ak”u\n- p”ak”unhpsa → \"my pot too\" → root p”ak”u + nhpsa → \"too\"\n\nSo \"nhpsa\" = \"too\" — so -psa = additive (\"too\")\n\nBut -psa appears in:\n- aq”ipsa → \"the cave too\"\n- p”ak”unhpsa → \"my pot too\"\n- yapsanpsa → \"in our1+2 field too\" → has \"sanpsa\"\n\nNow, -psa is additive.\n\nBut yapsanpsa → in our1+2 field too → so \"san\" = our1+2?\n\nThis matches the pattern: -sa = possessive (our1+2), -psa = \"too\"\n\nSo:\n- -sa = possessive (our1+2)\n- -psa = \"too\"\n- -txi = \"is it?\"\n- -na = \"in the [place]\"\n- -t”a = \"from\"\n\nNasal suffixes:\n- -nha → \"my house\" → utnha\n- -ma → \"your bed\" → ishma\n\nSo accumulates:\n\nNow, back to:\n\n1. utnhantxi\n\nRoot: utn → \"my house\"\n\nSuffixed: -hantxi → likely -ha (nasal) + -ntxi?\n\nBut no such suffix.\n\nAlternatively, could be -ha (nasal) + -ntxi?\n\nBut -ntxi not in list.\n\nWait: is there a possibility that -hantxi is built from a nasal and a case?\n\nNote that in markstxi → is it our1+2 town? → mark + stxi\n\nstxi → composed of -stxi → suffix -txi?\n\nIn markstxi → mark + stxi → so -stxi → is it?\n\nBut in chushuntxi → is it in the corner? → chush + untxi → so -untxi?\n\nNo, chushuntxi → \"is it in the corner?\" → root chush + untxi?\n\nBut -ntxi → not recognized.\n\nWait — in chushuntxi → \"is it in the corner?\" → likely root chush (corner) + untxi → but \"untxi\" = \"in the corner?\"\n\nBut in ishinhna → \"in my bed\" → ishin + hna → so -hna = \"in\"\n\nSimilarly, utnha = \"in my house\"? But \"utnha\" is \"my house\" — not \"in my house\"\n\nContradiction?\n\nWait — in ishinhna → \"in my bed\" — so \"in\" is a case suffix.\n\nSo likely -na or -hna = in?\n\nBut aq”na → \"in the cave\" → so -na = in the [place]\n\nishinhna → \"in my bed\" → root ishin + hna → what does hna mean?\n\nhna → could be \"in the\" with possessive?\n\nBut ishma → \"your bed\" → ish + ma → so -ma = your\n\nThus: possession via -ma, -na, -p”a?\n\n- -p”a → his\n- -ma → your\n- -na → in the cave?\n\nBut aq”na → in the cave → so -na = in the → specific place\n\nSimilarly, ishinhna → in my bed → so root ishin + hna → hna = in the bed?\n\nBut hna is nasal suffix.\n\nNow, nasal suffixes eat vowels if they keep theirs.\n\nSo if nasal suffix has its own vowel, it consumes the preceding vowel.\n\nIn ishinhna → ish + hna → ish ends with \"h\", so vowel before h? No — ish ends with consonant.\n\nSo no vowel to consume.\n\nIn utnha → utn + ha → utn ends with \"n\", no vowel.\n\nBut in \"utnha\" → the \"n\" is the consonant of root.\n\nSo the nasal suffix -ha is added, no vowel to consume → okay.\n\nNow, back to:\n\nutnhantxi → root utn + hantxi?\n\nCould be utn + ha + ntxi → but -txi is a suffix.\n\nBut the rule says suffixes are: -p”a, -t”a, -psa, -na, -txi\n\nSo likely:\n\n- utn → root\n- -ha → nasal suffix → \"my\"\n- -txi → question → \"is it?\"\n\nSo utnhantxi → is it in my house?\n\nBut the structure: should the nasal and case be combined?\n\nCheck yapsanpsa → \"in our1+2 field too\" → yap + sanpsa\n\nsanpsa → -sa + -psa → our1+2 + too → in our1+2 field too\n\nSimilarly, utnhantxi → if -ha = \"my\", -txi = \"is it\", then \"is it in my house?\"\n\nBut do we have a \"in\" marker?\n\nIn ishinhna → root ishin + hna → is in my bed\n\nSo -hna = \"in the bed\"\n\nSimilarly, aq”na → aq + na → in the cave\n\nSo -na = \"in the [place]\"\n\nBut in utnha → \"my house\" → no -na\n\nSo if \"my house\" is the noun, and we add -txi, it becomes a question.\n\nBut where does \"in\" come from?\n\nPerhaps the -txi is always \"is it\", so \"is it my house?\" → but not \"in my house?\"\n\nBut aq”ipsa → \"the cave too\" → root aq + ipsa → \"too\"\n\nNo in.\n\nBut in aq”na → \"in the cave\" → \"in\"\n\nSo only when -na is present is \"in\" there.\n\nSo for \"is it in my house?\", we need -na and possessive.\n\nBut utnhantxi → no -na\n\nRoot is utn → -ha → \"my house\", and -txi → \"is it?\"\n\nSo perhaps \"is it my house?\" → meaning \"is it the house?\"\n\nBut \"in my house\" vs \"my house\" — in Jaqaru, do possessive and location overlap?\n\nBut in markstxi → \"is it our1+2 town?\" → mark + stxi → so no -na, so \"is it the town?\"\n\nSimilarly, yaputxi → \"is it the field?\"\n\nSo is it [something]? → -txi → question mark.\n\nSo \"utnhantxi\" → could be \"is it my house?\"\n\nBut is there a possessive?\n\nWe have -ha → \"my\" → so it is \"is it my house?\"\n\nBut in utnha → \"my house\" → so in this case, utnhantxi → likely \"is it my house?\"\n\nBut why is -ha not consuming a vowel?\n\nRoot \"utn\" → ends with \"n\" → no vowel → fine.\n\nAs per rule: nasal suffix consumes vowel if they keep theirs → here, -ha keeps \"a\" → so it keeps its own vowel → but no vowel before → so no consumption → okay.\n\nNow 2. yapp”psa\n\nRoot: yap → \"the field\" → yaputxi → \"is it the field?\"\n\nSo root yap → field\n\nyapp”psa → yap + p”psa\n\np”psa → what?\n\nSuffixes: -p”a → possessive → -psa → \"too\"\n\nSo \"p”psa\" → possibly a split?\n\nBut no such suffix.\n\nWait: p”a is possessive → \"his\", \"your\", etc.\n\nSo is yapp”psa = \"his field too\"?\n\nBut the answer guide says: 2. yapp”psa — his field too\n\nYes! So yapp”psa = \"his field too\"\n\n- yap → field\n- p”a → possessive → \"his\"\n- psa → \"too\"\n\nBut does \"p”a\" + \"psa\" = \"his too\"?\n\nPossibility: \"p”a\" + \"psa\" may be combined, with elision.\n\nBut in p”ak”unhpsa → \"my pot too\" → p”ak”u + nhpsa → \"nhpsa\" = \"too\" — so \"psa\" part is \"too\"\n\nIn aq”ipsa → \"the cave too\" → aq”ip + sa → \"ipsa\" → but \"ipsa\" = \"too\"? Or is it possessive + too?\n\n\"aq”ipsa\" → \"the cave too\" → so if \"ipsa\" = \"too\", and -p”a is not there, how?\n\nWait -p”a\" is listed as one of the suffixes.\n\nBut aq”ipsa → aq”i + psa → so \"ipsa\" = \"too\"\n\nSimilarly, p”ak”unhpsa → p”ak”u + nhpsa → \"nhpsa\" → \"too\"\n\nSo \"psa\" = \"too\"\n\nAnd -p”a\" = possessive\n\nSo for \"his field too\" → root yap + p”a + psa → but written as yapp”psa → so the \"p”a\" and \"psa\" are combined → likely with elision.\n\nBut no vowel before \"p”a\"? In yap → ends with \"p\"? No — yap → ends with \"p\", so no vowel.\n\nSo \"yap\" + \"p”a\" → no vowel to consume → so no elision → yapp”a\"\n\nThen yapp”a\" + \"psa\" → now \"a\" at end of \"p”a\" → if \"psa\" comes after, it may consume the \"a\"?\n\nBut rule: oral suffixes consume vowel if it belongs to another suffix.\n\nSpecifically:\n\n- Oral suffixes always consume the preceding vowel — but only if the vowel belongs to another suffix.\n\nIn this case, \"psa\" is a case suffix? It's the \"too\" marker.\n\nThe rule says: \"oral suffixes consume the preceding vowel if it belongs to another suffix\"\n\nSo if a vowel comes before an oral suffix, and that vowel belongs to another suffix, then it is consumed.\n\nSo in yapp”psa → yap + p”a + psa\n\nBut p”a is possessive → oral suffix? Yes.\n\npsa is also oral suffix → \"too\" → oral suffix.\n\nSo vowel before \"p”a\" — in \"yap\" → ends with \"p\" → no vowel → so no vowel to consume.\n\nThen after \"p”a\" → \"p”a\" ends with \"a\" → vowel.\n\nNow \"psa\" comes after → so vowel \"a\" before \"psa\"?\n\nThis vowel belongs to \"p”a\"?\n\n- The rule says: \"consume the vowel if it belongs to another suffix\"\n\nSo if the vowel \"a\" in \"p”a\" belongs to the suffix \"p”a\", then it is not consumed.\n\nBut in the suffix \"p”a\", the vowel \"a\" is part of the suffix — so it belongs to \"p”a\", not to another.\n\nTherefore, the rule says: consume only if the vowel belongs to another suffix.\n\nSo if the vowel is part of the suffix, it doesn't belong to another → so not consumed.\n\nTherefore, no consumption.\n\nSo yapp”psa = yap + p”a + psa → \"his field too\"\n\nYes — matches given answer.\n\nNow 3. yapup”psa\n\nyap + up”psa → what?\n\n\"up”psa\" → u + p”psa?\n\nBut -p”a → possessive → \"his\"\n\n- p”psa\" → \"through the\"?\n\nCompare: qucxap”a → \"through the lake\" → qucx + ap”a → so -ap”a = through?\n\nBut ap”a → is a root of \"through\"?\n\nWait qucxap”a → \"through the lake\"\n\nqucx → lake?\n\nBut qucxst”psa → \"from our1+2 lake too\" → so qucx + st”psa → from", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11656.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "redacted_solution_hint_mask1", + "sample_index": 1, + "output": "Step 1: Identify the root and suffix patterns in the given examples.\n\nRoots and their common suffixes:\n- Root: aq” → \"cave\"\n- Suffixes:\n - -na → \"in the cave\"\n - -psa → \"too\" (used in \"cave too\" → \"aq”ipsa\")\n - -t”a → \"from the town\" (e.g., markp”t”a = from his town)\n - -txi → question: \"is it in the corner?\" (chushuntxi)\n - -nha → \"my house\" (p”ak”unhpsa → my pot too; utnha → my house)\n - -ma → \"the town\" (marka → the town)\n - -p”a → possessive (e.g., chushp”a = his corner)\n - -t”a → from possessive place (markp”t”a = from his town)\n\nStep 2: Analyze the rules for suffix elision.\n\nRule: Vowel elision occurs when a suffix consumes the preceding vowel.\n\n- Oral suffixes (like -na, -t”a, -txi, -psa):\n - Always consume the vowel if it belongs to another suffix (not root)\n - If the vowel belongs to root, leave it.\n\n- Nasal suffixes (-nha, -ma):\n - Consume the vowel if they keep theirs (i.e., if they are not borrowing from root)\n - Leave it if they give up theirs (i.e., if root's vowel is used)\n\nStep 3: Observe the structure in given examples:\n\nExample: aq”ipsa → \"the cave too\"\n- Root: aq”\n- Suffix: -ipsa → combines -ip + -sa\n- -psa is “too”, and -ip is derived from -na (in the cave) with elision\n- aq”ipsa → aq” + ipsa → elision of the vowel in -na when forming -ipsa\n\nSimilarly, qucxap”a → \"through the lake\"\n- Root: qucx\n- Suffix: -ap”a → \"through\"\n- No elision here — vowel retained\n\nqucxst”psa → \"from our1+2 lake too\"\n- Root: qucx\n- Suffixes: -st”p”a → st” + p”a → “from our lake too”\n- -t”a = from, -psa = too\n- “our1+2” shows possessive and distributive marker\n\nchushp”a → \"his corner\"\n- root: chush\n- suffix: -p”a → possessive → “his”\n\nchushuntxi → \"is it in the corner?\"\n- root: chush\n- suffix: -untxi → -un (for “in”) + -txi (question)\n- -txi is a question suffix → attached to root\n\nmarka → \"the town\"\n- root: mark\n- suffix: -a → definite article\n\nmarkp”t”a → \"from his town\"\n- root: mark\n- suffix: -p”t”a → -p”a (his) + -t”a (from)\n- So -p”a + -t”a → \"from his town\"\n\nmarkstxi → \"is it our1+2 town?\"\n- root: mark\n- -stxi → -s + txi → “is it [our] town?”\n- -s? likely possessive (our) → combined with -txi (question)\n\nutamt”a → \"from your house\"\n- root: utam → house\n- suffix: -t”a → from → so “from your house”\n\nutnha → \"my house\"\n- root: ut → house (utnha)\n- suffix: -nha → “my house” → nasal suffix\n\np”ak”u → \"the pot\"\n- root: p”ak\n- suffix: -u → definite article?\n\np”ak”unhpsa → \"my pot too\"\n- root: p”ak\n- -unhpsa → -un + hpsa\n- -nha → “my” → nasal suffix → consumes vowel if it keeps its own\n- -psa → “too”\n- So “my pot too”\n\nyaputxi → \"is it the field?\"\n- root: yapu → field\n- -txi → question → “is it in the field?”\n\nyapsanpsa → \"in our1+2 field too\"\n- root: yapu\n- -s → possessive \"our\"\n- -n → \"in\"\n- -psa → \"too\"\n- So \"in our field too\"\n\nWait: yapsanpsa → “in our1+2 field too”\n\nSo in this, we see:\n- -s → possessive (\"our\")\n- -n → \"in\"\n- -psa → \"too\"\n- Possessive suffix is before the vowel?\n\nBut the prefix -n is not clear. More plausible: -n is attached to root → “in” → then -psa → “too”\n\nNow analyze the target words:\n\n1. utnhantxi\n- Root: utn → possibly \"my house\" (utnha), so utn = my\n- Then -hantxi → -ha? -ntxi?\n- But -txi is the question form → “is it in the house?”\n- So utnhantxi → likely “is it in my house?”\n\nBreak it down:\n- utn → my\n- -ha → but not a suffix — look for structure\n- utnha → my house\n- -txi → is it in the corner?\n- So perhaps utnha + txi → but that would be utnhatxi\n\nBut the word is utnhantxi → has \"hantxi\" → could be a merged form?\n\nAlternative: -n → in → then -txi → question\nSo: utnha → my house → then attach with -txi?\n\nBut no elision.\n\nWait: look at \"markstxi\" → mark + stxi → is it our town?\n\nSimilarly, \"yaputxi\" → is it the field?\n\nSo \"utnhantxi\" → root utn → my house → + -txi → is it in my house?\n\nBut why is there “hantxi”? The word is utnhantxi.\n\nCould it be root: utn, then -hantxi?\n\nNo — known suffixes are -na, -t”a, -txi, -nha, -ma, -psa\n\nBut see: in p”ak”unhpsa → p”ak + unhpsa → unhpsa → -nha (my) + -psa (too)\n\nSo elision occurs when nasal suffix consumes vowel.\n\nSo in \"utnha\" → utn + ha → nasal suffix -nha consumes the vowel?\n\nWait: root can be ut → \"house\" → root ut → ha → becomes utnha?\n\nThen “n” inserted?\n\nAlternatively, root is u → and suffix -t”a → from → can consume?\n\nMore plausible: utnha = my house\n\nThus, utnhantxi = my house + -txi → is it in my house?\n\nBut the word is \"utnhantxi\" — has \"hantxi\"\n\nIn markstxi → mark + stxi → so s + txi\n\nSimilarly, yaputxi → yapu + txi\n\nSo pattern: root + txi → is it [place]?\n\nThus, utnhantxi → root = utn → my house → + txi → “is it in my house?”\n\nBut why \"hantxi\" and not \"utnha + txi\"?\n\nPossibly, the suffix -txi merges with root → so only one element.\n\nBut in markstxi → mark + stxi → prefix not clear.\n\nBut notice: markstxi → mark + stxi → “is it our town?”\n\nSimilarly, yaputxi → yapu + txi → “is it the field?”\n\nSo the structure is root + suffix → root + txi = “is it [place]?”\n\nThus, utnhantxi → root = utn → my house → + txi → “is it in my house?”\n\nSo translation: is it in my house?\n\nBut the root is probably utn → “house” in some form? But utnha is “my house” → so utn must be just “house” with a possessive?\n\nWait: utnha → my house → so root is ut → with -nha\n\nSo root: ut → house → with -nha → “my house”\n\nSo utnhantxi → utn + hantxi → maybe a typo?\n\nBut no. The word is utnhantxi — likely root + hantxi?\n\nBut only -txi is a question suffix.\n\nSo only possible if -txi is attached.\n\nThus, likely: utn + hantxi → utn + ha (from -nha?) + txi?\n\nBut -nha is already consumed.\n\nAlternative: the full suffix is -nha + txi → but no known rule for that.\n\nIn our examples:\n- chushuntxi → chush + untxi → un + txi → is it in the corner?\n\nchush → corner → untxi → un (in) + txi (question)\n\nSimilarly, markstxi → mark + stxi → s (our) + txi → is it our town?\n\nSo pattern: root + s + txi → is it our town?\n\nBut s is possessive, not inherent.\n\nSo question suffix -txi is attached directly after some vowel.\n\nIn yaputxi → yapu + txi → is it the field?\n\nSo structure: root + txi → is it [place]?\n\nSo back to utnhantxi → root = utn → my house → but my house is utnha → so utnha is the base.\n\nBut here it's utnhantxi → if it's utnha + txi → then it would be utnhatxi, not utnhantxi.\n\nBut the word is written as utnhantxi → the “h” and “a” may be “ha” from -nha?\n\nPossibility: the root is \"utn\" and the suffix is -hantxi?\n\nNo known suffix.\n\nWait — look at word: utnhantxi\n\nCompare with yaputxi (is it the field?) — yapu + txi\nCompare with markstxi (is it our town?) — mark + stxi\nCompare with chushuntxi (is it in the corner?) — chush + untxi\n\nSo the pattern is: base + [prefix] + txi → with [prefix] being possessive or locative?\n\nIn chushuntxi → untxi → un (in) + txi\nIn markstxi → stxi → s (possessive \"our\") + txi\nIn yaputxi → txi → directly attached to root\n\nBut in utnhantxi — we have utnhantxi\n\nBreak into: utn + hantxi?\n\nBut no such suffix.\n\nWhat if -hantxi is -ha (from nasal) + -txi (question)?\n\nBut nasal suffix -nha consumes vowel.\n\nSo if root is ut → then -nha would consume the “u”?\n\nSo utnha → ut + nha → “my house”\n\nSo ut → root, then nha → nasal suffix → consumes “u” → becomes “utnha”? Because -nha suffix consumes the vowel before it?\n\nWait: rule for nasal suffix:\n- consume the vowel if they keep theirs, but leave it if they give up theirs.\n\nSo if root has “u”, and nasal suffix -nha comes after, and it “keeps” its own vowel? But -nha doesn't have vowel — it has “nha”\n\nSo rules:\n- nasal suffixes: consume the vowel if they keep theirs, but leave it if they give up theirs\n\n“keep theirs” — if the nasal suffix has a vowel that it can hold, like -nha?\n\nBut it has “ha” → so it keeps the “a”?\n\nSo if the root has “u”, and nasal suffix adds -nha → does it consume the “u”?\n\nPossibility: yes, if the nasal suffix “keeps” its vowel — but “ha” has a vowel → so it keeps it → so it consumes the preceding vowel?\n\nYes — like in p”ak”unhpsa → \"my pot too\"\n\nRoot: p”ak → has “a” → suffix: -unhpsa → -nha (nasal) + -psa\n\nIf -nha consumes the “a” → so p”ak” → becomes p”uk → then p”uk + hpsa → p”ukhpsa?\n\nBut it's written as p”ak”unhpsa — so the “a” is present?\n\nWait — original: p”ak”u → \"the pot\"\np”ak”unhpsa → \"my pot too\"\n\nThe change: a “n” inserted → becomes \"unhpsa\" → so p”ak → p”ak”un → so “a” is still present?\n\nBut “a” is not consumed — so does nasal suffix not consume?\n\nWait — rule says: consume the vowel if they keep theirs.\n\nBut “nha” has “a” — so it keeps its vowel → so it consumes the preceding vowel?\n\nSo in p”ak” → if root has “a”, and nasal suffix -nha (keeping “a”) → consumes root’s “a” → so p”ak” → becomes p”uk” → then -nha → p”uknha → then -psa → p”uknhasa?\n\nBut word is p”ak”unhpsa → so later \"unhpsa\" → u is there.\n\nPossibility: “unhpsa” → “un” + “hpsa” — so the “n” is attached to “u”?\n\nSo “u” is root → then nasal suffix -nha → consumes “u” → becomes “unh”?\n\nBut root is “p”ak” → so “p”ak” → p”ak\n\nAdd “unhpsa” — becomes p”ak”unhpsa — so “a” is still pronounced.\n\nSo maybe the vowel is preserved.\n\nBut in that case, nasal suffix does not consume.\n\nContradiction.\n\nAlternative: nasal suffixes consume the vowel only if they are “giving up” their own vowel.\n\nIn -nha, if “ha” is not used, but is borrowed → then they keep their vowel?\n\nRule clarification:\n- consume the vowel if they keep theirs, but leave it if they give up theirs\n\nSo if nasal suffix has its own vowel (like -nha has “a”), then it “keeps” it → so it consumes the preceding vowel.\n\nIf it gives up its vowel, it leaves the preceding vowel.\n\nIn p”ak”unhpsa → the “a” in root is consumed → so root p”ak” becomes p”uk”?\n\nBut in the word it's written as p”ak”unhpsa — “a” is there.\n\nBut perhaps it's a grapheme — the “a” is part of the root, and the nasal makes it “unhpsa” — so means “my pot too”\n\nSimilarly, in utnha — root ut → with -nha → “my house”\n\nSo the “nha” is attached → the root “u” is consumed → so becomes “unh”?\n\nYes — like in English, “go” + “to” → “got” — internal vowel change.\n\nSo via elision: when nasal suffix borrows from root, if it keeps its own vowel, it consumes the root vowel.\n\nSo in utnha → root: ut → vowel “u” → nasal suffix -nha → has “a” → keeps vowel → consumes “u” → so becomes “unh” → then the root \"ut\" becomes “un” after elision?\n\nSo root: ut → after -nha → unha? → but written as utnha — probably just the form.\n\nSo elision is internal — the vowel is dropped.\n\nSimilarly, in utnhantxi → we have:\n\n- root: utn → which might be “my house” → “[my] house” + -txi?\n\nBut “my house” is “utnha”\n\nSo to form a question, add -txi → makes utnha + txi → utnhatxi?\n\nBut the word is utnhantxi — has “hantxi”\n\nAh — perhaps the “h” and “a” are part of the nasal suffix — and the “n” is attached to the root?\n\nPossibly, the structure is:\nroot + nasal + question\n\nLike: chushp”a → chush + p”a → his corner\n\nchushuntxi → chush + untxi → in corner?\n\nSo in markstxi → mark + stxi → is it our town?\n\nSimilarly, yaputxi → yapu + txi → is it the field?\n\nSo in utnhantxi → root + hantxi → but “hantxi” is not a suffix.\n\nBut “hantxi” might be “ha” + “txi” → but “ha” is not a suffix.\n\nWait — look at question form: all questions end with -txi.\n\n- chushuntxi → in the corner?\n- markstxi → is it our town?\n- yaputxi → is it the field?\n\nSo every question has -txi at the end.\n\nSo utnhantxi → must end with -txi → so must be root + something + txi\n\nSo the full base is utnhan — then + txi → so utnhantxi\n\nBut what is the structure of \"utnhan\"?\n\nCompare to:\n- utnha → my house\n- markstxi → mark + stxi → “stxi” = “our + txi”\n- chushuntxi → chush + untxi → “untxi” = “in + txi”\n\nSo in “utnhantxi” → utn + hantxi → hantxi might be “in + our” or “my + in”?\n\nNo.\n\nOnly known locative is -n → “in” → appears in:\n- qucxst”psa → from our1+2 lake too → has “st” → might be “in”?\n- yapsanpsa → in our1+2 field too → has “an” → “in”?\n\nYes — in yapsanpsa → “an” → “in”\n\nSimilarly, yapsanpsa → in our field too → so -an = “in”\n\nSo locative suffix is -an → “in”\n\nSo when -an is attached, it consumes the preceding vowel if it is not root’s?\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11980.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "redacted_solution_hint_mask1", + "sample_index": 2, + "output": "Step 1: Identify the base roots and affixes in the given examples.\n\nWe are given a list of Jaqaru words and their English translations. The structure involves roots and affixes with specific rules for vowel elision.\n\nRoots and affixes:\n- Possessor affixes:\n - -p”a → \"his\", \"your\", \"our\" etc.\n - -sa → \"in\", \"from\" depending on context\n- Case affixes:\n - -p”a → marka → \"the town\"\n - -t”a → markp”t”a → \"from his town\"\n - -txi → ishinhna → \"in my bed\", markstxi → \"is it our1+2 town?\"\n- Oral affixes:\n - Always consume the vowel before them\n - Consume vowel if it belongs to another suffix\n- Nasal affixes:\n - Consume vowel if they keep theirs, leave if they give up theirs\n- Specific roots:\n - aq\" → cave\n - qucx → lake\n - chush → corner\n - mark → town\n - utam → house\n - p“ak” → pot\n - yap → field\n - qaqat”a → from the cliff\n\nStep 2: Analyze vowel elision rules.\n\nRule: \n- Oral suffixes always consume the preceding vowel → so if a root has a vowel and an oral suffix follows, the vowel is dropped.\n- Nasal suffixes: consume the vowel if they keep theirs (i.e. if they possess a vowel), otherwise leave it (if they give it up).\n- Example: \"utamt”a\" → from your house → utam (house) + t”a (from), so \"t”a\" takes the vowel and becomes \"t”a\" without elision.\n- \"utnha\" → my house → nasal suffix -na → consumes vowel if it keeps it. If -na keeps \"a\", it consumes the vowel from root.\n\nBut note: \"utnhantxi\" — has \"nha\" and \"txi\". \"nha\" is nasal, and \"txi\" is case.\n\nStep 3: Break down each target.\n\n1. utnhantxi\n\n- utnha = my house → root utam + -nha → nasal suffix takes \"a\"\n- utnhantxi → adds -txi → is it in my house?\n\nCompare: ishinhna = in my bed → bed root + in\nmarkstxi = is it our1+2 town? → mark + st + txi → st is possessive (our), txi case\n\nSo -txi = \"is it...\" (question), used in questions.\n\nThus, utnhantxi = is it in my house?\n\nBut \"utnhantxi\" has \"nha\" → me, \"txi\" → question. So:\n\n→ is it in my house?\n\n2. yapp”psa\n\n\"yap\" = field\n\n\"yapp”psa\" — has \"p”a\" → possessive → \"his\" or \"our\"?\n\nBut target says \"his field too\"\n\nSo structure:\n- yap → field\n- p”a → his\n- psa → \"too\" suffix → same as \"too\" in \"aq”ipsa\" = the cave too\n\n\"aq”ipsa\" → aq + ip + sa → \"the cave too\"\n\n\"p”ak”unhpsa\" → my pot too → p”ak”u + un + hpsa → hpsa = too\n\nSo -psa = \"too\"\n\nSo \"yapp”psa\" = his field too → yap + p”a + psa\n\nVowel elision: does p”a affect the vowel?\n\nRoot: yap → ends in \"a\"\n→ p”a → oral suffix → consumes the preceding vowel → so \"a\" is dropped → \"yap\" → \"yap\" has \"a\", so after p”a, \"a\" is consumed → becomes \"yap\" → \"yap\" without the \"a\"?\n\nBut in \"yapp”psa\", it's spelled yapp”psa — so \"p\" after \"a\", suggesting vowel not consumed?\n\nWait — rule: oral suffixes consume the vowel only if it belongs to another suffix.\n\nBut p”a is a possessive? Is it oral?\n\nFrom the rules:\n\n\"oral suffixes\": always consume the vowel if it belongs to another suffix.\n\nBut looking at the list:\n\n- -p”a (possessor?) — seems to be eaten with vowel if follows vowel\n- -sa → in (in the cave)\n- -t”a → from (from his town)\n- -txi → is it?\n\nBut -nha, -ma → nasal affixes.\n\nPossessor affixes are often nasal? Or is \"p”a\" oral?\n\nCheck: \"chushp”a\" = his corner → chush + p”a → \"his corner\"\n\n\"markp”t”a\" = from his town → mark + p”t”a → p”t”a → a nasal? p”t”a → t”a may be nasal?\n\nBut t”a is in \"markt”a\"? \"marka\" → \"the town\", \"markp”t”a\" → from his town\n\nSo p”t”a → possessive + case?\n\nPossibly p”a is a nasal possessive?\n\nRule says: nasal suffixes consume the vowel if they keep theirs, but leave it if they give up theirs.\n\nIn \"chushp”a\", p”a → \"his\" → vowel \"u\" in chush is not consumed → so p”a must have taken over the vowel?\n\nchush → ends in \"u\", p”a → adds \"a\" → becomes chushp”a → \"his corner\"\n\nNo vowel elision → so p”a is nasal, and keeps \"u\" → so it consumes nothing? But it has its own vowel.\n\nRule: \"consume the vowel if they keep theirs, but leave it if they give up theirs\"\n\nSo if a nasal suffix has its own vowel (like p”a has \"a\"), it keeps it and consumes only if the vowel from root is \"theirs\" — but actually the rule says: consume if they keep theirs → so when they keep theirs (i.e. when they take the vowel from root), they consume it?\n\nWait: re-read:\n\n\"nasal suffixes consume the vowel if they keep theirs, but leave it if they give up theirs\"\n\nSo if nasal suffix keeps a vowel (that is from the root), it consumes it.\n\nIn \"chushp”a\" → chush ends with \"u\", p”a adds \"a\" → so \"u\" remains — so p”a does not consume the \"u\" → so it must have given up its own vowel? But it has an \"a\".\n\nContradiction.\n\nAlternatively: the nasal suffix consumes the vowel from the root only if it keeps its own vowel.\n\nBut in \"chushp”a\", vowel \"u\" remains → so p”a must have given up the vowel → so it only takes \"a\" for possessive.\n\nWait — but the root ends in \"u\" → so a vowel.\n\nAfter affix: chushp”a → \"his corner\" — \"u\" is present.\n\nSo p”a has its own vowel — \"a\" — so it \"keeps\" its own vowel — so it should consume the vowel from root?\n\nBut the vowel \"u\" remains → contradiction.\n\nUnless the p”a is not consuming the root vowel.\n\nPerhaps the affixes are applied in order, and if they have their own vowel, they preserve it.\n\nRule: \"nasal suffixes consume the vowel if they keep theirs, but leave it if they give up theirs\"\n\n\"keep theirs\" → if the nasal suffix has its own vowel, it keeps it and consumes the root vowel?\n\nBut in \"chushp”a\", the root ends with \"u\", and \"p”a\" has \"a\", so it keeps its own vowel, so should consume root's vowel — but no, \"u\" remains → so must be that it only consumes if it keeps the vowel from root?\n\nThat would make no sense.\n\nAlternative reading:\n\n\"consume the vowel if they keep theirs\" → \"their\" refers to the root vowels.\n\nSo nasal suffixes consume the root vowel if they are taking it (i.e. if the vowel belongs to them), or if they \"keep\" it?\n\nThis is confusing.\n\nTry using known examples.\n\n\"p”ak”unhpsa\" = my pot too\n\np”ak”u = pot → root\n\nunhpsa = my pot too → \"un\" is nasal? \"un\" → nasal, possibly \"my\" → nasal suffix\n\n\"un\" → (-nha) or (-una)? likely -un → my\n\nSo \"p”ak”u\" + \"un\" → already has \"un\" → then \"hpsa\" → \"too\"\n\n\"un\" is a nasal suffix — likely consumes vowel from root?\n\nRoot: p”ak”u → ends with \"u\"\n\nSo after \"un\" — if un consumes the vowel, \"u\" is dropped — becomes p”ak” + un → p”ak”un\n\nBut in \"p”ak”unhpsa\", it is written as \"p”ak”unhpsa\" — so has \"u\" before \"h\"\n\n\"unhpsa\" — \"u\" present.\n\nSo if nasal suffix consumes root vowel, the \"u\" should be missing.\n\nBut it's there → so must be that the nasal suffix \"un\" is giving up its vowel → so leaves the root vowel.\n\n\"un\" has its own vowel, \"u\", so if it gives it up → leaves root vowel.\n\nSo rule: nasal suffix consumes root vowel only if it keeps its own vowel.\n\nIn \"p”ak”unhpsa\":\n- \"un\" has vowel \"u\" — so it keeps its own vowel → so should consume root vowel → root ends in \"u\", so \"u\" is consumed → should not be in word.\n\nBut it is present → contradiction.\n\nUnless \"un\" is not the nasal suffix.\n\nPerhaps suffixes are applied as:\n\n- Root + nasal suffix → if nasal suffix has vowel → consumes root vowel → removed\n\nBut in \"p”ak”unhpsa\", root \"p”ak”u\" has \"u\", then \"un\" → if un consumes \"u\", it should be gone.\n\nBut it's not.\n\nSo perhaps the nasal suffix is not consuming the vowel.\n\nWait: \"p”ak”u\" = pot → root\n\"p”ak”unhpsa\" = my pot too → so \"un\" = my → nasal? \"un\" → seems like \"my\"\n\nBut the word has \"u\" — so root vowel remains.\n\nThus, the nasal suffix \"un\" must be giving up its vowel → so it leaves the root vowel → thus, no consumption.\n\nRule: nasal suffixes consume the vowel if they keep theirs, leave if they give up theirs.\n\nSo in \"p”ak”unhpsa\":\n- nasal suffix \"un\" has vowel \"u\" — so keeps it → should consume root vowel → but root vowel is present → contradiction.\n\nAlternative: the root ends in \"u\", and the nasal suffix is attached — if it keeps its own vowel, it consumes the root vowel.\n\nBut it doesn't → so maybe \"un\" does not have a vowel of its own.\n\n\"un\" → \"u\" is root vowel.\n\nBut \"un\" ends in \"n\" — perhaps it's formed from -n → and adds \"u\"?\n\nNo — \"unhpsa\" — likely \"un\" is a nasal possessive.\n\nPerhaps the nasal suffix is -na, -ma, -nha, which may be derived from -n.\n\nIn \"utnha\" = my house → root \"utam\" + -nha → \"nha\" has \"a\", so it has its own vowel → keeps it → so should consume root vowel?\n\nRoot \"utam\" → ends in \"a\" → so after -nha → does it drop \"a\"?\n\n\"utnha\" — has \"a\" at end → so root vowel present.\n\nSo if -nha has its own vowel, keeps it → should consume root vowel → but \"a\" remains → contradiction.\n\nUnless the rule is the opposite.\n\nWait — \"marka\" = the town → root \"mark\" + -a → but -a is not listed as nasal.\n\nList of nasal affixes: -nha, -ma\n\n\"chushuntxi\" = is it in the corner? → chush + unt + txi\n\n\"unt\" → not in list.\n\n\"markstxi\" = is it our1+2 town? → mark + st + txi\n\n\"st\" — is possessor?\n\n\"chushuntxi\" — is it in corner? → so \"unt\" may be \"in\", \"in\"?\n\n\"qucxst”psa\" = from our1+2 lake too → qucx + st + psa → st = our1+2, psa = too\n\n\"st\" is possessive → likely from \"p”a\" or \"sa\"\n\nFrom rule: possible oral suffixes: -p”a, -sa, -t”a, -txi\n\nBut -sa is oral? Or nasal?\n\nIn \"aq”na\" = in the cave → aq + na → na = in → nasal suffix\n\n\"qucxst”psa\" = from our1+2 lake too → qucx + st + psa → st = our, psa = too\n\nSo -st → likely possessive with \"s\" and \"t\"\n\nBut t”a is listed as case → possibly -st is a variant.\n\nIn \"markp”t”a\" = from his town → mark + p”t”a → p”t”a → p”a + t”a — two affixes?\n\nPossibility: affixes are applied sequentially.\n\n\"p”t”a\" → may be p”a + t”a\n\n\"p”a\" — possessive → \"his\"\n\"t”a\" — case → \"from\"\n\nSo \"mark\" + \"p”a\" + \"t”a\" → from his town\n\nIn \"chushp”a\" → chush + p”a\" = his corner\n\n\"chushuntxi\" = is it in the corner? → chush + unt + txi? But unt not in list.\n\n\"unt\" → possibly \"in\" or \"t\" from \"t”a\"?\n\n\"unt\" → could be \"un\" + \"t\" → un = my, t = in?\n\nBut \"ishinhna\" = in my bed → ish + in + hna → ish + in → in bed?\n\n\"ish\" = my, \"in\" = in, \"hna\" = bed?\n\nNot consistent.\n\nBack to targets:\n\n1. utnhantxi\n\nRoot: utam (house) → modified by -nha (my) → utnha = my house\n\nThen -txi = is it [in]?\n\nSo \"utnhantxi\" = is it in my house?\n\nYes — matches pattern in \"ishinhna\" = in my bed, \"markstxi\" = is it our1+2 town?\n\nSo -txi = question \"is it?\"\n\nSo answer: is it in my house?\n\n2. yapp”psa\n\nRoot: yap = field\n\n- p”a = possessive → his\n\n- psa = too\n\nNow, vowel elision: after \"yap\", vowel is \"a\"\n\n- p”a\" is a possessive affix — is it oral or nasal?\n\nFrom examples:\n- p”a\" in chushp”a → his corner → no elision → \"u\" remains → so no consumption → so p”a\" is not consuming root vowel.\n\nRule: oral suffixes always consume the vowel if it belongs to another suffix\n\np”a\" → in \"chushp”a\", root has \"u\", p”a\" has \"a\" — so p”a\" has its own vowel — so if it keeps it, it should consume the root vowel?\n\nBut \"u\" is there → so must be that p”a\" gives up the vowel → so it does not consume it.\n\nThus, p”a\" is a nasal suffix that \"gives up\" its vowel → so leaves the root vowel.\n\nThus, \"yap\" + \"p”a\" → \"yapp”a\" → with \"a\" from root preserved.\n\nThen adds \"psa\" — \"too\"\n\n\"psa\" is a suffix — no vowel elision rule given.\n\nExample: \"p”ak”unhpsa\" = my pot too → so \"hpsa\" = \"too\"\n\nSimilarly, \"aq”ipsa\" = the cave too → so \"ipsa\" = too\n\nSo \"psa\" = too\n\nThus, yapp”psa = his field too\n\n3. yapup”psa\n\nRoot: yap = field\n\n- p”a = his\n\n- psa = too\n\nBut now: \"yapup”psa\"\n\nSpelled with \"up\" — suggests that after \"yap\", vowel \"a\" is followed by \"p\", so \"a\" is not consumed.\n\nSo likely \"p”a\" is a nasal possessive that gives up its vowel → so vowel from root remains.\n\nThen \"psa\" = too.\n\nBut why \"up”\" instead of \"p”a\"?\n\n\"yapup”psa\" — has \"p\" after \"a\" — so it's \"yap\" + \"p\" + \"u\" + \"psa\"\n\nMore likely: \"yap\" + \"p”a\" → becomes \"yap\" + \"p”a\" with \"a\" preserved.\n\nBut in \"yapp”psa\" it is \"yapp”psa\" — so \"p\" after \"a\", then \"p”a\" — so the \"a\" is preserved.\n\nIn \"yapup”psa\" — similar, with \"up”\" — possibly typo?\n\nWait — the word is \"yapup”psa\"?\n\nGiven: \"yapup”psa\"\n\nIn the problem:\n\n\"3. yapup”psa\"\n\nBut the target says: \"through the field too\"\n\n\"through\" — is that in the list?\n\n\"qucxap”a\" = through the lake\n\nSo \"qucx\" = lake, \"ap”a\" = through?\n\n\"qucxap”a\" = through the lake\n\nSo \"ap”a\" = through\n\n\"qucxst”psa\" = from our1+2 lake too → st = our, psa = too\n\n\"qucx\" + \"st\" + \"psa\" = from our1+2 lake too\n\n\"qucxap”a\" = through the lake\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12163.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "redacted_solution_hint_mask1", + "sample_index": 3, + "output": "We are given a set of Jaqaru words and their translations, along with a detailed rule system for suffixes and vowel elision. We are to translate three specific Jaqaru words into English:\n\n1. utnhantxi \n2. yapp”psa \n3. yapup”psa \n\nWe will analyze the structure and rules step by step.\n\n---\n\n### Step 1: Understand the suffix system\n\nThe problem specifies that each word has a root and up to three suffixes. The suffixes are categorized:\n\n- **Possessor suffixes**:\n - -p”a (used with possessive markers)\n - -sa (also possessive)\n- **Case suffixes**:\n - -p”a (locative or case?)\n - -t”a (from possessive?)\n - -txi (question form: “is it…”)\n- **Oral vs. nasal suffixes**:\n - Oral suffixes: \"always consume the vowel\" if it belongs to another suffix, but \"leave it if it belongs to the root\".\n - Nasal suffixes: \"consume the vowel if they keep theirs, but leave it if they give up theirs\".\n\nAlso, there are root forms and specific case markers:\n\n- Roots:\n - utnha → \"my house\"\n - marka → \"the town\"\n - chushp”a → \"his corner\"\n - p”ak”u → \"the pot\"\n - aq”ipsa → \"the cave too\"\n - qaqat”a → \"from the cliff\"\n\n---\n\n### Step 2: Identify structure of each word\n\n#### Word 1: utnhantxi\n\n- Root: utnh- → from \"utnha\" = \"my house\"\n- Suffixes: -t”a, -txi?\n\nLet’s look at the pattern of -txi:\n\n- qucxst”psa → \"from our1+2 lake too\" → contains -txi\n- markstxi → \"is it our1+2 town?\" → contains -txi\n- yaputxi → \"is it the field?\" → contains -txi\n\nSo: -txi = “is it...?”\n\nAlso:\n- case suffixes:\n - -p”a → locative?\n - -t”a → from?\n - -psa → from... too?\n - -na → in?\n\nNow: utnhantxi\n\n- Root: utnha (my house)\n- -t”a? → from my house?\n- -txi → is it...?\n\nBut the word ends in -t”a + -txi → possible structure: [utnh] + [t”a] + [txi]\n\nBut is -t”a a case suffix?\n\nCompare:\n- utamt”a → \"from your house\"\n- utnha → \"my house\"\n- so: -t”a → “from”?\n\nYes: in \"utamt”a\" = \"from your house\", and root = \"utnha\" → \"house\"\n\nSimilarly:\n- marka → \"the town\"\n- markp”t”a → \"from his town\"\nSo \"mark\" + \"p”t”a\" → “from his town”\n\nWait: actually \"markp”t”a\" → from his town → so -p”t”a = from possessive?\n\nBut earlier we had:\n\nPossessor suffixes:\n- -p”a\n- -sa\n\nCase suffixes:\n- -p”a\n- -t”a\n- -txi\n\nIn the case of:\n- markp”t”a → from his town → so root: marka (town), suffix: p”t”a → possessor? But p”t”a is not listed.\n\nWait: the suffixes given are:\n\n- possessor: -p”a, -sa\n- case: -p”a, -t”a, -txi\n- nasal: -nha, -ma → consume vowel if they keep theirs, else leave\n\nBut in markp”t”a → p”t”a — is this a blend?\n\nWait: marka → the town \nmarkp”t”a → from his town\n\nPossibility: the root is \"mark\", then a case suffix?\n\nBut p”t”a — does that include possessor?\n\nPerhaps the suffix -t”a is “from” and is attached to a possessed noun.\n\nBut in markp”t”a, the \"p”t”a\" — could it be \"p”a\" + \"t”a\"?\n\nBut \"p”a\" is a possessor suffix.\n\nAlso, \"his\" is not directly in the list — but \"chushp”a\" = his corner → so \"p”a\" = his\n\nThus, p”a = possessive of \"his\"\n\nThen \"p”t”a\" = from his?\n\nBut that would be structure: root + p”a + t”a?\n\nBut that would be quite long.\n\nAlternatively, perhaps suffixes are attached in sequence.\n\nLet’s look at all given word forms.\n\n---\n\n### Step 3: Functional patterns\n\nLook at the translation of \"utamt”a\" → from your house \n\"utnha\" → my house\n\nSo -t”a → from\n\nSimilarly:\n- markp”t”a → from his town \nThen: mark + p”a + t”a → from his town\n\nSimilarly:\n- chushuntxi → is it in the corner? → root chushp”a + t”a? \nBut chushp”a is \"his corner\", so chushuntxi → is it in the corner?\n\nBut t”a is not in the list as “in”.\n\nWait: earlier:\n\n- chushuntxi → is it in the corner?\n\n- markstxi → is it our1+2 town?\n\nSo -txi = is it?\n\nAnd:\n\n- chushp”a = his corner\n- chushuntxi = is it in the corner?\n\nSo “in” is likely a marked case — perhaps -nha or -na?\n\nWe have:\n- aq”na → in the cave\n- p”ak”unhpsa → my pot too\n- aq”ipsa → the cave too\n\nSo “in” appears in -na → aq”na\n\nThus, -na = in?\n\nNow, what happens with vowel elision?\n\nRule:\n- Oral suffixes: always consume the vowel if it belongs to another suffix, but leave it if it belongs to the root.\n- Nasal suffixes: consume vowel if they keep theirs, but leave if they give up theirs.\n\nSo when suffixes are added, the vowel of the previous element may be deleted depending on whether the suffix “takes” the vowel.\n\nLook at:\n\n**Example: p”ak”u → the pot** \n**p”ak”unhpsa → my pot too**\n\nStructure: p”ak”u + unhpsa?\n\nUnhpsa — is it \"my\" + \"pot too\"?\n\n“my” → probably -p”a \n“too” → -psa?\n\nSo p”ak”u → root \np”ak”unhpsa → root + -unhpsa?\n\nBut -unhpsa?\n\nBreak down: -unhpsa → -u? → possible split?\n\nRoot: p”ak”u → “the pot”\n\nNow, p”ak”unhpsa → my pot too\n\nPossibly: root + -p”a (my) + -psa (too)\n\nBut in between: vowel in root is “u” → is it consumed?\n\nRoot ends in “u”\n\nSuffix -p”a begins with “p” — not a vowel.\n\nBut the rule: oral suffixes consume the vowel if it belongs to another suffix.\n\nBut “p”a” is a possessor suffix — is it oral?\n\nSuffix types:\n- possessor: -p”a, -sa → oral?\n- case: -p”a, -t”a, -txi → oral?\n- nasal: -nha, -ma → nasal?\n\nSo suffixes marked as oral: -p”a, -sa, -t”a, -txi — these are oral, so they consume the vowel if it belongs to another suffix (i.e., not the root)\n\nBut nasal suffixes: only -nha, -ma → nasal\n\nSo in p”ak”unhpsa → root: p”ak”u → ends in “u”\n\nThen we have -unhpsa?\n\nBut -unhpsa → likely compound: -u? -nha? -psa?\n\nWait: perhaps broken as: -unhpsa — meaning -u + -nha + -psa?\n\nBut -nha is nasal — so consumes vowel?\n\nBut root ends with “u” — the vowel belongs to the root?\n\nSo if the nasal suffix -nha wants to consume it, only if it keeps its own vowel.\n\nBut -nha has vowel “a” → so it keeps its own? Then it consumes the root’s vowel?\n\nSo in p”ak”u + -nha + -psa → the root’s “u” is consumed?\n\nSo we get: p”ak” → then + nha psa?\n\nBut word is p”ak”unhpsa — so u is present → “u” appears?\n\nWait — the word is written with “u”, so “p”ak”u” → root, then “unhpsa” — so after “u” comes “n” — so the root’s vowel is preserved?\n\nBut the rule says: oral suffixes consume the vowel if it belongs to another suffix.\n\nIn this case, if the suffix is added and it’s oral, and the vowel belongs to the root, then it is consumed?\n\nBut here, the vowel “u” is not consumed — it’s preserved.\n\nSo perhaps the vowel belongs to the root, and the suffix is oral — so it should be consumed — contradiction?\n\nWait — let’s look at:\n\n**aq”na → in the cave**\n\nRoot: aq”ipsa → cave too → so \"aq”ipsa\" has “-ipsa”\n\naq”na → in the cave\n\nSo root: aq”ip? → in cave?\n\nBut aq”na → in the cave\n\nPossibly root: aq”ip → in cave?\n\nNot clear.\n\nAnother example:\n\n**qucxap”a → through the lake**\n\nqucx → lake? \nqucxap”a → through the lake? \nSo -p”a → through? or locative?\n\nqucxst”psa → from our1+2 lake too → so -st”psa?\n\nRoot: qucx → lake?\n\nqcx → lake?\n\nqucx → lake \nqucxap”a → through the lake → might be case -p”a = through?\n\nqucxst”psa → from our1+2 lake too — from + lake too?\n\nSo \"-t”psa\" — suspect that -t”psa = from + too?\n\nBut \"t”psa\" is not a standard suffix.\n\nWait: let's look at the pattern of \"my\" and \"too\".\n\nWe see:\n\n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too\n\n→ So -unhpsa = my + too?\n\nBut written as \"unhpsa\"\n\nSimilarly: \n- aq”ipsa → the cave too → has -ipsa \n- aq”na → in the cave → root aq”+na?\n\nSo root aq” based on aq”na\n\nAnother: \n- qaqat”a → from the cliff → so -t”a = from?\n\nYes, matches earlier — utamt”a = from your house\n\nSo: -t”a = from\n\nAnd -txi = is it?\n\nAnd -psa = too?\n\nUsed in:\n- aq”ipsa → the cave too → -ipsa → so -psa?\n- p”ak”unhpsa → my pot too → -unhpsa → likely -u + -nha + -psa?\n\nBut -nha? Where is that?\n\nWe have:\n- aq”na → in the cave → so -na → in?\n\nRoot: aq” → cave?\n\nSo aq”na → in the cave\n\nAlso: yapsanpsa → in our1+2 field too → so in our field too → -sanpsa?\n\n- sanpsa → in + our + field too?\n\nSo -npsa → -na (in) + -psa (too)?\n\nThus, -na = in \n- psa = too \n- t”a = from \n- t”xi = is it?\n\nNow: root + case + possessive?\n\nSteps:\n\nWe have:\n- Root → base noun\n- Suffixes added in order, with vowel elision rules.\n\n---\n\n### Step 4: Apply to given words\n\n#### 1. utnhantxi\n\nRoot: utnha → my house\n\nSuffixes:\n- -t”a → from\n- -txi → is it?\n\nSo likely: from my house? — but is it?\n\nBut structure: utnha + t”a + txi → utnhantxi\n\nBut vowel elision?\n\nRoot ends in “a”\n\nNext suffix: -t”a — is this oral? Yes.\n\nRule: oral suffixes consume the vowel if it belongs to another suffix.\n\nIn this case, the vowel “a” belongs to the root.\n\nDoes the suffix -t”a consume it?\n\nYes — because it is oral and the vowel belongs to a different suffix (i.e., the root), so it should be consumed.\n\nBut in the word utnhantxi → it is written as \"utnhantxi\" → so “a” is preserved?\n\n\"utnha\" ends in a → then \"t”a\" → so after \"a\" comes \"t”a\" → so \"a\" is not consumed?\n\nBut according to rule: oral suffix consumes vowel if it belongs to another suffix → so if the vowel belongs to the root, and the suffix is oral, it should be deleted.\n\nThus, in normal order, root ends with “a”, then suffix -t”a → oral → consumes the vowel → so only \"utnh\" + \"t”a\" + \"txi\"\n\nSo becomes: utnh + t”a + txi → utnh t”a txi → but written without vowel?\n\nBut word is \"utnhantxi\" → has “a” in between.\n\n\"utnhantxi\" → so after \"utnh\" → “a” → then “ntxi”?\n\nSo the vowel is preserved.\n\nContradiction?\n\nUnless the vowel is not consumed.\n\nPossibility: the suffix -t”a has a vowel — so the root's vowel is only consumed if the suffix is adding its own vowel and it doesn’t belong to it.\n\nBut the rule says:\n\n\"oral suffixes always consume the vowel if it belongs to another suffix\"\n\nSo: if the vowel belongs to the root → it is consumed.\n\nSo in this case, the root ends in “a” → vowel belongs to root → oral suffix -t”a adds “t”a” → which includes vowel → so consumes root’s vowel.\n\nSo root becomes \"utnh\" → then -t”a → so \"utnh\" + \"t”a\" → \"utnht”a\" → then -txi → \"utnht”txi\"\n\nBut written as \"utnhantxi\" — has “a” after “utnh” → so an extra “a”?\n\nSo perhaps I have the wrong root.\n\nutnha → root?\n\nBut what if root is \"utnh\" and the suffix is added?\n\nBut the word \"utnha\" is given — so root is \"utnha\"\n\nPerhaps the elision only happens between root and suffix that are adjacent.\n\nLet’s look at another example: \n- markstxi → is it our1+2 town?\n\nmarka → the town \nmarkstxi → is it our1+2 town? → so -stxi?\n\ns and t? → -s + t”a + txi?\n\nBut -t”a is from?\n\nBut here, markstxi → not from.\n\nWait: markstxi → “is it our1+2 town?” — so “our1+2” is not possessive.\n\nPossessors:\n- -p”a → his\n- -sa → ?\n\nIn chushp”a → his corner → p”a\n\nIn chushuntxi → is it in the corner? → so “in” + “corner”?\n\nBut “in” is likely -na?\n\nIn aq”na → in the cave → so -na = in\n\nSo in chushuntxi → in + corner → chush + n + t”xi → but t”xi?\n\nWait: chushuntxi → chush + un + txi?\n\n“un” — is that -na?\n\nBut -na is a suffix.\n\nSo perhaps the root is chush → corner, then -na → in → then -txi → is it?\n\nBut chushp”a → his corner → so p”a → his\n\nSo chushuntxi → in the corner? → so root chush → corner → -na → in → -txi → is it?\n\nBut written as \"chushuntxi\" — so \"un\" is part of it.\n\nBut “un” — is it -u + -n?\n\nNo, because -n is not a suffix.\n\nBut -nha? – nasal?\n\nIn p”ak”unhpsa → un + h + psa — so un = u + n?\n\nPerhaps the form is root + case suffix, and vowel elision occurs between root and suffix.\n\nNow back to utnhantxi.\n\nRoot: utnha → \"my house\"\n\nSuffixes: -t”a → from, -txi → is it?\n\nSo: from my house? → but in English, “is it from my house?”\n\nBut the phrasing is “is it from my house?”\n\nYes — likely.\n\nBut the word is utnhantxi — contains “a” in the middle.\n\nCould the root be \"utnh\" and the full form utnh + na + t”a + txi? No — because -na is in?\n\nWait — we see no \"in\" here.\n\nAnother possibility: the root is \"utnh\", and -a is part of a suffix that comes after.\n\nBut available suffixes: -na, -t”a, -txi, -psa\n\nIn utnhantxi → “antxi” → likely -t”a + -txi?\n\nSo t”a + txi?\n\nSo suffixes: -t”a and -txi\n\nRoot: utnha → my house\n\nSo -t”a = from? → from my house?\n\n- t”a → from → so \"from my house\"\n\nBut question form? -txi → is it?\n\nSo entire phrase: \"is it from my house?\"\n\nYes.\n\nSo translation", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11909.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — [TARGET ANSWER REDACTED]\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— qaqsa\n 5. in your corner — chushumna\n\n 6. in your corner too — chushmanpsa\n\n 7. from your corner too — chushumt”psa\n\n 8. is it from the cave? — aq”it”txi\n\n 9. is it the house? — utatxi", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "redacted_solution_hint_mask3", + "sample_index": 0, + "output": "We are given a set of Dyirbal sentences with translations, and we are to translate three new sentences (17, 18, 19) into English using the provided linguistic rules.\n\nStep-by-step breakdown:\n\n1. **Core word order**: OSV (Object-Subject-Verb) \n - O: object (noun with article) \n - S: subject (noun with article) \n - V: verb \n\n2. **Articles**:\n - balan → baNgul → men, animals \n - bayi → baNgul → men, animals \n - bala → baNgu → all other things (objects, women, dangerous animals)\n\n Note: All nouns are preceded by an article.\n\n3. **Adjective formation**: \n - “that is always being [Ved]” = [N]-nay-muNa or -l-muNa (with -n, -l, or -ñu suffixes) \n - “that is always [Ving]” → [N]-ñu, -y-muNa \n - Generally, the suffix -n, -l, -ñu shows the state of being always V-ing\n\n4. **Subject marking**:\n - If word ends in vowel and has 2 syllables → -Ngu \n - If ends in vowel and >2 syllables → -gu \n - If ends in consonant → -Du \n\n5. **Pattern for \"A is making B tired\" or \"A is causing B to be X\"** \n - Form: [A] + \"is making\" + [B] + \"tired\" → [A] (object) + [subject] + \"is making\" + [B] + \"tired\" \n - \"tired\" = biNgunman \n - \"making\" = baNgun in context (though upstream examples show \"A is making B\" = A + [subject] + \"is making\" + B + \"tired\")\n\nNow, examine each target:\n\n---\n\n**17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman**\n\nStructure: \n- balan = object (female entity) \n- ñalNga = subject (noun) \n- baNgul = article for subject \n- NumaNgu = \"the man that is always being followed\" (Numa = man; -Nay-muNa = \"that is always being followed\") \n- guniymuNagu = \"that is always searching\" (guni- = search; -y-muNa = always V-ing) \n- bambunman = \"fat\" (mambunman = fat)\n\nSo: \nObject = balan ñalNga → \"the woman who is always searching\" \nSubject = baNgul NumaNgu → \"the man that is always being followed\" \nBut wait — order is Object-Subject-Verb, and the verb is implied by the participle.\n\nBut note: the form is [Object] [Subject] [Verb-adj]\n\nParsing: \n- balan ñalNga = the woman who is always searching \n- baNgul NumaNgu = the man that is always being followed \n- guniymuNagu → participle of \"seeking\" (searching) \n- bambunman → fat\n\nBut the entire phrase is structured as: \n[Object] [Subject] [that is always being followed] [that is always searching] [fat]?\n\nNo — the components are:\n\n- balan ñalNga → object (the woman) \n- baNgul NumaNgu → subject (the man that is always being followed) \n- guniymuNagu → \"that is always searching\" → must attach to the subject? \n- bambunman → adjective of the object?\n\nWait — look at example 15: \n\"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\" \n→ \"The quiet boy is looking at the tired lizard.\" \n\"biñéiriñ\" = quiet → adjective \n\"biNgun\" = tired → adjective \n\"ñalNgaNgu\" = lizard → modified by -Ngu (2 syllables ending in vowel)\n\nThus, adjectives go before the noun, and they describe the noun.\n\nSo in 17: \n- balan ñalNga = object → \"the woman who is always searching\" \n - \"ñalNga\" = “searching” → but \"ñalNga\" ends in vowel and has 2 syllables? \n - \"ñalNga\" → 3 syllables: ña-l-nga → 3 syllables → should end in -gu? But it's not. \n - Wait: article is baNgul, so the noun is \"ñalNga\" → but article comes before noun.\n\nWait — structure: \n- balan ñalNga → object (the woman) \n- baNgul → article \n- NumaNgu → \"the man that is always being followed\" \n- guniymuNagu → \"that is always searching\" \n- bambunman → \"fat\"\n\nBut where does the verb go?\n\nFrom example 1: \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\" \n\"booze is making the man that is always being blamed tired\" \n→ \"bayi\" = subject (booze) → subject? No — actually, \"bayi yaóa\" = \"booze is making\" (O-S-V)\n\nSo: O = bayi (booze), S = yaóa (man), V = gurugugu → making tired? But \"biNgunman\" is the adjective.\n\nActually: \n\"bayi yaóa ... biNgunman\" = \"booze is making the man tired\" \n→ The verb is implied by the object? No — \"yaóa\" is the subject, and \"biNgunman\" is the adjective of the subject.\n\nBut in example 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\" \n→ \"booze is making the man that is always being blamed tired\" \n→ \"NunéaymuNa\" = \"the man that is always being blamed\" → applies to yaóa \n→ \"gurugugu\" = making \n→ \"biNgunman\" = tired\n\nSo it's: [O] [S] [attribute] [verb] [result]\n\nBut in syllabus: \n“V →A: V that is always being Ved” → so possibilites: \n- -n, -l-muNa, -ñu, -y-muNa → modals\n\nSo \"Numa\" = man \n- NumaNgu → man that is always being followed → because -Nay-muNa → \"being followed\" \n- guniymuNagu → that is always searching → guni- + -y-muNa → always searching \n- bambunman → fat\n\nSo: \nThe structure is: \n[Object] [Subject] [that is always [V]ing] [that is [A]]\n\nSo the full sentence is: \n\"The woman who is always searching is making the man that is always being followed fat?\"\n\nBut the order is OSV. So object first.\n\nIn 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ O: balan ñalNga → the woman who is always searching \n→ S: baNgul NumaNgu → the man that is always being followed \n→ guniymuNagu → \"that is always searching\" → but this should go with an object? Or is it modifying the subject?\n\nWait — look at example 4: \n\"bala yila wura baNgul bargandu biNgundu guniñu.\" \n→ \"the tired wallaby is searching for the little feather\" \n→ \"yila\" = wallaby → object \n\"baNgul bargandu\" = for the little feather → object \n\"biNgundu\" = tired \n\"guniñu\" = searching\n\nBut structure: O → S → V → Result \nActually: \"the tired wallaby is searching for the feather\" → so verb at end?\n\nWait — no: the verb is not a separate verb; \"guniñu\" = \"is searching\", so in OSV: \nO = yila (wallaby), S = bargandu (feather), V = guniñu (is searching)? → no, that would be O-S-V\n\nBut elements: \n\"yila\" = wallaby \n\"baNgul bargandu\" = for the feather → but this is object? \n\"biNgundu\" = tired → adjective of wallaby \n\"guniñu\" = searching → verb?\n\nSo order: O + S (with attribute) + V → not clear.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ O = bayi (booze) \n→ S = yaóa (man) \n→ attribute = NunéaymuNa → \"that is always being blamed\" \n→ verb = gurugugu → “making” \n→ result = biNgunman → “tired”\n\nSo verb is not directly “is making” — the verb is a separate action.\n\nIn 17: \n- balan ñalNga → object \n- baNgul NumaNgu → subject \n- guniymuNagu → adjective → \"that is always searching\" → likely modifies the subject \n- bambunman → \"fat\" → modifies the object?\n\nWait — but bambunman would go with the object.\n\nSo: \n\"the woman who is always searching is making the man who is always being followed fat\"\n\nYes — fits.\n\nIs \"making\" implied? Yes, in the pattern of examples: \n- A makes B [adjective] \n- So in example 1: \"booze is making the man tired\" \n- So in 17: \"the woman is making the man fat\"\n\nSo full translation: \n“The woman who is always searching is making the man who is always being followed fat.”\n\nBut check ending: “bambunman” → fat → yes.\n\nBut is \"ñalNga\" modifying the object?\n\n\"ñalNga\" → \"searching\" → with -ga ending, vowel → 3 syllables → should have -gu → but it has -ga → not marked.\n\nWait — but article is baNgul on the subject, so noun is \"NumaNgu\" — no.\n\n\"ñalNga\" → noun? → \"ñalNga\" = woman searching? \n\nBut in example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"the quiet boy is looking at the tired lizard\" \n\"biñéiriñ\" = quiet → adjective \n\"biNgun\" = tired → adjective \n\"ñalNgaNgu\" = lizard → modified by -Ngu → 2 syllables (ñalNga → 3? ña-l-nga → 3) → should be -gu → but it's -Ngu.\n\nWait: ñalNga → 3 syllables → ends in vowel → should be -gu → but it is -Ngu → contradiction.\n\nNo — in example 15: \n\"ñalNgaNgu\" → \"lizard\" → so the noun is \"ñalNga\" → with article \"baNgul\", and suffix -Ngu → must be because it has 2 syllables?\n\nPossibly: “ñalNga” = 3 syllables → error? Or minimal word?\n\nBut in the rule: \n“Subject and its attributes get the ending: -Ngu if ends in vowel and has two syllables”\n\nSo if a noun ends in vowel and has two syllables → -Ngu\n\n\"ñalNga\" → 3 syllables → should be -gu\n\nBut in 15: \"ñalNgaNgu\" — so it's using -Ngu → contradiction\n\nAlternatively: the suffix is applied to the entire noun phrase?\n\nWait — the noun is not \"ñalNga\", it's \"ñalNga\" + \"Ngu\" = \"the lizard\"\n\nSo the noun has 3 syllables → should get -gu → but it has -Ngu\n\nThus, maybe the rule has an exception.\n\nWait — example 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" \n\"yila\" = wallaby → 3 syllables → ends in vowel → should get -gu → but it's not marked.\n\nSo perhaps the article is separate, and the noun doesn't get suffix.\n\nBut in example 3: \"baban waymin bambun baNgu éugaNgu éamiman\" \n\"baban\" → \"sugar\" → 3 syllables → ends in vowel → should get -gu → has -Nu? \n\nNo — article is baNgu → so “baban” is object → no suffix.\n\nThen why in example 5: \"balan malayigara baNgu garandu biNgunman\" \n\"malayigara\" = smoke → 5 syllables → ends in vowel → should get -gu → but no suffix.\n\nUnless suffixes go only on modified nouns.\n\nBack to 17.\n\nWe see that:\n- balan → object\n- ñalNga → part of object: woman who is always searching → \"ñalNga\" = searching → -y-muNa or -ñu?\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father\" \n\"Numa\" = man → \"Numa guli\" → \"that is always being followed\" → -guli → -l-muNa → similar to -l-muNa\n\nIn 17: \"guniymuNagu\" → -y-muNa → “that is always searching”\n\nSo \"ñalNga\" is being used as a participle meaning “searching” → so the object is “the woman who is always searching”\n\nSubject: baNgul NumaNgu → man that is always being followed\n\nResult: bambunman → fat\n\nSo the structure is: \n[woman who is always searching] is making [man that is always being followed] fat.\n\nThus: \n**17. The woman who is always searching is making the man who is always being followed fat.**\n\n---\n\n**18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu**\n\n- bala → object \n- diban → noun → fat → \"diban\" \n- bilmbalmuNa → \"the mother-in-law that is always pushing\" → \"bilmba\" = pushing → -l-muNa → “that is always pushing” → so the object is “the fat mother-in-law that is always pushing” \n- baNgun → article for subject \n- biñéiriñéu → \"the lizard\" → adjective \"looking\" → \"biñéiriñ\" = quiet → so \"biñéiriñéu\" = looking at? \n In example 15: \"biñéiriñ\" = quiet → so \"biñéiriñéu\" = “the one that is always looking” → → \"looking\" \n- guniñu → \"searching\" → but verb?\n\nBut order is OSV.\n\nSo: \nObject: bala diban bilmbalmuNa → the fat mother-in-law that is always pushing \nSubject: baNgun biñéiriñéu → the lizard that is always looking \nVerb: guniñu → searching?\n\nBut \"guniñu\" is \"is searching\", not the verb of the sentence.\n\nIn example 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"the tired wallaby is searching for the little feather\" → so \"guniñu\" is the verb\n\nSo here: \"guniñu\" = verb → \"is searching\"\n\nBut who is searching? The subject?\n\nSo: the object is [fat mother-in-law that is always pushing] \nThe subject is [lizard that is always looking] \nThe verb is \"is searching\"?\n\nBut there's no object of \"searching\".\n\nWait — the structure is OSV — so the verb must go at the end.\n\nBut no object mentioned.\n\nWait — example 10: \"balan duNan baNgul yiriñéilagu guniñu\" → \"The dragonfly is searching for the stinging tree.\" \n→ \"duNan\" = dragonfly → subject? But it starts with balan → object?\n\n\"balan\" → object → so \"the dragonfly\" must be the object?\n\nBut in 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ \"The dragonfly is searching for the stinging tree\" \n\"duNan\" → dragonfly → subject\n\nBut \"balan\" → object\n\nSo it's O-S-V with the verb at end.\n\nBut in 10: \"balan\" = object → \"the dragonfly\" — which is odd.\n\nUnless \"duNan\" is the subject.\n\nBut \"duNan\" = dragonfly → comes after baNgul → after article.\n\nThe article baNgul → subject → so \"duNan\" is the subject → \"the dragonfly\"\n\nThen \"baNgul yiriñéilagu\" → \"for the stinging tree\" → object of \"is searching\"\n\nSo \"yiriñéilagu\" → stinging tree → object\n\nSo structure: O + S + V → but O is missing?\n\nIn 10: \"balan\" → object \n\"duNan\" → subject \n\"baNgul\" → article for subject \n\"yiriñéilagu\" → object of \"searching\" \n\"guniñu\" → verb\n\nSo sentence: \"The [something] is searching for the stinging tree\" → \"The [something]\" = balan → so balan = something (what?) → but balan is article.\n\nThus, possibly: \"The [object] [subject] is searching for [object]\"\n\nSo vanished participle?\n\nBack to 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ bala → object \n→ diban → noun \n→ bilmbalmuNa → \"that is always pushing\" → so \"the fat mother-in-law that is always pushing\" \n→ baN", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12540.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "redacted_solution_hint_mask3", + "sample_index": 1, + "output": "Step 1: Identify the word order. The problem states OSV (object-subject-verb), with articles preceding nouns.\n\nStep 2: Identify article system:\n- balan → objects (e.g., sugar, smoke, death adder)\n- bayi → men, dangerous animals (e.g., death adder, drunk man)\n- bala → all other things (e.g., mother-in-law, lizard, stone)\n\nStep 3: Adjective and attribute suffixes:\n- V → A: “that is always being Ved” or “that is always Ving Ns”\n- Pattern: -n, -l-muNa → “that is always being [Ved]”\n- Examples:\n - “blaming the mother that is always following death adders” → balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\n - “becoming tired” → biNgunman → “the tired man”\n\nStep 4: Determine how attributes go:\n- Attributes are attached to nouns via suffixes:\n - If noun ends in vowel and has 2 syllables → -Ngu\n - More than two syllables → -gu\n - Ends in consonant → -Du\n\nStep 5: Analyze example 17:\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak down:\n- balan → object\n- ñalNga → noun → \"quiet\" or \"quiet boy\"?\n → \"ñal\" likely means \"quiet\"\n → \"ñalNga\" may be a noun form; often in phrases like \"the quiet one\"\n → According to example (15): bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan → “the quiet boy is looking at the tired lizard”\n → So \"ñalNga\" = quiet boy → noun meaning \"quiet one\"\n- baNgul → subject → men or dangerous animals → “the quiet boy” makes sense as subject here\n- NumaNgu → \"the man that is always being followed\" → Numa = man; -gu ending implies >2 syllables → \"that is always being followed\"\n- guniymuNagu → \"that is always searching\" → guni = search; -ymuNa → the \"that is always searching\" construction\n- bambunman → \"fat\", adjective → \"fat man\"\n\nSo:\n- balan ñalNga → \"the quiet one\" (object)\n- baNgul NumaNgu → \"the man that is always being followed\" (subject)\n- guniymuNagu bambunman → \"that is always searching for the fat man\"\n\nThus: The quiet one is making the man that is always being followed search for the fat man.\n\nBut this contradicts OSV. In OSV, object-subject-verb.\n\nWait: examples like 1 → bayi yaóa NunéaymuNa baNgu gurugugu biNgunman → “Booze is making the man that is always being blamed tired” → So structure is [A] is making [B that is always being C] D\n\nPattern:\n- [A] → agent, subject\n- [B] → patient, object\n- [B] has adjectives: “that is always being blamed” → used to modify the object\n- Verb: “is making” → A → V → A: “making” turns into “is making”\n\nSo in all cases, the structure is:\n[AGENT] is making [OBJECT THAT IS ALWAYS BEING VERBED] [ADJECTIVE]\n\nBut in line (17): balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nbalan → agent? Object?\n\nObserve:\n- (1): balan yabu → \"the strong man is blaming\" → balan = subject? But balance is object in English.\n\nWait — recheck structure in (1):\n\"boozing is making the man that is always being blamed tired\" → so \"boozing\" is the cause.\n\nIn (1): bayi yaóa → \"boozing\" → verb agent?\nBut baNgul → man that is being blamed → object\n\nActually, examine:\n(1): bayi yaóa → Booze is making → “boozing” is the verb agent\nThen: NunéaymuNa → man that is always being blamed → object\nThen: baNgu → “the” → so baNgul is actually subject?\n\nWait, no: English says \"booze is making the man that is always being blamed tired\"\n\nSo verb is “making” → passive: “is being blamed”\n\nBut the structure is: agent → verb → object (with attributes)\n\nExample (2): balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\n→ \"The strong man is blaming the mother that is always following death adders\"\n→ So balan = subject (strong man)\n→ yabu = verb (blaming)\n→ bimabanéalNaymuNa = object (mother that is always following) \n→ baNgul yaóaNgu guliNgu Nunéañu → further attributes of mother?\n\nNo: in (2), baNgul is object? But baNgul = \"the mother\" → so \"mother\" is the object?\n\nWait: \"The strong man is blaming the mother that is always following death adders.\"\n\nSo: subject (strong man) → verb (blaming) → object (mother with attribute)\n\n→ So the structure is: [S] [V] [O] where O has attributes\n\nThen (3): sugary is making the healthy mother-in-law fat → balan waymin → sugar\n→ bimabanéalNaymuNa → mother-in-law (that is always being blamed?) — no\n\nIn (3): balan waymin bambun baNgu éugaNgu éamiman\n→ \"Sugar is making the healthy mother-in-law fat\"\n→ balan = sugar → agent\n→ waymin = adjective → “healthy”?\n→ bambun = mother-in-law\n→ baNgu → article\n→ éugaNgu → article for “fat”? → éamiman → “fat”\n\nSo structure: [agent] is making [object] [adjective]\n\nThe adjective applies to the object, and appears after the noun.\n\nBut attributes like “that is always being V-ed” use -l-muNa suffixes.\n\nIn (5): balan malayigara baNgu garandu biNgunman\n→ “The smoke is making the scorpion tired”\n→ malayigara → smoke\n→ baNgu → article\n→ garandu → scorpion\n→ biNgunman → tired\n\nSo: [agent] is making [object] [adjective]\n\nSo general pattern:\nAgent → verb → object → adjective (with -man, -NaymuNa, etc.)\n\nNow go to (17): balan ñalNga baNgul NumaNgu guniymuNagu bambunman\n\n- balan → agent (object, in word order)\n- ñalNga → noun → “quiet” → likely \"quiet one\"\n- baNgul → subject → \"man\"\n- NumaNgu → “man that is always being followed” → -gu suffix → >2 syllables → makes sense\n- guniymuNagu → “that is always searching” → guni = search → -ymuNa suffix → “that is always searching”\n- bambunman → “fat man”\n\nBut structure is OSV: object-subject-verb\n\nBut here: balan ñalNga → object? → agent?\n\nIn all examples, the first noun is the agent (like “boozing”, “smoke”, “strong man”)\n\nExample (1): bayi yaóa → booze is making → “boozing” is agent\n\nBut bayi (man) + yaóa → “boozing”?\n\nNo — in (1): bayi yaóa → “boozing” → the word “yaó” is the verb?\n\nBut “yaóa” is used in (1) → “boozing”\n\nSo “yaóa” is a verb → issue?\n\nBut in (5): malayigara → smoke → noun\n\nSo likely, the verb is embedded or implicit.\n\nWait — look at the verb in the sentence.\n\nIn (1): “is making” — implied by structure\n\nSo all sentences have “is making” as the verb, so the verb is missing in the form — it's implied.\n\nThus, the structure is:\n[AGENT] → [object] → [subject] → [attribute]?\n\nNo — order is OSV: object-subject-verb → so:\n\n1. O S V → object, subject, verb → but verb is not separate\n\nBut in all cases, the verb is “is making” — it's a verbal construction.\n\nSo actually, the full construction is:\n[AGENT] is making [THE OBJECT] [attribute]\n\nBut in the examples, the agent is the first noun.\n\nIn (1): bayi yaóa → “boozing” → is the agent? → so “boozing is making…”\n\nThen “the man that is always being blamed” → object\n\nSo: agent → object → attribute\n\nBut word order is O S V → so object-subject-verb\n\nThus: verb is last → “is making” is the verb → so last item is the verb?\n\nBut all sentences have the verb “is making” → so the last word is the verb? But not present.\n\nWait: no verb is written — only nouns and attributes.\n\nSo likely, the verb “is making” is implied.\n\nThen the structure is: [O] [S] [attribute] → where O = agent, S = object, attribute = describing the object\n\nBut in (1): bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\n→ “boozing is making the man that is always being blamed tired”\n\nSo: O: “boozing” (yaóa) → agent\nS: “the man” (NunéaymuNa) → object\nAttribute: “that is always being blamed” → NunéaymuNa → “man that is always being blamed”\n→ “tired” → biNgunman\n\nBut the word order is O S V → so O first, then S, then verb → but verb is missing.\n\nIn the sentence, there is no explicit verb — only the structure suggests it.\n\nThus, all sentences have the verb “is making” implied.\n\nThus, the pattern:\n[AGENT] is making [THE OBJECT THAT IS ALWAYS [VERBING]] [ADJECTIVE]\n\nOr: [AGENT] is making [S] [VERBING] [ADJECTIVE]\n\nNow in (17): balan ñalNga baNgul NumaNgu guniymuNagu bambunman\n\nBreak down:\n- balan → agent\n- ñalNga → noun → \"the quiet one\"? → likely \"quiet boy\" or \"quiet one\"\n- baNgul → subject (the man)\n- NumaNgu → “the man that is always being followed” → so S has attribute\n- guniymuNagu → “that is always searching”\n- bambunman → “fat man”\n\nWait — FOCUS: is this “making” or is it different?\n\nIn (2): “The strong man is blaming the mother that is always following death adders”\n\nSo verb is “blaming” → so “blaming the mother → agent is strong man”\n\nSo the verb is expressed with the agent.\n\nBut in (1): “boozing is making the man tired” → so the verb is implied.\n\nSo perhaps in all cases, the verb is “is making” — so the last element is the verb.\n\nBut in the sentence, the last segment is “bambunman” — which is an adjective.\n\nSo likely, the structure is:\nAGENT is making OBJECT [attribute]\n\nThus:\n- Agent: balan ñalNga → “the quiet one” (agent)\n- Object: baNgul NumaNgu → “the man that is always being followed” → subject\n- Attribute: guniymuNagu bambunman → “that is always searching for the fat man”\n\nBut “guriymuNagu” → “searching” → so “searching for the fat man”\n\nSo: “The quiet one is making the man that is always being followed search for the fat man.”\n\nBut “man that is always being followed” — that is the object.\n\nThen “searching for fat man” — that’s the verb.\n\nBut the pattern says OSV: object-subject-verb.\n\nBut here, object is “man that is always being followed”, subject is “quiet one”, verb is “searching” → not matching.\n\nWait — perhaps the verb is “is making” → agent makes object.\n\nThen the attribute is attached to the object.\n\nSo: “The quiet one is making the man that is always being followed [search for fat man]”\n\nBut “search for” is a verb, so it shouldn't be part of the adjective.\n\nBut in (10): balan duNan baNgul yiriñéilagu guniñu\n→ “dragonfly is searching for the stinging tree”\n\nSo “searching for” → guniñu → “searching for”\n\nSo the construction: V → A: “that is always Ving” → used to modify the noun.\n\nIn (10): “searching for” → is “guli” or “guliñu” — here, guniñu → so guni = search + -ñu → “searching”\n\nSo suffix indicates verb action.\n\nSo “guniymuNagu” → “searching” with -ymuNa → “that is always searching”\n\nSo guniymuNagu = “that is always searching”\n\nSo in (17): “guniymuNagu bambunman” = “that is always searching for the fat man”\n\nSo object (S) has attribute: “that is always searching for the fat man”\n\nTherefore, full sentence:\nThe quiet one is making the man that is always being followed search for the fat man.\n\nBut “quiet one” — is ñalNga a noun meaning “quiet one”?\n\nFrom (15): bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan → “the quiet boy is looking at the tired lizard”\n\n→ biñéiriñ = quiet; ñalNgaNgu → “quiet one” (with -Ngu)\n\nSo ñalNga → “quiet one” without -gu\n\nSo in (17): balan ñalNga → “the quiet one” (agent)\n\nbaNgul → “the man”\n\nNumaNgu → “man that is always being followed” → -gu → >2 syllables → valid\n\ngulinymuNagu → “that is always searching”\n\nbambunman → “fat man”\n\nSo: The quiet one is making the man that is always being followed search for the fat man.\n\nBut is “quiet one” a noun? In (15), \"the quiet boy\" — so yes.\n\nBut do we need to clarify?\n\nYes — final translation for 17:\n\nThe quiet one is making the man that is always being followed search for the fat man.\n\nNow (18): bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\n\n- bala → agent → “the fat doctor” or “a thing”\n- diban → adjective → “fat”\n- bilmbalmuNa → “the one that is always pushing stones” → “bilmba” + “-lmuNa” → “that is always pushing”\n\n- baNgun → article\n- biñéiriñéu → “the one that is always being looked at” → “looking at” — “biñéiri” = look; -ñéu → passive? — suffix\n- guniñu → “searching for” — guni = search; -ñu\n\nWait — from (13): bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\n→ “mother-in-law that is always pushing stones is looking at the smoke”\n\n→ “waymindu” = searching? No — waymin = healthy → waymindu = has many? → change\n\nIn (13): “dibanbilmbalNaymuNagu” → “that is always pushing stones” → so “diban” = fat; “bilmba” = pushing; “l-muNa” = always\n\nSo “dibanbilmbalNaymuNagu” = the one that is always pushing stones\n\nSimilarly, in (18): bilmbalmuNa → “that is always pushing stones”\n\nSo bilmbalmuNa = \"the one that is always pushing stones\"\n\nThen baNgun → article for the subject\n\nbiñéiriñéu → “that is always being looked at” → from (15): “biñéiriñ” = look → “biñéiriñéu” → passive → “being looked at”\n\nguliñu → “searching for”\n\nBut verb is “is making” → agent is bala\n\nSo: “The fat doctor is making the one that is always pushing stones look at the one that is always being looked at?”\n\nBut “guliñu” = “searching for”\n\nInconsistent.\n\nLook again:\n\nStructure: bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\n\nAgent: bala → doctor (fat)\nAttribute of agent: diban = fat → “fat doctor”\n\nThen object: bilmbalmuNa → “the one that is always pushing stones”\n\nThen: baNgun → article\nThen: biñéiriñéu → “that is always being looked at” → object attribute\nThen: guniñu → “searching for”\n\nBut “guliñu” = searching for → so final structure: “searching for [what]”?\n\nNo — in (10): balan duNan baNgul yiriñéilagu guniñu → dragonfly is searching for stinging tree\n\nSo here: “searching for” → with object?\n\nBut no object.\n\nSo perhaps “searching for” is modifying the subject.\n\nBut the subject is “the one that is always pushing stones”\n\nSo: “is making [S] [attribute] [searching for...]”\n\nBut the search is for what? Not specified.\n\nBut in (18): agent is making the one that is always pushing stones search for the one that is always being looked at?\n\nBut that doesn’t make sense.\n\nWait — from (15): \"quiet boy is looking at the tired lizard\" → biñéiriñ → looking at\n\nSo biñé", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13315.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "redacted_solution_hint_mask3", + "sample_index": 2, + "output": "Step 1: Identify article patterns and noun categories. \nFrom the examples, we see that:\n- All nouns are preceded by articles:\n - balan → women, dangerous animals, objects\n - bayi → men, animals\n - bala → all other things\n\nStep 2: Analyze the structure: OSV (Object-Subject-Verb), with attributes on the noun.\n\nA → V (\"make A\") → \"A-man\" \nV → A → \"that is always being Ved\" or \"that is always Ving Ns\"\n\nSuffix patterns:\n- Nouns ending in vowel with two syllables → end in -Ngu\n- Nouns ending in vowel with more than two syllables → end in -gu\n- Nouns ending in consonant → end in -Du\n\nStep 3: Decode each phrase.\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n- balan = object (a woman, dangerous animal, etc.) \n- ñalNga = noun (ñalNga = \"quiet\", \"still\"? But check structure) \n- baNgul = subject (man/animal) \n- NumaNgu = \"strong\" + -Ngu → \"strong man\" \n- guniymuNagu = \"that is always searching\" → V → A pattern: \"searching\" = guni-, -muNa → \"that is always searching\" \n- bambunman = \"fat\" (bambun → fat) + -man → \"fat man\"? But this is a noun ending in vowel with two syllables → should end in -Ngu? → bambunman ends in -man → no -Ngu → must be noun with attribute\n\nBut note: in sentence 8: “bayi gubimbulu biNgun baNgu gurugugu éagunman” → \"Booze is making the tired doctor fall asleep\" \nHere: gubimbulu → tired (tired = gubimbulu?) → ends in vowel (u), 4 syllables → would take -gu → yes → gubimbulu → tired → makes sense.\n\nSo: \n- \"that is always Xing\" → X + -muNa → e.g., guni + muNa → \"that is always searching\" \n- \"that is always being Xed\" → X + -n → e.g., yaóaNgu → \"always being blamed\" → \"being blamed\" → yaóa + Ngu → in (2) “blaming the mother that is always following death adders” → “following” = guli + -muNa → guliNaymuNa → \"that is always following\" → yes.\n\nSo pattern:\n- A + Ngu → \"the A-man\"\n- Verb + -muNa → \"that is always being V-ed\" or \"that is always V-ing\"\n - For V-ing → append -muNa\n - For being V-ed → V + -n → e.g., yaóaNgu → being blamed\n\nBut in (2): “the strong man is blaming the mother that is always following death adders”\n> balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu \nBreaking down:\n- \"yabu\" = strong\n- \"bimabanéalNaymuNa\" = \"the man that is always being strong\" → no → wait — actually: “bimabanéalNaymuNa” → bimabaneal → \"strong\"? But it's a noun? \n\nMore accurately: in (2): \"bimabanéalNaymuNa\" → subject is \"strong man\" → “bimabanéal” → almost \"strong\" → but look: “yabu” = strong → so subject = \"strong man\" → \"bimabanéalNaymuNa\" = “strong man” → 'bimabanéal' → if “yabu” is the strong, why is the man described with bimabanéal? \n\nWait: perhaps “bimabanéal” is “man that is always being strong”? No — clearly, the structure is: \nS (strong man) = “yabu” + “baNgun” → no — “balan” is object, “yabu” is adjective on subject?\n\nActually look: sentence 2: \n\"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"the strong man is blaming the mother that is always following death adders\" \nSo: \n- balan → object (what is being blamed?) \n- yabu → adjective on subject → “strong man” → “yabu bimabanéalNaymuNa” = strong man \n→ bimabanéalNaymuNa → N → \"the man that is always being strong\"? — but “being strong” doesn’t make sense. \n\nMore likely: “yabu” = “strong” → \"the strong man\" → subject \n\"bimabanéalNaymuNa\" → infected with suffix → \"that is always strong\"? → no — it ends in -NaymuNa → strong → winning? \n\nWait: in (1): \"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"booz is making the man that is always being blamed tired\" \n→ \"yaóa\" = being blamed → “yaóa” + “NunéaymuNa” → “the man that is always being blamed” → yes → “yaóa” + \"NunéaymuNa\" = being blamed → so verb + -NaymuNa → that is always being Ved → “being blamed”\n\nSimilarly, in (2): “guliNgu Nunéañu” = “following death adders” → “guli” + “NaymuNa” → “that is always following” → yes → guli + NAYmuNa\n\nSo rule:\n- \"V + NAYmuNa\" = \"that is always V-ing\" \n- \"V + NajmuNa\" → but in (1): yaóa + NunéaymuNa → yes \n- also: \"V + n\" → being V-ed → e.g., yaóaNgu → being blamed? But yaóaNgu → same as yaóa → but with -N? → \"yaóaNgu\"\n\nIn (1): “yaóa” + “NunéaymuNa” = being blamed → which is a verbal adjective \nIn (2): “yaóaNgu” = “the mother that is always being blamed” → wait no — (2): “yaóaNgu” is the adjective on the mother → “the mother that is always being blamed” → “yaóaNgu” → being blamed → meaning: “the mother that is always being blamed” → so “yaóaNgu” = “that is always being blamed” \nIs “yaóaNgu” = “being blamed” → yes → “N” → being → “N” vowel → becomes -N → in the article area → but N + gu?\n\nWait: in (2): “baNgul yaóaNgu” = “the mother that is always being blamed” \nSo: “yaóaNgu” = “that is always being blamed” → so “being blamed” = “yaóa” + “N” → conjugated to “-N” → “yaóaN” → but it's “yaóaNgu” → why -gu?\n\nNote: “yaóaNgu” → ends in vowel (u), and has 3 syllables → more than two → should end in -gu → yes → so “yaóaNgu” = “being blamed” → adjective → implies “that is always being blamed”\n\nThus: \n- “V + -NaymuNa” = “that is always V-ing” \n- “V + -Nagu” = “that is always being V-ed”\n\nSo: \nFor (17): \nbalan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ object = balan + ñalNga → “the quiet woman” \n→ subject = baNgul + NumaNgu → “the strong man” \n→ verb = guniymuNagu → “that is always searching” \n→ attribute = bambunman → “fat” (bambun → fat)\n\nSo: “The quiet woman is making the strong man that is always searching fat.”\n\nWait — is it making? “A → V” → “make A” \nSo “balan ñalNga” → “quiet woman” \n“baNgul NumaNgu” → “strong man” \n“guniymuNagu” → “that is always searching” \n“bambunman” → “fat” → so object → “fat man”?\n\nBut structure: OSV → Object-Subject-Verb → “The quiet woman is making the strong man that is always searching fat.”\n\nBut “making the man that is always searching fat” → means the man becomes fat → yes.\n\nSo (17): The quiet woman is making the strong man that is always searching fat.\n\nBut need to check noun endings.\n\n“ñalNga” → begins with vowel → 2 syllables? ñal → 2 syllables → ends in vowel → so should take -Ngu? \nBut it's “ñalNga” → ends in a → vowel → 2 syllables → should end in -Ngu? → but it’s “ñalNga” → no -gu or -Ngu → contradiction?\n\nWait: noun suffix rule: \n- if ends in vowel and has two syllables → -Ngu \n- if ends in vowel and more than two syllables → -gu \n- ends in consonant → -Du\n\n“ñalNga” → ñal → 2 syllables → ends in a → vowel → must take -Ngu → so should be \"ñalNgaNgui\"? But form is “ñalNga” → so perhaps it’s not the full noun.\n\nWait: from (15): “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” \n→ “the quiet boy is looking at the tired lizard” \n“biñéiriñ” → “quiet” → has 2 syllables? → ends in vowel → should take -Ngu → appears as “biñéiriñ” — no -Ngu → unless it’s not the adjective.\n\nBut look: “biñéiriñ” → subject? → “the quiet boy” = “bayi biñéiriñ” → so “biñéiriñ” = “quiet” → 2 syllables → should end in -Ngu → but doesn't → contradiction?\n\nUnless the adjective attaches directly.\n\nWait: in (15): “biñéiriñ” → with no suffix → but must have → check the full phrase.\n\nActually: “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” \n→ “the quiet boy is looking at the tired lizard” \n→ “biñéiriñ” → quiet → so → adjective → 2 syllables → ends in vowel → should take -Ngu → but it is “biñéiriñ” — no -Ngu → contradiction?\n\nUnless it’s “biñéiriñ” is the full form and suffix is implied.\n\nWait — look at (13): “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” \n→ “the mother-in-law that is always pushing stones is looking at the smoke” \n“dibanbilmbalNaymuNagu” → “that is always pushing stones” → diban → pushing → \"diban\" + \"bilmbal\" → \"pushing\" → \"dibanbilmbalNaymuNa\"? → has -NaymuNa → yes → pushing = diban + NAYmuNa → so the noun is “dibanbilmbalNaymuNa” → that is \"the mother-in-law that is always pushing stones\"\n\nSo the pattern is: the noun ends with the adjective + NAYmuNa → so \"that is always V-ing\" → V + NAYmuNa\n\nSimilarly: in (15): “biñéiriñ” → quiet → adjective → should be → “biñéiriñ” → but no -Ngu → unless “biñéiriñ” is not the adjective.\n\n“biñéiriñ” → 2 syllables? bi-ñé-i-ri-ñ → more than 2 → 5 syllables? → bi-ñé-i-ri-ñ → 5 → yes → ends in vowel → more than two syllables → should end in -gu → so should be “biñéiriñgu” → but it is “biñéiriñ” → contradiction?\n\nWait — perhaps the adjective is \"biñéiriñ\" and it's an exception — or the suffix is only for nouns with the same structure.\n\nWait — in (15): “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” \n→ object = bayi (boy) \nsubject = biNgun (tired) → \"tired man\"? → “biNgun” → ends in vowel → 2 syllables → should be -Ngu → yes → “biNgun” → “tired” → so “biNgun” = “tired” \n→ “baNgul” = subject → “lizard” \n→ “ñalNgaNgu” = “quiet” → ends in u → vowel → 3 syllables? ñal-nga-? → no: “ñalNgaNgu” → after “N” → “-Ngu” → so it ends in a vowel → and after N → so it has -Ngu suffix → so noun → “quiet one” → “ñalNga” base + -Ngu → yes → 3 syllables → two or more? → yes → so -Ngu → ok.\n\nSo suffix attached to the noun → so “ñalNga” → with -Ngu → “ñalNgaNgu”\n\nSo rule: the noun gets the suffix based on syllables and ending.\n\nNow back to (17): \nbalkan ñalNga → balan → woman → object \nñalNga → \"quiet\" → 3 syllables? ña-lN-ga → 3 syllables → ends in vowel → more than two → should take -gu → so should be “ñalNgaGu” → but it's “ñalNga” → so must be missing suffix?\n\nBut in the sentence: “balan ñalNga baNgul NumaNgu guniymuNagu bambunman”\n\n“balian” → is “bala” or “balan” → “bala” is other things, “balan” = women/animal → so “bala” → used for objects?\n\nBut “bana” is not here → so “bala” might be used broadly.\n\nWait — in (17): \"balan\" → object → so woman \n\"ñalNga\" → adjective → \"quiet\" → 3 syllables → ends in vowel → should have -gu → so base would be \"ñalNga\" → forms \"ñalNgaGu\" → but written as \"ñalNga\" → so likely \"ñalNga\" is the base and suffix is implied — or the suffix is attached in the structure.\n\nBut look at (14): “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” → “mother-in-law that is always pushing stones” → “dibanbilmbalNaymuNagu” → \"pushing stones\" — has NAYmuNa → “pushing” = diban + NAYmuNa\n\nSimilarly, in (15): “biñéiriñ” → “quiet” → no suffix → but in (15) it’s “biñéiriñ” and “biNgun” → “tired” → “biNgun” → ends in vowel, 2 syllables → must have -Ngu → so “biNgun” → yes → so when a noun ends in vowel and has two syllables → takes -Ngu → so “biNgun” → “biNgun” → yes.\n\n“biñéiriñ” → 5 syllables → ends in vowel → more than two → should take -gu → so “biñéiriñgu” — but it is written as “biñéiriñ” → contradiction?\n\nUnless “biñéiriñ” is not the adjective.\n\nWait — in (15): “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” \n→ “the quiet boy is looking at the tired lizard” \nSo: “bayi” = boy \n“biñéiriñ” = quiet → so adjective \n“biNgun” = tired → subject? → “biNgun” → should end in -Ngu → it does — “biNgun” → with -N → so “biNgun” = “tired” → and ends in vowel → 2 syllables → yes → so it has suffix.\n\nBut “biñéiriñ” → no suffix → even though 5 syllables → so exception? Or perhaps the adjective is attached without suffix?\n\nBut in (2): “bimabanéalNaymuNa” → “that is always being strong” → “bimabanéal” + “NaymuNa” → the noun has -NaymuNa → so focused on agent.\n\nBack to (17): \n\"bala\" is used for non-women, non-animals → but here \"balan\" is used for woman → so must be \"quiet woman\" → but “ñalNga” → quiet → so base noun → must take suffix → unless the adjective is a separate stem.\n\nPerhaps the \"object\" is \"quiet woman\" → so \"bala\" or \"balan\" — here \"bala\" is not used — \"balan\" is used → so object is female.\n\nNow: “ñalNga” → quiet → needs suffix → 3 syllables → vowel → → should be “ñalNgaGu” → but written as “ñalNga” → likely typo or it's allowed.\n\nAlternatively, “ñalNga” is the full form → and suffix not appended for adjectives? But in other cases it is.\n\nIn (1): “NunéaymuNa” → “always being blamed” → “yaóa” + “NaymuNa” → so verb + -NaymuNa → not on noun.\n\nSo", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11889.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "redacted_solution_hint_mask3", + "sample_index": 3, + "output": "We are given a set of Dyirbal sentences with translations, and we are to translate three new sentences (17, 18, 19) into English, using the established linguistic rules.\n\nStep 1: Understand the structure.\n\n- Word order is OSV (Object – Subject – Verb).\n- Nouns are preceded by articles:\n - balan: women, dangerous animals/objects\n - bayi: men, animals\n - bala: all other things\n- The verb–object structure is key: verb followed by the verb-modifying attribute suffix.\n- Adjective-like attributes are formed with:\n - V → A: “that is always being Ved” or “that is always Ving”\n - Ending patterns:\n - -n → -l-muNa → “that is always being [V]ed”\n - -ñu → -y-muNa → “that is always [V]ing”\n - -ñu → -nay-muNa → “that is always [V]ing”\n - “that is always Ving N” → V + -N + -nay-muNa → e.g., \"that is always following the mother\" → \"baNgul yaóaNgu banéalmuNagu munduman\"\n- The suffix -Ngu appears on nouns ending in vowel with 2 syllables; -gu on those with >2 syllables; -Du if ending in consonant.\n- “make A” construction: A-man → used when a substance causes a change in a person/entity.\n\nNow, break down each target sentence:\n\nSentence 17: \n**balan ñalNga baNgul NumaNgu guniymuNagu bambunman**\n\n- balan → woman\n- ñalNga → noun; agrees with \"balan\" → subject (woman) → must be a woman with attribute\n- baNgul → men/animals → subject (subject is \"baNgul\", so this is the person being affected)\n- NumaNgu → “the strong one” → subject of the action (the strong one)\n- guniymuNagu → “that is always searching”\n- bambunman → “fat”\n\nSo: \n→ A woman who is always searching (guniymuNagu) is making the strong man (NumaNgu) fat (bambunman).\n\nBut \"make A\" structure: \"A-man\" → so \"makes the strong man fat\" → “makes the strong man fat” → “is making the strong man fat”\n\nBut here, the object is \"baNgul\", so \"the strong man\", and the verb is \"guniymuNagu\" → \"is always searching\" → that's a state, not a verb of causation.\n\nWait — there's a pattern from (1), (5), (8), etc. where a substance (e.g. booze) \"is making X tired\" → \"is making the X tired\" → so “is making” is a transitive verb acting on a subject.\n\nBut here, \"balan ñalNga\" → woman, and the structure is: \n[balan ñalNga] [baNgul NumaNgu] [guniymuNagu bambunman]\n\nBut there’s no clear \"make\" verb.\n\nAlternatively, look at sentence 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" → “Booze is making the man that is always being blamed tired.” \n→ so “denial” → “being blamed” → “-nay-muNa” → “that is always being blamed”\n\nSo in sentence 17: \nguniymuNagu → ends in -u? → \"guniymuNagu\" → ends in \"u\", so can form -nay-muNa → “that is always searching”\n\nThus: guniymuNagu → “that is always searching” → attribute of the woman.\n\nAnd bambunman → “fat”\n\nSo the woman is (that is always searching) → making the strong man fat?\n\nBut no “make” verb.\n\nWait — look at (3): \n\"balan waymin bambun baNgu éugaNgu éamiman\" → \"Sugar is making the healthy mother-in-law fat.\"\n\n→ So \"balan waymin\" = sugar \n→ \"baNgu éugaNgu\" = the healthy mother-in-law \n→ \"éamiman\" = fat → \"making fat\"\n\nSo the causative verb is implied — the first noun (X) causes Y to become Z.\n\nSo in 17: \n\"balan ñalNga\" = the woman (who is always searching) \n→ but is it sugar or booze? No — balan is for women, and this whole thing has no causative marker — but \"make\" is present in the grammar.\n\nBut in sentence 17, the object is baNgul NumaNgu → “the strong man” → and the attribute is guniymuNagu bambunman → “that is always searching and fat”?\n\nWait — “guniymuNagu” + “bambunman” → “that is always searching and fat” → but in (1), it's “being blamed” → “NunéaymuNa” → “that is always being blamed”\n\nSo “guniymuNagu” → similar to “guni” → “searching” → “that is always searching”\n\nSo perhaps the structure is: \nX → Y → Z → \"X is making Y (that is always searching and fat)\"\n\nBut here, the object is baNgul NumaNgu → the strong man\n\nSo: “The woman that is always searching is making the strong man fat?”\n\nBut “fat” → “bambunman” → but in (3), “bambun” → “fat” → so “bambunman” → “fat man” → “the strong man is fat”\n\nBut in (1), “biNgunman” → “tired man” → so “man” with attribute.\n\nSo “baNgul NumaNgu” is “the strong man” → and “guniymuNagu bambunman” → “that is always searching and fat”?\n\nBut that would be the strong man having the attributes. So the woman is making the strong man fat?\n\nBut no “make” verb used — yet in (3), sugar makes mother-in-law fat.\n\nSo in (17), “balan ñalNga” → the woman → causes the strong man → fat?\n\nBut why is “guniymuNagu” attached?\n\nPossibility: “guniymuNagu” is not modifying the man — it's the woman.\n\nSo: “The woman who is always searching is making the strong man fat.”\n\nBut is “guniymuNagu” the woman’s attribute?\n\nYes — from pattern: V → A: V-ification → “that is always Ving”\n\nSo “guniymuNagu” → “that is always searching”\n\nSo the woman is always searching.\n\nThus: The woman that is always searching is making the strong man fat.\n\nNow sentence 18: \n**bala diban bilmbalmuNa baNgun biñéiriñéu guniñu**\n\n- bala → thing (non-woman, non-man)\n- diban → fat\n- bilmbalmuNa → “that is always pushing”\n- baNgun → subject → “the one who is”\n- biñéiriñéu → “lizard”\n- guniñu → “little feather”\n\nSo: \nA fat thing (diban) that is always pushing (bilmbalmuNa) is following (baNgun) the lizard that is looking for the little feather?\n\nWait — structure is OSV.\n\nO: bala diban bilmbalmuNa → fat thing that is always pushing \nS: baNgun biñéiriñéu → the lizard \nV: guniñu → little feather\n\nBut “following” is not in the verb — but from (12): \n\"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"The fat doctor is pushing the big stone.\"\n\nSo here: “diban” → fat → “is pushing” → “bilmbalmuNa” → “that is always pushing” → so same structure.\n\nSo: “The fat thing that is always pushing is following the lizard that is looking for the little feather?”\n\nBut “guli” → “searching” → here “guniñu” → “little feather” → so “looking for”\n\nBut in (10): “bala yila wura baNgul bargandu biNgundu guniñu” → “The tired wallaby is searching for the little feather.”\n\nSo guniñu = little feather → “searching for the little feather”\n\nBut here, the verb is “biñéiriñéu” → “lizard” → so “the lizard is looking for the little feather”\n\nSo the object is “guniñu” — so verb is “is looking for”\n\nBut “following” → look at (9): \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → “The mother-in-law that is always pushing stones is looking at the smoke.”\n\n→ so “looking at” → “biñéiriñéu” → “looking at”\n\nSo “baNgun biñéiriñéu” = the lizard\n\nThen “guniñu” = the little feather\n\nBut what verb? The verb is missing.\n\nIn OSV, verb is last.\n\nSo the verb must be “is looking for” → “guniñu” → but in (10), “wura” → “searching for” → so “wura” = searching for\n\nHere, no verb?\n\nWait — the token order: \nbala diban bilmbalmuNa baNgun biñéiriñéu guniñu\n\nSo:\n- O: bala diban bilmbalmuNa → fat thing that is always pushing\n- S: baNgun biñéiriñéu → lizard\n- V: guniñu → little feather\n\nSo verb is \"guniñu\"? But \"guniñu\" means “little feather”\n\nBut from (10): “wura” → “searching for” → not “little feather”\n\nSo likely, “guniñu” is the object, and the verb is “is searching for” — but we don’t have it.\n\nWait — perhaps “biñéiriñéu” is the verb?\n\nNo — “biñéiriñéu” is a noun (lizard)\n\nOnly nouns and articles are used.\n\nSo how do we get verbs?\n\nCheck the patterns:\n\nIn sentence 1: “baNgul” + “yaóaNgu” → “being blamed” → “NunéaymuNa” → so “being blamed” → “-nay-muNa”\n\nIn sentence 5: “malayigara” → “the smoke” → “making the scorpion tired” → “biNgunman”\n\nSo verb: “tired” → “biNgunman”\n\nIn sentence 15: “biñéiriñ” → “the quiet boy” → “is looking at” → “biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” → “The quiet boy is looking at the tired lizard.”\n\nSo “biñéiriñ” = boy → “is looking at” → verb is “biñéiriñ” → but “biñéiriñ” is a noun.\n\nAh! Mistake.\n\nLook: “biñéiriñ” → “quiet” → in (15): “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” → “The quiet boy is looking at the tired lizard.”\n\n→ so “biñéiriñ” is the adjective → “quiet boy” → subject → “is looking at” → verb is implied by context.\n\nBut “is looking at” is not a separate verb — the verb is “biñéiriñ” = “quiet” → no.\n\nWait — the structure is: [subject] [adj] [verb]?\n\nBut in (15): \"biñéiriñ biNgun\" → \"quiet boy\" → and then \"baNgul\" → \"lizard\" → \"mugurugu buóan\" → “tired” → so “is looking at” is not expressed.\n\nBut in (10): “bala yila wura baNgul bargandu biNgundu guniñu” → wallaby is searching for the little feather → “wura” = searching for\n\nSo “wura” = verb “searching for” → noun meaning.\n\nSo in (18): “guniñu” → could mean “is looking for” → but it's a noun.\n\nWait — in (10), “wura” = searching for → so “wura” → verb meaning.\n\nSimilarly, in (15): “biñéiriñ” = quiet → no.\n\nBut in (9): “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” → “The mother-in-law that is always pushing stones is looking at the smoke.”\n\n→ “waymindu” → “that is always pushing” → “dibanbilmbalNaymuNagu” → “pushing stones” → “is looking at” → “buóan” → smoke → so “is looking at”\n\n“biñéiriñéu” → would be “lizard” → but only if it’s a noun.\n\nSo in (18): “baNgun biñéiriñéu” → “the lizard” → the subject\n\n“guniñu” → “the little feather”\n\nSo if the verb is “is looking for” → then “guniñu” must be the object, and “is looking for” must be a verb phrase.\n\nBut “guniñu” is a noun.\n\nOnly possible if “guniñu” is the object of a verb formed from a root.\n\nBut from (10): “wura” → “searching for” → “wura” → verb (searching for)\n\nSimilarly, in (13): “dibanbilmbalNaymuNagu” → “always pushing stones”\n\nIn (18): “bilmbalmuNa” → “that is always pushing” → verb preposition?\n\nNo — “bilmbalmuNa” → “that is always pushing” → so the noun “diban” → fat → “that is always pushing”\n\nSo “bala diban bilmbalmuNa” = the fat thing that is always pushing\n\nThen S: “baNgun biñéiriñéu” → the lizard\n\nThen V: “guniñu” → little feather\n\nSo what is “guniñu”?\n\nIn (10): “wura” → “searching for” → so “wura” is a verb form.\n\nIn (15): “bali” → “is looking at” → not captured.\n\nBut in (9): “looking at” — “biñéiriñéu” — could “biñéiriñéu” be the verb?\n\nNo — “biñéiriñéu” = “lizard”\n\nOnly forms like “guli” or “wura” are verbs.\n\nSo likely, in (18), “guniñu” is the object, and the verb is “is searching for” — which is “wura” — but “wura” is missing.\n\nWait — in the sentence: “bala diban bilmbalmuNa baNgun biñéiriñéu guniñu”\n\nNo verb root.\n\nPerhaps “biñéiriñéu” is a verb form?\n\nBut from (15): “biñéiriñ biNgun baNgul” → “boy is looking at” — “biñéiriñ” is adjective.\n\nIn (15): “biñéiriñ” → “quiet” → so not verb.\n\nIn (19): “bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan”\n\n→ “The boy is looking at the smoke that is always being followed”\n\n→ “bargan” → “quiet” → adjective\n\nSo “gubimbuluNunéanaymuNagu” → “that is always being followed”\n\nSo verb forms are in suffixes like -nay-muNa → for being V-ed.\n\nSo back to (18): the only verbs are those forming -nay-muNa or -y-muNa or -ñu.\n\nIn (18), “guniñu” → likely “little feather” → object.\n\nThe verb must be missing — but it’s the last word.\n\nUnless “guniñu” is the verb.\n\nBut “guniñu” → in (10): “wura” → “searching for”\n\nIn (10): “wura” → “searching for” → so “wura” is a verb.\n\nSimilarly, “mugurugu” → “falling asleep” → in (8) → “gurugugu” → “tired” → “éagunman” → “falling asleep”\n\nSo “guri” → “tired” → “-nay-muNa” → “being tired”\n\nOnly patterns: verbs are in roots that form attributes.\n\nSo in (18), “guniñu” = “little feather” → object.\n\nSo the structure: [O] [S] [V] = fat thing that is always pushing — following — the lizard — looking for the little feather?\n\nNo — “guniñu” is last.\n\nOnly possible if “guniñu” is the verb, which it’s not.\n\nWait — perhaps the verb is “look” or “follow” — and “biñéiriñéu” is the object?\n\nNo.\n\nFrom (9): “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” → “mother-in-law that is always pushing stones is looking at the smoke”\n\nSo subject: mother-in-law that is always pushing \nverb: “looking at” \nobject: smoke\n\nBut “looking at” is not a word — implied.\n\nSimilarly, (10): “searching for” — “wura”\n\nSo in (18), the verb is likely “is searching for” — which comes from “wura”\n\nBut “wura” is not in the sentence.\n\nUnless “guniñu” is being used as the object of a verb meaning “searching for”.\n\nSo the fat", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + 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Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The word order is OSV (O: object, S: subject, V: verb), NA (N: noun, A:\nadjective).\n A →V (‘make A’): A-man.\n V →A: V ‘that is always being Ved’ ‘that is always Ving Ns’\n -n -l-muNa N-. . . -l-Nay-muNa\n -ñu -y-muNa N-. . . -nay-muNa\n Every noun is preceded by an article:\n O S\n balan baNgun women, dangerous animals and objects\n bayi baNgul men, animals\n bala baNgu all other things\n\n The subject and its attributes get the ending\n • -Ngu, if the word ends in a vowel and has two syllables;\n • -gu, if the word ends in a vowel and has more than two syllables;\n • -Du, if the word ends in a consonant; D is a stop articulated in the same place in the mouth as the final sound of the word.\n\n (a) The grasshopper is neither a woman nor a dangerous animal, but takes the same article,\n so it must be the “old woman” from the myth. The linguist thought that baNgun\n bundiñéu in example (14) was an error.\n\n (b) 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n [TARGET ANSWER REDACTED]\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n [TARGET ANSWER REDACTED]\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n [TARGET ANSWER REDACTED]\n\n (c) 20. The little wallaby is looking at the dragonfly.\n bayi yiriñéila baNgul bargandu wuraNgu buóan.\n 21. The aunt that is always being followed is bending the feather.\n bala yila baNgun mugunanéagu banéalmuNagu waóuman.\n 22. The sleeping possum is ignoring the loud noise.\n bala muNga baNgul midindu éagundu Naéin.\n 23. The caterpillar is searching for the man that is always carrying stones.\n bayi yaóa dibandimbanaymuNa baNgul bayimbambu guniñu.\n\nTenth International Olympiad in Linguistics (2012). 2\nIndividual Contest Solutions", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "redacted_solution_hint_mask0", + "sample_index": 0, + "output": "We are given a set of Menominee verb forms and their English translations, along with structural rules. The task is to translate four English sentences into Menominee, using the pattern observed in the provided examples.\n\nStep-by-step derivation:\n\n1. **I begin to eat it** \n - \"begin\" is associated with root *kewǣp*, as in *kewǣpeqtaq* (\"we1+2 begin\") and *wǣpohnæw* (\"he begins walking\"). \n - \"to eat\" is linked to *-aht*, as seen in *kepītahtæq* (\"we1+2 come eating it; we1+2 bring it in our mouths\") and *ketāwahtæq* (\"we1+2 bite, gnaw a hole in it\"). \n - In *ketāwahtæq*, \"bite\" and \"gnaw\" are associated with *-aht*, which is \"by mouth\". Thus, *-aht* = \"by mouth\" or \"eating\". \n - So, \"begin to eat\" → *kewǣp* + *aht* → *kewǣpaht*? \n - However, the given solution in the guidance has: **new¯æpahtan** \n - Look at *nekāwāhpem* (\"I fall over laughing\") — contains *ne-* (I), *kā* (movement), *wāh* (fall), *pem* (laughing). \n - Consider that *newāckesan* = \"I cut around it\" — *new* (I), *āck* (cut around). \n - Compare: *new¯æpahtan* — I + *¯æpaht* \n - \"begin\" root: *wǣp*, which is *wǣpohnæw* (\"he begins walking\") → *wǣp* + *ohnæw* \n - We need a verb combining *begin* and *eat* → something with *wǣp* and *aht*? \n - But *wǣp* is not directly linked to eating. \n - However, in the provided solution: **new¯æpahtan** \n - Break it: *new* = I (from nepītohnæm → I walk → ne-) \n - *¯æp* = from *wǣp*? Possibly *wǣp* with vowel change? \n - Note: vowel length rule: if both first vowels are short, second becomes long. \n - In *wǣpohnæw*, both vowels are short → second becomes long? But *wǣpohnæw* has *ohnæw*, so not always. \n - Alternatively, is *¯æp* a derived form of *wǣp*? \n - In *wackōhnæw* → \"he walks roundabout\" → *wack* is related to \"around\". \n - But *wǣp* is the root for \"begin\". \n - Now, look at *ketāwahtæq* — \"we1+2 bite, gnaw a hole in it\" → contains *aht* (by mouth) \n - So eating = *aht* \n - \"I begin to eat\" → I + begin + eat \n - What is the beginning verb? *kewǣp* is used in \"we1+2 begin\", so *kewǣp* is the root. \n - But *new¯æpahtan* — could be *ne-* (I) + *wǣp* (begin) + *aht* (by mouth) → *ne* + *wǣp* + *aht* → *newǣpaht* \n - With vowel length: rule says if both first vowels are short, second becomes long. In *newǣpaht*, first two vowels: *e*, *a* — both short? \n - But *wǣp* has *a* — if both are short, second vowel becomes long → so *wǣp* → *w¯æp*? \n - Yes: *wǣp* → if first two vowels short → *w¯æp* \n - So *new¯æpahtan* = I + *w¯æp* (begin) + *aht* (by mouth) → \"I begin to eat it\" \n - Matches.\n\n2. **we1+2 lay it flat by hand** \n - \"lay flat by hand\" → transitive verb, \"by hand\" = *-en* \n - \"lay flat\" → possibly related to \"place down\", \"put down\" \n - Look at: *nepītohnæm* = I walk here \n - *pahkǣsam* = he cuts it off \n - *kekēskahtæq* = we1+2 bite it through \n - *kek¯awenæq* is given as the solution in guidance → “we1+2 lay it flat by hand” \n - *kek* = we1+2 \n - *aw* = ? \n - *en* = lay down? \n - *-en* = by hand — appears in *nekǣtahan* = I pry it out by tool → *-aht*, not *-en* \n - *nekǣtahan* = prying → *-tahn* → but *-en* is by hand \n - *nepītohnæm* = I walk here → *tohn* → \"here\" \n - Is there a root for \"lay\" or \"place\"? \n - *kēskenam* = he breaks it through by hand → *kēs* + *ken* → *ken* = through? \n - *kewǣpānæhkæq* = we1+2 begin to dig → *pānæhkæ* = digging \n - *pāhkaham* = he opens it by tool → *pāhka* + *ham* → tool \n - *tawǣsam* = he cuts a hole → *taw* + *a* + *sam* \n - But in guidance: *kek¯awenæq* = we1+2 lay it flat by hand \n - So: *kek* = we1+2 \n - *aw* — possible root for \"place\"? \n - *aw* could be a base meaning \"to place\", \"to lay\" \n - *en* = by hand (as in *-en*) — appears in *-en* marking \n - Look at *kawāham* = he fells it by tool → *kaw* + *āham* → *āham* = by tool? \n - *pāhkeqtaw* = he opens up — *pāhk* + *eqtaw* \n - But *kepītahtæq* = we1+2 come eating — \"come eating\" \n - No direct “lay flat” \n - But *kek¯awenæq* seems to match structure: \n - *kek* = we1+2 \n - *aw* — verb root (possibly “lay”) \n - *en* = by hand \n - *-næq* = suffix? \n - Compare to *kawāham* → *kaw* + *āham*, so second vowel is long? \n - In *kek¯awenæq*, we have *¯a* → long a → so first two vowels short → second becomes long? \n - In *aw*, if both first vowels are short, second becomes long → so *aw* → *¯aw* \n - But *kek¯awenæq* has *¯a*, not *¯aw*. \n - Wait: *kek¯awenæq* — vowel: k-e-k-¯a-w-e-n-æ-q \n - First vowel: e (short), second: a (becomes long → ¯a) — yes, rule applies: if both first two are short, second becomes long. \n - So root *aw* → becomes *¯aw* → but word is *¯awen* → so *¯aw* is root with long vowel. \n - Thus, *kek¯awenæq* = we1+2 lay it flat by hand → makes sense.\n\n3. **he digs a hole** \n - \"he digs\" → verb for digging \n - Looking at examples: *kewǣpānæhkæq* = we1+2 begin to dig → *pānæhkæ* \n - Structure: *pānæhkæ* → *pān* = dig? *-æhkæ* = digging? \n - In guidance: solution is *taw¯anæhkæw* \n - So: *taw* = ? \n - *tawǣsam* = he cuts a hole → *taw* + *a* + *sam* → cutting a hole \n - So *taw* = cut, pierce? \n - But digging → not cutting \n - *kewǣpānæhkæq* = we1+2 begin to dig → so *pānæhkæ* = digging \n - So digging = *pānæhkæ* \n - But with subject: *he* → not *we1+2* \n - So *he digs* → must be *he* + *digging* \n - In the list: *kewǣpānæhkæq* → we1+2 begin to dig → root *pānæhkæ* \n - *kew* = we1+2 \n - So *pānæhkæ* = digging \n - Then *he* → must use a root with *k* or *p*? \n - *wackōhnæw* = he walks roundabout → *wack* (around) \n - *ket¯ohnæw* = he walks out \n - *kawāham* = he fells it by tool \n - *pāhkaham* = he opens it by tool \n - Any verb for \"dig\"? \n - *kewǣpānæhkæq* has *pānæhkæ* → so *pānæhkæ* is the verb form for \"digging\" \n - But for \"he digs\", we need to remove *kew-* (we1+2) \n - So is *pānæhkæ* used with *he*? \n - Look at guidance: he digs a hole → *taw¯anæhkæw* \n - *taw* = cut a hole → but *cut* is not same as *dig* \n - *taw* + *an* → *tawan*? \n - *taw¯anæhkæw* → *taw* (cut), *¯an* (long a), *æhkæ* (digging), *w*? \n - But *w* is at end? \n - Final form: *taw¯anæhkæw* = he digs a hole? \n - Compare to *kewǣpānæhkæq* → we1+2 begin to dig \n - Root is *pānæhkæ* → *pān* + *æhkæ* → digging \n - But *taw¯anæhkæw* — if *taw* is base, and *anæhkæ* is digging? \n - But in *kawāham*, *kaw* = fell → *a* (by tool) \n - In *tawǣsam*, *taw* = cut → *a* (hole) \n - So *taw* = cut → similar to dig? \n - But \"dig a hole\" → \"cut a hole\"? Close. \n - Is *taw¯anæhkæw* = he cuts a hole? But \"cuts a hole\" is not \"digs a hole\" \n - However, in Menominee, \"dig a hole\" may be expressed by a form with *taw* root? \n - Alternatively, is *pānæhkæ* used for digging, and with *he* = *k*? \n - But no example for he + dig \n - Guidance gives *taw¯anæhkæw* \n - Note: *taw¯anæhkæw* — *taw* = cut → *an* → long a → *anæ* → then *hkæw* \n - But *kewǣpānæhkæq* = begin to dig → *pānæhkæ* \n - So perhaps *pānæhkæ* is root for digging \n - But for he, what root? \n - Another possibility: dig = *pān* \n - But he digs → *pānæhkæw*? \n - But guidance solution is *taw¯anæhkæw* \n - We must accept that the given solution is *taw¯anæhkæw* \n - And since *taw* means \"cut a hole\", and \"dig a hole\" is similar, perhaps it's acceptable \n - Also, the vowel length: both first vowels short → second becomes long \n - In *taw¯anæhkæw*: t-a-w-¯a-n-æ-h-k-æ-w \n - First two vowels: a, w? w is consonant \n - First vowel: a (in *taw*) → first vowel short \n - Then *¯a* → long a → so does the rule apply? \n - Rule: if both first vowels in the word are short, second becomes long \n - So in *taw¯anæhkæw*, vowels: a (short), ¯a (long) → so second vowel is long because first is short? \n - Since only one vowel at start, first vowel is a — short \n - Only one vowel? *taw* — first vowel a (short), next is ¯a (long) — so the rule applies: if both first two vowels are short → second becomes long \n - Here, only one short vowel at beginning → so the rule may not trigger? \n - But in *kewǣpānæhkæq*: k-e-w-ǣ-p-ā-n-æ-h-k-æ-q \n - First two vowels: e, ǣ (both short) → so second becomes long → *ā* \n - So rule applies when first two vowels are short → second becomes long \n - In *taw¯anæhkæw*, first vowel a (short), second vowel ¯a (long) → so the second is long → rule applied \n - Thus, the word has a long vowel due to rule \n - And *taw* = cut → may be used for \"dig\" \n - Perhaps in Menominee, \"dig a hole\" is via *taw* root \n - Or it's a different root, but solution given is *taw¯anæhkæw* \n\n4. **he walks out** \n - \"he walks out\" → example: *ket¯ohnæw* = he walks out \n - In list: *wǣpohnæw* = he begins walking \n - *ket¯ohnæw* = he walks out → exactly matches \n - So this one is clear.\n\nFinal translations:\n\n- I begin to eat it → **new¯æpahtan** \n- we1+2 lay it flat by hand → **kek¯awenæq** \n- he digs a hole → **taw¯anæhkæw** \n- he walks out → **ket¯ohnæw**\n\nAll derived from pattern: verb stems with subjects, prefixes for person, suffixes for manner (by hand, by tool, etc.), and vowel length rule applied when first two vowels are short → second becomes long.\n\n\\boxed{b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw}", + "generated_tokens": 3624, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw", + "score_fraction": 1.0, + "exact": 1.0, + "matched_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "missed_units": [], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 1.0, + "ioling_exact_accuracy": 1.0, + "ioling_matched_units": 4.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 1.0, + "ioling_strict_substring_reward": 1.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9429.0, + "ioling_final_answer_chars": 67.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "redacted_solution_hint_mask0", + "sample_index": 1, + "output": "We are given a list of Menominee verb forms and their English translations, along with a verb structure guide. The task is to translate four sentences into Menominee:\n\n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out \n\nWe analyze each based on the provided patterns and examples.\n\n---\n\n**1. \"I begin to eat it\"**\n\n- \"I begin\" → from the list: \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is a root.\n- \"begin to eat\" → \"eat\" is likely derived from \"by mouth\" or \"in mouth\".\n- The form \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → contains \"waht\" which may relate to \"mouth\".\n- \"I bite\" → \"nekāwāhpem\" = I fall over laughing → not relevant.\n- But \"ketāwahtæq\" has \"ket\" (out) and \"waht\" (by mouth) → possibly \"eat by mouth\"?\n- In the guidance, \"kepītahtæq\" = we1+2 come eating it → \"come eating\" → so \"eating\" is possible via “taht”.\n- \"taht\" appears in \"kepītahtæq\" → and \"kepī\" means \"come\", so \"come eating it\" → so “eat” is a root.\n- But we need \"I begin to eat it\".\n- Recall: \"wǣpohnæw\" = he begins walking → “wāp” + “ohnæw” = \"begin walking\"\n- So \"begin\" root is \"wāp\" or \"wǣp\"\n- “begin to eat” → begin + eat\n- What is the verb for “eat” in Menominee?\n- Look at: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → may be “bite” = eat → so “bite” ≈ “eat”\n- But “I begin to eat” → the root for “begin” is \"wǣp\"\n- What about \"new¯æpahtan\"? Given in guidance: \"I begin to eat it\" → **new¯æpahtan**\n- Let's parse: \"new\" = I (from ne- to I), \"¯æp\" = begin (from wǣp), \"ah\" = by hand? But \"eat\" → \"paht\" = \"by mouth\"?\n- \"paht\" appears in \"ketāwahtæq\" → \"wāht\" → possibly \"by mouth\", \"eating\"?\n- So \"new¯æpahtan\" = I begin to eat it → matches directly\n- So answer: **new¯æpahtan**\n\n---\n\n**2. \"we1+2 lay it flat by hand\"**\n\n- \"lay it flat\" → flatness → what is “flat”?\n- In examples: \"nepītohnæm\" = I walk here → not relevant.\n- \"pāhkeqtaw\" = he opens up → opening\n- \"kek¯awenæq\" is given as the answer in the guidance → \"we1+2 lay it flat by hand\"\n- Check components:\n- \"kek\" = we1+2 (from ke-)\n- \"aw\" = perhaps \"lay\"\n- \"en\" = by hand (from \"en\" in \"pītenam\" = pass here, \"enk\" = by hand?)\n- In the verb table: \"en\" = by hand\n- \"aw\" = from \"pahk\" = open (but \"aw\"?) — perhaps “aw” is “lay”\n- Look at: \"kewǣpānæhkæq\" = we1+2 begin to dig → “pān” = dig?\n- “pāh” = open, so “pā” might be related\n- “kepītahtæq” = we1+2 come eating → “pī” = pass\n- “kek¯awenæq” → kek = we1+2, aw = lay, en = by hand → fits\n- Root \"aw\" likely means \"lay flat\"\n- So “we1+2 lay it flat by hand” → **kek¯awenæq**\n\n---\n\n**3. \"he digs a hole\"**\n\n- \"he digs a hole\" → digging\n- Known form: \"k¯esk\" = through, \"k¯eskahtæq\" = we1+2 bite it through\n- \"k¯anæhkæ\" = digging → in the table: \"-¯anæhkæ\" = digging\n- \"k¯anæhkæ\" = digging → the root is “kān”?\n- But we need \"he digs a hole\"\n- \"k¯anæhkæ\" is listed as \"digging\"\n- Who? \"he\" → so root \"k\" with \"anæhkæ\" → \"k¯anæhkæw\"?\n- In guidance: \"he digs a hole\" → **taw¯anæhkæw**\n- Wait — \"taw\" = pierce — not digging?\n- But in table: \"tawǣsam\" = he cuts a hole in it → “cut a hole”\n- \"taw\" = pierce, cut\n- But \"dig a hole\" → digging vs cutting\n- What is the distinction?\n- \"k¯anæhkæ\" = digging → root \"k\"\n- So \"he digs a hole\" → \"k¯anæhkæw\"? But \"w\" at end?\n- \"w\" in table: \"wǣpohnæw\" = he begins walking → \"w\" = he\n- So \"he\" = w or k?\n- In table: \"k¯anæhkæ\" = digging → but no person marker?\n- Be careful: verbs have person prefixes.\n- In examples:\n - \"kewǣpeqtaq\" = we1+2 begin → \"ke\" = we1+2\n - \"kawāham\" = he fells it by tool → \"ka\" = he\n - \"nekāweqtam\" = I lie down → \"ne\" = I\n- So person markers:\n - \"ke\" = we1+2\n - \"ka\" = he\n - \"ne\" = I\n\nSo \"he\" = k (in initial consonant) → \"k\" root\n- \"k¯anæhkæ\" = digging → so \"he digs\" → **k¯anæhkæ**\n- But guidance says: \"he digs a hole\" → **taw¯anæhkæw**\n- Wait — contradiction.\n\nWait, check guidance: \nIn official solution: \n“he digs a hole: taw¯anæhkæw”\n\nBut \"taw\" means \"cut\" → \"pierces\", \"cuts\", \"cuts a hole\" → so \"taw\" = cut a hole \n\"digging\" vs \"cutting a hole\"\n\nIn Menominee, \"digging\" may be a different root.\n\nBut the form: \"taw\" = cut, so “cut a hole” → may be used for digging?\n\nBut the examples say:\n- \"tawǣsam\" = he cuts a hole in it → so “cut a hole”\n- \"pāhkaham\" = he opens it by tool → opening\n- \"nekǣtahan\" = I pry it out by tool → pry\n\nSo \"taw\" = cut → \"cut a hole\" → fits “dig a hole”?\n\nBut digging is more earth-moving, cutting is slicing.\n\nBut in the list, \"k¯anæhkæ\" is unmarked, and \"k¯an\" appears in the verb table.\n\nIn the verb table: \"-¯anæhkæ\" = digging\n\nSo root \"k\" = he → \"k¯anæhkæ\"\n\nBut guidance says: \"he digs a hole: taw¯anæhkæw\"\n\nWait — “w” at end? In “wǣpohnæw” = he begins walking → “w” = he\n\nSo “taw¯anæhkæw” = he cuts a hole → not digging\n\nBut the target is “he digs a hole”\n\nContradiction.\n\nWait — perhaps the guidance is error?\n\nNo — in official solution row: \n\"he digs a hole: taw¯anæhkæw\"\n\nBut taw = cut — not dig\n\nBut digging = \"k¯anæhkæ\"\n\nSo is there a typo?\n\nWait — check the verb table directly:\n\n“-¯anæhkæ” = digging\n\nNo person marker → so \"he\" would be \"k¯anæhkæ\"\n\nBut person marker \"k\" is in \"kawāham\" = he fells → so \"ka\" = he\n\nSo \"k¯anæhkæ\" = he digs\n\nBut guidance says taw¯anæhkæw\n\ntaw = cuts a hole → so \"he cuts a hole\"\n\nSo \"dig a hole\" ≠ \"cut a hole\"\n\nThus, the intended form must be **k¯anæhkæ**\n\nBut guidance says taw¯anæhkæw → which is “he cuts a hole”\n\nSo is the translation incorrect?\n\nWait — perhaps in Menominee, \"dig\" and \"cut\" are interchangeable?\n\nBut the root for digging is explicitly listed as “-¯anæhkæ”\n\nAnd “k” = he → so “he digs” = k¯anæhkæ\n\nBut let's confirm with another example.\n\n\"pītenam\" = he passes it here — \"pī\" = pass, \"ten\" = here\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkaham\" = he opens by tool\n\nNo digging verb.\n\nOnly digging is “-¯anæhkæ”\n\nSo \"he digs a hole\" → k¯anæhkæ\n\nBut guidance says taw¯anæhkæw\n\nWait — is \"taw\" the root for digging?\n\nNo — \"taw\" = cut\n\nBut \"taw\" = pierce → cutting\n\nSo we must trust the pattern, not the guidance for derivation.\n\nFrom verb structure:\n\n- digging = \"-¯anæhkæ\" (as listed)\n- agent: \"he\" = \"k\"\n→ so \"k¯anæhkæ\"\n\nBut why guidance says taw¯anæhkæw?\n\nPossibly typo.\n\nWait — look: \"tawǣsam\" = he cuts a hole in it → so “cut a hole”\n\nBut “dig a hole” is different.\n\nThus, the correct form for \"he digs a hole\" is **k¯anæhkæ**\n\nBut — is “dig” really “anæhkæ”? Possibly.\n\nAlternatively, is there another form?\n\nNo — only one digging verb.\n\nTherefore, despite guidance, we infer: \n\"he digs a hole\" → **k¯anæhkæ**\n\nBut in guidance: \"he digs a hole: taw¯anæhkæw\" — clearly a mistake?\n\nWait — look back: in the verbal table:\n\n“-¯anæhkæ” = digging\n\nYes — so root is \"k¯anæhkæ\" → for “he”\n\nSo answer: **k¯anæhkæ**\n\nBut the guidance says taw¯anæhkæw → perhaps they used \"taw\" for hole?\n\nNo — \"taw\" is for cutting.\n\nAlternatively, is \"dig\" the same as \"cut a hole\"?\n\nIn context, \"he digs a hole\" might be paraphrased as \"cuts a hole\"?\n\nBut \"dig\" is more intentional.\n\nBut in the verb list, no other verb for digging.\n\nThus, the correct verb is **k¯anæhkæ**\n\nBut guidance says taw¯anæhkæw — must we trust it?\n\nWait — in the verb table, the line says:\n\n“-¯anæhkæ” = digging → and “k¯anæhkæ” is not given — but “kawāham” is “he fells by tool” → “k” = he.\n\nSo “k¯anæhkæ” = he digs\n\nYes.\n\nThus, despite guidance, we derive: **k¯anæhkæ**\n\nWait — but “taw” is root → and “taw” is for “cut”\n\nSo we conclude: \"he digs a hole\" → k¯anæhkæ\n\nBut check the full guidance: \n\"he digs a hole: taw¯anæhkæw\"\n\nThis must be an error — because taw = cut\n\nSo we go by pattern.\n\nProceed.\n\n---\n\n**4. \"he walks out\"**\n\n- \"walks out\" → “out” root?\n- \"wackōhnæw\" = he walks roundabout, by a detour → “roundabout”\n- \"wǣpohnæw\" = he begins walking → “begin walking”\n- \"wack\" = around\n- \"kēskenam\" = he breaks it through by hand\n- \"ketǣnam\" = he takes it out by hand → “takes it out”\n- “out” = ket? → \"ket\" → out\n- In “kewǣpānæhkæq” = we1+2 begin to dig → no out\n- \"ketǣnam\" = he takes it out by hand → so \"out\" = ket\n- So \"he walks out\" → \"he walks\" + \"out\"\n- “walks” → from “wǣp” = begin → \"wǣp\" = begin; “wak” = walk? → “wack” = around\n- “wackōhnæw” = he walks roundabout → so “wack” + “ohnæw”?\n- “ohnæw” = walking?\n- “wǣpohnæw” = he begins walking → so “wǣp” = begin; “ohnæw” = walk?\n- So “ohnæw” = walk?\n- So “he walks out” = “he walks” + “out”?\n- But “out” is “ket”\n- So “ket” + “ohnæw”?\n- \"ketohnæw\" = he walks out?\n- In guidance: \"he walks out: ket¯ohnæw\"\n- Yes — matches.\n\nThus, \"he walks out\" → **ket¯ohnæw**\n\nNote: “ket” = out, “ohnæw” = walk\n\nThus, derived.\n\n---\n\nFinal answers:\n\n1. I begin to eat it → new¯æpahtan \n2. we1+2 lay it flat by hand → kek¯awenæq \n3. he digs a hole → k¯anæhkæ \n4. he walks out → ket¯ohnæw\n\nNote: Despite guidance saying \"taw¯anæhkæw\" for digging, the verb table explicitly says \"-¯anæhkæ\" = digging, and \"k\" = he, so \"k¯anæhkæ\" is correct.\n\nThus, answers are:\n\n\\boxed{b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: k¯anæhkæ; b.4: ket¯ohnæw}", + "generated_tokens": 3328, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: k¯anæhkæ; b.4: ket¯ohnæw", + "score_fraction": 0.75, + "exact": 0.0, + "matched_units": [ + "b.1", + "b.2", + "b.4" + ], + "missed_units": [ + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.75, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 3.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.75, + "ioling_strict_substring_reward": 0.75, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 8847.0, + "ioling_final_answer_chars": 64.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "redacted_solution_hint_mask0", + "sample_index": 2, + "output": "We are given a set of Menominee verb forms with their meanings and a verb structure guide. The task is to translate four English sentences into Menominee, using the patterns observed in the provided forms.\n\n---\n\nStep 1: Identify the required translations.\n\n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out \n\nWe analyze each using the provided verb templates and known patterns.\n\n---\n\n1. \"I begin to eat it\"\n\n- \"begin\" = wæp (e.g., wæpohnæw = he begins walking)\n- \"to eat\" = eating by mouth → \"-aht\" prefix/appendix (e.g., ketāwahtæq = we1+2 bite, gnaw a hole in it; \"by mouth\" → -aht)\n\nThus, \"I begin to eat it\" should involve:\n- \"begin\" = wæp\n- \"by mouth\" = -aht\n- \"I\" = ne- (as in nekāweqtam = I lie down)\n\nBut look at the pattern: \"begin to eat\" → begin + by mouth\n\nFrom the example:\n- ketāwahtæq = we1+2 bite, gnaw a hole in it → \"bite\" = ke-, \"by mouth\" = -aht, \"we1+2\" = ke- (but ke- is also \"we1+2\" in some cases)\n\nWait — look at guidance:\n\n> \"I begin to eat it: new¯æpahtan\"\n\nSo the given answer is **new¯æpahtan**\n\nBreak it down:\n- \"new\" = I (as in nekāweqtam = I lie down → \"ne-\" = I)\n- \"¯æp\" = begin (wæp is begin, so ¯æp might be a variant)\n- \"aht\" = by mouth → eating by mouth\n- \"an\" = could be a suffix\n\nWait — the pattern suggests:\n- \"new\" = I\n- \"¯æp\" = begin (from wæpohnæw = he begins walking → wæp = begin)\n- \"aht\" = by mouth (as in -aht = by mouth)\n\nSo \"new¯æpahtan\" = I begin (to) eat it\n\nThis matches perfectly.\n\nThus, **b.1 = new¯æpahtan**\n\n---\n\n2. \"we1+2 lay it flat by hand\"\n\n- \"we1+2\" = ke- or kek (as in kekēskahtæq = we1+2 bite it through)\n- \"lay flat\" → laying down, flat\n- \"by hand\" → -en (as in \"by hand\" → -en)\n\nLook at the verb:\n- nepītohnæm = I walk here → \"I walk here\"\n- pāhkeqtaw = he opens up → \"open up\"\n- \"by hand\" appears in forms like nepītohnæm — \"here\" is a locative, not flat.\n\nBut look at this:\n- kek¯awenæq = we1+2 lay it flat by hand → given in guidance.\n\nBreak down:\n- kek = we1+2 (as in kekēskahtæq)\n- aw = lay? → like \"pahk\" = open, \"pāh\" = open\n- en = by hand?\n\nWait — \"aw\" may be a root for \"lay\"?\n\nNote: \"pahkǣsam\" = he cuts it off → not direct\n\nBut look at \"ne-awk\" = I open? Not directly.\n\nNote from pattern:\n- \"we1+2 lay it flat by hand\" → asked for\n- In guidance: \"we1+2 lay it flat by hand: kek¯awenæq\"\n\nSo: kek¯awenæq\n\nBreak:\n- kek → we1+2\n- aw → lay?\n- en → by hand?\n\nYes — and \"by hand\" is marked with -en (e.g., \"ne- kāwāhpem\" = I fall over laughing — not matching)\n\nEarlier: \"ne- kāweqtam\" = I lie down — \"kāweqtam\"\n\nBut in \"pītenam\" = he passes it here — \"pass\"\n\nWhat about \"kaw\" = down (as in kawāham = he fells it by tool)\n\n\"aw\" may be from \"kaw\" → \"lay down\"?\n\nYes — \"lay flat\" = \"lay down\" → kaw → down\n\nSo kek + aw + en → we1+2 lay it flat by hand\n\n\"en\" = by hand\n\nThus, \"kek¯awenæq\" = we1+2 lay it flat by hand\n\nSo **b.2 = kek¯awenæq**\n\n---\n\n3. \"he digs a hole\"\n\n- \"he\" → k- (as in kawāham, kēskenam, kewǣpānæhkæq)\n- \"digs\" → digging → look at form: \"k¯eskanæhkæ\" → seems close\n\nGiven in guidance: \"he digs a hole: taw¯anæhkæw\"\n\nIs this correct?\n\nWait — taw = pierce; \"tawǣsam\" = he cuts a hole in it → \"cuts a hole\"\n\nSimilarly, \"taw\" = cut, pierce\n\nDoes \"dig\" = \"cut a hole\"?\n\nYes — in context, \"digs a hole\" is semantically equivalent to \"cuts a hole\" or \"opens a hole\"\n\n\"taw\" → cut, \"an\" → by hand? \"an\" = may be \"by hand\"\n\n\"¯anæhkæw\" = digging?\n\nEarlier: \"k¯eskanæhkæ\" — \"k\" = he, \"eska\" = cut through, \"hkæ\" = digging?\n\nBut taw → pierce/excavate?\n\nIn \"tawǣsam\" = he cuts a hole in it → matches \"cuts a hole\"\n\nSo \"he digs a hole\" = \"he cuts a hole\" → taw + something?\n\nNow, compare:\n- \"k¯eskanæhkæ\" = he digs (as opposed to \"breaks it\")\n- but \"taw\" = cut → also cuts a hole\n\nIs \"taw\" used for digging a hole?\n\nYes — tawǣsam = cuts a hole\n\nSo \"he digs a hole\" → taw + ? → likely taw + something\n\nNow, \"taw¯anæhkæw\" → taw (cut), ¯an (by hand), æhkæw (digging?) — but \"hkæw\" is odd.\n\nWait — the given answer in guidance: \"he digs a hole: taw¯anæhkæw\"\n\nBut look at \"k¯eskanæhkæ\" — that’s he digs.\n\nWait — is \"k\" (he) for digging?\n\nIn the verb table:\n- k¯eskanæhkæ — appears not listed, but \"k¯eskanæhkæw\" might be it?\n\nNo — in guidance, it says: \"he digs a hole: taw¯anæhkæw\"\n\nBut let’s analyze:\n\n\"taw\" = cut \n\"an\" = by hand? — appears in \"nekǣtahan\" = I pry it out by tool → \"by tool\"\n\n\"en\" = by hand? — in \"kawāham\" = by tool → \"ah\" = by tool\n\nWe find:\n- \"by tool\" = -ah \n- \"by hand\" = -en (from \"pahk\" = open; \"pāh\" = open; \"pahk\" = open; pahk = open; nepītohnæm = I walk here — no)\n\nBut in \"nekāweqtam\" = I lie down — no\n\n\"pāhkeqtaw\" = he opens up — \"pāh\"\n\nWait — \"pāh\" = open; \"pā\" = open?\n\nIn \"pāhkaham\" = he opens it by tool → \"pāh\" + \"kaham\" = open by tool\n\nSo:\n- by hand = -en (e.g., \"by hand\" suffix)\n- by tool = -ah\n\nThus, \"he digs a hole\" → likely \"he cuts a hole by hand\"\n\nSo: taw + ? + en?\n\nBut the given form is taw¯anæhkæw\n\nBreak down:\n- taw → cut\n- ¯an → long a, by hand? (an → by hand)\n- æhkæw → digging?\n\nBut \"hkæw\" = digging? In list: \"k¯eskanæhkæ\" = digging?\n\nYes — \"k¯eskanæhkæ\" = he digs\n\nBut in guidance, it says he digs a hole → taw¯anæhkæw?\n\nContradiction?\n\nWait — is there a verb \"dig a hole by hand\"?\n\nLook back at list:\n\nkewǣpeqtaq = we1+2 begin \nkewǣpānæhkæq = we1+2 begin to dig \nkewǣpānæhkæq → related to digging\n\n\"we1+2 begin to dig\" = kewǣpānæhkæq\n\nSo \"begin to dig\" → kewǣpānæhkæq\n\nThus \"he digs\" → non-begin, he digs\n\nSo \"he digs a hole\" → root = k, suffix = digging\n\nLook at: k¯eskanæhkæ — not in list\n\nBut \"k¯eskanæhkæ\" is missing.\n\nWait — the form \"k¯eskanæhkæ\" is not listed.\n\nBut \"k¯eskanæhkæ\" is likely a variant.\n\nBut guidance says: \"he digs a hole: taw¯anæhkæw\"\n\nCould taw be used for dig?\n\n\"tawǣsam\" = he cuts a hole in it → clearly cuts a hole → so taw = cuts a hole → \"he cuts a hole\"\n\nSo \"he digs a hole\" is a synonym of \"he cuts a hole\"?\n\nYes — in context, \"digs a hole\" = \"cuts a hole\"\n\nSo \"he digs a hole\" = taw + ? → by hand?\n\n\"taw\" → cuts → by hand?\n\nSo need -en?\n\nBut \"taw¯anæhkæw\" — where does \"hkæw\" come from?\n\n\"taw\" + \"¯an\" + \"æhkæw\"\n\n\"æhkæw\" = digging?\n\nBut \"w\" = he?\n\nIn \"wackōhnæw\" = he walks roundabout\n\n\"wack\" = around\n\n\"ahnæw\" = walks\n\nSo \"wackōhnæw\" = he walks around\n\nSo \"hkæw\" = something?\n\nBack to list:\n\n- kewǣpānæhkæq = we1+2 begin to dig\n- kewǣpānæhkæq → begin to dig\n- k¯eskanæhkæ — not listed\n\nBut in guidance: the answer is *taw¯anæhkæw*\n\nSo despite doubts, the given solution says: \"he digs a hole: taw¯anæhkæw\"\n\nSo must accept it.\n\nThus, **b.3 = taw¯anæhkæw**\n\n---\n\n4. \"he walks out\"\n\nWe are told:\n- \"he walks out\" → look for \"he walks out\"\n\nFrom list:\n- kewǣpeqtaq = we1+2 begin\n- kepītahtæq = we1+2 come eating it\n- wǣpohnæw = he begins walking\n- ketǣnam = he takes it out by hand\n- ket¯ohnæw = he walks out\n\nYes — \"he walks out\" = ket¯ohnæw\n\n\"ke\" = he? (k in others is he, ke in others)\n\nIn \"kēskenam\" = he breaks it → k = he\n\nIn \"ketǣnam\" = he takes it out by hand → ke = he\n\nSo \"ke\" = he\n\n\"¯ohnæw\" = walks out\n\n\"w\" is walking → wǣp = begin walking\n\nSo \"ohnæw\" = walks out?\n\nYes — \"wǣpohnæw\" = he begins walking\n\n\"ohnæw\" = walks\n\nSo \"ke\" + \"t\" + \"ohnæw\" → pattern?\n\n\"ket\" → walks out?\n\nYes — in guidance: \"he walks out: ket¯ohnæw\"\n\nSo final form: **b.4 = ket¯ohnæw**\n\n---\n\nFinal answers:\n\nb.1: new¯æpahtan \nb.2: kek¯awenæq \nb.3: taw¯anæhkæw \nb.4: ket¯ohnæw\n\n\\boxed{b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw}", + "generated_tokens": 2861, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw", + "score_fraction": 1.0, + "exact": 1.0, + "matched_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "missed_units": [], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 1.0, + "ioling_exact_accuracy": 1.0, + "ioling_matched_units": 4.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 1.0, + "ioling_strict_substring_reward": 1.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7332.0, + "ioling_final_answer_chars": 67.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "redacted_solution_hint_mask0", + "sample_index": 3, + "output": "We are given a list of Menominee verb forms and their English translations, along with a verbal structure and morphological patterns. We are to translate four English phrases into Menominee.\n\n---\n\n**Target translations:**\n\n1. I begin to eat it \n2. we1+2 lay it flat by hand \n3. he digs a hole \n4. he walks out \n\n---\n\nStep 1: Identify relevant verb roots and affixes from the provided table.\n\nFrom the guidance:\n\n- \"begin\" → *kewǣp*, *wǣpohnæw* (he begins walking), *kewǣpānæhkæq* (we1+2 begin to dig) \n → \"begin\" is root *kewǣp* or *wǣp*, with variations in form.\n\n- \"eat\" → not directly in list, but \"bite, gnaw a hole in it\" is *ketāwahtæq*, and \"bite it through\" is *kekǣtohnæq*. \n However, \"by mouth\" is marked with *-aht*. \n → \"eat\" is likely via *-aht* meaning \"by mouth\", and \"begin to eat\" would involve *begin* + *by mouth*.\n\nLook at: \n- *ketāwahtæq* = we1+2 bite, gnaw a hole in it \n- *ketǣnam* = he takes it out by hand \n- *kekēskahtæq* = we1+2 bite it through \n\nBut “begin to eat” = \"begin\" + \"by mouth\"\n\nWe already have: \n- *wǣpohnæw* = he begins walking \n- *wǣp* is the root for begin \n→ So, \"I begin to eat it\" = *I* + *begin* + *by mouth*\n\nFrom the vocabulary: \n- *newāckesan* = I cut around it \n- *new* is not clearly \"begin\" \n- *kepītahtæq* = we1+2 come eating it; we1+2 bring it in our mouths → suggests \"eating\" is with *-aht*\n\nBut “begin to eat” → likely from *wǣp* (begin) + *-aht* (by mouth)\n\nLook at: *wǣpohnæw* = he begins walking → so *wǣp* is \"begin\"\n\nIn the guidance, it says: \n\"• I begin to eat it: new¯æpahtan\" → this is given in the solution, so we can confirm the form.\n\nBut we are to derive it.\n\nWe see: \n- *newāckesan* = I cut around it → new = cut? \n- *ne- I*, *wāck* = cut around → so *new* = cut\n\nBut \"begin\" = *wǣp*, *kewǣp* also\n\nNow, for \"begin to eat\": \n- \"eat\" = by mouth → *-aht* \n- \"begin\" = *wǣp* \n- \"I\" = *ne-* \n\nSo *ne-wǣp-aht*? → But that doesn't match form. \n\nWe also have: *kepītahtæq* = we1+2 come eating it → so *aht* = eating by mouth \n\nBut *new¯æpahtan* is listed as translation in the guidance → so we accept: \n→ I begin to eat it = *new¯æpahtan* \n\nLet’s analyze this: \n- *new* → possibly \"cut\" or \"begin\"? Not clear \n- *¯æp* → possibly from *wǣp*, with vowel length \n- *aht* → eating by mouth \n- *an* → I \n\nAh — *new* may be from *wǣp* with a morpheme shift? \n\nWait: *newāckesan* = I cut around it → so *new* = cut \nBut *new¯æpahtan* = I begin to eat it — a different meaning \n\nCould this be a compound? \n\nAlternative: look at verb for \"bite\" = *ketāwahtæq* → \"bite, gnaw\" by mouth\n\n\"begin to eat\" → perhaps \"begin\" + \"bite by mouth\"\n\nBut *wǣp* + *aht*? \n\nWe have: \n- *wǣpohnæw* = he begins walking \n- *wǣp* is the root \n- *-ohnæ* = walking \n- *-aht* = by mouth \n\nPerhaps *wāp* or *wǣp* + *aht*? \n\nBut no direct form. \n\nIn the guidance solution: \n→ \"I begin to eat it: new¯æpahtan\" \n\nWe accept this form, and verify its components:\n\n- *ne-* = I \n- *wǣp* = begin \n- *aht* = by mouth \n- *an* = suffix for \"it\" or marking of transitivity?\n\nWait: *an* at end → *new¯æpahtan* → ends with *an*\n\nIn the list: *nekāweqtam* = I lie down → ends with *tam* \n*nekāwāhpem* = I fall over laughing → ends with *pem* \n*nekǣtahan* = I pry it out by tool → ends with *han* \n*nepītohnæm* = I walk here → ends with *m*\n\nSo *an* is not a known personal ending.\n\nBut *newāckesan* = I cut around it — ends with *an* \n→ So *an* = final marker?\n\nBut *new¯æpahtan* ends in *an*, so likely it is a past or action with *an* \n\nAlso, the rule: \"If both first vowels in the word are short, the second becomes long\" → e > ¯æ \n\nSo *wǣp* → if both vowels short, second becomes long → *wǣp* → *w¯æp*? \n\nYes: *wǣp* (first vowel a, second e) — if both short, e becomes ¯æ → so *w¯æp* \n\nSo *ne-w¯æp-aht-an*? \n\nBut that’s *new¯æpahtan* — fits.\n\nSo: \n- *ne-* = I \n- *w¯æp* = begin \n- *aht* = by mouth \n- *an* = transitivization or object marker? \n\nBut *ne-w¯æp-aht-an* → \"I begin to eat it\" → plausible.\n\nThus, **I begin to eat it = new¯æpahtan**\n\n---\n\nSecond: we1+2 lay it flat by hand \n\n\"lay it flat\" → flat = *flat*? \n\nWe look for verbs meaning \"lay\" or \"place flat\"\n\nLook at: \n- *pāhkeqtaw* = he opens up \n- *pahk* = open → *pāhk* → open \n- *kewǣpānæhkæq* = we1+2 begin to dig \n- *kekāw* → seen in *kek¯awenæq* \n- *kek¯awenæq* = we1+2 lay it flat by hand → in solution!\n\nSo the form is given: *kek¯awenæq*\n\nBreak it down: \n- *ke-* = we1+2 \n- *k¯aw* = lay? (from \"kaw\" = down) \n- *en* = flat? \n- *æq* = by hand? \n\nNote: *kaw* = down — could \"lay flat\" be \"down by hand\"?\n\nBut *kaw* = down, as in \"kawāham\" = he fells it by tool — still not clear \n\nBut *kek¯awenæq* is the form given in solution → likely correct.\n\nMorphology: \n- *ke-* = we1+2 \n- *k¯aw* = lay down? \n- *en* = flat? \n- *æq* = by hand \n\nYes, fits: \"lay it flat by hand\" → so we accept this.\n\n→ **we1+2 lay it flat by hand = kek¯awenæq**\n\n---\n\nThird: he digs a hole \n\nLook for verb for \"dig\" or \"dig a hole\"\n\nGiven: *kewǣpānæhkæq* = we1+2 begin to dig \n→ \"begin to dig\" → *kewǣpānæhkæq*\n\nAlso: *k¯ānæhkæ* = digging (in guidance, listed under \"digging\" root)\n\nIn the verb table: \n- *-¯anæhkæ* = digging\n\nSo \"he digs a hole\" = *he* + *digging*\n\n\"he\" = *k-* \n\"digging\" = *¯anæhkæ* \n→ *k¯anæhkæw*?\n\nWait: *w* at end? \nLook at *kewǣpānæhkæq* → has *w* at end? No → *q*\n\nBut *kewǣpānæhkæq* has *q* at end → perhaps not.\n\nNote: *k¯anæhkæ* = digging \nBut what about the \"he\" prefix?\n\nWe have: *kawāham* = he fells it by tool → *k-* = he \nSo likely *k- + digging* = *k¯anæhkæw*?\n\nBut where is the \"w\"?\n\nLook at *wackōhnæw* = he walks roundabout → ends with *w*\n\nIn table: *-ohnæ* = walking \nBut digging → *-anæhkæ*?\n\nAlso, *tawǣsam* = he cuts a hole in it → cuts a hole → so \"hole\" is used in that.\n\nIs \"dig a hole\" = *k¯anæhkæw*?\n\nBack to guidance: \"he digs a hole: taw¯anæhkæw\"\n\nWait — *taw* = pierce → not dig.\n\nBut *taw* = pierce, *w* = he? \n*he* = *k-*, not *t-*\n\nBut *taw¯anæhkæw* → starts with *taw*\n\nCan *taw* = dig?\n\nLook: *tawǣsam* = he cuts a hole in it — cuts a hole → so *taw* = cut a hole → so *taw* = make a hole?\n\n\"cut a hole\" → makes sense → \"dig a hole\" = probably similar action.\n\n\"dig\" in Menominee: likely *taw* + *anæhkæ* + *w*?\n\nBut *taw¯anæhkæw* — \"he\" is marked by *w*?\n\nIn *kawāham* = he fells it by tool → *k-* = he → so he = *k-* \n\nBut *tawāham*? Not in list.\n\nBut *tawǣsam* = he cuts a hole in it → \"cuts a hole\" → same as \"dig\"?\n\nLikely: *taw* = cut, so \"cut a hole\" → so \"dig a hole\" = *taw* + *anæhkæ*?\n\nBut form: *taw¯anæhkæw*\n\nWe see *w* at the end — is that the verb root or the person?\n\nIn *wackōhnæw* = he walks roundabout → *w* at end → likely \"he\"\n\nIn *kekēskahtæq* = we1+2 bite it through → *eqta* = ——, *q* = we1+2\n\nSo marker at end: \n- *q* = we1+2 \n- *w* = he \n\nThus, *taw¯anæhkæw* → *taw* = cut a hole, *anæhkæ* = digging-related, *w* = he → \"he digs a hole\"\n\nYes, fits.\n\nThus: **he digs a hole = taw¯anæhkæw**\n\n---\n\nFourth: he walks out \n\nWe have: \n- *wǣpohnæw* = he begins walking \n- *ket¯ohnæw* = he walks out → this is given in solution \n\nCheck: \n- *ket* = out \n- *ohnæ* = walking \n- *w* = he? \n- *w* at end → likely he \n\nSo *ket¯ohnæw* = he walks out \n\nYes, \"walks out\" = *ket* + *ohnæ* + *w* → *ket¯ohnæw*\n\nIn the guidance: \"he walks out: ket¯ohnæw\"\n\nThus confirmed.\n\n---\n\nFinal translations:\n\n1. I begin to eat it → new¯æpahtan \n2. we1+2 lay it flat by hand → kek¯awenæq \n3. he digs a hole → taw¯anæhkæw \n4. he walks out → ket¯ohnæw \n\n\\boxed{b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw}", + "generated_tokens": 2905, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw", + "score_fraction": 1.0, + "exact": 1.0, + "matched_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "missed_units": [], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 1.0, + "ioling_exact_accuracy": 1.0, + "ioling_matched_units": 4.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 1.0, + "ioling_strict_substring_reward": 1.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7546.0, + "ioling_final_answer_chars": 67.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #1. The Menominee verb forms have the following structure:\n\n intransitive verb:\n kaw down -¯ahpe laughing -m I ket out -¯anæhkæ digging -q we1+2 k¯esk through -eqta —— -w he ne- I pahk off -ohnæ walking\n ke- we1+2 p¯ahk open\n transitive verb:—— he p¯ıt hither\n -ah by tool taw pierce -an I -aht by mouth wack around -æq we1+2 -en by hand w¯æp begin -am he -es cutting\nIf both first vowels in the word are short, the second becomes long (e > ¯æ).\n\n (a) • kek¯eskahæq: we1+2 chop it through, break it through by tool\n • nep¯ahkenan:\n – I open, uncover it by hand ( p¯ahk), !\n – I break it off, tear it offby hand ( pahk) !\n • w¯æp¯ahpew: he begins laughing\n (b) • I begin to eat it: new¯æpahtan\n • we1+2 lay it flat by hand: kek¯awenæq\n • he digs a hole: taw¯anæhkæw\n • he walks out: ket¯ohnæw", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 0, + "output": "We are given a set of Nooni sentences spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden** into English. We must use the linguistic rules and examples provided.\n\n---\n\n### Step 1: Understand the structure and tense rules\n\nFrom the problem:\n\n- **Tense markers**:\n - Past: `V᷅` (e.g., `cí` = past)\n - Future: `V́` (with `nú` or `nú géː`, `nú bóy`, `nú yúː`)\n - \"Just now\" or \"about to\": `fé`, `čí`, `tɔ̀`, `bɛ̂ː`, `cí nɔ̂ː`, etc.\n\n- **Word order**: `S T V O (lé) L D`\n - S = subject\n - T = tense\n - V = verb\n - O = object\n - L = place\n - D = day\n\n- **\"To see\" = `yɛn lé` → after consonant: `lé → é` (so `yɛn é`)\n\n- **1st person prefix**:\n - `n-` → `mb-` (e.g., `nb` → `mb`)\n - `nk/ng` → `ŋk/ŋg`\n - `nn` → `n`\n\n- **After –̂, –᷆, –̀ → –́ becomes –̌** (e.g., `tɔ̀` → `tɔ̌` in some cases)\n\n---\n\n### Step 2: Identify day names and their cycles\n\nGiven days:\n- Bvutfu (day 1)\n- Bvusɔw\n- Bvuzhi\n- Bvukema\n- Bvuŋka\n- Bvuŋkaden\n\nFrom examples:\n- \"The day after tomorrow is Bvutfu\" → sentence 5: `fɔ̀ shě ntfǔː nú bvútfu᷅`\n- \"Tomorrow is Bvuŋkaden\" → sentence 8: `ntfǔː nú bvûŋka᷆ːde᷆n`\n- \"The day before yesterday was Bvuŋka\" → sentence 11\n\nThis indicates a weekly cycle, probably 7 days. We don’t need full calendar, just relative days.\n\n---\n\n### Step 3: Analyze each target sentence\n\n#### 16. `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː`\n\n- Structure: `Day nǔ fɔ̀ shě ntfǔː`\n- `fɔ̀ shě ntfǔː` → “The day after tomorrow is Bvutfu”\n- But here: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` → \"On Bvusɔw, the day after tomorrow is Bvutfu\"\n\nWait — but \"the day after tomorrow\" is a future reference. So rephrasing:\n→ \"On Bvusɔw, the day after tomorrow is Bvutfu\"\n\nBut check existing examples:\n- Sentence 5: \"The day after tomorrow is Bvutfu\" → `fɔ̀ shě ntfǔː nú bvútfu᷅`\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow is X\"\n\nThus: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` = \"On Bvusɔw, the day after tomorrow is Bvutfu\"\n\n✔️ Translation: **On Bvusɔw, the day after tomorrow is Bvutfu**\n\n---\n\n#### 17. `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\n- Subject: `me` = I\n- Tense: `ŋgéː` → future (from rule: future = `nú géː`, `nú bóy`, `nú yúː`)\n- Object: `nyɛ́n` → \"the thief\"\n- Verb: `kèŋkfǔ` = \"steal\"\n- `lé` = \"saw\" (to see) → after consonant → `lé → é`, so `yɛn é`\n- Day: `ɛ̀bɛ̀n` = \"the woman\"\n\nSo: \"I will see the thief (saw) the woman?\"\n\nWait — structure: `S T V O (lé) L D`\n\nBut `nyɛ́n` is object, `kèŋkfǔ` is verb, `lé` is after verb (object of \"see\"), so:\n\n→ \"I will see the thief (who saw) the woman?\"\n\nNo — `kèŋkfǔ lé` = \"will steal and see\"?\n\nWait: `kèŋkfǔ` = \"steal\", `lé` = \"see\" → this is a compound?\n\nBut look at sentence 14: `bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n` → \"Today, we will steal the car\"\n\nSo `géː` = future, `cɔ́ŋ` = steal, `mutù` = car\n\nSo `kèŋkfǔ` = \"steal the yam\", from sentence 2.\n\nSo `kèŋkfǔ lé` = \"steal and see\"? Or \"steal the [thing] that was seen\"?\n\nBut the structure is: `S T V O (lé) L D`\n\nPossibly: \"I will [see] the thief\" → `me nú ŋgéː nyɛ́n lé`?\n\nBut verb is `kèŋkfǔ`, so likely: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\nSo: \"I will (the thief) steal the woman\" — makes no sense.\n\nAlternative: \"I will (the thief) see the woman and steal?\"\n\nNo.\n\nBut sentence 17: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\nLooking at sentence 2: `wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w` → \"On Bvusɔw, you(sg) will steal the yam\"\n\nSo `cɔ́ŋ kèŋkfǔ` = \"steal the yam\"\n\nSimilarly, `kèŋkfǔ` = steal the yam → object is yam\n\nHere, `kèŋkfǔ lé` — `lé` after verb → \"see\" → object of \"see\"\n\nSo perhaps it’s **\"I will see (the thief) stealing the woman\"**?\n\nBut the syntax seems to be: `[S] [T] [V] [O] [lé] [L] [D]`\n\nOnly one object → `nyɛ́n` is object of `kèŋkfǔ`?\n\nBut `lé` appears after, so likely `lé` is a separate verb.\n\nPossibility: `kèŋkfǔ` = verb, `lé` = to see → so \"I will see the thief stealing the woman\"\n\nBut \"stealing the woman\"? That doesn’t make sense.\n\nFrom sentence 15: `bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy` → \"They saw me at the market just now\"\n\nSo `yɛn lé` = \"saw X\"\n\nThus: `kèŋkfǔ lé` = \"steal and see\", but more likely: **\"steal the woman\"** and separately **\"see\" the thief**?\n\nWait — if `kèŋkfǔ` is \"steal\", and `lé` is separate, then:\n\n\"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\"\n\n→ \"I will (the thief) steal the woman\" → missing \"the\"\n\nBut `nyɛ́n` is object → so \"the thief steals the woman\"\n\nBut then `lé` is extra — unless it’s an object of \"see\"\n\nSo maybe: I will see the thief steal the woman\n\n→ \"I will see the thief stealing the woman\"\n\nThat fits sentence 15 where `yɛn lé` = saw + something\n\nSo: \"I will see the thief stealing the woman\"\n\nBut the day is `ɛ̀bɛ̀n` → the woman? Or reference?\n\nWait: `lé` is after the verb → so likely `lé` is the verb \"to see\", and `nyɛ́n` is the object of \"see\", and `kèŋkfǔ` is something else?\n\nBut only one verb?\n\nAlternative interpretation: misordering.\n\nWait — maybe `kèŋkfǔ` is \"steal\", and `lé` is \"saw\", so the whole phrase is \"**I will (the thief) steal the woman (that was seen)**\"\n\nNo.\n\nFrom sentence 2: `wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w` → \"On Bvusɔw, you will steal the yam\"\n\nSo verb = \"steal\", object = \"the yam\"\n\nSimilarly: `kèŋkfǔ` = steal the yam → object is yam\n\nBut here: `kèŋkfǔ lé` — `lé` after → so perhaps \"steal the woman\" and \"see\" is part of it?\n\nBut structure is `S T V O (lé) L D`\n\nSo likely: `kèŋkfǔ` = verb, `nyɛ́n` = object, `lé` = place? No — `lé` is \"see\", so must be an object of \"see\"\n\nBut there’s no \"see\" verb in the base form.\n\nWait — the verb \"see\" is `yɛn lé`\n\nSo \"I will see the thief stealing the woman\" → this would be `me nú ŋgéː nyɛ́n yɛn kèŋkfǔ lé ɛ̀bɛ̀n` — which is not what we have.\n\nWe have `kèŋkfǔ lé` — not `yɛn kèŋkfǔ lé`\n\nSo likely: the verb is `kèŋkfǔ` (steal), and then `lé` is attached → since after consonant, `lé → é`, so `kèŋkfǔ é`\n\nBut no — “steal the woman”?\n\nAnd “the woman” is the day? Unlikely.\n\nWait — sentence 7: `wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ` → \"You heard the thief a long time ago\" → `cɔ̌ŋ` = \"the thief\"\n\nSo `kèŋkfǔ` = \"the yam\" → so object is yam\n\nSo `kèŋkfǔ` = \"the yam\"\n\nSo why is `nyɛ́n` there? Object?\n\nThus: `me nú ŋgéː nyɛ́n kèŋkfǔ` = \"I will see the thief steal the yam\" — no, that’s not right.\n\nAlternative: `kèŋkfǔ` = \"steal\", `nyɛ́n` = object → \"the thief steals\"?\n\nThen `lé` = see → so \"I will see the thief steal the yam\"?\n\nBut the day is `ɛ̀bɛ̀n` — \"the woman\"\n\nSo perhaps: \"I will see the thief stealing the woman\"?\n\nYes — that fits the pattern.\n\nIn English: \"I will see the thief stealing the woman\"\n\nAnd the structure:\n- `me` = I\n- `nú ŋgéː` = future\n- `nyɛ́n` = the thief\n- `kèŋkfǔ` = steal (with implied object)\n- `lé` = \"see\"\n- `ɛ̀bɛ̀n` = the woman\n\nBut how is \"the woman\" the object of \"see\"?\n\nPossibly: \"the thief stealing the woman\"\n\nSo it's a complex verb construction: **\"see (someone) stealing (something)\"**\n\nSo: \"I will see the thief stealing the woman\"\n\nThat fits all rules.\n\nThus: **On Bvuŋkaden, I will see the thief stealing the woman**\n\nBut the day is `ɛ̀bɛ̀n` → the woman → so yes.\n\nSo translation: **I will see the thief stealing the woman**\n\nBut the sentence starts with “me nú ŋgéː” → “I will”\n\nSo full: **I will see the thief stealing the woman**\n\n✔️\n\n---\n\n#### 18. `wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn`\n\n- `wvù` = he\n- `tɔ̀ nɔ̂ː` = \"a long time ago\" (past)\n- `yɛ᷅n` = \"saw\"\n- `bèsèn` = \"the woman\"\n- `ě` = past tense marker (from rule: past = V᷅, `cí`, `nɔ̂ː`)\n- `bvúmbòn` = \"Bvumbon\"\n\nSo: \"He saw the woman (a long time ago) on Bvumbon\"\n\nBut `ě` is used after `bèsèn` — so `bèsèn ě` = \"the woman was\"\n\nBut `yɛ᷅n` = saw — so \"he saw the woman (on Bvumbon)\"\n\nThe day is at the end.\n\nSo: \"He saw the woman on Bvumbon a long time ago\"\n\nBut the structure: `S T V O (lé) L D`\n\n- S: `wvù`\n- T: `tɔ̀ nɔ̂ː` = past (a long time ago)\n- V: `yɛn` = see\n- O: `bèsèn` = woman\n- L: `bvúmbòn` = day\n- D: none?\n\nBut `ě` appears earlier — is it tense?\n\nRule: past tense = `V᷅`, and `cí`, `bɛ̂ː`, `nɔ̂ː` — here `nɔ̂ː` is in the tense prefix.\n\nActually, in sentence 7: `wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ` → \"You (sg) heard the thief a long time ago\" — `tɔ̀ nɔ̂ː` = past\n\nSo `tɔ̀ nɔ̂ː` = past, with object\n\nSo `tɔ̀ nɔ̂ː` = past time → represents \"a long time ago\"\n\nThus: `wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn`\n\n→ \"He a long time ago saw the woman (on Bvumbon)\"\n\nBut `ě` is after object → so? `bèsèn ě` = the woman was?\n\nThat would be passive.\n\nBut \"he saw the woman\" is active.\n\nSo likely `ě` is distractor or part of tense.\n\nWait — in sentence 7: `wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ` — \"heard\", `yo᷅w` = thief, `cɔ̌ŋ` = the thief\n\nSo `yo᷅w` = object → `cɔ̌ŋ` is the noun\n\nThus `yɛn` is verb, object `cɔ̌ŋ`\n\nSo in sentence 18: `yɛ᷅n` = \"saw\", object `bèsèn` = woman, then `ě` = past marker?\n\nBut the marker is already in `tɔ̀ nɔ̂ː`\n\nPossibility: `ě` is \"on Bvumbon\" → but no.\n\n`bvúmbòn` is the day → so likely `bèsèn ě bvúmbòn` = \"the woman was on Bvumbon\"\n\nBut the sentence says \"he saw the woman on Bvumbon\" — not \"the woman was on Bvumbon\"\n\nSo likely: `yɛ᷅n bèsèn ě bvúmbòn` = \"he saw the woman on Bvumbon\"\n\nThus: \"He saw the woman on Bvumbon a long time ago\"\n\n✔️ Translation: **He saw the woman on Bvumbon a long time ago**\n\n---\n\n#### 19. `bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n`\n\n- `bèsèn` = the woman\n- `nǔ` = \"on\" (preposition for day)\n- `bóy` = \"will help\"\n- `tɔ́` = tense → future (from rule: future = `nú géː`, `nú bóy`, `nú yúː`)\n- `fɔ̀wǎy` = \"the market\"\n- `bvúzhı᷇ːde᷆n` = the day after Bvuzhi\n\nSo: \"On Bvuzhiden, the woman will help the market\"?\n\nBut “help the market” is odd.\n\nCheck sentence 3: `kwɔ᷆ːn nǔ bóy fí me bvúzhí` → \"On Bvuzhi, the woman will help me\"\n\nSo `bóy` = \"help\", object = me\n\nSo `bóy fí` = help me\n\nThus: `bóy fɔ̀wǎy` = help the market\n\nBut \"the market\" = `fɔ̀wǎy`\n\nSo: \"The woman will help the market on Bvuzhiden\"\n\nSo day is `bvúzhı᷇ːde᷆n` = the day after Bvuzhi = Bvuzhiden\n\n✔️ Translation: **On Bvuzhiden, the woman will help the market**\n\nNote: the day is named after the previous day.\n\n---\n\n### Final translations:\n\n16. On Bvusɔw, the day after tomorrow is Bvutfu \n17. I will see the thief stealing the woman \n18. He saw the woman on Bvumbon a long time ago \n19. On Bvuzhiden, the woman will help the market \n\nNow, confirm with known patterns:\n\n- Sentence 5: \"The day after tomorrow is Bvutfu\" → uses `fɔ̀ shě ntfǔː`\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → uses `yɛn é` due to consonant\n- Sentence 12:", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10245.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 1, + "output": "We are given a series of Nooni sentences and their English translations across different days of the week. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, using the established linguistic rules.\n\n---\n\n### Step 1: Identify the tense and structure patterns\n\nFrom the provided examples:\n\n- **Tense markers**:\n - Past: `nɔ̂ː` (e.g., \"was\", \"heard\", \"found\")\n - Future: `nú` (e.g., \"will\")\n - Present (today): `bɛ̂ː` (e.g., \"today\") or `cí` (past), `tɔ̀ nɔ̂ː` (long time ago)\n - “Just now” or “be about to”: `géː` or `bóy` (e.g., “I am about to”)\n\n- **Verb structure**:\n - `S T V O (lé) L D`\n - “to see” = `yɛn lé` → after consonant: `lé → é`\n - `A T B` = “A is B” / “A was B” (where T is tense)\n\n- **1st person singular**:\n - `n-` becomes `mb-` (e.g., `nb` → `mb`)\n - `nk` → `ŋk`, `nn` → `n`\n\n---\n\n### Step 2: Analyze known examples for temporal expressions\n\nWe observe days in the cycle:\n\n- Bvutfu (yesterday)\n- Bvusɔw → used in sentence 2\n- Bvuzhi → used in 3\n- Bvukema → used in 8–11\n- Bvuŋka → used in 4–7, 12–15\n- **Bvuŋkaden** → target day (16–19)\n\nBackward and forward temporal expressions in the data:\n\n- “The day after tomorrow” → `fɔ̀ shě ntfǔː` → sentence 5 → **next day after tomorrow** = Bvutfu\n- “Tomorrow” → sentence 8 → `ntfǔː nú bvûŋka᷆ːde᷆n` → tomorrow is Bvuŋkaden\n- “The day before yesterday” → sentence 11 → `kefwé cí nú bvûŋka` → the day before yesterday was Bvuŋka\n- So the days follow a cycle:\n - Bvufu → yesterday\n - Bvusɔw → ?\n - Bvuzhi → ?\n - Bvukema → ?\n - Bvuŋka → today\n - **Bvuŋkaden** → tomorrow\n\nThus, **Bvuŋkaden = tomorrow** from Bvuŋka.\n\n---\n\n### Step 3: Translate sentence by sentence\n\n---\n\n#### 16. `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.`\n\n- `bvúsɔ̀w` = on Bvusɔw\n- `nǔ` = you (sg)\n- `fɔ̀ shě ntfǔː` = the day after tomorrow is Bvutfu\n\nWait: “fɔ̀ shě ntfǔː” = the day after tomorrow is Bvutfu?\n\nFrom sentence 5: \n> \"The day after tomorrow is Bvutfu\" → sentence 5 → `fɔ̀ shě ntfǔː nú`\n\nSo `fɔ̀ shě ntfǔː` = the day after tomorrow is Bvutfu → this is a fact.\n\nTherefore, this sentence: \n\"On Bvusɔw, the day after tomorrow is Bvutfu.\"\n\nBut that doesn't make sense chronologically because Bvusɔw occurred earlier — we are on Bvuŋkaden.\n\nWait — the day after tomorrow is Bvutfu?\n\nBut Bvutfu is earlier in the week.\n\nFrom (b): the days are ordered:\n\n> Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\nSo: \nOrder: Bvutfu → Bvuŋka → Bvuzhi → Bvukema → Bvuŋkaden → Bvuzhiden → Bvusɔw → Bvumbon → back to Bvutfu\n\nSo Bvusɔw is **after** Bvuŋkaden.\n\nTherefore, “the day after tomorrow is Bvutfu” → 2 days after tomorrow\n\nBut from Bvuŋkaden: \n- Tomorrow → Bvuzhiden \n- Day after tomorrow → Bvusɔw \n- Day after that → Bvumbon \n- Day after that → Bvutfu\n\nSo “the day after tomorrow” from Bvuŋkaden is **Bvusɔw**, not Bvutfu.\n\nWait: contradiction?\n\nBut in sentence 5:\n\n> “The day after tomorrow is Bvutfu”\n\nThat was on Bvusɔw.\n\nSo on Bvusɔw, day after tomorrow = Bvutfu.\n\nSo the cycle must be:\n\nOn Bvusɔw: \n- day after tomorrow = Bvutfu\n\nSo from Bvusɔw:\n- tomorrow = Bvuzhi \n- day after tomorrow = Bvukema \n- day after that = Bvuŋka \n- day after that = Bvuzhiden \n- day after that = Bvusɔw → no\n\nAlternatively, the cycle might be:\n\nFrom earlier: \n- On Bvukema: tomorrow = Bvuŋkaden \n- On Bvuŋka: day before yesterday = Bvuŋka → sentence 11: \"The day before yesterday was Bvuŋka\"\n\nOn Bvuŋka: \"The day before yesterday was Bvuŋka\" → impossible.\n\nSentence 11: \"kefwé cí nú bvûŋka\" → the day before yesterday was Bvuŋka → so on current day, day before yesterday was Bvuŋka.\n\nSo current day = Bvukema?\n\nBut sentence 8 says: \"Tomorrow is Bvuŋkaden\" → on Bvukema → so current day = Bvukema → tomorrow = Bvuŋkaden\n\nSo:\n- Bvukema → tomorrow = Bvuŋkaden\n- Then day before yesterday = Bvuzhi?\n\nBut sentence 11: “the day before yesterday was Bvuŋka” → so on Bvukema? → day before yesterday = Bvuŋka\n\nThus:\n- Bvukema → day before yesterday = Bvuŋka\n\nSo the order is:\n... → Bvuŋka → Bvukema → Bvuŋkaden → ...\n\nSo order: Bvuŋka → Bvukema → Bvuŋkaden → (next) → ?\n\nFrom (b): days are: \nBvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\nCheck positions:\n- Bvutfu → 0\n- Bvuŋka → 1\n- Bvuzhi → 2\n- Bvukema → 3\n- Bvuŋkaden → 4\n- Bvuzhiden → 5\n- Bvusɔw → 6\n- Bvumbon → 7\n\nSo sequence: \nEach day is one step after the previous.\n\nNow, on day D, what is the day \"n days later\"?\n\nBack to sentence 5: “The day after tomorrow is Bvutfu” → on Bvusɔw.\n\nBvusɔw → position 6 \nDay after tomorrow → position 8 → Bvumbon → not Bvutfu.\n\nBut Bvutfu is position 0.\n\nSo unless it's a cycle of 8 days, day after tomorrow = (6 + 2) mod 8 = 0 → Bvutfu → yes!\n\nSo:\n- Start at Bvusɔw (6)\n- +2 → Bvutfu (0)\n\nSo the day after tomorrow = Bvutfu → correct.\n\nSimilarly, in sentence 8: “Tomorrow is Bvuŋkaden” → on Bvukema (3) → tomorrow = 4 → Bvuŋkaden → yes.\n\nSo the days go in order, with wraparound when needed.\n\nThus, from a day X, add k → next day is (k + offset)\n\n---\n\nNow, back to sentence 16:\n\n`bvúsɔ̀w nǔ fɔ̀ shě ntfǔː`\n\n- On Bvusɔw, the day after tomorrow is Bvutfu.\n\nBut the sentence is **spoken on Bvuŋkaden**, not on Bvusɔw.\n\nSo this is not a sentence about the day Bvusɔw — it is just stating a fact: \n\"On Bvusɔw, the day after tomorrow is Bvutfu.\"\n\nSo translation is: \n**On Bvusɔw, the day after tomorrow is Bvutfu.**\n\nBut the context is Bvuŋkaden — so we are speaking from there, and stating a fact that on Bvusɔw, the day after tomorrow is Bvutfu.\n\nYes — consistent with the cycle.\n\nSo (16): \"On Bvusɔw, the day after tomorrow is Bvutfu.\"\n\n---\n\n#### 17. `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.`\n\nPattern:\n- `me` = I\n- `nú` = will (future)\n- `ŋgéː` = “be about to” (future)\n- `nyɛ́n` = the thief (subject)\n- `kèŋkfǔ` = the yam (object)\n- `lé` = to see → after consonant: `lé → é` → so `nyɛ́n kèŋkfǔ é` → “the thief saw the yam”\n- `ɛ̀bɛ̀n` = the woman\n\nWait — structure: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\nSo: “I will be about to see the thief the woman?”\n\nNo. That doesn't make sense.\n\nPossibility: `nyɛ́n kèŋkfǔ lé` → “the thief saw the yam” → “the thief saw the yam” → but then “the woman”?\n\nStructure: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\nWikipedia-style grammar: \"to see\" = yɛn lé → with object\n\nBut here: `nyɛ́n kèŋkfǔ lé` — the thief saw the yam\n\nThen `ɛ̀bɛ̀n` — the woman?\n\nBut that doesn’t match.\n\nAlternative: is `lé` used with object = thief, and “the woman” is the subject?\n\nNo.\n\nWait — example 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → today, we will steal the car → “we” = subject, “steal” = verb, “car” = object\n\nExample 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → they saw me at the market just now → \"they saw me\" → yɛn me → object = me\n\nSo `yɛn O lé` = \"to see O\"\n\nThus, syntax: \n**subject + verb + object + lé**\n\nSo here: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\n= \"I will be about to see the thief the woman?\"\n\nDoesn’t make sense.\n\nBut in example 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → on Bvutfu, the woman saw the market\n\nSo \"saw the market\" → \"yɛn wáy\"\n\nSo \"the woman saw the market\" → subject = woman, verb = saw, object = market\n\nSo in 17: `nyɛ́n kèŋkfǔ lé` → subject = thief, verb = see, object = yam\n\nThen `ɛ̀bɛ̀n` → the woman → who?\n\nBut subject is \"me\" → I will be about to see the thief the woman?\n\nDoesn’t work.\n\nWait — maybe it's \"I will be about to see the thief (who) sees the woman?\"\n\nNo.\n\nAlternative: \"I will be about to see the (thief) in the woman\" — no.\n\nWait: perhaps \"kèŋkfǔ\" is not the object?\n\nBut no other objects.\n\nCould it be \"I will be about to see the yam (with the woman)\"?\n\nNo.\n\nAnother idea: perhaps it's a mistranslation of \"I will be about to see the woman with the yam\"?\n\nNo.\n\nWait — in list (b), the days are: \nBvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\nSo days are ordered — we know what \"tomorrow\" is.\n\nBut the sentence is on Bvuŋkaden.\n\nSentence 17: `me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n`\n\nThe key is the tense: `nú ŋgéː` → future — \"will be about to\"\n\nSo: \"I will be about to see [someone] the woman?\"\n\nNo.\n\nWait — perhaps the object is \"the yam\", and \"ɛ̀bɛ̀n\" is the subject?\n\nNo — subject is \"me\".\n\nWait — perhaps it's a compound: “see the thief in the woman”?\n\nBut no such expression.\n\nAlternative: is “kèŋkfǔ” the verb?\n\nNo — verb is \"see\" = yɛn or yɛn lé.\n\n\"steal\" = cɔ́ŋ, \"help\" = bóy, \"kill\" = yó, \"choose\" = mbóy, \"saw\" = yɛn\n\nSo here, verb is \"see\" → yɛn.\n\nSo: subject: me \ntense: nú ŋgéː (future) \nverb: yɛn (to see) \nobject: nyɛ́n kèŋkfǔ → the thief with the yam?\n\nBut there's no such phrase.\n\nWait — in example 13: “the woman saw the market” → “yɛn wáy”\n\nSo object is market.\n\nSo object here is \"kèŋkfǔ\" — the yam.\n\nSo \"the thief\" is the subject of the verb \"see\"?\n\nNo — the structure is: `me nú ŋgéː nyɛ́n kèŋkfǔ lé` → I will be about to see the thief the yam?\n\nBut “the thief the yam” → doesn’t exist.\n\nWait — perhaps \"kèŋkfǔ\" is the place?\n\nNo.\n\nAnother idea: maybe the object is \"the woman\", and \"the thief\" is the subject?\n\nNo.\n\nWait — look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → today, we will steal the car (mutù) → ɛ̀bɛ̀n → woman → object?\n\nNo — \"mutù\" = car → object.\n\n\"ɛ̀bɛ̀n\" = woman → object? But no — \"we will steal the car\" — car is object.\n\nSo \"ɛ̀bɛ̀n\" is used as object in 14? No — “mutù ɛ̀bɛ̀n” = the car the woman? No.\n\nWait — sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “we will steal the car the woman”?\n\nNo — no such phrase.\n\nWait — example 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → “on Bvutfu, the woman saw the market”\n\nSo \"yɛn wáy\" — saw the market\n\nSo object = market\n\nThus, in 17: “nyɛ́n kèŋkfǔ lé” → the thief saw the yam\n\nThen “ɛ̀bɛ̀n” — the woman — is not part of it.\n\nBut it's at the end.\n\nUnless it's “I will be about to see the thief, the woman”?\n\nBut it’s not grammatical.\n\nAnother possibility: typo or misreading.\n\nWait — is it possible “kèŋkfǔ” is the subject and “lé” is the verb?\n\nNo — “kèŋkfǔ” = the yam → object.\n\nWait — compare to sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → they saw me at the market just now → \"yɛn me\" → saw me\n\nSo: object after \"yɛn\" is \"me\"\n\nSo structure: [subject] [tense] [verb] [object] [lé]?\n\nNo — \"yɛn me lé\" — object = me\n\nSo object is before \"lé\"? Or after?\n\nIn 15: \"yɛ᷅n me lé fɔ̀wǎy\" — they saw me at the market → \"me\" = object, \"fɔ̀wǎy\" = place\n\nSo object comes before place.\n\nIn sentence 17: `nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n` → it has object before \"lé\", then \"ɛ̀bɛ̀n\" — which may be place?\n\nBut \"ɛ̀bɛ̀n\" = the woman — not a place.\n\nUnless \"ɛ̀bɛ̀n\" = place — no.\n\nWait — is there a place in the sentence?\n\nNo.\n\nAnother possibility: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé\" = \"I will be about to see the thief (who) stole the yam?\"\n\nNo — \"kèŋkfǔ\" = yam, not \"stole\".\n\n\"steal\" = cɔ́ŋ\n\nSo no.\n\nWait — could \"kèŋkfǔ\" be a verb?\n\nNo — in context, \"steal the yam\" is \"cɔ̌ŋ kèŋkfǔ\"\n\nSo \"kèŋkfǔ\" is the object", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10731.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 2, + "output": "We are given sentences in Nooni spoken on different days, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden**, using the provided grammatical rules and examples.\n\n---\n\n### Step 1: Understand the day system and tense marking\n\nFrom the examples:\n- Days: Bvutfu, Bvusɔw, Bvuzhi, Bvukema, Bvuŋka, Bvuŋkaden\n- Tense markers:\n - Past: `V᷅` or `nɔ̂ː` (with `nɔ̂ː` after verb)\n - Future: `nú` + future marker (`géː`, `bóy`, `yúː`)\n - Present/now: `bɛ̂ː` (today), `cí` (past), `tɔ̀ nɔ̂ː` (long time ago), `tɔ̀` (after), `nú` (future)\n\nTense patterns:\n- `A T V O L D` → subject, tense, verb, object, place, day\n- Tense markers:\n - past: `nɔ̂ː` (after verb), or `V᷅`\n - future: `nú` + future marker (e.g., `nú géː`, `nú bóy`, `nú yúː`)\n - \"no longer\" or \"just now\" often marked by `bɛ̂ː` or `cí`\n\nTransformations:\n- First person singular: `n-` → `mb` (e.g., `nb` → `mb`)\n- `nk/ng` → `ŋk/ŋg`\n- `nn` → `n`\n\nAlso, after `-̂`, `-᷆`, `-̀`, the `-́` becomes `-̌`\n\n---\n\n### Step 2: Identify patterns in translation\n\nWe analyze the known translations:\n\nExample (1): `fɔgò cǐ nú bvúmbòn` → \"Yesterday was Bvumbon\" \n→ `cǐ` = past, `nú` = was → past tense of \"day\" \n→ tense: `cǐ` = past → \"yesterday\", `nú` = \"is/was\"\n\nExample (2): `wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w` → \"On Bvusɔw, you(sg) will steal the yam\" \n→ `yúː` = future → \"will steal\" \n→ `nú` used with `yúː` → future marker\n\nExample (3): `kwɔ᷆ːn nǔ bóy fí me bvúzhí` → \"On Bvuzhi, the woman will help me\" \n→ `bóy` = future (after `nǔ`) → \"will help\"\n\nSo:\n- `nú` with `géː` → \"will / about to\" (future)\n- `nú bóy` → future (to happen)\n- `nú yúː` → future (to happen)\n- `bɛ̂ː` → today\n- `tɔ̀ nɔ̂ː` → long time ago\n- `ní` → past (possibly `cí`)\n- `cí` → past (e.g., \"yesterday\", \"the day before\")\n\nAlso:\n- `yɛn lé` = \"to see\"\n- After consonant: `lé → é` → so `yɛn é` = \"saw\"\n\nExample (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"The day after tomorrow is Bvutfu\"\n→ `ntfǔː nú` = \"the day after tomorrow\" \n→ future tense with `nú`\n\nExample (6): `wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n` → \"Today, he killed the woman\"\n→ `bɛ̂ː` = today\n→ `yo᷅kwɔ᷆ːn` → killed (killed, goes from `kwɔ` to `yo₂kwɔ`, with `n` realization)\n\nNote: `kwɔ᷆ːn` → `yo᷅kwɔ᷆ːn` → may reflect past tense with voice?\n\nBut the result is \"killed\".\n\nWe see `bɛ̂ː` = today \n`cí` = past \n`nɔ̂ː` = past tense on noun based verb\n\nTense markers:\n- Future: `nú géː`, `nú bóy`, `nú yúː`\n- Present: `bɛ̂ː` (today)\n- Past: `nɔ̂ː` (after verb), `cí` (past), `tɔ̀ nɔ̂ː` (long ago)\n\n---\n\n### Step 3: Parse each sentence (spoken on Bvuŋkaden)\n\n---\n\n**16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.**\n\nStructure:\n- `bvúsɔ̀w` = day\n- `nǔ` = \"you(sg)\"\n- `fɔ̀` = past tense verb (from `fɔ̀` → \"was\")\n- `shě` = \"the\" (determiner for day?)\n- `ntfǔː` = \"the day after tomorrow\"\n\nBut `fɔ̀ shě ntfǔː` → must be \"the day after tomorrow was\" \nBut at the end, `nǔ` meaning \"you\" — so \"you will have the day after tomorrow\"?\n\nWait — look at example (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"The day after tomorrow is Bvutfu\"\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow was\"\n\nBut here: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` → \"On Bvusɔw, you(sg) had the day after tomorrow?\"\n\nThat doesn’t make sense.\n\nWait — perhaps the verb is `shě` = \"to be\"?\n\n`fɔ̀` is past tense marker.\n\nSo: `fɔ̀ shě` = \"was\"\n\n`ntfǔː` = \"the day after tomorrow\"\n\nSo: \"you were the day after tomorrow\" — wrong.\n\nWait.\n\nAnother idea: `ntfǔː` introduces the day.\n\nIs it “the day after tomorrow is [something]”?\n\nBut here it’s `nǔ fɔ̀ shě ntfǔː` = \"you were the day after tomorrow\" — still wrong.\n\nPerhaps `ntfǔː` is the day name?\n\nBut we already have `bvúsɔ̀w` as day.\n\nAlternative: `fɔ̀ shě ntfǔː` = \"was the day after tomorrow\"\n\nSo `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` = \"On Bvusɔw, you were the day after tomorrow\"?\n\nNo.\n\nWait — example (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"the day after tomorrow is Bvutfu\"\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow was\" — interpreted as 'is' → future tense.\n\nBut here, it’s a past claim: `fɔ̀ shě ntfǔː` might mean \"was [the day after tomorrow]\"\n\nSo: \"On Bvusɔw, you were the day after tomorrow?\" doesn’t make sense.\n\nPerhaps it’s a misreading.\n\nWait — what if `fɔ̀ shě ntfǔː` = \"the day after tomorrow [was]\" → so the phrase is \"On Bvusɔw, you were [the day after tomorrow]\"?\n\nStill nonsense.\n\nWait — perhaps it’s a reference to a day being *when* something happened.\n\nAnother clue: Example (11): `kefwé cí nú bvûŋka` → \"The day before yesterday was Bvuŋka\"\n\nSo:\n- `cí` = before yesterday\n- `nú` = was\n- So \"the day before yesterday was Bvuŋka\"\n\nSimilarly:\n- `ntfǔː` = the day after tomorrow\n- `fɔ̀` = past tense (was)\n- So `fɔ̀ shě ntfǔː` = the day after tomorrow was (i.e., happened)\n\nSo: \"On Bvusɔw, you were the day after tomorrow\" — still odd.\n\nBut no subject says \"you were the day after tomorrow\".\n\nWait — perhaps it's a word order error.\n\nWhat if it's \"On Bvusɔw, the day after tomorrow was\" — but who?\n\nThe subject is `nǔ` → \"you\"\n\nSo: \"On Bvusɔw, you were the day after tomorrow\"?\n\nStill not likely.\n\nWait — is there a different verb?\n\nLook at (13): `kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅` → \"On Bvutfu, the woman saw the market\"\n\nSo `yɛn lé` = \"saw\", `lé → é` when after consonant.\n\nSo `yɛ᷅n` = \"saw\", `lé → é` in `é` after consonant.\n\nBack to 16: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː`\n\nCompare with (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"the day after tomorrow is Bvutfu\"\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow is\" → interpreted as future implied?\n\nBut past tense → \"was\"\n\nWait — maybe the verb `shě` is \"to be\", and `fɔ̀` is tense?\n\nPerhaps `fɔ̀` is the tense marker for past (like `nɔ̂ː`), so \"was\"\n\nSo `fɔ̀ shě` = \"was\"\n\nThus: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` = \"On Bvusɔw, you were the day after tomorrow\" — still doesn't make sense.\n\nBut no other day is called \"the day after tomorrow\".\n\nAlternative: Perhaps `ntfǔː` is a day name.\n\nWe have: Bvutfu, Bvusɔw, Bvuzhi, Bvukema, Bvuŋka, Bvuŋkaden.\n\nSo `ntfǔː` = Bvutfu?\n\nIn example (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"the day after tomorrow is Bvutfu\"\n\nSo `ntfǔː` = \"day after tomorrow\"\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow was\"\n\nThen `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` → \"On Bvusɔw, you were the day after tomorrow\"?\n\nNo.\n\nWait — is it \"you were [on] the day after tomorrow\"?\n\nThat is: \"you were on the day after tomorrow\"\n\nBut \"on\" is not expressed.\n\nBut look at other structures.\n\nExample (3): `kwɔ᷆ːn nǔ bóy fí me bvúzhí` → \"On Bvuzhi, the woman will help me\"\n\nSo day is marked at beginning: `On Day X, verb`\n\nSo here: `bvúsɔ̀w` = day → \"On Bvusɔw,\"\n\nThen: `nǔ fɔ̀ shě ntfǔː` → \"you were the day after tomorrow\"?\n\nBut \"day after tomorrow\" isn't a time in the day.\n\nWait — could \"fɔ̀ shě\" = \"was\" and \"ntfǔː\" = \"the day after tomorrow\" so \"the day after tomorrow was\" → \"was the day after tomorrow\" — but on what day?\n\nMaybe misreading.\n\nAnother idea: perhaps the structure is `S T V O L D`\n\nSo: `nǔ` = subject (you)\n`fɔ̀` = tense (past)\n`shě` = verb (to be)\n`ntfǔː` = object (the day after tomorrow)\n\nSo \"you were the day after tomorrow\"\n\nBut that’s not grammatical.\n\nUnless \"day after tomorrow\" is a place?\n\nNo.\n\nBut in (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"The day after tomorrow is Bvutfu\"\n\nSo \"the day after tomorrow\" = a day name\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow was\"\n\nThus, \"On Bvusɔw, you were [on] the day after tomorrow\" → no.\n\nWait — \"you were on\" is not in structure.\n\nWait — maybe it's \"you were [the one who was on] the day after tomorrow\"\n\nStill odd.\n\nAlternative: Could `shě` be \"to have\"?\n\nNo — no evidence.\n\nAnother possibility: “fɔ̀ shě” is a day name?\n\nNo — `fɔ̀` is tense.\n\nWait — in (1): `fɔgò cǐ nú bvúmbòn` → \"yesterday was Bvumbon\"\n\nSo `cǐ` = past tense, `nú` = was\n\nHere: `fɔ̀` = past, `shě` = be, `ntfǔː` = the day after tomorrow\n\nSo \"you were the day after tomorrow\" → perhaps a misstatement.\n\nBut maybe it’s “you will be the day after tomorrow” — but `fɔ̀` = past.\n\nNo.\n\nWait — could it be a typo or alternative reading?\n\nNote: Sentence 16: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː`\n\nCompare with sentence 5: `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"The day after tomorrow is Bvutfu\"\n\nSo in that case, `fɔ̀ shě ntfǔː` is a phrase that means \"the day after tomorrow is\"\n\nSo structure: `[fɔ̀ shě ntfǔː] nú [day]` = \"the day after tomorrow is [day]\"\n\nBut in 16, it's `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` → \"On Bvusɔw, you were [the day after tomorrow]\"\n\nWait — unless `fɔ̀ shě ntfǔː` means \"on the day after tomorrow\", like \"the day after tomorrow\" as a unit.\n\nBut \"you were on the day after tomorrow\" — possible.\n\nBut “on” is not in the grammar.\n\nWait — is there a \"was on\" verb?\n\nBut the only \"on\" is marked by day name.\n\nAnother idea: perhaps \"bvúsɔ̀w\" is not the day, but the verb?\n\nNo — `bvúsɔ̀w` is a known day name (like Bvusɔw), so it must be the day.\n\nSo: \"On Bvusɔw, you were the day after tomorrow\" — grammatical only if “day after tomorrow” is a person.\n\nUnlikely.\n\nWait — another clue: example (11): `kefwé cí nú bvûŋka` → \"the day before yesterday was Bvuŋka\"\n\nSo `cí` = day before yesterday\n\nSimilarly:\n- `ntfǔː` = day after tomorrow\n- `fɔ̀` = past tense\n- `shě` = to be\n\nSo `fɔ̀ shě ntfǔː` = the day after tomorrow was\n\nSo “you were the day after tomorrow” → still odd.\n\nBut perhaps it's \"you were the one who was on the day after tomorrow\" — no.\n\nWait — could “nǔ” be part of a noun?\n\nNo — in (2): `wɔ̀ nǔ yúː` = \"you will steal\"\n\nSo `nǔ` = you (sg)\n\nSo subject.\n\nAlternative possibility: linguistic error — maybe the day is `ntfǔː`, and the sentence is about a past occurrence.\n\nBut days do not attach to verb like that.\n\nWait — look at (11): `kefwé cí nú bvûŋka` → \"the day before yesterday was Bvuŋka\"\n\nSo: time reference = `cí` (day before yesterday), tense = `nú` (was), day = Bvuŋka\n\nSo in (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"the day after tomorrow is Bvutfu\" (future)\n\nSo `fɔ̀ shě ntfǔː` = \"the day after tomorrow was/is\"\n\nBut here: `bvúsɔ̀w nǔ fɔ̀ shě ntfǔː` = \"On Bvusɔw, you were the day after tomorrow\"\n\nNo.\n\nPerhaps it's a misordering.\n\nAnother idea: Perhaps `fɔ̀ shě` is a time expression.\n\nWait — in (3): `kwɔ᷆ːn nǔ bóy fí me bvúzhí` → \"On Bvuzhi, the woman will help me\"\n\nSo \"On Day X, Subject will [verb] Object\"\n\nIn (16): \"On Bvusɔw, you were [the day after tomorrow]\"\n\nOnly if “being” is used.\n\nBut no.\n\nWait — is there a possibility that `ntfǔː` is not \"the day after tomorrow\", but the day name?\n\nIn (5): `fɔ̀ shě ntfǔː nú bvútfu᷅` → \"the day after tomorrow is Bvutfu\"\n\nSo `ntfǔː` is the time expression, `nú` links to day.\n\nBut here, `bvúsɔ̀w` is the day, and `fɔ̀ shě ntfǔː` is the time event.\n\nSo the sentence might be: \"On Bvusɔw, you were in the day after tomorrow\" — but again, no.\n\nPolling the phrase: the only grammatical explanation is that “you were the day after tomorrow” is a non-standard use.\n\nAlternative interpretation: maybe “fɔ̀ shě” = “was on”, and “ntfǔː” = “the day after tomorrow”\n\nBut “on” is not there.\n\nWait — in (4): `wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː` → \"On Bvuŋka, he found the book\"\n\nSo \"On Bvuŋka, he found\"\n\nSo in (16): \"On Bv", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + 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"ioling_format_error": 1.0, + "ioling_response_chars": 10882.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 3, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden** into English.\n\nWe need to infer the grammatical rules and then apply them to the target sentences.\n\n---\n\nStep 1: Identify the core grammatical structure from given examples.\n\nGeneral structure:\n- A T nú B → A is B / A was B (T = tense)\n- S T V O (lé) L D → Subject + Tense + Verb + Object + place + day\n- \"to see\" = yɛn lé (after consonant → lé → é)\n\nTense markers:\n- past: V᷅ (e.g., fɔ̀wǎy in \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\")\n- present/future: \n - ∅ (neutral): \"Today\"\n - fut: V́ (e.g., yúː in \"On Bvusɔw, you(sg) will steal the yam\")\n - past: V + nɔ̂ː (e.g., wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → \"On Bvusɔw, you will steal...\")\n - future: \"nú géː\" / \"nú bóy\" / \"nú yúː\"\n\nTense markers per day:\n- past: basic tense with nɔ̂ː\n- future: can be in forms like:\n - nú géː → \"will be about to\"\n - nú bóy → \"will\"\n - nú yúː → \"will\"\n\nAlso: \n- after –̂, –᷆, –̀: –́ → –̌ \n → So if a verb has a tone at the end, after a specific letter, the high tone becomes low: e.g., “fɔ̀wǎy” → “fɔ̀w̌y” as seen in \"fɔ̀wǎy bvúmbòn\"\n\nAlso: \n- 1st person: \n - n- → mb (e.g., nb → mb) \n - nk → ŋk, ng → ŋg \n - nn → n\n\nNow, look at tense markers tied to days:\n\nExample:\n- \"The day after tomorrow is Bvutfu.\" → fɔ̀ shě ntfǔː nú bvútfu᷅ \n → \"ntfǔː\" means \"the day after tomorrow\", and it's marked with \"nú\" → future pattern\n\n- \"The day before yesterday was Bvuŋka.\" → kefwé cí nú bvûŋka \n → \"cí\" = past, so \"was\"\n\n- \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"ntfǔː\" (tomorrow) + \"nú\" → future\n\nSo:\n- \"ntfǔː\" = tomorrow\n- \"cí\" = past (was)\n- \"fɔ̀ shě\" = the day after tomorrow? Actually in sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\" → so \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\"\n\nSo:\n- fɔ̀ shě ntfǔː = the day after tomorrow \n- ntfǔː = tomorrow \n- cí = past \n- yúː = future (will) \n- bɛ̂ː = today \n- tɔ̀ nɔ̂ː = a long time ago (past away from today)\n\nThus:\n- tense markers:\n - present: bɛ̂ː (today)\n - past: cí (past), tɔ̀ nɔ̂ː (some time ago)\n - future: nú (will), with following:\n - nú géː = will be about to\n - nú bóy = will (do)\n - nú yúː = will (do)\n\nAlso: \"yɛn\" means \"to see\", and when after consonant, \"lé\" → \"é\"\n\nSo: \"yɛn lé\" → \"yɛn é\" (after consonant)\n\nNow, the sentences to translate (on Bvuŋkaden):\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ \"On Bvúsɔw, the day after tomorrow\"\n\nWait — better: pattern?\n\nFrom earlier:\n\nExample: \n\"On Bvusɔw, you(sg) will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\n\nSo:\n- wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ → subject (you), future (yúː), verb (steal), object (yam), day (Bvúsɔw)\n\nSo structure: [subject] [tense] [verb] [object] [day]\n\nTherefore:\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː → **On Bvúsɔw, the day after tomorrow**? \nBut \"nǔ\" is not subject. Wait — in past tense, not subject.\n\nLook: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\n\"nǔ\" is likely the tense marker here.\n\nIn example 2: wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w \n→ wɔ̀ (you), nǔ (tense: future), yúː (will), cɔ́ŋ (steal), kèŋkfǔ (yam), bvúsɔ̀w (day)\n\n\"nǔ\" is attached to the verb — this is a tense marker for future.\n\nSo in 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ Subject: ? \nBut no subject. So perhaps \"the day after tomorrow\" is the subject?\n\nBut \"fɔ̀ shě ntfǔː\" is the day after tomorrow.\n\nSo: \"On Bvúsɔw, [the day after tomorrow] is...\" → no.\n\nWait — another example:\n\n\"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n \n→ ntfǔː (tomorrow), nú (future), bvûŋka (day)\n\nSo in 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \nWe see \"fɔ̀ shě\" = the day after tomorrow \nSo is \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow\" — so it is a day name?\n\nBut in “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu” \nSo phrase “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nThus, in 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː → likely means “On Bvúsɔw, the day after tomorrow is...” — but no object.\n\nWait — no completion. But the sentence may be missing a verb.\n\nBut no — look at structure: no verb in this sentence.\n\nAnother possibility: the day is being named.\n\nWait — from sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n\n\nSo “ntfǔː nú [day]” → future\n\nSimilarly, sentence 5: \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅\n\nSo: [day] + nú + day name\n\nSimilarly, sentence 11: \"The day before yesterday was Bvuŋka\" → kefwé cí nú bvûŋka → past (cí), on day\n\nSo: for future day: [day name] + nú + target day name\n\nBut in 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\n\n\"nǔ\" is likely a future tense marker → may be substituted for \"nú\" in some cases?\n\nBut in example 2: future → \"nǔ yúː\" → \"you will steal\"\n\nSo \"nǔ\" is part of future tense with future verb.\n\nBut no verb here.\n\nSo likely: \"On Bvúsɔw, the day after tomorrow\" — but that's incomplete.\n\nWait — is “bvúsɔ̀w” the day?\n\nYes — Bvúsɔw is a day name.\n\nBut the sentence is “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nCould be: “On Bvúsɔw, [the day after tomorrow]?”\n\nBut still, for it to make sense, it must be a statement about a day.\n\nCompare with sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n \n→ future + day name\n\nSentence 5: \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅\n\nSo: [day] + nú + day name\n\nSo \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — perhaps \"On Bvúsɔw, the day after tomorrow\" is a statement? But what?\n\nWait — maybe mistake: perhaps \"nǔ\" is the tense, and “fɔ̀ shě” is the day, so:\n\n“On Bvúsɔw, the day after tomorrow” → not complete.\n\nBut in the pattern, when a future day (like \"day after tomorrow\") is mentioned, it is marked with \"ntfǔː nú [day]\" (as in 5)\n\nSo here, no \"nú\", only \"nǔ\"\n\nPerhaps “nǔ” is a variant of “nú”?\n\nIn sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → “On Bvutfu, the woman saw the market”\n\n“nɔ̂ː” = past\n\nIn sentence 17: me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n \n→ I will be about to see the thief? \n“nú ŋgéː” = future, “nyɛ́n” = to see (yɛn), “lé” → “é” after consonant → so “nyɛ́n é”\n\nSo “see the thief”\n\n“ɛ̀bɛ̀n” = the woman\n\nSo me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n → I will be about to see the thief\n\n“l’é” → after consonant → becomes “é”\n\nSimilarly: 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn \n→ “he heard the thief [a long time ago]?” \n“tɔ̀ nɔ̂ː” = long time ago (past), “yɛ᷅n” = saw, “bèsèn” = the thief, “ě” → likely a verb (to be), “bvúmbòn” = Bvumbon\n\n“ě” — from previous: “bɛ̂ː” = today, “tɔ̀ nɔ̂ː” = long ago\n\nSo in example 7: “you(sg) heard the thief a long time ago” → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → “heard”\n\nSo “yɛ᷅n” = saw (yɛn), after consonant → “yɛ᷅n” → “yɛ̂n” → becomes “yɛn” with tone?\n\nWait: “yɛn” is to see → in 18: yɛ᷅n → after consonant → but word is “yɛ᷅n” — so tone shift?\n\nRule: after a consonant: lé → é → so yɛn → yɛ́n → yɛ̂n → yɛ̌n → yɛn? With tone change.\n\nBut in 18: wvù tɔ̀ nɔ̂ː yɛ᷅n → “he saw the thief” — past tense.\n\nSo likely “yɛن” → “yɛن” — or pronounced as “yɛن” → so “saw”\n\nBack to 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\n\n“nǔ” → future tense marker (as in “you will steal” → wɔ̀ nǔ yúː)\n\n“fɔ̀ shě ntfǔː” → “the day after tomorrow”\n\nSo: “On Bvúsɔ̀w, the day after tomorrow” → but still incomplete.\n\nBut this is a statement about a future day — perhaps it is stating that “on Bvúsɔw, the day after tomorrow is [something]” — but no day after?\n\nWait — is “bvúsɔ̀w” the day, and the sentence is saying that “the day after tomorrow” is a future event?\n\nNo — the sentence is on Bvuŋkaden — so it's talking about other days.\n\nWait — perhaps the sentence is: “On Bvúsɔw, the day after tomorrow [is something]” — but missing object.\n\nBut all sentences in the list have a subject, verb, object, or location.\n\nWait — perhaps “nǔ” is not future, but a day name?\n\nBut “bvúsɔ̀w” is a day — so that can't be.\n\nAnother idea: perhaps “fɔ̀ shě ntfǔː” is a day name, and “bvúsɔ̀w” is the day.\n\nBut in known example: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo likely here: “On Bvúsɔw, the day after tomorrow is [not given]” — but no day.\n\nUnless it's a typo or missing?\n\nBut let’s look at structure again.\n\nIn example 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “On Bvuŋka, he found the book” \n→ wvù (he), tɔ̀ nɔ̂ː (past), bɔ᷅ŋ (found), ŋwà (book), bvûŋka (day)\n\nSo structure: [subject] [tense] [verb] [object] [day]\n\nNow 16: bvúsɔ̀w nǔ fɔ̀ shě ntfǔː — only two noun phrases.\n\nUnless “bvúsɔ̀w” is subject? But it's a day — like \"On Bvúsɔw\" — which is a day.\n\nSo likely: “On Bvúsɔw, the day after tomorrow” — but that doesn't make sense as a full sentence.\n\nWait — from sentence 10: dìɛ̀msɛ̌n nú yɛ́n wvù lě → “The man is about to see him”\n\n“nú” for “is about to” → future\n\nSimilarly, “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → I will be about to see the thief\n\nSo “nú ŋgéː” = future, “nyɛ́n” = see, “lé” → “é”\n\nSo any “nú” or “nǔ” with high tone is future.\n\nIn 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — \"nǔ\" = future, \"fɔ̀ shě\" = day, \"ntfǔː\" = day?\n\nBut “fɔ̀ shě ntfǔː” = the day after tomorrow — so “the day after tomorrow” is a time expression.\n\nSo the only way this makes sense is if it is saying “On Bvúsɔw, the day after tomorrow” — but again, incomplete.\n\nAlternatively, could \"nǔ\" be attached to \"fɔ̀ shě\" to form a verb?\n\nNo — \"fɔ̀ shě\" is not a verb.\n\nFrom example 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → you will steal the yam on Bvúsɔw\n\nSo verb is after “yúː”\n\nSo in 16, “nǔ” is likely a future tense marker before a verb — but no verb appears.\n\nUnless the verb is missing.\n\nBut look at the list again — all others have verbs.\n\nPerhaps it's a standalone statement: “On Bvúsɔw, the day after tomorrow” — meaning that Bvúsɔw is the reference day, and the day after tomorrow is a future time.\n\nBut what is being said?\n\nWait — background: \"Bvuŋkaden\" is a day — and this sentence is spoken on it.\n\nBut no event.\n\nAnother possibility: maybe it's a calendar statement, like “On Bvúsɔw, the day after tomorrow is [something]” — but something is missing.\n\nBut in sentence 5: “The day after tomorrow is Bvutfu” — so “fɔ̀ shě ntfǔː nú bvútfu᷅”\n\nSimilarly, in sentence 8: “Tomorrow is Bvuŋkaden” → ntfǔː nú bvûŋka᷆ːde᷆n\n\nSo pattern: [time expression] + nú + day name\n\nSo in 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" — if “nǔ” is “nú”, then it would be “bvúsɔ̀w nú fɔ̀ shě ntfǔː” — meaning “On Bvúsɔw, the day after tomorrow is [something]”\n\nBut what is [something]? Not specified.\n\nUnless the sentence is missing the day name.\n\nBut in the problem, it's given as is.\n\nPerhaps the structure is: [day] + [time expression] → but the time expression is “fɔ̀ shě ntfǔː” = the day after tomorrow\n\nSo “On Bvúsɔw, the day after tomorrow” — perhaps it's meant to be “On Bvúsɔw, the day after", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10502.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. [TARGET ANSWER REDACTED]\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. [TARGET ANSWER REDACTED]\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. [TARGET ANSWER REDACTED]\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. [TARGET ANSWER REDACTED]\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. me ncí nɔ̂ː nfı᷅dìɛ̀msɛ̌n bvúsɔ̀w.\n 21. The thief stole the yam just now. cɔ̌ŋ nɔ̂ː cɔ᷅ŋ kèŋkfǔ.\n 22. On Bvuŋkaden, I will hear the car. me nú nyúː nyów mutù bvûŋka᷆ːde᷆n.\n 23. Today, the woman will kill the man. kwɔ᷆ːn nǔ géː yó dìɛ̀msɛ̌n ɛ̀bɛ̀n.\n 24. Today, the man saw you(sg). dìɛ̀msɛ̌n bɛ̂ː yɛ᷅n wɔ̀ lě ɛ̀bɛ̀n.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 0, + "output": "We are given a set of Inuktitut sentences and their translations, with rules for verb and noun derivation. Our goal is to translate five new sentences into Inuktitut using the provided linguistic patterns.\n\n---\n\n### Step 1: Understand the core structures\n\nFrom the problem, we have three general schemas:\n\n1. **X-(q) V–** → 'X V (himself)' → reflexive; when no object, verb is simple \n e.g., *Aanniqtutit* → \"You hurt yourself\"\n\n2. **X-(q) Y-(r)mik V–si–** → 'X V a Y' → transitive, object is indefinite, marked with -mik (with -r before if indefinite) \n e.g., *Iluaqhaijiup aarqijaatit* → \"The doctor cured you\" \n Here: \"iluaqhaiji\" (doctor) + \"up\" (definite subject) + \"aarqijaatit\" → cured you; but object \"you\" is definite, so no -mik. Wait — actually, in sentence 4: *Iluaqhaijiup aarqijaatit* → doctor cured you → object is definite, so no -mik. \n But in sentence 6: *Angatkuq iluaqhaijimik aarqisijuq* → \"The shaman cured a doctor\" → object is \"a doctor\" (indefinite) → object has -mik.\n\n Pattern: \n - if object is indefinite → object has -mik \n - if object is definite → no -mik \n - indefinite object: includes forms like *nanuq-mik*, *iluaqhaijimik* \n - definite object: *iluaqhaiji* (without -mik)\n\n Also: nouns with definite subject use -up (e.g., *inuuhuktuit*), with possessive:\n - \"your\" → -(q) → -(it) or -(vit)\n - subject: -(q) becomes -(it) or -(vit) when possessive\n\n3. **X-up Y-(q) V–** → 'X V the Y' \n e.g., *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" \n Here: \"Qingmi\" (dog) + \"up\" (definite) + \"ilinniaqtitsijiit\" → hurt + \"your teacher\" \n → \"ilinniaqtitsijiit\" = \"your teacher\" \n → \"your\" = \"ilinniaq\" → ilinniaqtitsijiit → possessive form of \"teacher\" with -it\n\n---\n\n### Step 2: Derive pattern for each of the target sentences\n\n---\n\n#### 19. The shaman hurt you.\n\n- Subject: \"the shaman\" → *angatkuq* \n- Verb: \"hurt\" → \"aanniqtut\" (from sentence 3: *Aanniqtutit* = \"you hurt yourself\") → base verb *aanniqtut*, with -it for reflexive (you hurt yourself)\n\n- Object: \"you\" → definite → no -mik \n- Subject is definite → use -up \n→ *Angatkuq aanniqtutit* → \"The shaman hurt you\"\n\nBut check structure: \nIn sentence 3: *Aanniqtutit* → \"you hurt yourself\" → reflexive \nIn sentence 2: *Inuuhuktuup iluaqhaiji qukiqtanga* → \"the boy shot the doctor\" \n→ so verb: *qukiqtanga* → \"shot\" → transitive with definite object\n\nSo for transitive verb with definite object → no -mik \nWith indefinite → object ends in -mik\n\nHere: object = \"you\" → definite → so no -mik → verb ends in -it\n\nSo: *Angatkuq aanniqtutit*\n\nBut is *angatkuq* the form for \"the shaman\"? \nSentence 6: *Angatkuq iluaqhaijimik aarqisijuq* → \"the shaman cured a doctor\" → so yes, *angatkuq* = \"the shaman\"\n\nSo sentence 19: **Angatkuq aanniqtutit**\n\n---\n\n#### 20. The teacher saw the boy.\n\n- Subject: \"the teacher\" → must be *ilinniaq*? \n Sentence 10: *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" \n → \"ilinniaqtitsijiit\" = \"your teacher\" \n → So teacher → base form *ilinniaq* \n → definite → *ilinniaq-up*?\n\nBut verbs: \"saw\" — where is this?\n\nSentence 1: *Qingmivit takujaatit* → \"your dog saw you\" \n→ *takujaatit* → saw you → verb with -it\n\nSo verb for \"saw\" = *takuj* → with suffix -a (after t?) → *takujaatit*\n\nStructure: \nSubject: \"the teacher\" → definite → use -up → *ilinniaq-up* \nObject: \"the boy\" → definite → so object not marked with -mik \nVerb: saw → *takuj* → transitive → *takujaatit*? \nBut in sentence 1: *Qingmivit takujaatit* → \"your dog saw you\" → subject = \"your dog\" → possessive → \"qinmivit\" = *qingmi* + it (your) + -vit? \n\"qingmi\" → dog → \"qingmivit\" → your dog → used -vit \n\nSo for definite subject → -up; for possessive → -it or -vit \n\nSo \"the teacher\" → *ilinniaq-up* \n\"the boy\" → *inuuhuktu* (from sentence 2: \"the boy\") — base noun\n\nSo: *ilinniaq-up inuuhuktu takujaatit*?\n\nCheck grammar: \nSentence 2: *Inuuhuktuup iluaqhaiji qukiqtanga* → \"the boy shot the doctor\" → subject is definite → -up → object is definite → no -mik → verb ends with -a-t? — *qukiqtanga* → looks like verb with -a-t?\n\nBut verb pattern: \n- verb base: *qukiq* → shot \n- suffix: -ta → *qukiqtanga* — consonant + -t → suffix after consonant → *-t* → *-qtanga*?\n\nRule: verb receives:\n- -j after vowel\n- -t after consonant\n\nIn sentence 2: *qukiqtanga* → after consonant → -t → so *-qtanga*?\n\nSimilarly, in sentence 1: *takujaatit* → after vowel? \"takuj\" → vowel? \"a\" → vowel → so -j after vowel → *takujaatit* → so suffix -j\n\nSo verb: saw → base form *takuj* → after vowel → -j → *takuj* → base? Then *takuj* + *a* + *t*?\n\nWait: *takujaatit* → \"saw\" → so after \"a\" → -j → so *takuj* → ends with j?\n\nPossibly: *takuj* → saw → with -j after vowel → so *takuj* + something?\n\nIn sentence 1: *takuj* → saw → preceded by subject → *qingmivit* → \"your dog\" → verb is *takujaatit* → *takuj* + *a* + *a* + *t*?\n\nNo — apparent form: *takujaatit* → likely: base *takuj*, then -a-tit → -a for vowel? No.\n\nWait: verb pattern:\n\n- after vowel → -j → so *takuj* (after \"a\") → *takuj* + *j* → *takuj*? \nBut \"takuj\" is already there.\n\nBetter: in sentence 1: *qingmivit takujaatit* → the verb is *takujaatit* \nIt ends with -it\n\n- \"takuj\" → base word \n- then -a → infix? \n- then -t → after consonant? \n- then -it?\n\nActually, likely: verb base *takuj* → \"saw\" \n- with object → -a-t → used in both cases? \nIn sentence 1: *takujaatit* — includes -a, -t, -it \n\nNo clear base.\n\nBut look at sentence 1: *qingmivit takujaatit* → saw you \nsentence 2: *inuuhuktuup iluaqhaiji qukiqtanga* → shot doctor → verb = *qukiqtanga* \n→ ends with -tanga → after consonant → -t-suffix?\n\nPattern: \n- when after consonant → -t suffix → *qukiqtanga* → *qukiq* + *t* + *anga* \n- when after vowel → -j suffix → *takuj* (but in sentence 1, *takujaatit* — not just *takuj*)\n\nAnother idea: the verb is formed by:\n- base verb root\n- affix: -j after vowel; -t after consonant\n- then person endings\n\nIn sentence 1: *takujaatit* → for 2nd person → -it? \nYes: \"you\" → appears in both cases → \"you\" → -it\n\nIn sentence 2: *qukiqtanga* → \"the doctor\" → 3rd person → -a-t? — but no person ending?\n\nWait: sentence 2: \"the boy shot the doctor\" → boy is subject → 3rd person → should have ending?\n\nSentence 2: *Inuuhuktuup* → \"the boy\" → 3rd person singular → ending -up?\n\nThen verb: *qukiqtanga* → so -t after consonant → because \"qukiq\" ends with q → consonant → so -t → *qukiqtanga* → and no person ending → because object is definite and 3rd person?\n\nBut sentence 1: *qingmivit takujaatit* → \"your dog saw you\" → subject = 1st person? → \"your dog\" → possessive → verb ends in -it → 2nd person?\n\nNo — \"you\" → object → 2nd person → verb has -it\n\nSo verb: when object is 2nd person → -it \nWhen object is 3rd person → no? But sentence 1: object is \"you\" → 2nd person → -it\n\nSentence 2: object is \"doctor\" → 3rd person → verb is *qukiqtanga* → ends with -a-t? → no person suffix?\n\nRule says: verb has person endings if:\n- in first two: -utit (2), -uq (3)\n- in third: -ait (2/3), -anga (3/3), -atit (3/2)\n\nBut sentence 2: *inuuhuktuup iluaqhaiji qukiqtanga* → subject = 3rd person → should have ending?\n\n\"inuuhuktuup\" → \"the boy\" → 3rd person → so should be -uq?\n\nBut it's *inuuhuktuup* — not ending in -uq → so why?\n\nWait: in Inuktitut, subject marker is on noun: for definiteness — -up → for 3rd person — no person suffix?\n\nHmm.\n\nBack to grammar.\n\nLook at sentence 4: *iluaqhaijiup aarqijaatit* → \"the doctor cured you\" → object = \"you\" → 2nd person → verb ends in -it → *aarqijaatit* → *aarqij* + *a* + *t* + *it* → after consonant → -t, and -it (2nd person)\n\nSimilarly, sentence 6: *angatkuq iluaqhaijimik aarqisijuq* → \"the shaman cured a doctor\" → object = \"a doctor\" → indefinite → object has -mik → verb = *aarqisijuq* → ends with -uq → 3rd person?\n\nSo verb:\n- with 2nd person object → -it \n- with 3rd person object → -uq \n- based on whether object is definite or not\n\nBut rule says: person endings:\n- in first two: -u-tit ‘2’, -u-q ‘3’ \n- in third: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’\n\nSo when object is definite → person ending comes in \nWhen object is indefinite → object marked with -mik → person ending still applies?\n\nYes.\n\nSo verb suffix: \n- for “saw” → base form: from sentence 1 → *takujaatit* → has -it → so 2nd person → object = “you” → so 2nd person object → verb = *-it*\n\nSo for “saw” → base = *takuj* → then after vowel → -j → so *takuj* → *takuj* + ? → but in sentence 1: *takujaatit* — the -j is present after vowel “a”?\n\n“takuj” → ends in j → so base verb is *takuj*, then added suffixes.\n\nBut in sentence 1: *takujaatit* → let's break down:\n- takuj → saw\n- a → infix?\n- jaat → from *j* + *a* + *t*?\nNo — better: *takuj* + *a* + *t* + *it* → infix and verb suffix?\n\nActually, in Inuktitut, the verb of “saw” is *takua* or *takuj* — likely *takuj* with -j after vowel.\n\nSo for transitive verb with definite object → verb has suffix:\n- after consonant → -t\n- after vowel → -j\n- then person ending\n\nSo for “saw” with object = definite (you) → 2nd person → -it → so verb = *takujaatit*\n\nYes → matches sentence 1.\n\nSo for “saw” → verb base *takuj* → with -j after vowel → *takuj* → then *takuj* + *a* + *t* + *it*? Wait — no clear suffix.\n\nBut sentence 1: *takujaatit* → appears as whole.\n\nWe can use structure:\n\n- subject: \"the teacher\" → *ilinniaq-up* \n- object: \"the boy\" → *inuuhuktu* → definite → no -mik \n- verb: \"saw\" → must be in 3rd person (object is 3rd person) → so verb ends in -uq?\n\nRule: if object is 3rd person → verb has -uq? \nIn sentence 2: the boy (3rd person) shot the doctor → verb *qukiqtanga* → not -uq\n\nSentence 2 verb: *qukiqtanga* — no -uq\n\nSentence 1: object = \"you\" → 2nd person → verb ends in -it → *takujaatit*\n\nSo when object is 2nd person → -it \nWhen object is 3rd person → ? → seems to be -a-t at end?\n\nIn sentence 2: *qukiqtanga* — ends with -anga → which is a valid form?\n\nIn sentence 5: *Qingmiq iputujait* → \"you speared the dog\" → 2nd person → verb ends in -it\n\nSo for \"saw\", with object = boy (3rd person) → verb should be *takuj* + *a* + *t* + *anga*? → *takujatanga*?\n\nBut in sentence 2: *qukiqtanga* → no -a?\n\nWait — word \"qukiq\" → and then -tanga → so likely verb is base *qukiq* → with -t after consonant → -tanga\n\nSimilarly, \"takuj\" → after vowel → -j → so *takuj* — but if no -j, only -t?\n\nBut in sentence 1: *takujaatit* → after “a” → vowel → -j? → -j after vowel → so *takuj* → *takuj* + -a? Then -t? Then -it?\n\nPossibly: structure is:\n- root verb\n- after vowel → -j\n- after consonant → -t\n- person suffix: 2nd → -it, 3rd → -uq or -anga?\n\nBut in sentence 2: object is 3rd person → verb ends in -anga → *qukiqtanga*\n\nSimilarly, should apply to “saw”?\n\nSo verb for “saw” with 3rd person object → *takujatanga*?\n\nBut in sentence 1: with 2nd person → *takujaatit* → not *takujatit* — difference?\n\nIn sentence 1: *takujaatit* → has -it → 2nd person \nIn sentence 2: *qukiqtanga* → ends with -anga → 3rd person\n\nSo pattern:\n- verb: if after vowel → -j\n- if after consonant → -t\n- person ending:\n - 2nd person object → -it\n - 3rd person object → -anga\n\nYes — so for sentence 20: \"the teacher saw the boy\" \n→ object = boy → 3rd person → verb = *takujatanga*\n\nBut wait — \"saw\" → base root? Is it *takuj*? Yes — from sentence 1.\n\nSo verb = *takujatanga*\n\nSubject: \"the teacher\" → *ilinniaq-up*\n\nObject: \"the boy\" → *inuuhuktu* → definite → no -mik\n\nSo full: *ilinniaq-up inuuhuktu takujatanga", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11411.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 1, + "output": "We are given a structure for Inuktitut, with specific patterns for verb forms, noun modifications, and possessive marking.\n\nLet’s analyze the grammatical rules step by step to translate the target sentences.\n\n---\n\n### Key Rules from the problem:\n\n1. **Noun structure:**\n - Base noun + (q) → often indicates definite object or subject without definite object.\n - If noun acts as **indefinite object**, it takes **-r** before -mik: \n Example: **nanuq** → **nanu-r-mik**\n So: *nanuq* (polar bear) → *nanu-r-mik* when object (indefinite)\n - **-q** appears on object or subject when definite.\n - For \"your\", use **-it** instead of -(q), and **-vit** instead of -up.\n\n2. **Verb patterns:**\n - Structure 1: `X-(q) V–` → \"X V (himself)\" → reflexive \n → e.g., *Aanniqtutit* = \"You hurt yourself\" (reflexive)\n - Structure 2: `X-(q) Y-(r)mik V-si–` → \"X V a Y\" \n → \"a\" = indefinite object marker; Y gets -mik with -r before it\n e.g., *iluaqhaijiup aarqijaatit* → \"The doctor cured you\"\n - Structure 3: `X-up Y-(q) V–` → \"X V the Y\" \n → object is definite; Y has -(q), so not -mik\n e.g., *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\"\n\n3. **Verb suffixes:**\n - Verb ends with:\n - **-j** after vowel\n - **-q** after consonant\n - Person markers:\n - First two schemas:\n - -u-tit → 2nd person\n - -u-q → 3rd person\n - Third schema:\n - -a-it → 2nd/3rd person (2 or 3)\n - -a-nga → 3rd person\n - -a-atit → 3rd person\n\n4. **Possessive marking:**\n - \"your\" → replace -(q) with -it, -up with -vit\n\n---\n\nNow, go sentence by sentence.\n\n---\n\n### 19. The shaman hurt you.\n\n- Subject: \"the shaman\" = \"Angatkuq\"\n- Verb: \"hurt\" → from example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\"\n- \"hurt\" → \"aanniqtutit\" → \"You hurt yourself\", so the verb form for \"hurt\" is base + -ut (like -q or -t) with person suffix.\n\nIn example 6: \"cured\" = \"aarqisijuq\" → suffix -si– + -juq → likely base verb root + -si + -juq\n\nIn \"aanniqtutit\" → \"hurt yourself\" → base verb root \"aanniqt-\" with suffix -ut → -ut it (ending)\n\nSo \"hurt\" → base verb form + -t → -ut → takes suffix -ut when subject is 1st person (you)\n\nBut here, subject is \"the shaman\" → third person, object is \"you\" → definite object.\n\nSo pattern 2: `X-(q) Y-(r)mik V-si–` → object has -mik with -r if indefinite.\n\nBut \"you\" is definite → so \"you\" gets -q → → \"vit\"?\n\nWait: \"you\" = \"takujaatit\" → example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = -q + -it? \"takujaatit\" = \"you\"\n\nIn example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n→ \"your\" = -it (replaces -(q)) \n→ \"you\" = -q + -it → ends in -it\n\nWait: \"takujaatit\" → so \"you\" is marked with -it?\n\nIn \"The boy shot the doctor\" (2): \"Inuuhuktuup iluaqhaiji qukiqtanga\" \n→ \"Inuuhuktuup\" = \"the boy\" → -up? \n→ \"iluaqhaiji\" = \"the doctor\" → definite object → so -q? \n→ verb: \"qukiqtanga\" → verb of \"shot\"\n\nSo rule:\n- Definite object: noun + -(q)\n- Indefinite object: noun + -(r)mik\n\nDefinite object: no -(r), just -(q)\n\nSo:\n19. \"The shaman hurt you\"\n\nSubject: \"the shaman\" → \"Angatkuq\" → definite → so \"Angatkuq\"\nObject: \"you\" → definite → so \"you\" → in Inuktitut, \"you\" is \"takujaat\" → with -it for \"your\" or \"you\"\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" is \"takujaatit\"\n\nSo \"you\" with -it → definite \"you\"\n\nSo verb: \"hurt\" → base must be \"aanniqt\" → check example 3: \"Aanniqtutit\" → \"You hurt yourself\"\n\n→ So verb root is \"aanniqt\" → suffix -ut → -ut for reflexive\n\nBut here, it's not reflexive → object is \"you\" → definite → so structure 2?\n\nWait — in example 5: \"Qingmiq iputujait\" → \"You speared the dog\"\n\n→ \"You\" = 1st person → \"Qingmiq\" → verb \"iputujait\"\n\n→ verb: -jait → -j at end, consonant before → after consonant, add -q → so iputujait\n\nIn \"Aanniqtutit\" → reflexive → no object → so verb ends with -ut\n\nIn \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n→ \"iluaqhaiji\" = the doctor → definite object → -q\n\n→ verb: \"qukiqtanga\" → ends with -anga → after consonant → -anga for 3rd person? \n→ subject is \"the boy\" → -up → 3rd person? No — \"the boy\" is 3rd person → but he is subject → so subject marker?\n\nIn \"takujaatit\" → you → 2nd person → -it?\n\nLet’s look at person suffixes:\n\nFrom guidance:\n- Two schemata:\n - -u-tit → 2nd person\n - -u-q → 3rd person\n- Third schema: -a-it → 2nd or 3rd, -a-nga → 3rd, -a-atit → 3rd/2nd\n\nIn example 1: \"Qingmivit takujaatit\" → \"your dog saw you\"\n\n→ \"you\" (object) = takujaatit → ends in -it → so 2nd person?\n\nBut \"saw\" → verb root?\n\n\"Qingmivit\" → \"your dog\" → \"Qingmi\" + -vit → \"your\" → -vit (replaces -up)\n\n\"takujaatit\" → \"you\" → -it → 2nd person\n\nSo verb must be in 2nd person → -u-tit?\n\nSo verb root: \"takuj\" → \"saw\" → takuj + -ujait? → \"takujaatit\" = -a-it?\n\nWait — structure:\n\nIn example 1: \"Qingmivit takujaatit\" → so verb is \"takujaatit\"\n\n→ How is \"saw\" formed?\n\nIf the verb is in 2nd person → -u-tit\n\nSo \"takuj\" + -u-tit → \"takujuit\"? But it's \"takujaatit\"\n\n→ perhaps \"takuj\" + -a-it → -a-it → 2nd person?\n\nIn example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n\"qukiqtanga\" → after consonant → -q → then -anga → -anga → 3rd person?\n\nSubject: \"the boy\" → \"Inuuhuktuup\" → -up → 3rd person?\n\nSo person suffix on verb → -q → for 3rd person?\n\nBut -q is after consonant → so verb root \"qukiq\" → + -q → \"qukiqt\" → + -anga → \"qukiqtanga\"\n\nSo verb suffix: after consonant → -q → then -anga → for 3rd person?\n\nWait — example 5: \"Qingmiq iputujait\" → \"You speared the dog\"\n\n→ \"you\" = 1st person → verb ends with -jait? → -j after consonant?\n\n\"Qingmiq\" → \"you\" → no person marker? Wait — \"Qingmiq\" = \"you\" → 1st person — is 1st person marked?\n\nOnly examples with 1st person are \"you hurt yourself\" (3) and \"you fell\" (11)\n\nIn 3: \"Aanniqtutit\" → \"You hurt yourself\" → verb = \"aanniqtut\" → -ut → reflexive?\n\nIn 11: \"Ukiakhaqtutit\" → \"You fell\" → verb = \"ukiakhaqtut\" → -ut?\n\nSo in both, reflexive → verb ends in -ut → -ut as in -t + -ut → so -ut?\n\nFor non-reflexive, object → object with -mik?\n\nIn 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\"\n\n→ subject: \"the boy\" → -up → 3rd person\n→ object: \"the doctor\" → -q → definite\n→ verb: -q + -anga → 3rd person → -anga?\n\nIn 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\"\n\n→ subject: \"The doctor\" → iluaqhaijiup → up → 3rd person\n→ object: \"you\" → aarqijaatit → \"you\" = -it → 2nd person → which is -u-tit?\n\nBut verb is \"aarqijaat\" → ends in -aat? → -a-at → very close to -a-atit?\n\n\"aarqijaatit\" → ends in -it → so verb form?\n\nBut in 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\"\n\n→ subject: \"Angatkuq\" → 3rd person → -q (definite)\n→ object: \"a doctor\" → \"iluaqhaijimik\" → has -mik → indefinite? → \"a doctor\" = indefinite → so -mik → with -r → iluaqhaiji → iluaqhaijimik → yes → has -mik → and -r?\n\n\"iluaqhaiji\" → root → \"iluaqhaiji\" → add -mik → so -mik → only if indefinite?\n\nYes — pattern: for indefinite object → add -mik with -r before → nanuq → nanu-r-mik\n\n\"iluaqhaiji\" → \"doctor\" → definite → so should have -q → but it has -mik → so it's indefinite?\n\nBut \"a doctor\" → indefinite → so yes → indefinite object → → noun with -mik\n\nAnd verb: \"aarqisijuq\" →?\n\n\"aarqisijuq\" → likely \"cure\" → root \"aarqis\" → + -juq\n\nIn 4: \"aarqijaatit\" → \"cured you\" → \"you\" = second person → verb = -a-it?\n\n\"aarqijaatit\" → ends in -it → so -a-it?\n\nBut in 6: \"aarqisijuq\" → ends in -uq → not -it → so 3rd person?\n\nSubject is \"shaman\" → 3rd person → so verb should be 3rd person → -q → ending?\n\nIn 6: verb = \"aarqisijuq\" → after consonant → -q → then -uq?\n\nRule: verb suffix:\n- -j after vowel\n- -q after consonant\n- person marker\n\nSo \"aariqisij\" → consonant → add -q → \"aarqisijuq\"\n\nSo -q → for 3rd person?\n\nThus:\n- 3rd person verb → -q + (person suffix)\n- 2nd person → -u-tit? But in 4, verb = \"aarqijaatit\" → ends with -it → so -a-it?\n\nNow compare structure:\n\nIn 19: \"The shaman hurt you\"\n\nSubject: \"the shaman\" → definite → \"Angatkuq\" → -q\nObject: \"you\" → definite → so \"takujaatit\" → -it\nVerb: \"hurt\" → root \"aanniqt\" → pattern from example 3: \"aanniqtutit\" → reflexive → verb = -ut\n\nBut here, object is definite → so structure 3: X-up Y-(q) V– ?\n\nWait — structure 3 is: X-up Y-(q) V– → \"X V the Y\"\n\nSo if object is definite, use that structure.\n\nBut here the object is \"you\" → which is 2nd person → so should it be Y-(q)?\n\n\"you\" in Inuktitut is marked with -it → not -q → -it for 2nd person?\n\nIn example 1: \"your dog saw you\" → \"takujaatit\" → \"you\"\n\nIn example 4: \"iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" → \"you\" = aarqijaatit → -it → so 2nd person → marked with -it\n\nSo \"you\" → definite → marked with -it\n\nBut in structure 3: X-up Y-(q) V– → object is marked with -q\n\nBut \"you\" is not marked with -q → it's with -it\n\nSo perhaps the rule is:\n\n- For definite object: if it is a specific person (you, me, he, etc.), it may be marked with -it or -q depending on person\n\nIn structure 3: \"X-up Y-(q) V–\" → if Y is the object, and it's a specific person or noun, it takes -q?\n\nBut in examples:\n- \"iluaqhaijiup aarqijaatit\" → \"doctor\" + \"you\" → doctor is definite → marked with -up (subject), you is marked with -it → not -q\n\nActually, the object is marked with -it → not -q → so perhaps pattern 3 is only for object with -q?\n\nWait — look at rule:\n\n> If a noun gets the ending -q when it is either a definite object or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending -mik when it is an indefinite object.\n\nSo:\n- Definite object → gains -q\n- Indefinite object → gains -r before -mik\n\nSo \"you\" is definite → should gain -q → so you = \"takujaat\" + -q = \"takujaaqt\"?\n\nBut in example 1: \"takujaatit\" → ends in -it → not -q\n\nBut \"takujaat\" → base → \"you\"\n\nIn \"Qingmivit takujaatit\" → \"your dog saw you\" → verb is \"takuj\" → with -a-it? or -u-tit?\n\nWait — the verb in \"saw\" is not given — but in 11: \"Ukiakhaqtutit\" → \"You fell\"\n\n\"Ukiakhaqtutit\" → \"you\" = subject → so \"you fell\" → verb = \"ukiakhaqtut\"\n\nSo verb root is not directly tied.\n\nBut from examples, we see:\n\n- Reflexive: verb ends in -ut\n- Other: verb has person suffix\n\nSo for 19: \"The shaman hurt you\"\n\nSubject: shaman → \"Angatkuq\" → definite → -q\nObject: you → definite → so you = \"takujaat\" + -q → \"takujaaqt\"\n\nVerb: hurt → root \"aanniqt\" → for 3rd person → should have -q → but in reflexive it's -ut\n\nIn \"aanniqtutit\" → reflexive → 1st person → verb = -ut\n\nSo for 3rd person → verb = -u-q → after consonant → so -q suffix?\n\nBut \"aanniqt\" → consonant → add -q → \"aanniqtq\" → then person suffix?\n\nThe verb pattern:\n- After consonant → add -q\n- After vowel → add -j\n\nSo for root \"aanniqt\" → ends in -t → consonant → so add -q → \"aanniqtq\"\n\nThen person suffix (3rd person) → -u-q\n\nSo verb → \"aanniqtq-u-q\" → \"aanniqtq-uq\" → \"aanniqtquq\"?\n\nBut in example 6: \"angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor\n\nVerb: \"aarqisijuq\" → root \"aarqis\" → consonant → add -q → \"aarqisq\" → then -uq → so \"aarqisijuq\" → likely \"aarqis\" + -j (after consonant) + -uq?\n\n\"aarqis\" → consonant → + -j → \"aarqisj\" → + -uq → \"aarqisjuq\"?\n\nBut it's \"aarqisijuq\" → so -j is in between?\n\nPossible that it's \"aarqisij\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11146.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 2, + "output": "We are to translate the following English sentences into Inuktitut, using the grammatical rules and examples provided.\n\nWe are given the general structure of Inuktitut sentences:\n\n1. X-(q) V– → “X V (himself)” (reflexive; transitive verb without object interpreted as reflexive)\n2. X-(q) Y-(r)mik V-si– → “X V a Y” (X acts on Y, Y is indefinite object)\n3. X-up Y-(q) V– → “X V the Y” (X acts on definite Y)\n\nRules for possessive:\n- “your” replaces -(q) with -it, -(up) with -vit\n\nVerb suffixes:\n- -j after vowel, -t after consonant\n- person marking:\n - in (1) and (2): -utit (2nd), -uq (3rd)\n - in (3): -a-it (2nd/3rd), -a-nga (3rd/3rd), -a-atit (3rd/2nd)\n\nAdditionally:\n- If a noun is a definite object or subject of a sentence with no definite object → it takes -q\n- When a noun is an indefinite object → it takes -r before -mik (e.g., nanuq → nanu-r-mik; iluaqhaiji → iluaqhaiji-mik)\n\n---\n\n### 19. The shaman hurt you.\n\n- “The shaman” = Angatkuq (from example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor)\n- “hurt” → inuktitut verb: aanniqtang (from example 3: \"Aanniqtutit\" → you hurt yourself)\n- \"hurt you\" → transitive verb with object “you”\n- “you” is a definite object → so object gets -q\n- Structure: X (Angatkuq) + object (you → -it) + verb\n\nBut in structure 2: X-(q) Y-(r)mik V-si–\n\n- X = shaman → Angatkuq\n- Y = you → you is definite → ends with -q → but since it's a definite object, it takes -q → “you” → “it” is implied\n- However, the verb in structure 2 has -si\n- But “hurt” → check examples:\n - “aanniqtutit” = you hurt yourself → reflexive\n - So “aanniqtanga” = hurt (intransitive?) — no, it's used in transitive\n\nLook at example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"cured\" = aarqisijuq\n\nSo “cured” = aarqisijuq → so “hurt” = aanniqtang?\n\nBut in example 3: “Aanniqtutit” = you hurt yourself → implies verb root = aanniqt- → with -utit for 2nd person\n\nIn example 1: “Qingmivit takujaatit” = your dog saw you → “saw” = takujaatit → root takuj-\n\nSo verb formation: root + suffix\n\nLet’s analyze verb suffixes:\n\n- The verb suffixes are:\n - -j after vowel\n - -t after consonant\n- Person markers:\n - 2nd person: -utit (in 1 & 2), -a-it (in 3)\n - 3rd person: -uq, -a-nga, -a-atit\n\nSo for “hurt”:\n- Root = aanniqt? → from “aanniqtutit” → so root = aanniqt → verb = aanniqt + suffix\n\nIn “aanniqtutit” → 2nd person, reflexive → object is “you”, so verb = aanniqtutit → after vowel → -utit → -t after vowel? No → -t after consonant?\n\naanniqtutit:\n- aanniqt → ends with q → consonant → so should get -t → yes → aanniqt-t → aanniqtut? → aanniqtut → then -it → aanniqtutit → yes\n\nSo:\n- verb root: aanniqt\n- suffix: -t (after consonant) + -it (for 2nd person)\n\nNow, “the shaman hurt you”:\n- Subject: shaman → Angatkuq (definite subject)\n- Object: you → definite → so object gets -q → you → “it” → becomes “uit”?\n- But note: rule says: if noun is definite object or subject without definite object → it gets -q\n- So “you” → “uit” → so we use “uit” → and since object is definite → it is not marked with -mik\n- But in structure 2: X-(q) Y-(r)mik V-si– → for indefinite object → takes -r before -mik\n\nHere, “you” is definite → so no -mik → just -q\n\nSo structure: X-(q) Y-(q) V– ?\n\nBut both subject and object are definite?\n\nWait, Example 3: “Aanniqtutit” = you hurt yourself → reflexive → no object specified\n\nExample 4: “Iluaqhaijiup aarqijaatit” = the doctor cured you → subject definite (iluaqhaiji), object definite (you) → “cured you” → verb = aarqijaatit → has -it → 2nd person?\n\nActually: “you” → in object → definite → so gets -q → “uit” — so “iluaqhaijiup aarqijaatit” → doctor cured you → “cured” = aarqijaat?\n\nRoot: aarqi → aarqisijuq → “cured” → so “aarqijaat” → -j after vowel? aarqi → ends with i → vowel → so -j → aarqija → then -at? → -a- (definite object?) → but -it → person?\n\nIn example 6: “Angatkuq iluaqhaijimik aarqisijuq” → shaman cured a doctor → object is a doctor → indefinite → doctor → iluaqhaiji → with -mik → so iluaqhaijimik → root iluaqhaiji → ends with i → vowel → get -j → then -mik → so iluaqhaijimik\n\nBut object is indefinite → marked with -mik\n\nIn example 4: “iluaqhaijiup aarqijaatit” → doctor cured you → object “you” is definite → does it get -q?\n\n“you” → object → definite → so should be “uit” → so “aarqijaatit” → has -it → 2nd person.\n\nSo only the person is marked.\n\nSo general pattern:\n- If object is definite → object noun takes -q\n- If object is indefinite → object noun takes -r before -mik\n\nThus, in 19: “The shaman hurt you”\n- Subject: shaman → Angatkuq\n- Object: you → definite → takes -q → “uit”\n- Verb: hurt → root aanniqt → with -t (after consonant) + -it (2nd person)\n\nSo verb = aanniqtutit → but with object?\n\nWait — structure not matching.\n\nWe have X-(q) Y-(q) V– → but X-(q) is for definite subject?\n\nIn example 4: “iluaqhaijiup aarqijaatit” → subject is definite → iluaqhaiji → has -up → so definite subject uses -up → so subject with -up → definite\n\nSimilarly, “Angatkuq” → definite → so no change → Angatkuq\n\nObject: “you” → definite → so “uit” → so “Angatkuq uit aanniqtutit”?\n\nBut is that the rule?\n\nCheck example 3: “Aanniqtutit” → you hurt yourself → reflexive → verb = aanniqtutit → object is “yourself”\n\nSo when object is definite → noun takes -q → so “you” → “uit”\n\nThus: “The shaman hurt you” → Angatkuq uit aanniqtutit\n\nBut is “uit” a valid form?\n\nCompare with “you” → in examples:\n- example 1: “Qingmivit takujaatit” → your dog saw you → object is “you” → “you” → “it” → “vit” → but that's after your → possessive\n\n“Your” → replaces -(q) with -it → “q” → “it”\n\nSo in base form, “you” is -it → so “uit” → is that the same?\n\nIn example 1: “Qingmivit” → “your dog” → “Qingmi” → “your” → so q → it → q → it → so “qingmi-it” → qingmivit\n\nSo “you” base → -it → in non-possessive → “uit”?\n\nYes — in example 4: “iluaqhaijiup aarqijaatit” → “the doctor cured you” → “you” → “uit”\n\nSo yes → definite object → “uit”\n\nSo 19 → Angatkuq uit aanniqtutit\n\nBut verb is “aanniqtutit” → aanniqt (root) + -t (after consonant q) + -it (2nd person)\n\nYes.\n\nBut in example 5: “Qingmiq iputujait” → you speared the dog → “you” is subject → first person → verb = iputujait → root iputuj → -j after vowel? u → vowel → -j → iputuj → then -ait → ait → ait = -a-it? — person?\n\ni is vowel → root = iputuj → ends with j → consonant → so after consonant → -t → iputujt → then -ait → is that a person marker?\n\nWait — “iputujait” — structure: “you” — subject → first person → should get -a-it (from rule) — in schema 3: X-up Y-(q) V– → first person → subject → X-up → so “up” → so verb gets -a-it → yes\n\nSo when subject is first person → verb gets -a-it\n\nIn example 3: “Aanniqtutit” → you hurt yourself → first person → verb ends with -utit → not -a-it → contradiction?\n\nWait — example 3: “Aanniqtutit” → you hurt yourself → no object → reflexive → so first person → reflexive → verb = aanniqtutit → which has -utit → which is second person?\n\nWait — error.\n\nIn example 3: “Aanniqtutit” → you hurt yourself → subject is “you” → first person\n\nBut in the rule: in schema 1: X-(q) V– → “X V (himself)” → so reflexive → first person → should use -utit or -uq?\n\n-utit is 2nd person → uq is 3rd\n\nBut “you” → first person\n\nSo why -utit?\n\nHmm.\n\nPossibly the rule applies to transitive verbs with reflexive meaning.\n\nActually, in example 1: “Qingmivit takujaatit” → “your dog saw you” → subject: “your dog” → definite → uses -vit → which is from -q → it → -vit → so -it → replaced by -vit\n\nBut “the dog” → “takujait” → root takuj → ends with j → consonant → suffix -t → takujt → then -ait → ait → -a-it? → but it's -ait → not -a-it\n\nWait — “takujaatit” → after vowel? taj → t after j? Not clear.\n\nRoot: takuj → ends with j → consonant → so suffix -t → takujt → then -ait → an -a-it?\n\nBut ait → is that a person marker?\n\nThe rule says:\n- in 1st two schemata: -utit ‘2’, -uq ‘3’\n- in 3rd schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’\n\nSo only when schema 3 is used (subject with -up) → persons marked with -a-it, etc.\n\nExample 1: “Qingmivit takujaatit” → subject = “your dog” → not -up → so schema 1? → but subject has -it → so is it schema 1?\n\nSchema 1: X-(q) V– → subject with -q → “your dog” → “Qingmivit” → -q → -it → so schema 1 → verb should have -utit or -uq\n\nBut “takujaatit” → ends with -it → not -utit → so contradiction.\n\nUnless -it is for different person.\n\nPerhaps “takuj” → root → vowel after? a → vowel → so -j → takujj → no.\n\ntakuj → ends with j → consonant → so suffix -t → takujt → then -ait?\n\nMost likely: the verb suffix is -j after vowel, -t after consonant → then person marking.\n\nFor \"saw\" → takujaatit → root takuj → after consonant → -t → takujt → then -ait → which may be -a-it → so 2nd or 3rd person.\n\nBut subject is “your dog” → so third person — subject → should be -uq?\n\nSo verb should end with -uq?\n\nBut it ends with -it → contradiction.\n\nWait — closer look: the sentence is “Qingmivit takujaatit” → your dog saw you → object is “you” → definite → so object gets -q → “uit” → so the verb is “takujatit” → with -it → which is 2nd person → but subject is third person → so why -it?\n\nPerhaps the person marker is on the verb for the object?\n\nThis is confusing.\n\nAlternative: the verb ending reflects the object.\n\nBut example 4: “iluaqhaijiup aarqijaatit” → doctor (3rd person) cured you (2nd person) → verb ends with -it → 2nd person → yes → so person marking is on the object.\n\nSimilarly, example 5: “Qingmiq iputujait” → you (1st person) speared the dog → verb ends with -ait → which is -a-it → 1st or 2nd?\n\n“you” → subject → so first person → verb should have first person ending.\n\nIn schema 3: X-up Y-(q) V– → subject first person → X-up → so verb gets -a-it (for 1st or 2nd person?)\n\nRule says -a-it ‘2/3’ — so both 2nd and 3rd? — not 1st.\n\nContradiction.\n\nExample 11: “Ukiakhaqtutit” → you fell → first person → verb ends with -utit → which is 2nd person? → again, not 1st.\n\nPossibly the person markers are misassigned.\n\nLook at example 3: “Aanniqtutit” → you hurt yourself → first person → -utit → which is 2nd person — contradiction.\n\nWait — is it possible that “you” in example 3 is 2nd person?\n\nBut it says “you hurt yourself” — so first person.\n\nUnless in Inuktitut, “you” has two forms: “you” (2nd) vs “yourself”\n\nPerhaps the verb person is determined by the object.\n\nBut in example 4: doctor (3rd) cured you (2nd) → verb ends with -it → 2nd person → yes\n\nExample 5: you (1st) speared the dog → verb ends with -ait → ait → is -a-it? → 2nd or 3rd?\n\nIn list, “iputujait” → with “you” as subject.\n\nBut -a-it is 2nd/3rd → not 1st → so can't be.\n\nUnless the schema is different.\n\nWait — list of examples:\n\n1. Qingmivit takujaatit — your dog saw you → verb = takujaatit → subject 3rd (dog), object 2nd (you) → verb ends with -it → 2nd person → matches.\n\n2. Inuuhuktuup iluaqhaiji qukiqtanga — the boy shot the doctor → boy (1st?) → shot (3rd person?) → verb = qukiqtanga → ends with -a-nga? → no — ends with -a-nga? \"qukiqtanga\" — ends with -nga → so -a-nga → 3rd person → object is doctor (3rd) — so verb for 3rd person.\n\n3. Aanniqtutit — you hurt yourself → first person — verb ends with -utit → -utit is for 2nd person? → but should be 1st.\n\n4. Iluaqhaijiup aarqijaatit — doctor cured you → doctor (3rd), you (2nd) → verb ends with -it → 2nd person → matches.\n\n5. Qingmiq iputujait — you speared the dog → you (1st), dog (3rd) → verb ends with -ait → -a-it → which is for 2nd/3rd → not 1st.\n\n6. Angatkuq iluaqhaijimik aarqisijuq — shaman cured a doctor → shaman (3rd), doctor (indefinite) → verb ends with -ijuq → -a-nga? — no — \"aarqisijuq\" — ends with -uq → 3rd person → matches.\n\n7. Nanuq qaijuq — polar bear came → 3rd person — verb qaijuq → ends with -uq → 3rd → matches.\n\n8. Iluaqhaijivit inuuhuktuit aarqijanga — your doctor cured your boy → doctor (3rd), boy (2nd) → verb ends with -anga → -a-nga → 3rd person → object is 2nd → so verb", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11860.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 3, + "output": "We are to translate the following English sentences into Inuktitut, using the provided linguistic patterns and examples.\n\n---\n\nStep 1: Identify the grammatical patterns from the given examples.\n\nGeneral structure:\n\n1. **X-(q) V–** → \"X V (himself)\" → reflexive (no object, subject = object)\n2. **X-(q) Y-(r)mik V-si–** → \"X V a Y\" → transitive with indefinite object (Y has -(r)mik)\n3. **X-up Y-(q) V–** → \"X V the Y\" → transitive with definite object (Y has -(q), no -(r)mik)\n\nAdditional rules:\n- \"your\" → replace -(q) with -it, -up with -vit\n- definite object or subject without object → noun gets -q\n- indefinite object → noun gets -r before -mik → e.g., nanuq → nanu-r-mik; iluaqhaiji → iluaqhaiji-mik\n- verb suffixes:\n - -j after vowel, -t after consonant\n - person endings:\n - first two schemas: -u-tit (2nd person), -u-q (3rd person)\n - third schema: -a-it (2/3), -a-nga (3/3), -a-atit (3/2)\n\nNote: Reflexive verbs (no object) → imply subject harms itself → use schema 1.\n\n---\n\nNow, translate each of the target sentences.\n\n---\n\n**19. The shaman hurt you.**\n\n\"the shaman\" → Angatkuq \n\"hurt\" → aanniqtanga (from sentence 3: Aanniqtutit → \"you hurt yourself\"; from 6: Angatkuq iluaqhaijimik aarqisijuq → \"the shaman cured a doctor\" → so \"cure\" is aarqisijuq)\n\nSo \"hurt\" is aanniqtanga.\n\n\"you\" → you = -(q) → but \"you\" is object → definite object → so use pattern 3: X-up Y-(q) V– → but \"hurt\" is transitive.\n\nWait: \"the shaman hurt you\" = agent (shaman) → object (you)\n\nSo schema: X-(q) Y-(q) V– → \"X V Y\", where Y is definite object → so \"you\" gets -q.\n\n\"you\" → in sentence 3: Aanniqtutit → \"You hurt yourself\" → \"you\" is subject → reflexive → so \"you\" as subject → -q → implies reflexive.\n\nBut here, \"you\" is object → still definite object → so it gets -q.\n\nSo:\n- X = Angatkuq (shaman)\n- Y = you → in Inuktitut, \"you\" is \"takujaat\" (from sentence 1: Qingmivit takujaatit → \"your dog saw you\" → \"you\" is object → takujaat? Wait, \"saw you\" → \"takujaatit\" → so object \"you\" → takujaat → suffix -it)\n\nWait: \"takujaatit\" → \"saw you\" → subject is \"your dog\" → \"Qingmivit\" → so \"dog\" is agent, \"you\" is object.\n\nSo object \"you\" = takujaat → so \"you\" → takujaat.\n\nIn sentence 3: Aanniqtutit → \"You hurt yourself\" → so \"you\" is subject → reflexive → so \"you\" as agent → -q → \"takujaat\" → with -t → aanniqtutit → so the verb is aanniqt– + -t → because it ends with consonant → -t.\n\nSo verb \"hurt\" → aanniqt– + -t → aanniqtut\n\nNow, in \"The shaman hurt you\" → shaman (Angatkuq) → agent → definite → so Angatkuq → has -q? — Yes, definite subject → gets -q.\n\nObject \"you\" → definite → so gets -q → takujaat.\n\nBut \"you\" as object → in sentence 1: takujaatit → so verb ends with -it → because it's the 2nd person object?\n\nWait, look at the verb endings.\n\nIn sentence 1: Qingmivit takujaatit → \"your dog saw you\" → verb = takujaatit → 3rd person object? Or 2nd?\n\nWait: \"saw you\" → so agent (your dog) → sees object (you) → so object is \"you\" → so object suffix.\n\nBut \"you\" is the object → so it's a definite object → so takes -q → but in sentence 1: \"takujaatit\" → \"you\" is object → so \"takujaatit\" → verb ends in -it.\n\nIn the pattern, it says:\n- verb suffix: -j after vowel, -t after consonant\n\n\"takujaat\" → ends with consonant (t) → so should get -t → so takujaat-t → takujaatit → yes.\n\nNow, who is the subject?\n\n\"your dog\" → Qingmivit → subject → \"your\" → so -(q) becomes -it → so Qingmivit → from \"dog\" → likely \"qingmi\" → with -it → \"Qingmivit\"\n\nSo \"your dog\" = Qingmivit → so for definite subject → -it → yes.\n\nNow, back to our sentence: shaman hurt you.\n\n- shaman → Angatkuq → definite → so -q → Angatkuq → correct.\n- you → object → definite → so takujaat (base) → + -t → takujaatit\n- verb: \"hurt\" → from sentence 3: Aanniqtutit → \"you hurt yourself\" → verb is aanniqtut → so root is aanniqt → suffix -t → because verb ends after consonant.\n\nSo \"hurt\" → aanniqt– + -t → aanniqtut\n\nNow, transitive with definite object → schema 3: X-(q) Y-(q) V– → so X is shaman → Angatkuq → so Angatkuq aanniqtutit?\n\nWait — but \"aanniqtutit\" → \"you hurt yourself\" → so the verb form is aanniqtut + -it\n\nSo in this case, object is \"you\" → so object gets -it?\n\nBut in pattern, when object is definite, it has -q → but when it's 2nd person, it may have person-specific suffix?\n\nWait — the verb is for 2nd person object?\n\nIn sentence 1: Qingmivit takujaatit → \"your dog saw you\" → object is \"you\" → 2nd person → so verb ends with -it?\n\nYes — takujaatit → -it → because it's 2nd person object?\n\nLook at the patterns:\n\n- First two schemata: -u-tit (2), -u-q (3)\n- Third schema: -a-it (2/3), -a-nga (3/3), -a-atit (3/2)\n\nBut in schema 3: X-up Y-(q) V– → so if object is definite → Y-(q)\n\nBut in \"you\", it's 2nd person → so does it get -it?\n\nIn sentence 1: object is \"you\" → verb = takujaatit → so -it → so for 2nd person object → suffix -it\n\nSimilarly, in sentence 3: Aanniqtutit → \"you hurt yourself\" → verb = aanniqtut + -it → so again -it\n\nSo person suffix attached to verb.\n\nSo for \"hurt\" with object \"you\" (2nd person), verb → aanniqt + -t → aanniqtut → then -it → aanniqtutit?\n\nBut \"aanniqtut\" ends with -t — so after consonant → so -t → then add person suffix?\n\nWait — the rule says: verb receives:\n- -j after vowel, -t after consonant\n- then person ending\n\nSo the person suffix comes after the consonant suffix?\n\nIn sentence 3: Aanniqtutit → verb = aanniqt + -t → aanniqtut → then -it → so aanniqtutit → so person suffix -it is added.\n\nSimilarly, in sentence 1: takujaat → ends with consonant → takujaat → + -t → takujaatit → then \"it\" for 2nd person?\n\nSo yes — the person suffix is added *after* the consonant suffix (or vowel -j).\n\nThus, for transitive verb with definite object in 2nd person (you), verb ends with -it.\n\nSo for 19: \"The shaman hurt you\"\n\n- subject: shaman → Angatkuq → definite → so Angatkuq\n- verb: \"hurt\" → root aanniqt → + -t (after consonant) → aanniqtut → then add person suffix for 2nd person object → -it → aanniqtutit\n- object: \"you\" → definite → so takujaat → + -it? — but in sentence 1, \"you\" was \"takujaatit\" → so object gets -it?\n\nBut according to pattern, definite object → gets -q → so should be takujaatq?\n\nNo — in sentence 1: \"your dog saw you\" → \"takujaatit\" → so it ends with -it → not -q.\n\nWait — the rule says: \"if a noun gets the ending -q when it is either a definite object or a subject of a sentence that doesn’t have a definite object\"\n\nSo definite object → gets -q → but here we have \"you\" as object → definite → so should be takujaatq?\n\nBut in sentence 1: \"takujaatit\" → ends with -it → so contradiction?\n\nWait — look at the original sentence: \"Qingmivit takujaatit\" → meaning \"your dog saw you\"\n\n\"takujaatit\" → so object \"you\" → treated as \"you\" → so suffix -it → which may be from person marking.\n\nBut the rule says: definite object → gets -q → but here it’s not -q → it's -it → so perhaps the -q is only when the noun is a non-referential or indefinite object?\n\nWait — look at the pattern:\n\n\"X-(q) Y-(r)mik V-si–\" → indefinite object → Y-(r)mik → e.g., nanuq → nanu-r-mik\n\nBut \"iluaqhaiji\" → \"doctor\" → in sentence 2: \"inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → so doctor is definite → iluaqhaiji → no -r → no -mik\n\nIn sentence 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → iluaqhaijiup → definite → subject → so has -up → doctor is definite → so no -(r)mik\n\nBut in sentence 10: \"qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"your teacher\" → student → has \"your\" → so goes to it\n\nSo only when object is indefinite → it gets -r before -mik.\n\nExample: nanuq → nanu-r-mik\n\nSo in sentence 12: Angunahukti nanurmik qukiqsijuq → \"the hunter shot a polar bear\" → \"polar bear\" → nanurmik → indefinite → so has -r before -mik.\n\nSo for definite object → no -mik, just -q?\n\nBut in sentence 1: \"your dog saw you\" → object is \"you\" → definite → verb ends with -it → so \"takujaatit\"\n\nSo perhaps the noun \"you\" is special?\n\nBut in general, definite object → gets -q → so \"you\" should be takujaatq?\n\nBut in sentence 1, it's takujaatit → so perhaps the -q doesn't appear for pronouns?\n\nWait — in sentence 1: \"Qingmivit takujaatit\" → the object is \"you\" → which is a pronoun → so pronouns may not take -q?\n\nBut the rule says: \"a noun gets the ending -q when...\" — and \"you\" is a pronoun → not a noun.\n\nAh — important: the rule applies only to nouns → pronouns are exceptions.\n\nSo for nouns: definite object → gets -q → e.g., doctor → iluaqhaiji → definite → gets -q → iluaqhaiji\n\nBut pronouns (like you) → when used as object → may not take -q → instead, they take person suffix.\n\nIn sentence 1: object is \"you\" → takujaat → takujaatit → so -it → which is person suffix.\n\nIn sentence 3: \"you hurt yourself\" → aanniqtutit → again -it → so for 2nd person object → -it\n\nThus, the pattern for definite object with pronoun → takes person suffix — not -q.\n\nSo for \"you\" as object → it's a pronoun → so does not get -q → instead, the verb gets the person suffix.\n\nSo in 19: \"The shaman hurt you\"\n\n- subject: shaman → definite → Angatkuq → definite → so Angatkuq\n- verb: \"hurt\" → root aanniqt → + -t (after consonant) → aanniqtut → + -it (2nd person object) → aanniqtutit\n- object: \"you\" → pronoun → as object → so in form takujaat → with person suffix -it → takujaatit\n\nSo full sentence: Angatkuq takujaatit aanniqtutit?\n\nNo — in sentence 1: \"Qingmivit takujaatit\" → subject + verb → not verb + object\n\nThe structure seems to be: Subject + verb + object\n\nIn sentence 1: Qingmivit takujaatit → \"your dog saw you\" → so subject → verb → object\n\nSo syntax: X V Y\n\nBut in that case, Y is the object → so position is: subject + verb + object\n\nSo for \"the shaman hurt you\" → Angatkuq aanniqtutit takujaatit?\n\nNo — that would be \"the shaman hurt-you\", but \"takujaatit\" is the object form.\n\nBut in sentence 1: Qingmivit takujaatit → subject is \"your dog\", verb is \"saw\", object is \"you\" → so verb first, then object.\n\nIn sentence 3: Aanniqtutit → \"you hurt yourself\" → no object → reflexive → so verb alone.\n\nSentence 4: iluaqhaijiup aarqijaatit → \"the doctor cured you\" → subject → verb → object → so iluaqhaijiup aarqijaatit → so subject then verb then object.\n\nSimilarly, sentence 8: iluaqhaijivit inuuhuktuit aarqijanga → \"your doctor cured your boy\" → subject → verb → object\n\nSo order: subject → verb → object\n\nSo for 19: Angatkuq aanniqtutit takujaatit\n\nBut \"you\" as object → is it takujaatit? — in sentence 1, \"saw you\" → takujaatit → so yes.\n\nYes — object is \"you\" → so takujaatit\n\nNow, is \"you\" the definite object? Yes.\n\nBut does it get -q? — only for nouns — \"you\" is a pronoun → so it does not take -q → instead, it takes the person suffix in verb or object form.\n\nIn this case, object form → \"you\" → takujaat → + -it → takujaatit → correct.\n\nSo 19 → Angatkuq aanniqtutit takujaatit\n\nBut is \"aanniqtut\" the correct verb form?\n\nFrom sentence 3: Aanniqtutit → \"you hurt yourself\" → verb = aanniqtutit → so after -t → ends with -it → so the verb base is aanniqt → with -t → then -it → so aanniqtutit\n\nSo for \"hurt\" in 2nd person object → aanniqtutit\n\nSo yes.\n\nThus, 19: Angatkuq aanniqtutit takujaatit\n\nBut wait — in sentence 6: Angatkuq iluaqhaijimik aarqisijuq → \"the shaman cured a doctor\" → so verb is aarqisijuq → root aarqis → object is \"a doctor\" → indefinite → so iluaqhaijimik → with -mik\n\nSimilarly, in sentence 2: inuuhuktuup iluaqhaiji qukiqtanga → \"boy shot doctor\" → object \"doctor\" → definite → so iluaqhaiji → no -mik\n\nSo object definiteness affects whether it has -q or -mik.\n\nBut in this case, object is \"you\" → pronoun → so no -q or -mik → just takujaatit\n\nSo 19 → Angatkuq aanniqtutit takujaatit\n\nBut is \"aanniqt\" correct?\n\nSentence 3: Aanniqtutit → \"you hurt yourself\" → so \"hurt\" → yes\n\nSo 19 → Angatkuq aanniqtutit takujaatit\n\n---\n\n**20. The teacher saw the boy.**\n\n\"the teacher\" → in sentence 10: \"the dog hurt your teacher\" → so \"your teacher\" → so teacher → base likely \"ilinniaqt\" (dog in sentence 5: Qingmiup → so \"dog\" = qingmi)\n\nSentence 10: \"qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → \"your teacher\" → so teacher → ilinniaqt → with -it → ilinniaqtit\n\nSo teacher → ilinniaqt → definite → so ilinniaqt\n\n\"the boy\" → in sentence 2: inuuhuktuup iluaqhaiji qukiqtanga → \"boy\" is iluaqhaiji → definite → so iluaqhaiji\n\n\"sew\" → saw → in sentence 1: Qingmivit takujaat", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12282.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. The wolf saw your shaman.\n 14. Your polar bear hurt a boy.\n 15. Your hunter cured himself.\n 16. You shot the teacher.\n 17. You came.\n 18. You cured a hunter.\n\n (b) 19. [TARGET ANSWER REDACTED]\n 20. [TARGET ANSWER REDACTED]\n 21. [TARGET ANSWER REDACTED]\n 22. [TARGET ANSWER REDACTED]\n 23. [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "redacted_solution_hint_mask5", + "sample_index": 0, + "output": "Step-by-step derivation:\n\nWe are translating into Nooni, a language with specific grammatical and syntactic rules, and the sentences are spoken on **Bvumbon**, so we must use the tense and structure rules accordingly.\n\n---\n\n**Rule: Word order is S T V O L D**, with:\n- S = subject\n- T = tense\n- V = verb\n- O = object\n- L = place (optional)\n- D = day\n\nTense markers:\n- Past: **nɔ̂ː** (for actions completed before the reference point)\n- Future: **nú** (future), **nú géː** (future), **nú bóy** (later future), **nú yúː** (in the future, still to come)\n- “Just now” or “be about to” → **cí** (past) or **bɛ̂ː** (present) with a present-time verb; in specific cases, **cí** may appear with **nɔ̂ː** for just now or recently.\n- “Today” = **bɛ̂ː**\n- “Tomorrow” = **ntfǔː nú**\n- “The day after tomorrow” = **fɔ̀ shě ntfǔː**\n\nAlso, verbs:\n- To see = **yɛn** → after consonant → **lé** (with vowel change: lé > é)\n- “To help” = likely **nfí** (as seen in sentence 12: “me nú nfí dìɛ̀msɛ̌n” — “I am about to help the man”)\n- “To steal” = **cɔ́ŋ**\n- “To hear” = **bɛ̂ː** (as in “I hear”) — likely **bɛ̂ː** + object\n- “To kill” = **ɛ̀bɛ̀n** (as in sentence 6: “he killed the woman”)\n\nTone rules:\n- After falling / falling-low / low: high tone → becomes rising (–́ → –̌)\n\nSubject markers:\n- 1st person sg: **n-** → **nb > mb**, **nk → ŋk**, etc.\n\n---\n\nNow, translate each sentence:\n\n---\n\n**(20) On Bvusɔw, I helped the man.**\n\n- Day: Bvusɔw → encoded as **bvúsɔw** (from earlier examples like “On Bvusɔw, you will steal”)\n- Subject: I (1st person) → **me**\n- Verb: “helped” → past tense → **nfí** (as in “me nú nfí” in sentence 12)\n- Object: the man → **dìɛ̀msɛ̌n** (from sentence 12: “the man”)\n- No place → no L\n- Tense: past → uses **nɔ̂ː**, but in the pattern from the example: “On Bvusɔw, I helped the man” → found in earlier sentences like 18: “On Bvumbon, he saw us” → structure: **[Day] + [subject] + [tense + verb] + [object]**\n\nSo structure: **me nɔ̂ː nfí dìɛ̀msɛ̌n**\n\nBut tense marker for past is **nɔ̂ː**, and the verb “help” is **nfí** (from “me nú nfí” in future — so **nfí** is the base verb). In past, it's **nfí** with **nɔ̂ː**.\n\nSo: **me nɔ̂ː nfí dìɛ̀msɛ̌n**\n\nBut earlier: sentence 18: “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn” → “On Bvumbon, he saw us” → uses **nɔ̂ː** with verb.\n\nSo yes, past tense uses **nɔ̂ː**.\n\nSo: **me nɔ̂ː nfí dìɛ̀msɛ̌n**\n\nCheck tone: **nɔ̂ː** is long, falling. After this, **nfí** — no tone mark → middle tone. But tone rule: after falling or low, high tone becomes rising — but here no high tone. So likely okay.\n\nBut in sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” — “On Bvutfu, the woman saw the market” — uses **nɔ̂ː** + **yɛن** → so tone rule applies after a short falling tone? Doesn’t seem to change.\n\nSo accept: **me nɔ̂ː nfí dìɛ̀msɛ̌n**\n\n---\n\n**(21) The thief stole the yam just now.**\n\n- Subject: the thief → **bèsèn** (from sentence 6: “he killed the woman” — “he” = bɛ̂ː, “wom” = ɛ̀bɛ̀n; “thief” = bèsèn — seen in sentence 9: “the thief will find us” → “cɔ̌ŋ nú bóy bɔ́ŋ bèsèn” → “the thief”)\n- Verb: “stole” → past tense → **cɔ́ŋ**\n- Object: the yam → **kèŋkfǔ** (from sentence 2: “you will steal the yam” → “kèŋkfǔ”)\n- Time: “just now” → corresponds to **cí** (e.g., in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛن me lé” — so “nɔ̂ː” in past; “just now” often has **cí** or **nɔ̂ː**)\n\nWait: in sentence 5: “The day after tomorrow is Bvutfu” → future, so **fɔ̀ shě ntfǔː**\n\nBut “just now” appears in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛن me lé” → uses **nɔ̂ː**, not **cí**\n\nAlso sentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → past with **nɔ̂ː**\n\nSo “just now” = **nɔ̂ː** (recent past)\n\nThus: **bèsèn nɔ̂ː cɔ́ŋ kèŋkfǔ**\n\nStructure: subject (bèsèn) + tense (nɔ̂ː) + verb (cɔ́ŋ) + object (kèŋkfǔ)\n\nNo place.\n\nSo: **bèsèn nɔ̂ː cɔ́ŋ kèŋkfǔ**\n\nTone: cɔ́ŋ has no marking — likely defaults to middle. But may need to follow tone rules? But no falling or rising immediately before — so okay.\n\n---\n\n**(22) On Bvuŋkaden, I will hear the car.**\n\n- Day: **Bvuŋkaden** → from sentence 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n” → so **bvûŋka᷆ːde᷆n** = Bvuŋkaden\n- Subject: I → **me**\n- Verb: “will hear” → future tense → **nú** or **nú géː**? “I will hear” vs. “today I will hear” → future\n- In sentence 1: “On Bvumbon, I came to the market” → uses **me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy** → past\n- “I will choose the car” → “me nú mbóy mutù bvútfu᷅” → future\n\nSo “will” = **nú** + future form\n\nHear → base verb: **bɛ̂ː** (as in “he killed” = ɛ̀bɛ̀n; “he heard” = likely **bɛ̂ː**)\n\nStructure: **me nú bɛ̂ː mutù**\n\nBut object: the car → **mutù** (as in sentence 5: “I will choose the car” → “mutù bvútfu᷅”)\n\nSo: **me nú bɛ̂ː mutù**\n\nTime: day = **bvûŋka᷆ːde᷆n**\n\nSo full: **me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n**\n\nBut in earlier example: “On Bvutfu, I will choose the car” → “me nú mbóy mutù bvútfu᷅”\n\nHere: “On Bvuŋkaden, I will hear the car” → so **me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n**\n\nNote: “bɛ̂ː” is the base of hear, and “nú” is future.\n\nIs “hear” the same as “see”? No — “see” = yɛن, “hear” = bɛ̂ː.\n\nYes.\n\nSo: **me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n**\n\n---\n\n**(23) Today, the woman will kill the man.**\n\n- Day: today → **bɛ̂ː**\n- Subject: the woman → “kwɔ᷆ːn” (from sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn”)\n- Verb: “will kill” → future → **nú**\n- Base verb: “kill” → **ɛ̀bɛ̀n** (from sentence 6: “he killed”)\n- Object: the man → **dìɛ̀msɛ̌n**\n\nSo: **kwɔ᷆ːn nú ɛ̀bɛ̀n dìɛ̀msɛ̌n**\n\nTense: future — uses **nú**\n\nStructure: subject + tense + verb + object\n\nPlace: no — so no L\n\nThus: **kwɔ᷆ːn nú ɛ̀bɛ̀n dìɛ̀msɛ̌n**\n\n---\n\n**(24) Today, the man saw you(sg).**\n\n- Day: today → **bɛ̂ː**\n- Subject: the man → **dìɛ̀msɛ̌n**\n- Verb: “saw” → past tense → **yɛن** → becomes **lé** after consonant\n- Object: you(sg) → **nǔ**\n\nSo: **dìɛ̀msɛ̌n bɛ̂ː yɛن nǔ**\n\nBut in sentence 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛن me lé” → “yɛن” → after consonant → **lé**\n\nSo “saw” → **yɛن** → becomes **lé**\n\nThus: **dìɛ̀msɛ̌n bɛ̂ː lé nǔ**\n\nNo day marker needed — “today” is marked by **bɛ̂ː** at beginning.\n\nSo: **dìɛ̀msɛ̌n bɛ̂ː lé nǔ**\n\n---\n\nFinal translations:\n\n20. me nɔ̂ː nfí dìɛ̀msɛ̌n \n21. bèsèn nɔ̂ː cɔ́ŋ kèŋkfǔ \n22. me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n \n23. kwɔ᷆ːn nú ɛ̀bɛ̀n dìɛ̀msɛ̌n \n24. dìɛ̀msɛ̌n bɛ̂ː lé nǔ\n\nVerify all verb forms and tense markers with examples:\n\n- “helped” = past → **nfí** → correct (from “I am about to help” = “nfí”)\n- “stole” = past → **cɔ́ŋ** → correct\n- “will hear” = future → **nú bɛ̂ː** → correct (from “I will choose” → “nú mbóy”)\n- “will kill” → future → **nú ɛ̀bɛ̀n** → correct\n- “saw” → **yɛن → lé** after consonant → correct (sentence 15: “bɔ́ nɔ̂ː yɛن me lé”)\n\nTone rules: some tones may shift, but the given examples don’t require changes in tone due to high tone collapse — and no such marking is indicated.\n\nThus, final answers:\n\n\\boxed{c.1: me nɔ̂ː nfí dìɛ̀msɛ̌n; c.2: bèsèn nɔ̂ː cɔ́ŋ kèŋkfǔ; c.3: me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n; c.4: kwɔ᷆ːn nú ɛ̀bɛ̀n dìɛ̀msɛ̌n; c.5: dìɛ̀msɛ̌n bɛ̂ː lé nǔ}", + "generated_tokens": 2977, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: me nɔ̂ː nfí dìɛ̀msɛ̌n; c.2: bèsèn nɔ̂ː cɔ́ŋ kèŋkfǔ; c.3: me nú bɛ̂ː mutù bvûŋka᷆ːde᷆n; c.4: kwɔ᷆ːn nú ɛ̀bɛ̀n dìɛ̀msɛ̌n; c.5: dìɛ̀msɛ̌n bɛ̂ː lé nǔ", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7031.0, + "ioling_final_answer_chars": 150.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "redacted_solution_hint_mask5", + "sample_index": 1, + "output": "Step 1: Identify the grammatical structure and tense patterns from the given examples.\n\nFrom the problem, word order follows: S T V O L D (Subject + Tense + Verb + Object + Place + Day). \nTense markers are critical:\n\n- Past: V᷅ or cí (with \"cí\" meaning \"was\", used in past tense of certain verbs)\n- Present / today: bɛ̂ː (today), cí nɔ̂ː (the day before), tɔ̀ nɔ̂ː (a long time ago)\n- Future: V́ or nú (future with \"nú\") or nú géː (future), nú bóy (future), nú yúː (future)\n\nAlso, reconstruction of tense markers:\n- “just now” = cí (in past tense)\n- “about to” = bɛ̂ː (today), or \"bèsèn\" (today), or \"fɔ̀wǎy\" (market) for seeing\n- “hearing” = hear → verb is “yɛn” (to see), but “hear” is likely derived from that, possibly “bɔ́” or “kɛ̀”\n- “kill” = “bɛ̀n” appears in 6: “he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “he killed the woman”\n- “steal” = “cɔ́ŋ” (from 2: “you will steal the yam”)\n\nSo: \n- “steal” = cɔ́ŋ\n- “see” = yɛn\n- “help” = “fí” (from 3: “the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me”)\n- “hear” = inferred from “bèn” or “yɛn” → likely “bɔ́” or “yɛn” with modification\n\nStep 2: Identify the day references\n\nKnown days from the problem:\n- Bvutfu → appears in multiple days (yesterday, day after tomorrow, etc.)\n- Bvusɔw → appears in 2 and 6\n- Bvuŋka → 4, 5, 8\n- Bvuzhi → 3\n- Bvukema → 10, 11\n- Bvuŋkaden → 8, 22\n\nFrom 8: “Tomorrow is Bvuŋkaden” → future: tomorrow → “ntfǔː nú bvûŋka᷆ːde᷆n” → “ntfǔː” = tomorrow, “nú” = future, “bvûŋka᷆ːde᷆n” = Bvuŋkaden\n\nThus:\n- Tomorrow = ntfǔː nú\n- Today = bɛ̂ː\n- Just now = cí (past)\n- Future = nú + verb, or nú géː, nú bóy\n\nStep 3: Translate each item\n\n20. On Bvusɔw, I helped the man.\n\n- Subject: I = me\n- Verb: helped → “fí” (from “help” in 3: “helped me”)\n- Tense: On Bvusɔw → past tense marker: “nú” (for past on a specific day)\n- Day: Bvusɔw → bvúsɔw\n- Structure: me nú fí dìɛ̀msɛ̌n → but “dìɛ̀msɛ̌n” is “the man”\n- So: me nú fí dìɛ̀msɛ̌n\n\nBut check tense: “On Bvusɔw” → past, so use “nú” (past on a day)\n\nSo → me nú fí dìɛ̀msɛ̌n\n\n21. The thief stole the yam just now.\n\n- Subject: thief = yo᷅kwɔ᷆ːn (from 6: “he killed the woman” → “yo᷅kwɔ᷆ːn”)\n- Verb: stole = cɔ́ŋ\n- Tense: just now = cí (past)\n- Object: the yam = kèŋkfǔ\n- Structure: yo᷅kwɔ᷆ːn cí nɔ̂ː kèŋkfǔ\n\nTone: “cí” has a long vowel; tone → after –̂, –᷆, –̀ → –́ > –̌, but here no tone shift needed\n\nSo: yo᷅kwɔ᷆ːn cí nɔ̂ː kèŋkfǔ\n\n22. On Bvuŋkaden, I will hear the car.\n\n- Subject: I = me\n- Verb: hear → inference: “yɛn” is “see”, “hear” is similar → “yɛn” may be used\n- Tense: “will” → future → use “nú” (future), “nú bóy” → future meaning \"will\"\n- Day: Bvuŋkaden → bvûŋka᷆ːde᷆n\n- Object: the car → mutù\n\n→ me nú bóy yɛn mutù\n\nBut note: in 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “we will steal the car” → “géː” = future tense, “cɔ́ŋ” = steal\n\nSo “hear” → likely morphologically related to “see” → “yɛn”\n\nBut “hear” is not directly listed → see if any instance of hearing exists.\n\nIn 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “you heard the thief” → “yo᷅w” = thief, “cɔ̌ŋ” = heard\n\nSo “heard” = cɔ̌ŋ → verb “cɔ̌ŋ” = hear\n\nSo “hear” = cɔ̌ŋ\n\nTherefore: “I will hear the car” = me nú bóy cɔ̌ŋ mutù\n\nDay: On Bvuŋkaden → “nú bvûŋka᷆ːde᷆n” → but only if day is attached\n\nStructure: A (T) nú B → A is on B\n\nSo: me nú bóy cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\n\nBut order: (S T V O) L D → no place → so object → day at end\n\n→ me nú bóy cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\n\n23. Today, the woman will kill the man.\n\n- Subject: woman = nǔ\n- Verb: will kill = “bɛ̀n” (from “he killed” → 6: wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n)\n- Tense: “will” = future → use “nú” or “nú bóy”\n- “Today” = bɛ̂ː → use bɛ̂ː (today)\n- Object: man = dìɛ̀msɛ̌n\n- Structure: nǔ nú bóy bɛ̀n dìɛ̀msɛ̌n\n\nBut is “will” marked by “nú” or by “bóy”? From 14: “bèsèn nǔ géː cɔ́ŋ mutù” → “we will steal” → “bèsèn” = today → present future? \n\nWait: “bèsèn” = today, “nú” = future\n\nBut 14: “bèsèn nǔ géː cɔ́ŋ mutù” = Today, we will steal the car → so “bèsèn” marks present, “géː” marks future\n\nBut “bèsèn” is now used for “today”, with future verb\n\nIn 6: “Today, he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “bɛ̂ː” = today, “bɛ̂ː” is tense\n\nBut in 4: “On Bvuŋka, he found the book” → “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “tɔ̀ nɔ̂ː” = past\n\nFor future: 14 uses “bèsèn” with “géː” — so “bèsèn” may be today, and “géː” future\n\nSo “will” = géː?\n\nBut in 2: “On Bvusɔw, you will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ” — “yúː” = future\n\nIn 13: “On Bvutfu, the woman saw the market” — “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → “nɔ̂ː” = past, “yɛ᷅n” = saw\n\nIn 5: “The day after tomorrow is Bvutfu” → “fɔ̀ shě ntfǔː nú” → “nú” = future\n\nSo future = né, “nú” or “nú géː”\n\nIn 14: “Today, we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù”\n\nSo “will” = géː\n\nThus:\n- “will” = géː\n\nSo 23: nǔ nú géː bɛ̀n dìɛ̀msɛ̌n\n\n“Today” = bɛ̂ː → but used as day modifier? The sentence says “Today, the woman will kill” → so today is tense\n\nIn 14: “Today, we will steal” → “bèsèn” + verb\n\nBut in 6: “Today, he killed” → “bɛ̂ː” + verb\n\nSo today can be marked with bɛ̂ː or bèsèn?\n\nIn 23: “Today” → use bɛ̂ː\n\nBut “will” → géː\n\nSo: nǔ bɛ̂ː géː bɛ̀n dìɛ̀msɛ̌n\n\nStructure: Subject + Day (today) + future verb (géː) + verb + object\n\nBut in 14: “bèsèn” = today, and verb is “géː”\n\nIn 6: “bɛ̂ː” = today, verb is “bɛ̀n” — past\n\nThus, if verb is future, use “géː” with day “bɛ̂ː”?\n\nBut 14: bèsèn + géː → today, will\n\nSo perhaps “bɛ̂ː” is present, “bèsèn” is present with future\n\nBut bɛ̂ː is used in 6: “Today, he killed” → past\n\nThus, future with “today” = “bèsèn” + “géː”\n\nBut the sentence is “Today, the woman will kill” → so must use bèsèn + géː\n\nSo: nǔ bèsèn géː bɛ̀n dìɛ̀msɛ̌n\n\nBut is “bèsèn” only today?\n\nIn 11: “The day before yesterday was Bvuŋka” → “kefwé cí nú bvûŋka” → “kefwé” = day before yesterday\n\nBut no day-specific marker in 23 with \"bèsèn\"\n\n→ So likely future with today = “bèsèn géː”\n\nThus → nǔ bèsèn géː bɛ̀n dìɛ̀msɛ̌n\n\n24. Today, the man saw you(sg)\n\n- Subject: the man = dìɛ̀msɛ̌n\n- Verb: saw → yɛn (from “saw the market”)\n- Tense: today = bɛ̂ː or bèsèn?\n- Object: you(sg) = nǔ\n\nFrom 15: “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = just now, “yɛ᷅n” = saw\n\nSo “saw” = yɛn (inherited)\n\nIn 14: “we will steal” → “bèsèn nǔ géː cɔ́ŋ mutù”\n\nIn 15: “they saw me just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = just now\n\nThus, “today” = bɛ̂ː\n\nSo verb: yɛn\n\nStructure: dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ\n\nBut in 12: “I am about to help the man” → “me nú nfí dìɛ̀msɛ̌n”\n\nSo “about to” = “nú” (future)\n\nHere, “today” = bɛ̂ː\n\nThus: dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ\n\nBut in 15: “they saw me just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé” → “bɔ́” = just now, “yɛ᷅n” = saw\n\nSo “yɛn” = saw — correct\n\nThus: dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ\n\nNow, tone rules: after –̂, –᷆, –̀ → –́ > –̌\n\nBut no harm here.\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man → me nú fí dìɛ̀msɛ̌n \n21. The thief stole the yam just now → yo᷅kwɔ᷆ːn cí nɔ̂ː kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car → me nú bóy cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n \n23. Today, the woman will kill the man → nǔ bèsèn géː bɛ̀n dìɛ̀msɛ̌n \n24. Today, the man saw you(sg) → dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ\n\nNow check consistency.\n\nIn 20: On Bvusɔw → uses “nú” (past on a day) → me nú fí dìɛ̀msɛ̌n → correct\n\nIn 21: just now → “cí” → correct\n\nIn 22: future → “nú bóy” → correct\n\nIn 23: today + future → “bèsèn géː” → matches 14\n\nIn 24: today + saw → “bɛ̂ː” → matches 15 (just now uses “bɔ́” not “bɛ̂ː”) → but “today” is not “just now” → so “bɛ̂ː” is correct\n\nOne check: in 6, “today” = “bɛ̂ː”, “he killed” → bɛ̀n — past\n\nIn 14, “today” = “bèsèn”, “will steal” = “géː” — future\n\nSo “today” can be marked by bɛ̂ː or bèsèn depending on future?\n\nBut in 23, “will kill” → future → so use bèsèn géː\n\nIn 24, “saw” → past → so use bɛ̂ː\n\nYes — so past with today = bɛ̂ː, future with today = bèsèn géː\n\nThus all correct.\n\n\\boxed{c.1: me nú fí dìɛ̀msɛ̌n; c.2: yo᷅kwɔ᷆ːn cí nɔ̂ː kèŋkfǔ; c.3: me nú bóy cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n; c.4: nǔ bèsèn géː bɛ̀n dìɛ̀msɛ̌n; c.5: dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ}", + "generated_tokens": 3728, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: me nú fí dìɛ̀msɛ̌n; c.2: yo᷅kwɔ᷆ːn cí nɔ̂ː kèŋkfǔ; c.3: me nú bóy cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n; c.4: nǔ bèsèn géː bɛ̀n dìɛ̀msɛ̌n; c.5: dìɛ̀msɛ̌n bɛ̂ː yɛn nǔ", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7943.0, + "ioling_final_answer_chars": 158.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "redacted_solution_hint_mask5", + "sample_index": 2, + "output": "Step 1: Identify the core grammatical patterns from the examples.\n\nAll sentences follow a structure: \nSubject + Tense marker + Verb + Object (if any) + Place (optional) + Day (optional)\n\nTense markers:\n- Past: cí, tɔ̀ nɔ̂ː (e.g., \"on Bvumbon, I came\" → me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn)\n- Future: nú (used before existential or modal verbs), or nú géː (for \"will\" in future), or nú bóy (for \"will\" in aspectual future)\n- \"Today\" = bɛ̂ː (e.g., \"Today, he killed\" → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n)\n- \"Just now\" = cí (used with verb in past, e.g., \"just now\" = cí, as in \"he saw me just now\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ)\n\nNote: In sentence 7: “You(sg) heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” — here, \"tɔ̀ nɔ̂ː\" = long time ago (past), so \"cí\" = just now.\n\nStep 2: Analyze verb forms and transformations.\n\n\"Help\" → in example 12: “me nú nfí dìɛ̀msɛ̌n” → “I am about to help the man” \n“nfí” = help, “dìɛ̀msɛ̌n” = man \n→ “me nú nfí dìɛ̀msɛ̌n” → future (nú) + verb nfí (help) + object\n\n“See” → yɛn (O) lé, and after consonant → lé > é \nExample 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → \"They saw me at the market just now\" \n→ yɛn me lé = “saw me” (after consonant, lé > é)\n\nStep 3: Handle pronouns and subject prefixes.\n\n1st person singular: “n-” → becomes “mb” after certain consonants \n- “me” → subject (1st person sg), appears consistently in examples.\n\n“Thief” = yo᷅w (from 6: “he killed the woman” → “yo᷅kwɔ᷆ːn” = woman, \"yo᷅w\" = thief)\n\n“Man” = dìɛ̀msɛ̌n (from 12: “help the man”)\n\n“Car” = mutù (from sentence 5: “choose the car” → “mutù”)\n\n“Yam” = kèŋkfǔ\n\n“Woman” = nǔ bóy (from 3: “the woman will help me” → “kwɔ᷆ːn nǔ bóy”)\n\nStep 4: Translate each target sentence.\n\n20. “On Bvusɔw, I helped the man.” \n→ Day = Bvusɔw → use “nú” (for future or upcoming) \n→ “I” = me \n→ “helped” → past tense of “help”? But in example 12: “me nú nfí dìɛ̀msɛ̌n” → “I am about to help” (future), so “help” = nfí \n→ Past “helped” must be formed with tense marker. \nFrom example 12 (today, about to help): “me nú nfí” \nNow: On Bvusɔw → past or future? \nBvusɔw is not today’s day, so past = “cí”? But “on Bvusɔw” → past event? \nCheck: sentence 2: “On Bvusɔw, you(sg) will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → future \nSo “On X, Y will do Z” → use “nú” + V (for future) \nBut “helped” is past → not future → so indicate as past?\n\nBut no past structure for “on X, I helped” in examples.\n\nLooking at sentence 3: \"On Bvuzhi, the woman will help me\" → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “fí” = help → past form?\n\n“fí” appears in both \"help\" and \"helped\" from 3 and 12?\n\nWait: sentence 12: “me nú nfí dìɛ̀msɛ̌n” → “I am about to help” → future, not past.\n\nSentence 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “On Bvuzhi, the woman helped me” → past.\n\nSo “fí” = help → past tense \n“nfí” = future (with nú) \nThus, “helped” = fí in past\n\nSo: “On Bvusɔw, I helped the man” \n→ “me” + tense indicator? → on Bvusɔw = day → precede with “nú” \nBut in sentence 2: “On Bvusɔw, you(sg) will steal” → future → “nǔ yúː” → yúː = will \nSo for past: not “nú”, so need to use “cí” or “tɔ̀ nɔ̂ː”?\n\nBut Bvusɔw is not “today” → “today” = bɛ̂ː \nIn sentence 2: \"On Bvusɔw, you(sg) will steal\" → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → tense marker = yúː → future\n\nSo when “on X” and the action is future → use future verb (nú or yúː)\n\nWhen past → use past tense marker (fí) or with “cí”\n\nBut in no example do we have “on X, I helped” in past.\n\nHowever, sentence 3: “On Bvuzhi, the woman will help me” → “fí” → not future → contradiction.\n\nWait: sentence 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “fí” = help → and day is Bvuzhi \nBut there’s no tense marker like “nú” → is “fí” with no “nú” = past?\n\nCompare: sentence 12: “me nú nfí dìɛ̀msɛ̌n” → “I am about to help” → future\n\nSo when verb has “nú” → future, when not → past?\n\nYes. So in sentence 3: no “nú”, just “fí” → means past → “helped”\n\nSo for “On Bvusɔw, I helped the man” → past event → use “fí” → so: “me fí dìɛ̀msɛ̌n”?\n\nBut need day → “on Bvusɔw” → use “nú” for the day? \n\nLook at all day structure: \n- “On Bvusɔw” = “nú bvúsɔ̀w” → e.g., sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” \n- “On Bvutfu” = “nú bvútfu᷅” → sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu” → “nú” + day\n\nSo “on X” structure = “nú X”\n\nTherefore: “On Bvusɔw, I helped the man” → “me fí dìɛ̀msɛ̌n nú bvúsɔ̀w”\n\nBut is “fí” correct? \nYes, from sentence 3: past tense of help → “fí”\n\nAnd “me” → 1st person → remains “me”\n\nSo 20 → me fí dìɛ̀msɛ̌n nú bvúsɔ̀w\n\nStep 5: 21. “The thief stole the yam just now.”\n\n“just now” = cí (from sentence 7: “you heard the thief a long time ago” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → time marker = tɔ̀ nɔ̂ː = long ago; “cí” = just now)\n\nSo “just now” = cí → attached to verb\n\n“The thief” = yo᷅w \n“stole” = cɔ́ŋ → from sentence 2: \"you will steal\" → “cɔ́ŋ” → so “stole” = cɔ́ŋ\n\nThus: yo᷅w cɔ́ŋ kèŋkfǔ cí\n\nNote: The verb “cɔ́ŋ” has high tone — in sentence 2: “nǔ yúː cɔ́ŋ” → “will steal”\n\nNo tense marker needed — “cí” marks the time.\n\nSo → yo᷅w cɔ́ŋ kèŋkfǔ cí\n\nStep 6: 22. “On Bvuŋkaden, I will hear the car.”\n\n“On Bvuŋkaden” = “nú bvûŋka᷆ːde᷆n”\n\n“I” = me\n\n“will hear” = future → “nú” used with verb\n\n“hear” = from earlier: “saw” = yɛn lé → but hear? Not directly given.\n\nBut “heard” appears: \"you heard the thief\" → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “heard” = cɔ̌ŋ\n\nSo “hear” = cɔ̌ŋ (same verb)\n\nBut “will hear” → future → in examples, “will” = yúː or nú\n\nIn sentence 2: “will steal” → yúː\n\nIn sentence 5: “on Bvutfu, I will choose” → “me nú mbóy ncáw mutù bvútfu᷅” → “nú” + “mbóy” = choose → so “nú” = future\n\nIn sentence 14: “Today, we will steal” → “bèsèn nǔ géː cɔ́ŋ mutù” → “géː” = future\n\nSo “will” can be: \n- yúː → for “will steal” \n- nú + verb → for “I will choose”\n\n“hear” → cɔ̌ŋ (same as heard)\n\nSo “I will hear” = me nú cɔ̌ŋ mutù\n\nThen add day: “on Bvuŋkaden” → nú bvûŋka᷆ːde᷆n\n\nBut “nú” already used? Need to avoid repetition.\n\nStructure: “On X, I will hear” → “nú X, me nú cɔ̌ŋ mutù” → but that gives “on X, I will hear” — valid?\n\nBut in sentence 2: “On Bvusɔw, you will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → no “nú” with day → so day is attached directly.\n\nSo “nú + day” = “on day”\n\nSo verb tense: future → use “nú” with verb\n\nBut not used with day.\n\nThus: “On Bvuŋkaden, I will hear the car” → “me nú cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n” → but “nú” used twice?\n\nIn example 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → past time is not marked → only future → time is on day → “bvúsɔ̀w”\n\nSimilarly, in sentence 14: “Today, we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù” → not “on day”\n\nSo for “on X” and future → “X” is part of the clause → “me nú cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n”\n\nBut “nú” appears only once.\n\nIn sentence 8: “Tomorrow is Bvuŋkaden” → “ntfǔː nú bvûŋka᷆ːde᷆n” → “ntfǔː” = tomorrow → not “on”\n\nSo only for specific events: “on X” → “nú X”\n\nThus, \"On Bvuŋkaden, I will hear the car\" = me nú cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n\n\nBut “nú” used twice → is that valid?\n\nIn example 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu” → “nú” + day\n\nIn sentence 2: “On Bvusɔw, you will steal” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → no “nú” with verb → only “bvúsɔ̀w” at end\n\nSo structure: [subject] [tense] [verb] [object] [day] → day comes at end?\n\nBut in sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → day at end\n\nSo yes — day at end, after object.\n\nSo “me nú cɔ̌ŋ mutù nú bvûŋka᷆ːde᷆n” → has two “nú”?\n\nBut in 3: “nǔ bóy fí me bvúzhí” → no “nú” → only “bvúzhí” at end\n\nSo no “nú” with day.\n\nSo for “on X”, just “X” is appended → no extra “nú”\n\nThus: “me nú cɔ̌ŋ mutù bvûŋka᷆ːde᷆n”\n\nBut verb is “hear” → is “cɔ̌ŋ” used for “hear”? \nIn sentence 7: “you heard the thief” → “wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ” → “heard” → “cɔ̌ŋ” → so yes\n\nFuture: “will” = “nú” with verb\n\nSo: me nú cɔ̌ŋ mutù bvûŋka᷆ːde᷆n\n\nYes.\n\nStep 7: 23. “Today, the woman will kill the man.”\n\n“Today” = bɛ̂ː\n\n“the woman” = nǔ bóy\n\n“will kill” = “nú” + kill \n“kill” = from sentence 6: “he killed the woman” → “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” → “killed” = yo᷅kwɔ᷆ːn (thief killed woman) → verb is “kwɔ᷆ːn” → seems like “kill” is “kwɔ᷆ːn”\n\nSo “will kill” = nú kwɔ᷆ːn\n\nObject: “the man” = dìɛ̀msɛ̌n\n\nSo: nǔ bóy nú kwɔ᷆ːn dìɛ̀msɛ̌n bɛ̂ː\n\nOrder: S + T + V + O + D → correct.\n\nStep 8: 24. “Today, the man saw you(sg).”\n\n“Today” = bɛ̂ː\n\n“the man” = dìɛ̀msɛ̌n\n\n“saw” = yɛn (with lé) → in example 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw me at the market” → “yɛn me lé”\n\nSo “saw” = yɛn (object) + lé (after consonant → rendered as é)\n\nSo object = you(sg) = wɔ̀ (first person: “wɔ̀” = you)\n\nThus: dìɛ̀msɛ̌n yɛn wɔ̀ lé bɛ̂ː\n\nBut “lé” after consonant → becomes é → “lé” → “é”\n\nSo → dìɛ̀msɛ̌n yɛn wɔ̀ é bɛ̂ː\n\nAlso, in sentence 12: “me nú nfí dìɛ̀msɛ̌n” → no yɛn → but “see” is “yɛn” → verb\n\nSo yes.\n\nNow compile all:\n\nc.1 / 20: me fí dìɛ̀msɛ̌n nú bvúsɔ̀w \nc.2 / 21: yo᷅w cɔ́ŋ kèŋkfǔ cí \nc.3 / 22: me nú cɔ̌ŋ mutù bvûŋka᷆ːde᷆n \nc.4 / 23: nǔ bóy nú kwɔ᷆ːn dìɛ̀msɛ̌n bɛ̂ː \nc.5 / 24: dìɛ̀msɛ̌n yɛn wɔ̀ é bɛ̂ː\n\nFinal check:\n\n- 20: past help → fí, object man → dìɛ̀msɛ̌n, on Bvusɔw → nú bvúsɔ̀w → correct \n- 21: thief stole yam just now → cí → correct \n- 22: on Bvuŋkaden, I will hear car → me nú cɔ̌ŋ mutù bvûŋka᷆ːde᷆n → correct \n- 23: today, woman", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9166.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "redacted_solution_hint_mask5", + "sample_index": 3, + "output": "We are to translate the given English sentences into Nooni, spoken on **Bvumbon**, using the provided linguistic rules and examples.\n\n---\n\n**Step 1: Understand the structure of Nooni sentences**\n\nFrom the examples:\n\n- Word order: **S T V O L D** \n So: Subject + Tense + Verb + Object + Place + Day \n (S = subject, T = tense, V = verb, O = object, L = location, D = day)\n\n- \"to see\" = **yɛn** (O) + **lé** \n After a consonant: **lé → é** \n (e.g., yɛn lé → yɛn é)\n\n- Tense markers:\n - Past: **V᷅** (e.g., wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w) → \"you will steal\" on Bvusɔw \n - Past: **nɔ̂ː** (e.g., cí nɔ̂ː, tɔ̀ nɔ̂ː) \n - Future: **nú**, **nú géː**, **nú bóy**, **nú yúː** \n - \"just now\" = **bɛ̂ː** (present) or used with **cí** \n But note: \"just now\" appears with **bɛ̂ː** (e.g., 6: wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n → \"he killed the woman just now\")\n\n- For 1st person:\n - **n- + T/V** → **mb** (nb > mb), **ŋk → ŋg**, **nn > n**\n\n- Tonal rules:\n - After –̂, –᷆, –̀: –́ → –̌ \n (This affects tone changes in derived forms)\n\n---\n\n**Sentence 20: On Bvusɔw, I helped the man.**\n\n- \"I helped\" = 1st person, past tense, helping = verb form **nú** or **nú cí**? \n But \"help\" is not directly given. However, \"help\" is a verb: it should be **nú** (future) or **cí** (past). \n \"I helped\" = past, so **cí** \n Verb: \"help\" = **mbí**? Not directly given. \n But in sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"the woman will help me\", so \"bóy fí\" = \"will help\"\n\n So \"help\" = **fí** \n → \"I helped\" = **me cí fí** \n But is \"cí\" just tense? \n → Check: sentence 1: \"fɔgò cǐ nú bvúmbòn\" = \"Yesterday was Bvumbon\" → \"cǐ\" = past tense (cǐ = yesterday) \n Similarly, \"cí nɔ̂ː\" = \"last day\", etc.\n\n So **cí** is past tense in this context (as a part of V). \n But \"help\" = **fí**, so \"I helped\" = **me cí fí**\n\n Place? \"On Bvusɔw\" → D = **bvúsɔ̀w** \n Structure: S T V O L D \n O = man → **dìɛ̀msɛ̌n** (the man) \n L = ? (no place mentioned) → so no L \n D = bvúsɔ̀w \n\n So: **me cí fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n → But check tense: is \"cí\" the correct form?\n\n Look at sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → \"On Bvuŋka, he found the book\" \n → tense marker **nɔ̂ː** (past)\n\n Sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\" → future → **bóy**\n\n So **fí** appears without tense marker → in past context? \n In \"cí nɔ̂ː\" → \"yesterday was\", so **cí** is associated with past time, not tense.\n\n In fact, the tense marker is **nɔ̂ː** for past, **nú** (or nu) for future.\n\n In sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" → \"On Bvumbon, he saw us\" → uses **tɔ̀ nɔ̂ː** (past)\n\n So \"past\" = **T + nɔ̂ː** \n \"future\" = **T + nú**, **nú géː**, etc.\n\n \"Yesterday\" = **fɔgò cǐ** → **cǐ** is time word, not tense.\n\n So **cí** is a time word (day before yesterday), not tense.\n\n But in sentence 11: \"kefwé cí nú bvûŋka\" → \"The day before yesterday was Bvuŋka\" → \"cí\" is time reference.\n\n So **cí** = time, not tense.\n\n Then what is the tense of \"helped\"?\n\n In \"me nú mbóy ncáw mutù bvútfu᷅\" → \"On Bvutfu, I will choose the car\" → future → **nú**\n\n So the verb **fí** (help) in past context: should be **me cí fí**? → but where is the past tense marker?\n\n Wait — in sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"will help\" → \"bóy fí\" → **bóy** = future\n\n So **fí** is the verb, tense is marked by **bóy** or **cí**?\n\n But in sentence 3: \"nǔ bóy fí\" → future \n In \"me cí fí\" → past?\n\n But now observe: \"Today\" or \"just now\" uses **bɛ̂ː**.\n\n In sentence 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"you heard the thief a long time ago\" → past with **nɔ̂ː**\n\n In sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed\" → **bɛ̂ː** = today\n\n So tense markers:\n - **Today** = **bɛ̂ː**\n - **Past** = **nɔ̂ː**\n - **Future** = **nú**, **nú géː**, **nú bóy**, **nú yúː**\n - \"Just now\" = **bɛ̂ː** (as in 6)\n\n So for \"I helped\" (past), we use **cí** (as in time) + **fí**?\n\n But in sentence 3: \"kwɔ᷆ːn nǔ bóy fí me\" → \"will help\"\n\n So **bóy** = future, **fí** = verb\n\n Then for past: **me cí fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n But is \"cí\" time or tense?\n\n In 11: \"kefwé cí nú bvûŋka\" → \"day before yesterday was Bvuŋka\" → \"cí\" is time word\n\n So **cí** is not tense, but a time reference.\n\n So the tense of the verb must be marked by **nɔ̂ː** for past?\n\n In 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" → \"saw\" → **tɔ̀ nɔ̂ː** = past tense\n\n So \"helped\" must have **nɔ̂ː** → so **me nɔ̂ː fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n But wait: in sentence 3: \"nǔ bóy fí\" = future → so **bóy** = future \n In sentence 1: \"fɔgò cǐ\" = yesterday → time\n\n So no direct past tense verb with \"nɔ̂ː\" attached?\n\n But in sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě\" → \"saw us\" — so \"tɔ̀ nɔ̂ː\" = past tense\n\n So the verb \"see\" = yɛn → becomes yɛn é (after consonant), so \"yɛn é\"\n\n So for \"helped\", if past, tense = **nɔ̂ː**\n\n So: **me nɔ̂ː fí dìɛ̀msɛ̌n bvúsɔ̀w**?\n\n But is there a past form?\n\n Try to see if \"help\" appears in past in any sentence.\n\n Only in future: \"the woman will help me\" → use of **bóy**\n\n So for past: no verb form given directly.\n\n But in the pattern, we may assume **fí** is used with tense marker **nɔ̂ː** for past.\n\n Also, in sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\" → \"found\" → **tɔ̀ nɔ̂ː** = past\n\n So present tense = **bɛ̂ː**, past = **nɔ̂ː**\n\n So \"helped\" = **me nɔ̂ː fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n → But is this correct?\n\n Compare to 23: \"Today, the woman will kill the man\" → future → tense = **bɛ̂ː** for \"today\", verb = \"kill\" → so must be used with future marker?\n\n Let's go to sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"Today, we will steal the car\" → \"bèsèn\" = today, \"géː\" = future\n\n So \"today\" = **bèsèn**, future = **géː**\n\n Similarly, sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"On Bvutfu, the woman saw the market\" → past → **cǐ nɔ̂ː**\n\n So for today: **bèsēn** or **bɛ̂ː**?\n\n Sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed\"\n\n So **bɛ̂ː** = today\n\n Sentence 14: \"bèsèn nǔ géː\" → \"today, we will\" → **bèsèn** = today, but future verb\n\n So \"today\" can be **bɛ̂ː** or **bèsèn**?\n\n But in 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn\" → used **bɛ̂ː** \n In 14: \"bèsèn nǔ géː\" → used **bèsèn**\n\n Could it be that **bɛ̂ː** = just now, **bèsèn** = today?\n\n Sentence 7: \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"You heard the thief a long time ago\" → past\n\n Sentence 21: \"The thief stole the yam just now\" → must use **bɛ̂ː**\n\n So \"just now\" = **bɛ̂ː**\n\n So:\n\n - \"today\" = **bèsèn** \n - \"just now\" = **bɛ̂ː** \n - \"past\" = **nɔ̂ː**\n\n Now back to 20: \"On Bvusɔw, I helped the man\" \n → Day = **bvúsɔ̀w** \n → Verb = help → **fí** \n → Tense = past → **nɔ̂ː** \n → Subject = me → **me** \n → Object = man → **dìɛ̀msɛ̌n** \n → No place → so only V O D\n\n → **me nɔ̂ː fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n But is this acceptable?\n\n In sentence 3: \"kwɔ᷆ːn nǔ bóy fí me\" → \"will help me\" → so **bóy** is future tense\n\n So for past, we use **nɔ̂ː** → so verb: **fí**, tense: **nɔ̂ː**\n\n So 20 → **me nɔ̂ː fí dìɛ̀msɛ̌n bvúsɔ̀w**\n\n---\n\n**Sentence 21: The thief stole the yam just now.**\n\n- Subject: thief → **yo᷅kwɔ᷆ːn** (from sentence 6: \"he killed the woman\") \n- Verb: steal → **cɔ́ŋ** (in sentence 2: \"you will steal the yam\") → \"cɔ́ŋ\" \n- Object: yam → **kèŋkfǔ** (from sentence 2: \"steal the yam\") \n- Time: just now → **bɛ̂ː** (as in sentence 6)\n\n- Verb: \"stole\" = past → tense: **nɔ̂ː**? \n- But \"just now\" = **bɛ̂ː**, which may serve as tense marker\n\n- From sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed\" \n Here \"bɛ̂ː\" = today, verb = killed (which is past form)\n\n- Also, \"the thief\" = **yo᷅kwɔ᷆ːn**\n\n- \"Stole\" = **cɔ́ŋ** (from sentence 2: \"you will steal\")\n\n- So \"the thief stole\" = **yo᷅kwɔ᷆ːn nɔ̂ː cɔ́ŋ kèŋkfǔ**\n\n- Time: just now → so must use **bɛ̂ː**\n\n- So full: **yo᷅kwɔ᷆ːn nɔ̂ː cɔ́ŋ kèŋkfǔ bɛ̂ː**\n\n- But is tōne affected?\n\n- After **nɔ̂ː**, which is falling, we have **cɔ́ŋ** → tone changes? \n Rule: after –̂, –᷆, –̀: –́ → –̌ \n But here: **nɔ̂ː** → falling → followed by **cɔ́ŋ** → which may have tone unaffected?\n\n But no tone given → so default middle?\n\n But sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → \"you will steal\" → no tone on verb → so tone not given\n\n But in 6: \"he killed\" → tone on verb? Yes → **ɛ̀bɛ̀n** → high tone?\n\n So we preserve tone as per source.\n\n But in 21: no tone given → we assume no tone mark → so neutral\n\n- So: **yo᷅kwɔ᷆ːn nɔ̂ː cɔ́ŋ kèŋkfǔ bɛ̂ː**\n\n But is \"just now\" embedded in tense?\n\n In sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"Today, he killed\" → so **bɛ̂ː** is time and also marks present?\n\n So yes, **bɛ̂ː** = just now or today → used for both\n\n So here: \"just now\" = **bɛ̂ː**\n\n So 21: **yo᷅kwɔ᷆ːn nɔ̂ː cɔ́ŋ kèŋkfǔ bɛ̂ː**\n\n---\n\n**Sentence 22: On Bvuŋkaden, I will hear the car.**\n\n- \"I will hear\" = future tense \n- Verb: hear → from sentence 8: \"cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n\" → \"the thief will find us\" → \"bóy\" = future, verb = \"bɔ́ŋ\" (find)\n\n So \"hear\" = ? \n No direct form, but \"see\" = yɛn → \"yɛn lé\" → becomes yɛn é (after consonant)\n\n So \"hear\" = **yɛn**? \n But \"hear\" is not directly present.\n\n However, \"hear the car\" → object = car = **mutù ɛ̀bɛ̀n** (from sentence 14: \"steal the car\")\n\n So \"car\" = **mutù ɛ̀bɛ̀n**\n\n \"I will hear\" → 1st person, future → **me nú yɛn** \n In sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"The day after tomorrow is Bvutfu\" → tense = **nú**\n\n So future = **nú**\n\n But \"will hear\" = future → **n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9369.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. Rules:\n\n • word order:\n ( { )\n cí (past)\n – A (T) nú B ‘A is B’/‘A was B’, T = tense:\n ∅ (future)\n\n – S T V O (lé) L D\n\n (S = subject, V = predicate, O = object, L = place, D = day)\n\n ∗‘to see’ = yɛn (O) lé\n ∗after a consonant: lé > é\n\n tense ‘just now’/‘be about to …’ today < 3 days > 3 days\n • tense: past (V᷅) nɔ̂ː bɛ̂ː cí nɔ̂ː tɔ̀ nɔ̂ː\n future (V́) nú nú géː nú bóy nú yúː\n\n • 1st person sg: n- + T/V\n\n – nb > mb\n\n – nk/ng > ŋk/ŋg\n\n – nn > n\n\n • after –̂, –᷆, –̀: –́ > –̌\n\nAnswers:\n\n (a) 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː. Bvusɔw is the day after tomorrow.\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n. Today, I will see the yam.\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn. On Bvumbon, he saw us.\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n. On Bvuzhiden, we will come to the market.\n\n (b)\n Bvutfu, Bvuŋka, Bvuzhi, Bvukema, Bvuŋkaden, Bvuzhiden, Bvusɔw, Bvumbon.\n\n (c) 20. On Bvusɔw, I helped the man. [TARGET ANSWER REDACTED]\n 21. The thief stole the yam just now. [TARGET ANSWER REDACTED]\n 22. On Bvuŋkaden, I will hear the car. [TARGET ANSWER REDACTED]\n 23. Today, the woman will kill the man. [TARGET ANSWER REDACTED]\n 24. Today, the man saw you(sg). [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "redacted_solution_hint_mask6", + "sample_index": 0, + "output": "We are given a set of Jaqaru words with English translations and suffix rules. We must translate the given items using the pattern derived from the provided examples and suffix rules.\n\n---\n\nFirst, identify the root and suffix patterns.\n\nRoots and their verbal/case forms:\n\n- aq”ipsa → “the cave too” → root: *aq*; suffix -psa → “too”\n- aq”na → “in the cave” → root: *aq*; suffix -na\n- qucxap”a → “through the lake” → root: *qucx*; suffix -p”a\n- qucxst”psa → “from our1+2 lake too” → root: *qucx*; suffix -st”psa → “from our1+2 lake too”\n - -st” → seems like “from” + possessive (our1+2)\n - -psa → “too”\n- chushp”a → “his corner” → root: *chush*; suffix -p”a\n- chushuntxi → “is it in the corner?” → root: *chush*; suffix -untxi → “is it in?”\n- marka → “the town”\n- markp”t”a → “from his town” → root: *mark*; suffix -p”t”a → “from his” + -t”a = case?\n- markstxi → “is it our1+2 town?” → root: *mark*; suffix -stxi → “is it our1+2?”\n- ishinhna → “in my bed” → root: *ishin*; suffix -hna → “in”\n- ishma → “your bed” → root: *ish*; suffix -ma → “your”\n- p”ak”u → “the pot”\n- p”ak”unhpsa → “my pot too” → root: *p”ak*; suffix -unhpsa → “my pot too”\n- qaqat”a → “from the cliff” → root: *qqa*; suffix -t”a → “from”\n- yapsanpsa → “in our1+2 field too” → root: *yap*; suffix -sanpsa → “in our1+2 field too”\n\n---\n\nNow examine the suffix system:\n\n**Possessor suffixes:**\n- -p”a → neutral possessive (e.g., his, my, your)\n- -sa → also possessive, but not seen directly\n- -na → in the (in the cave) → seems like locative, attached to root\n- -t”a → from (e.g., from his town)\n- -txi → is it in? → interrogative?\n\n**Case suffixes:**\n- -psa → “too” or “also”\n- -txi → interrogative: “is it in X?”\n- -na → locative: “in”\n- -t”a → from\n\n**Vowel elision rules:**\n- Oral suffixes (like -p”a, -t”a, -txi) consume the preceding vowel **if it belongs to another suffix or to a different word**, but leave it if it's part of the root.\n- Nasal suffixes (like -nha, -ma) consume the vowel only if they keep theirs; otherwise, leave it.\n\nIn practice, from examples:\n- aq”na → “in the cave”: *aq* + *-na* → no vowel elision → aq”na\n- aq”ipsa → “the cave too”: *aq* + *-ipsa* → “too” → -psa attaches and elides the previous -i?\nWait: aq”ipsa = aq”i + psa → the \"i\" is left, with aspiration.\n\nBut look: qucxst”psa = from our1+2 lake too → root *qucx*, then -st”psa → has -st” and -psa → likely -st” is “from our1+2”, -psa = \"too\"\n\nSimilarly, chushp”a = his corner → chush + p”a\nchushuntxi = is it in the corner? → chush + untxi → -untxi = interrogative locative?\n\nmarkp”t”a = from his town → mark + p”t”a → “from his town”\nmarkstxi = is it our1+2 town? → mark + stxi → “is it our1+2?”\n\nSo likely:\n- -p”a → possessive marker (e.g., “his”, “my”, “your”)\n- -t”a → “from”\n- -txi → “is it in?” (interrogative)\n- -psa → “too” or “also”\n\nAlso note:\n- Our1+2 = “mine and yours” → so possessive marker “our1+2” → appears as -st in qucxst”psa → “our1+2” → -st?\n\nLook at:\n- qucxst”psa: from our1+2 lake too → -st”psa → so -st” is “our1+2” + “from”, with aspirated “t”?\n- markstxi: is it our1+2 town? → “our1+2” + -stxi (interrogative)\n\n→ So: “our1+2” is marked by -st (in -st”psa, -stxi)\n\n→ So:\n- -st” → “our1+2” + possessive or locative?\n- Also, in “from our1+2 lake too” = qucxst”psa → so the root *qucx* is modified by:\n - st” → our1+2\n - t”a → from?\n - psa → too?\n\nBut -st”psa → appears to be:\n- -st” → “our1+2” (with aspiration) \n- -psa → “too”\n\nBut the “from” is missing here. Wait: “from our1+2 lake too” → so “from” must be in root.\n\nWait—qucxap”a = “through the lake” → root qucx + p”a → “through”?\n\nThen qucxst”psa = “from our1+2 lake too” → might be: qucx + st” + t”a + psa?\n\nBut that seems messy.\n\nAlternatively, maybe “from” is expressed via suffix -t”a, and “our1+2” via -st” — and “too” via -psa.\n\nSo:\n- -st” → our1+2\n- -t”a → from\n- -psa → too\n- -txi → is it in?\n\nNow, possessive markers:\n- -p”a → his, my, your\n- -t”a → from (someone's)\n- -na → in\n- -txi → is it in?\n\nLet’s test with:\n\n**4. our1+2 cliff**\n\nRoot: *qqa* (from qaqat”a = from the cliff)\n\nSo, “our1+2 cliff” → root *qqa*, with possessive “our1+2” → -st”\n\nSo: *qqa* + *st”* → qqa st”?\n\nBut qaqat”a = from the cliff → root qqa + t”a → qqa t”a\n\nSo from = -t”a\n\nThen “our1+2 cliff” → just possessive + root → qqa st”?\n\nBut no case? Is there a locative?\n\nWell, “cliff” is a noun, so “our1+2 cliff” = possessive noun → so same as “his corner” = chushp”a → chush + p”a\n\nSo “our1+2 corner” → chushst”a?\n\nBut no such form.\n\nIn “chushp”a” = his corner → p”a\n\n“chushuntxi” = is it in the corner? → -untxi\n\nSo corner root: chush → p”a = his corner → p”a → plain poss\n\nSo possessive adds -p”a → “his”, “your”, “our1+2”\n\nSo “our1+2 cliff” → qqa + st” → qqa st”?\n\nBut is the “st” aspirated? Yes, in qucxst”psa → st” with aspiration\n\nSo: qqa st” → our1+2 cliff?\n\nBut earlier: qaqat”a = from the cliff → root qqa + t”a → qqa t”a\n\nSo “from the cliff” → qqa t”a\n\nThus, “our1+2 cliff” → qqa st” → likely\n\nBut what about vowel elision?\n\nWe must check if root has a vowel.\n\nRoot qqa → ends in a → no vowel before suffix?\n\nSo adding -st” → qqa st” → no elision issue.\n\nSo **4. our1+2 cliff → qqa st”**\n\nBut is that written as qqa st”? In the data, qaqat”a is spelled qaqat”a — so -t”a attached directly.\n\nSo qqa st” → qqa st”?\n\nYes.\n\nSo b.1 / 4.: **qqa st”**\n\n---\n\n**5. in your corner**\n\nRoot: corner → chush\n\nPossessive: your → -ma → see ishma → “your bed” = ish + ma\n\nSo “your corner” → chush + ma → chushma?\n\nBut “in your corner” → need locative.\n\n“in” is marked by -na → from “in my bed” = ishinhna → root ishin + hna → hna = in\n\n“in your bed” → would be ish + ma + hna → ishmanha?\n\nBut ishinhna → ishinhna\n\nSo \"in\" → -hna → attached to root\n\nSo corner → chush → chush + ma → your corner → chushma?\n\nThen add -na → in → chushma na?\n\nBut vowel elision?\n\nRoot: chush → ends with “h” → so adding -ma → chush + ma → chushma → no vowel to elide → vowels?\n\nchush → ends with “h” → no vowel — “ush” → so no vowel between root and suffix?\n\nPossibly, root ends with consonant → so -ma can attach → no elision.\n\nThen -na → after -ma → chushma + na → chushma na?\n\nBut is there a vowel before -na?\n\nIn ishinhna → ishin → ends with “n” → then hna → so h+na → no elision?\n\nWait: ishin → ends with “in” → then -hna → so “in” comes from -hna → and “in” is the locative.\n\nSo structure: root + locative suffix → root ends with consonant → no elision.\n\nSimilarly, chush + ma → your corner → chushma → then add -na → in → chushma na?\n\nSo **5. in your corner → chushma na**\n\nCheck pattern: ishinhna = in my bed → root ish + in + hna → ishin + hna → so “my” is ish → ish + in → ishin → then hna → so -hna = in?\n\nBut ishinhna → ishi + n + hna → so “n” is from root? Then hna → so root end and suffix vowel?\n\nWe can infer that -hna is the locative and directly follows.\n\nSo “in your corner” → your corner → your + corner → chushma → then in → -na → attached → chushma na\n\nSo **b.2 / 5.: chushma na**\n\n---\n\n**6. in your corner too**\n\n→ add “too” → suffix -psa\n\nSo from “in your corner” → chushma na → then add -psa → so chushma na psa?\n\nBut vowel elision: does the suffix -psa consume the vowel?\n\n- Oral suffixes consume the vowel if it belongs to another suffix.\n\nHere: -na is locative → root → vowel in -na?\n\n- -na has a vowel → “a”\n\nNow: suffix -psa → oral → consumes the preceding vowel **if it belongs to another suffix**\n\nBut the vowel “a” is part of -na → which is a locative suffix → and belongs to the locative.\n\nSo does -psa consume it?\n\nIn the list:\n\np”ak”unhpsa = my pot too → root p”ak → p”ak + unhpsa\n\nNote: unhpsa → has parts: -unh → ? -psa?\n\np”ak”unhpsa → root p”ak → then -unhpsa → ?\n\nAlso: p”ak”u = the pot → so -u is root ending?\n\np”ak”unhpsa → “my pot too”\n\nSo “my” → p”ak”u → p”ak” + u → so -u?\n\nThen -unhpsa? No.\n\nWait: p”ak”unhpsa → likely root p”ak → then -unhpsa → -unh → what?\n\nAlternatively, “my” is marked by -nha? But p”ak”u = the pot — no “my”\n\np”ak”u → the pot\n\np”ak”unhpsa → my pot too\n\nSo “my” → likely derived from root + -nha? But p”ak”u has no -nha\n\nPerhaps “my” = -nha?\n\nBut in ishinhna → “in my bed” → ishin + hna → “h” in root, “n” in hna → so hna = in + my?\n\nNo.\n\np”ak”unhpsa: let’s split → p”ak”u → pot → then -unhpsa?\n\nBut “too” → -psa → may be at end.\n\nPossibly the suffix -nha is nasal, and -psa is oral.\n\nBut p”ak”u = pot → root p”ak” → then -u → last vowel?\n\nThen p”ak”unhpsa → unhpsa → so it includes -unh and -psa?\n\n- unh → nasal?\n\nFrom nasal suffix rules: \"nasal suffixes consume the vowel if they keep theirs, but leave it if they give up theirs.\"\n\nSo -nha, -ma → nasal\n\nYes.\n\nIn ishinhna → root ishin → end with “h” → add -hna → so the “n” is from -hna → so the root “h” is kept, then “n” added → so no elision.\n\nSimilarly, ishma → “your bed” → root ish → add -ma → ish + ma → ishma → no elision.\n\nSo p”ak”u = pot → root p”ak” → ends with “u” → so no vowel to elide? Then -unhpsa?\n\nBut -nha is nasal → so -unh → nasal?\n\nBut it's attached to end.\n\nWait: p”ak”unhpsa → likely root p”ak” + -unhpsa\n\n- -unh → nasal? -nha → nasal → so -unh → possibly -u + -nh?\n\nBut u is root end.\n\nSo the root ends with “u” → adding nasal suffix -nh → consumes the root vowel?\n\nYes — in nasal suffix rules: \"consume the vowel if they keep theirs\"\n\nIf nasal suffix keeps its own vowel (e.g., uses “n” or “m”), it consumes the preceding vowel.\n\n“-nha” keeps the “a” → so it consumes the root vowel.\n\nSo if root ends in a vowel, and a nasal suffix like -nha comes after, and it keeps its “a”, it consumes the root vowel.\n\nIn p”ak”u → root ends with “u” → then -nha? → u is consumed?\n\nBut p”ak”u = the pot — no -nha → so perhaps only when possessive.\n\nBut p”ak”unhpsa → “my pot too” → so -unhpsa → -unh → nasal part → so -unh → consumes the root vowel?\n\nSo root p”ak” ends with “u” → then -unh → nasal suffix → consumes “u” → so no “u” → becomes p”ak” + unh → then psa?\n\n- unhpsa → unh + psa\n\nThen -psa = “too” → oral suffix\n\nNow, does -psa consume the vowel before it?\n\n- before -psa is “h” → no vowel → root ends with “h”? Wait — p”ak” → ends with “k” → “k” → consonant → so no vowel → so -unh → nasal, consumes nothing? Or “h” is from -unh?\n\np”ak” → ends in “k” → so no vowel → so -unh → can’t consume vowel → so stays?\n\nBut in p”ak”unhpsa → it’s written as such → so the “u” is gone?\n\nWait — maybe the root is *p”ak* → then -unh → so -u is part of suffix?\n\nPerhaps the root is actually *p”ak”* with a vowel?\n\nWe are not given the root, but pattern:\n\nIn “our1+2 cliff” → qqa → no vowel → qqa st” → fine\n\nBut for corner, chush → ends in “ush” → consonant → so -ma → no elision → chushma\n\nSimilarly, for “in your corner”, chushma na → na attaches → no vowel to elide → chushma na\n\nNow for “in your corner too” → add -psa after -na → so chushma na psa?\n\nNow — oral suffix -psa → consumes the preceding vowel if it belongs to another suffix.\n\nThe vowel in -na is “a” → which is part of the locative suffix -na → so “belongs to another suffix” → so the suffix -psa consumes it?\n\nTherefore, the “a” in -na is consumed → no vowel → so becomes chushma n psa?\n\nBut -na → -n → then -psa → so n + psa\n\nBut is “n” pronounced?\n\nIn the data, qucxst”psa → qucxst”psa → has “s” and then “t” → no elision?\n\nBut in “in our1+2 field too” → yapsanpsa → root yap → yapsanpsa → -sanpsa\n\nLikely -sanpsa", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11217.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "redacted_solution_hint_mask6", + "sample_index": 1, + "output": "We are given a set of Jaqaru words and their translations, along with rules for suffix attachment and vowel elision. We are to translate six items into Jaqaru.\n\nStep 1: Identify root and suffix patterns from examples.\n\nFrom the given:\n\n- aq”ipsa → the cave too → root: *aq* + *ipsa* (too) → suffix *-psa* (too), attached after vowel elision?\n- aq”na → in the cave → root: *aq* + *na* → suffix *-na* → case marker?\n- qucxap”a → through the lake → root: *qucx* + *ap”a* → perhaps *ap”a* = through? With aspiration?\n- qucxst”psa → from our1+2 lake too → *qucx* + *st”psa* → *st”p* = from + our1+2 + too? Suffix *-psa* = too\n- chushp”a → his corner → root: *chush* + *p”a* → possessive *-p”a* → \"his\"\n- chushuntxi → is it in the corner? → *chush* + *untxi* → *untxi* = is it in? → question form\n- marka → the town → root *mark*\n- markp”t”a → from his town → *mark* + *p”t”a* → possessive *-p”a* with case *-t”a* (from)\n- markstxi → is it our1+2 town? → *mark* + *stxi* → question + possessive\n- ishinhna → in my bed → *ishin* + *hna* → *hna* = in + my → possessive *-na*?\n- ishma → your bed → *ish* + *ma* → *ma* = your?\n- p”ak”u → the pot → root *p”ak*\n- p”ak”unhpsa → my pot too → *p”ak* + *unhpsa* → *unh* + *psa*? Possibly *-nha* (my) + *-psa* (too)\n- qaqat”a → from the cliff → *qaq* + *at”a* → *at”a* = from (case), *qaq* = cliff?\n- yapsanpsa → in our1+2 field too → *yap* + *sanpsa* → *sanpsa* = in + our1+2 + too?\n\nStep 2: Decode suffix patterns.\n\nWe have suffixes:\n\n- Possessor:\n - -p”a → genitive (his, her, your, etc.)\n - -sa → ? Possibly possessive for \"my\"?\n- Case markers:\n - -na → \"in\"\n - -t”a → \"from\"\n - -txi → \"is it in?\" (question form)\n- Additional: -nha, -ma → possessive?\n- -psa → \"too\"\n- Aspiration: mark ” indicates aspiration → relevant for *p”a*, *t”a*, etc.\n\nNow check root + suffix combinations.\n\nExamples:\n- chushp”a → his corner → *chush* + *p”a* → possession (his)\n- markp”t”a → from his town → *mark* + *p”t”a* → possessive *-p”a* and case *-t”a* → from his town\n- markstxi → is it our1+2 town? → *mark* + *stxi* → question + possessive\n- ishinhna → in my bed → *ishin* + *hna* → *hna* = in + my?\n- ishma → your bed → *ish* + *ma* → *ma* = your?\n- p”ak”unhpsa → my pot too → *p”ak* + *unhpsa* → *unh* → my? → *nha* + *psa* → my + too?\n- yapsanpsa → in our1+2 field too → *yap* + *sanpsa* → *sanpsa* = in + our1+2 + too?\n\nSo, the patterns:\n\nPossession:\n- -p”a → (his)\n- -ma → (your)\n- -nha → (my)\n- -sa → ? (possibly, from \"a\" root)\n\nCase:\n- -na → in\n- -t”a → from\n- -txi → is it in?\n\nSuffix attachment rules:\n\n1. Oral suffixes:\n - Always consume the preceding vowel\n - But if the vowel belongs to the root, leave it\n2. Nasal suffixes:\n - Consume vowel if they keep theirs, leave if they give up theirs\n\nSo, understanding vowel elision:\n\n- When a nasal suffix (like -nha, -ma) attaches, it may consume a vowel from the root if it keeps its own (i.e., if it has a vowel of its own), or leaves it if it gives up its vowel.\n\nBut in *ishinhna* → in my bed:\n\n- *ishin* → root\n- *hna* → nasal suffix → \"in\" and \"my\"\n- *hna* has its own vowel → so it keeps it? → but vowel from root is *i*? → ah, *ishin* has root vowel *i* → if nasal suffix *hna* has its own vowel *a*, it keeps it → so it consumes the root vowel? But is *ishin* changed to *ish*?\n\nLikewise, in *marka* → the town → no suffix? *mark* + *a*?\n\nIn *markp”t”a* → from his town → *mark* + *p”t”a* → *t”a* = case \"from\", *p”a* = his → need to combine.\n\nSo bare root + suffix.\n\nNow, targets:\n\n4. our1+2 cliff → \"from cliff\" — but \"our1+2\" = possessive\n\nWe have:\n- qaqat”a → from the cliff → *qaq* (cliff) + *at”a* → from\n→ so for \"our1+2 cliff\" → need possessive \"our\" + \"cliff\"\n\nWe have \"our1+2\" = *-na*? Or *-sa*?\n\nIn *qucxst”psa* → from our1+2 lake too → *qucx* + *st”psa* → *st”p* = from + our1+2 + too?\n\nBut how is \"our1+2\" marked?\n\nFrom *qucxst”psa* → *qucx* + *st”psa* → seems like *-st”p*? But likely *-t”a* is from, *-psa* is too?\n\nBut \"our1+2\" is a possessive marker.\n\nFrom *markstxi* → is it our1+2 town? → *mark* + *stxi* → use *stxi* → so *stxi* = possessive + question?\n\nBut in *qucxst”psa* → from our1+2 lake too → possessive + case (from) + too?\n\nSo what suffixes for \"our1+2\"?\n\nPossibility: *-sa* → for \"our1+2\"?\n\nBut *chushp”a* → his corner → \"his\" → *-p”a*\n\n*ishma* → your bed → *-ma*\n\nSo for \"our\" → likely *-sa*?\n\nSimilarly, *p”ak”unhpsa* → my pot too → *-nha* (my) + *-psa* (too)\n\nSo:\n- my = -nha\n- your = -ma\n- his = -p”a\n- our = -sa?\n\nTest: \"our1+2 cliff\"\n\nRoot: *qaq* (cliff)\n\nPossessive: *-sa* → \"our1+2\"\n\nCase: ? Is there a case needed?\n\n\"our1+2 cliff\" → just the thing → no \"in\", \"from\", etc.\n\nSo like \"marka\" → the town → just root + possessive?\n\nSo *qaq* + *sa*?\n\nBut is *sa* a suffix?\n\nNote: in *qucxst”psa* → poss + case → *st”psa*\n\nPossibly possessive suffixes:\n- -na → my\n- -ma → your\n- -p”a → his\n- -sa → our\n\nSo yes, *-sa* = our\n\nThen *qaq* + *sa* → qaqasa?\n\nBut do we see vowel elision?\n\nRoot: *qaq* → ends with *q*, so after *qaq*, add *sa* → no vowel between.\n\nSo *qaqasa* → plausible.\n\nBut in *qucxst”psa* → *qucx* + *st”psa* → *st”psa* has a vowel? Root ends with *x*, so adding suffix could consume prior vowel.\n\nBut *qucx* ends in consonant → *x*, not vowel → no vowel to consume.\n\nIn *chushp”a* → *chush* ends in *h*, not vowel → *p”a* added → no elision.\n\nIn *ishinhna* → *ishin* ends in *n* → vowel *i* before? *ishin* → *i* is before *sh*, so after *ishin*, vowel *i*?\n\nThen adding *hna* → nasal → *hna* has own vowel *a* → so it keeps it → consumes vowel from root? So *i* is consumed → becomes *ish* + *hna* → *ishhna*? But it is written *ishinhna* → likely root is *ishin*, suffix *hna* → so vowel *i* is consumed → but written as *ishin*?\n\nWait: *ishinhna* → two *i* together? Perhaps not.\n\nRoot might be *ishin* (bed), and suffix *hna* → but *h* is not a vowel → perhaps *h* is nasal?\n\nLikely: the root has a final vowel.\n\nFrom *p”ak”u* → the pot → root *p”ak* → ends with *k*, not vowel.\n\n*p”ak”unhpsa* → my pot too → *unhpsa* → *unh* + *psa* → *unh* = my?\n\nRoot: *p”ak* → after adding *unh*, we get *p”akunh* → consonant + consonant → no vowel.\n\nSo no vowel elision needed.\n\nSimilarly, *marka* → root *mark* → ends in *k*, suffix *a* → adding *a* → vowel after → no elision.\n\nBut *markp”t”a* → *mark* + *p”t”a* → *p”t”a* → has *t”a* → case suffix.\n\n*mark* ends in *k*, so vowel not present → no consumption.\n\nNow *qucxst”psa* → qucx + st”psa → *st”psa* → had vowel in root?\n\n*qucx* → ends in *x*, so no final vowel → so when adding *st”p*? But *st”psa* — might be *st”p* + *sa*?\n\nPerhaps *-st”p* = from + possessive?\n\nBut likely *-t”a* = from, *-psa* = too.\n\nBack to item 4: our1+2 cliff\n\nCliff = *qaq* → from *qaqat”a* = from the cliff → so *qaq* = cliff\n\nSo root = *qaq*\n\nPossessive = our1+2 → likely *-sa* → based on *-na*, *-ma*, *-p”a* as my, your, his → so *-sa* = our\n\nSo *qaq* + *sa* → qaqasa\n\nNo case, no question → so just possessive → likely qaqasa\n\nBut in *qucxst”psa* → from our1+2 lake too → has both *-t”a* and *-psa*\n\nHere, no case → so qaqasa\n\n→ b.1: qaqasa\n\n---\n\n5. in your corner\n\nCorner = chush\n\nYour → *-ma*\n\nCase: in → *-na*\n\nSo need to build *chush* + *ma* + *na*?\n\nBut suffix attachment: order matters? Are suffixes added in a particular order?\n\nWe have:\n- Possession after root?\n- Case after?\n\nLook at *chushuntxi* → is it in the corner? → root *chush* + *untxi* → so *untxi* = in + question?\n\n*chush* + *untxi* → so *untxi* = in + question form?\n\nBut we want \"in your corner\"\n\nSo \"in\" → *-na*, \"your\" → *-ma*?\n\nBut when combined: is *-ma* before or after *-na*?\n\nIn *ishinhna* → in my bed → *ishin* + *hna* → *hna* = in + my → so *-na* is part of the nasal suffix?\n\nIn *marka* → the town → no\n\nIn *markstxi* → is it our1+2 town? → *mark* + *stxi* → *stxi* = in (question) + possessive?\n\nBut *stxi* might be a combined suffix for \"in\" + question.\n\nWait — *chushuntxi* → is it in the corner? → so *untxi* = is it in?\n\nSo *-txi* = is it in? → question form\n\nSo for \"in\" → *-na* (not *-txi*)\n\nIn *ishinhna* → in my bed → likely has *-na* = in?\n\nBut *hna* = in + my?\n\nSo nasal suffix *-hna* → combines in and my?\n\nSimilarly, *-ma* = your?\n\nSo perhaps *-na* is only when standalone?\n\nBut in *markp”t”a* → from his town → *p”t”a* → *p”a* = his, *t”a* = from\n\nSo *-t”a* = from\n\nPossessive suffixes: -na, -ma, -p”a, -sa?\n\nBut -na = my? In *aq”na* → in the cave → *aq* + *na* → in the cave\n\nAnd *aq”na* = in the cave → so *-na* = in?\n\nBut in *ishinhna* = in my bed → *hna* → so *-hna* = in + my?\n\nAh — consistent.\n\nThus:\n- *-na* = in (but when combined with possessive, forms a compound suffix)\n\nPossessive nasal suffixes:\n- -nha → my\n- -ma → your\n- -p”a* → his\n- -sa → our\n\nAnd case:\n- -na → in\n- -t”a* → from\n- -txi → is it in?\n\nNow to build \"in your corner\"\n\nCorner = *chush*\n\n\"your\" → *-ma*\n\n\"in\" → *-na*\n\nBut how to attach?\n\nPossibly: suffixes add in order — or in a chain?\n\nWe see *chushuntxi* → corner + *untxi* → so *untxi* = in + question\n\nSimilarly, *markstxi* → our1+2 town → *stxi* = in + question?\n\nSo *-txi* = in (question)\n\nThus, for \"in\" (not question), use *-na*?\n\nBut if *-na* is a root vowel consumer?\n\nIn *chushp”a* → his corner → *chush* + *p”a* → no vowel consumption\n\nIn *chushuntxi* → *chush* + *untxi* → *untxi* has *u*, so root *chush* ends in *h* → no vowel?\n\nSo when adding *untxi*, vowel not from root → so no elision?\n\nSo suffixes may be added as a unit.\n\nPossibility: *-na* is for \"in\", and it can be combined with possessive.\n\nBut in *ishinhna* → *ishin* + *hna* → *hna* is a single suffix → so *-hna* = in + my\n\nSo *-na* and *-nha* are part of the same class.\n\nSimilarly, *-ma* = your?\n\nIs there a form for \"in your\"?\n\nWe don’t see it, but likely it's *chush* + *ma* + *na*?\n\nBut we have to follow elision rules.\n\nRule: nasal suffixes consume the vowel if they keep theirs, leave if they give up theirs.\n\n*chush* ends in *h* → no vowel → so no vowel to consume.\n\nSo if we add *-ma* → your → no vowel → so *chushma*\n\nThen add *-na* → in → would that consume a vowel?\n\nOnly if the vowel belongs to the root.\n\nRoot ends in *h* — not a vowel → so *na* can be added directly → *chushmana*?\n\nBut do we see that?\n\nNo — we see *chushp”a*, *chushuntxi*\n\nBut *chushp”a* → his corner → *p”a* → no vowel\n\nSimilarly, *chushuntxi* → *untxi* → has a vowel.\n\nSo perhaps the case suffix *-na* is a separate unit, and is not part of the nasal possessive.\n\nBut in *ishinhna* → *ish* (root) + *hna* → *hna* is used for both in and my.\n\nSo likely, each suffix is a single unit: -nha (my + in), -ma (your), -p”a (his), -sa (our)\n\nThen what about *-na* (in) alone?\n\nIn *aq”na* → in the cave → *a* + *na* → so root *aq* → then *na* → in?\n\nSo *na* = in\n\nThen *-nha* = in + my\n\nSo only when combined with possessive.\n\nSo \"in your corner\" — need \"in\" + \"your\" + \"corner\"\n\nSo \"your", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10748.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "redacted_solution_hint_mask6", + "sample_index": 2, + "output": "Step 1: Identify root and suffix patterns from the given examples.\n\nFrom the table:\n\n- Roots and their case/suffix patterns:\n - \"aq\" = cave → \"aq”ipsa\" (the cave too), \"aq”na\" (in the cave), \"aqxap”a\" (through the lake), \"aqxst”psa\" (from our1+2 lake too)\n - \"chushp”a\" = his corner → \"chushuntxi\" = is it in the corner?\n - \"marka\" = the town → \"markp”t”a\" = from his town, \"markstxi\" = is it our1+2 town?\n - \"utamt”a\" = from your house → \"utnha\" = my house → \"utamt”a\" = from your house\n - \"yaputxi\" = is it the field? → \"yapsanpsa\" = in our1+2 field too\n\nStep 2: Identify suffixes and their behavior.\n\nCase suffixes:\n- -p”a: possessive (e.g., chushp”a = his corner)\n- -t”a: from + possessor (e.g., markp”t”a = from his town)\n- -txi: interrogative (\"is it...?\") — as in chushuntxi, markstxi, yaputxi\n- -psa: \"too\", added to a root to indicate \"also\"\n- nasal suffixes (-nha, -ma): used in place of possessive or locative, with vowel elision rules\n- vowel elision rules:\n - Oral suffixes (like -t”a, -txi, -psa) consume the vowel before them **if it belongs to another suffix**\n - Nasal suffixes consume vowel **if they keep theirs**; leave if they give up theirs\n\nStep 3: Analyze each required translation.\n\n4. our1+2 cliff \n- Root: \"qaqat”a\" = from the cliff → implies \"cliff\" is the root \n- \"our1+2\" = possessive, so likely uses -p”a suffix → \"qaqat”ap”a\"? \n- But look: \"qaqat”a\" = from the cliff → root = \"qaqat\" \n- \"our1+2\" = same as \"we\" in root, so likely \"qaqat”ap”a\" → but check elision \n- \"qaqat”a\" has a vowel after \"t\" (t”a), so \"a\" is not elided. \n- Possessive suffix: -p”a → added directly. \n- Since \"our1+2\" is not a regular possessive like \"my\", but \"our\", and given \"qaqat”a\" already uses the root with \"t”a\", we infer that the possessive is formed by adding -p”a after the root. \n- So: **qaqat”ap”a**? \n- But consider: “our1+2 cliff” — not “from the cliff”, nor “in the cliff” → likely a direct use of possessive. \n- In \"qucxst”psa\" = from our1+2 lake too → possessive + from + with -st”psa → so \"our1+2\" = -p”a or -p”a with possessive \n- In \"markstxi\" = is it our1+2 town? → root \"marka\", suffix -stxi → so \"our1+2\" appears via -stxi \n- But -stxi is interrogative — so in \"chushp”a\", possessive is -p”a \n- In \"markstxi\" = is it our1+2 town? → possessive suffix = -st? Or is it -p”a? \n- \"marka\" → \"markp”t”a\" = from his town → possessive = -p”t”a? \n- Wait: \"marka\" → \"markp”t”a\" = from his town → so -p”t”a = from + possessor \n- So -p”a is still the base. Then “our1+2” attached via -p”a? \n- In \"markstxi\" → is it our1+2 town? → likely root \"marka\" + -stxi (interrogative), and possessive is implied in the question \n- But for \"our1+2 cliff\", we need a possessive form of \"cliff\" \n- \"qaqat”a\" = from the cliff → root = qaqat \n- To form \"our1+2 cliff\", likely use -p”a → qaqat”ap”a \n- But in \"qucxst”psa\" = from our1+2 lake too → \"qucx\" = through the lake → \"qucxap”a\" = through the lake (already has -p”a) → \"qucxst”psa\" = from our1+2 lake too → so \"st”psa\" = from + our1+2 + too \n- So \"our1+2\" is marked via suffix like -p”a or -st” \n- But \"extruding\" possessive seems to go with -p”a → so for “our1+2 cliff” → root \"qaqat\" + -p”a → qaqat”ap”a \n- But is there vowel elision? \n- \"qaqat\" ends with \"t\" → so the vowel after is \"a\" → root ends with consonant-vowel? \n- qaqat”a → has a final vowel. \n- So qaqat”a → root + final vowel, then add -p”a \n- The vowel in \"a\" belongs to the root. When adding -p”a (possessive), the rule says: oral suffixes consume the vowel if it belongs to another suffix → here, the suffix -p”a is oral → it consumes the vowel **only if the vowel belongs to another suffix**. \n- But no other suffix; it’s just the root → so vowel remains → qaqat”ap”a \n- But \"our1+2\" = special case, and \"from the cliff\" = qaqat”a → so \"our1+2 cliff\" = qaqat”ap”a \n- But check if this appears elsewhere. \n- In \"qucxap”a\" = through the lake → so \"qucx\" + \"ap”a\" → root + -p”a → implies -p”a is added \n- So format: root + -p”a \n- Thus, 4. our1+2 cliff → qaqat”ap”a \n\n5. in your corner \n- Root: \"chushp”a\" = his corner → root = chush \n- \"in your corner\" → locative \n- Look for locative patterns: \n- \"in the cave\" = aq”na → root aq” + -na → -na is nasal suffix \n- \"in my bed\" = ishinhna → root ishi + -nha → -nha = nasal → in → so locative suffix \n- \"in your bed\" = ishma → ish + ma → ma = nasal → so -ma = your \n- \"in your town\" = ? → \"markstxi\" = is it our1+2 town? → so not direct \n- \"in your corner\" → likely uses -ma or -na \n- \"his\" = chushp”a → so \"your\" = chush + ma → chushma \n- But with locative? \n- \"in my bed\" = ishinhna → root ishi + -nha → so -nha = locative in \"in\" \n- \"in your bed\" = ishma → root ish + ma → so ma → \"your\", but no locative suffix? \n- Size: ishma = your bed → so \"ma\" = your → \"inside\" or \"on\"? \n- But \"in\" is missing → maybe \"in\" is marked via -na or -ma? \n- \"in the cave\" = aq”na → so -na = in \n- \"in my bed\" = ishinhna → -nha → in? \n- \"in your town\" → not given, but \"markstxi\" = is it our1+2 town? \n- So -na or -nha = in \n- So \"in your corner\" → root \"chush\" + locative + your → \n- \"your\" = -ma \n- \"in\" = -na? \n- But -na is nasal → consumes vowel if it keeps its own \n- Root: chush → ends with \"sh\" → vowel? → chushp”a → has \"p”a\" → so root has no vowel? \n- chushp”a → chush + p”a → so root \"chush\" ends with consonant \n- Then adding suffixes: \n- -na (in) is nasal → consumes vowel **if it keeps its own**, but if it gives up, leaves \n- Since it gives up vowel (doesn't keep it), it leaves → so vowel from root is preserved \n- So chush + -ma (your)? \n- But \"in your corner\" → need both \"in\" and \"your\" \n- Compare: ishinhna → in my bed → root ishi + -nha → so locative -nha = in + my \n- \"in my bed\" → ishinhna → \"nha\" = in + my \n- So \"your\" = -ma \n- So \"in your corner\" → chush + -na? → but -na is in \n- But -na implies possessive? No, \"in my\" uses -nha \n- -nha = in + my \n- -ma = your \n- So perhaps \"in your corner\" = chush + -ma + -n? \n- No such suffix \n- But in \"chushp”a\" = his corner → possessive \n- \"in your corner\" → likely locative with your → possible \"chushma\" → but that's just your corner \n- But \"in\" not marked \n- Perhaps \"in\" is marked by -na → so chush + -na → with your? \n- Look at \"in the cave\" = aq”na → root aq” + -na → so -na = \"in\" \n- \"in my bed\" = ishinhna → root ishi + -nha → root ishi + -nha = in my bed \n- So both \"in\" and possessive \n- So -nha = in + my (possessive) \n- In \"in your corner\", we want \"in\" + \"your\" \n- So likely root + -ma → with -na? \n- But -na and -ma both nasal \n- Rule: nasal suffixes consume vowel if they keep theirs, but leave if they give up theirs \n- So if a nasal suffix gives up its vowel, it leaves it \n- In “in your corner”, if we use -ma (to mark \"your\"), and -na (to mark \"in\"), then:\n - Root: chush → no vowel\n - Add -na (in) → no vowel → okay\n - Add -ma (your) → after -na \n - Now: -na and -ma are both nasal → they compete \n - Vowel consumption only if the nasal keeps its own \n - But both are after root → root has no vowel \n - If -na gets the vowel, it keeps it → but root has no vowel \n - So no vowel for nasal to consume \n - So both suffixes go directly? \n - But \"in your corner\" = chush + -na + -ma? \n - But in \"ishinhna\" → root + -nha → only one suffix — implies that possessive and locative may be fused \n - In \"chushp”a\" → possessive only → p”a \n - In \"in your bed\" = ishma → ish + ma → so \"your\", no \"in\" \n - So \"in\" is not in \"isha\" → so \"in\" must come from a separate suffix \n - Only -nha and -na seem related to \"in\" \n - \"in the cave\" = aq”na → so -na = in \n - \"in my bed\" = ishinhna → -nha = in + my \n - So -na = in (general), -nha = in + my \n - So for \"in your corner\" → likely chush + -na + -ma → but -ma is \"your\", so what about the vowel? \n - Root ends with \"sh\", so after \"chush\", no vowel → adding -na → no issue → then -ma → after -na? \n - The rule: nasal suffixes consume vowel if they keep theirs \n - -na and -ma: neither keeps their vowel because there is no vowel to begin with \n - So both are added without consuming \n - So chush + na + ma? \n - But is that possible? \n - But in the examples, we have: \n - aq”na → in the cave → aq” + na \n - ishinhna → in my bed → ishi + nha \n - So \"your\" = -ma, \"in\" = -na \n - So \"in your corner\" → chush + na + ma → but order? \n - Probably phonological order → \"chushnama\"? \n - But \"chushna\" + \"ma\"? \n - But -na and -ma both nasal → when adjacent, maybe one eats the vowel? \n - Rule: nasal suffixes consume vowel if they keep theirs; if they give up theirs, leave \n - So if -na is first, it may take vowel from root if it keeps it — root has no vowel → so no \n - Then -ma adds after — consumes if it keeps — no vowel → so no consumption \n - So chushnama → but in \"ishinhna\" → ish + nha → so no vowel after root \n - So possible: chushnama \n - But original root: “chushp”a” → so root is chush, with p”a \n - Adding -na and -ma? \n - But no example of two nasal suffixes added \n - Alternative: \"in your corner\" = chush + ma → with -na being assumed? \n - But “in” not in “chushma” \n - Another idea: from \"marka\" → \"markstxi\" = is it our1+2 town? → no \"in\" \n - But \"in your corner\" — compare to “in the cave” = aq”na \n - So perhaps the \"in\" is given by -na, and your = -ma \n - So word = chushna + ma → chushnam a? → chushnama \n - But phonologically? \n - No example — but based on pattern, likely \n - However, in “in my bed” = ishinhna → “nha” → implies that when possessive and locative are together, it’s fused \n - But here, only \"your\" and \"in\" \n - So chush + na → in the corner → then with “your” → -ma \n - So chushnama \n - But root is chush, so chush + na + ma → chushnama \n - But \"chushna\" → in? → then \"ma\" → your → so in your corner \n - So 5. in your corner → chushnama \n\n6. in your corner too \n- \"too\" suffix = -psa (e.g., aq”ipsa = the cave too; yapsanpsa = in our1+2 field too) \n- So need to attach -psa \n- \"in your corner\" = chushnama → so chushnama + psa → chushnamapsa \n- But does -psa consume a vowel? \n- -psa is oral → consumes vowel if it belongs to another suffix \n- The vowel “a” in -na belongs to the root? Or is it a separate vowel? \n- Root: chush → ends with \"sh\" → no vowel → so the \"a\" in \"na\" is after root → so \"a\" is not from root \n- So in \"chushna\", the \"a\" is from -na → it belongs to the suffix -na \n- Now, adding -psa (oral suffix) → consumes vowel **if it belongs to another suffix** \n- The vowel “a” belongs to -na → so -psa consumes it → so \"a\" is deleted \n- Then final: chushnma + psa → chushnmapsa? \n- Order: -na is first → then -ma → then -psa \n- After -na and -ma, no vowel → so -psa added after \n- The vowel \"a\" in -na belongs to -na → so it is not \"belonging to another suffix\" → so -psa consumes it only if it belongs to another suffix \n- Rule: oral suffixes consume the vowel **if it belongs to another suffix** \n- So if the vowel belongs to -na, and -psa is added after, and -na is a suffix, then the vowel “belongs to another suffix” → so -psa consumes it → deletes the \"a\" \n- So chushna + ma + psa → chushnamapsa → with \"a\" gone → chushnma + psa → chushnmapsa \n- So 6. in your corner too → chushnmapsa \n\n7. from your corner too \n- \"from your corner\" → \"from\" = -t”a (as in markp”t”a = from his town) \n- \"your corner\" → chushma → but with \"from\" \n- So root: chush → + -ma (your) + -t”a (from) → chushmat”a? \n- But order? \n- Also \"too\" = -psa \n- So sequence: chushma + t”a + psa \n- Now, -t”a is oral → consumes vowel if it belongs to another suffix \n- The vowel in -ma is in \"a\" → belongs to -ma \n- -t”a added after — so vowel belongs to another suffix → so -t”a consumes it \n- So \"a", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11728.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "redacted_solution_hint_mask6", + "sample_index": 3, + "output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru, using the provided suffix rules and patterns.\n\n---\n\nFirst, analyze the known examples:\n\n1. **aq”ipsa** – the cave too \n → Root: *aq* + *ipsa* → \"the cave too\" \n2. **aq”na** – in the cave \n → *aq* + *na* → \"in the cave\" \n → Note: \"na\" is case suffix for location (in) \n3. **qucxap”a** – through the lake \n → *qucx* + *ap”a* → \"through the lake\" \n → *ap”a* likely means \"the lake\" \n4. **qucxst”psa** – from our1+2 lake too \n → *qucx* + *st”psa* → \"from our1+2 lake too\" \n → So *st”psa* = \"from our1+2 lake\" (with \"too\" suffix) \n → Suffix *-psa* = \"too\" (used in \"too\" cases) \n5. **chushp”a** – his corner \n → *chush* + *p”a* → \"his corner\" \n → *p”a* = possessive (his) \n6. **chushuntxi** – is it in the corner? \n → *chush* + *untxi* → \"is it in the corner?\" \n → *-txi* = interrogative (is it in?) \n7. **marka** – the town \n → *mark* + *a* → \"the town\" \n8. **markp”t”a** – from his town \n → *mark* + *p”t”a* → \"from his town\" \n → *p”t”a* = possessive + case \n9. **markstxi** – is it our1+2 town? \n → *mark* + *stxi* → \"is it our1+2 town?\" \n → *stxi* = question form (is it...?) \n10. **utamt”a** – from your house \n → *utam* + *t”a* → \"from your house\" \n → *t”a* = possessive for \"your\" \n11. **utnha** – my house \n → *utn* + *ha* → \"my house\" \n12. **utnha** → likely has *-ha* as possessive + locative? \n13. **yaputxi** – is it the field? \n → *yap* + *utxi* → \"is it the field?\" \n14. **yapsanpsa** – in our1+2 field too \n → *yap* + *sanpsa* → \"in our1+2 field too\" \n → *sanpsa* = \"in our1+2 field\" (with \"too\") → so *-psa* = \"too\"\n\n---\n\nNow the structure:\n\n### Suffixes and their effects:\n\n- **Possession**:\n - -p”a = (his) → *chushp”a*\n - -t”a = (your) → *utamt”a*, *markp”t”a*\n - -na = (in the cave) → *aq”na* → but also used in *p”ak”unhpsa* → \"my pot too\"\n - -ha = (my house) → *utnha*\n\n- **Case**:\n - -na → in (location: in the cave)\n - -t”a → from (origin: from your house)\n - -txi → interrogative: is it in the corner?\n\n- **\"Too\" suffix**:\n - -psa → used for \"too\": 'aq”ipsa', 'yapsanpsa', 'aqucxst”psa'\n\n- **Vowel elision rules**:\n - Oral suffixes (e.g., -na, -t”a, -txi) **consume the vowel** if it belongs to another suffix.\n - Nasal suffixes (-nha, -ma) **consume vowel if they keep theirs**, else leave.\n\nAlso, *our1+2* = shared possession (mine and yours)\n\n---\n\nNow analyze **target translations**:\n\n---\n\n**4. our1+2 cliff**\n\n- We need \"our1+2 cliff\"\n\n- Root: likely *qaq* (from *qqaqat”a* – from the cliff)\n\n→ *qaqat”a* = \"from the cliff\" → so root is *qaq* or *qaqa*\n\n→ So *qaaq* + something → \"our1+2 cliff\"\n\nLook at the pattern:\n\n- *qucxst”psa* → from our1+2 lake too → \"our1+2\" + \"lake\" + \"too\"\n- *markstxi* → is it our1+2 town?\n\nSo \"our1+2\" appears with:\n- *st”* or *st* in roots?\n\nIn *qucxst”psa*: \"our1+2 lake\" → stem = *qucxst”* → so *st”* is possessive + location?\n\nBut \"our1+2\" is not a suffix of its own. It appears via a form where the possessive is *-st”* (for \"our1+2\")?\n\nCompare:\n\n- *qucxst”psa* = from our1+2 lake too \n- *markstxi* = is it our1+2 town?\n\nSo *-st* or *-st”* = our1+2 possessive\n\nPossession:\n- -p”a → his\n- -t”a → your\n- -na → unspecified, but in *aq”na* = in the cave\n- -ha → my\n- So **our1+2** must be formed by a possessive like *-st”*?\n\nIn *qucxst”psa*, the root *qucx* (lake) has *st”* (our1+2) + *psa* (too)\n\nSo:\n- *qucx* (lake) → *qucxst”* = from our1+2 lake → then *psa* = \"too\"\n\nSo for \"our1+2 cliff\":\n- Cliff root: *qaqat”a* = from the cliff → root = *qaq*\n- So *qaq* + possession → *our1+2* → *st”*?\n\n→ *qaqst”a*? → *qaqst”a* = the cliff (our1+2)\n\nBut is it \"the cliff\" or \"from\"?\n\nWe want \"our1+2 cliff\" → likely just possessive + noun → like \"our1+2 cliff\" = *qaqst”a*\n\nBut *qaqat”a* = from the cliff → so without \"from\", the base is *qaq*? Or does *qaq* have *a* attached?\n\nWait: *qaqat”a* → root *qaqa* or *qaq*?\n\nPerhaps the root is *qaaq* (cliff) → and suffix *-t”a* → from\n\nSo without -t”a, just *qaaq*? But in the examples, the possessive appears in *st”*\n\n→ So for \"our1+2 cliff\", most likely: *qaqst”a*\n\nBut is there a form for \"in the cliff\"? No. We only want \"our1+2 cliff\" → so direct noun phrase: possessive + root\n\n→ Possessive for \"our1+2\" = *st”* (from examples: *qucxst”psa*, *markstxi*)\n\nSo: **qaqst”a**\n\nBut check vowel elision:\n\n- *qaq* → root → then *st”* → suffix that consumes vowel?\n\n→ In *chushp”a* → *chush* + *p”a* → no elision → both have vowel?\n\nBut in *qucxst”psa*: *qucx* + *st”* + *psa*\n\n- What is the vowel in *qucx*? *cx* → *qucx* = q + u + c + x → ends with *x*, no vowel?\n\nWait — *qucx* has no vowel? Then *st”* comes after → so how is *qucxst”* formed?\n\nIn *qucxst”psa*:\n- After *qucx*, no vowel → adding *st”* → no vowel conflict.\n\nBut in *chushp”a*: *chush* ends with *h* → then *p”a* → so *chushp”a* = no vowel elision\n\nIn *chushuntxi* → *chush* + *untxi* → no vowel issue\n\nSo *st”* is a nasal or possessive suffix, likely consumes vowel only if it belongs to another suffix.\n\nBut here, *qaq* ends with *q*, so no vowel → adding *st”* → no vowel to consume.\n\nSo *qaqst”a* is plausible.\n\nBut is there a form like *qaqst”a*?\n\nNote: \"from the cliff\" is *qaqat”a* → so *t”a* = from\n\nSo possessive *st”* = for \"our1+2\" → likely *qaqst”a* = our1+2 cliff\n\n→ So **4. qaqs”ta**? Wait — the mark is aspiration.\n\nIn *chushp”a*: *p”a* – the mark ” indicates aspiration\n\nSimilarly, *t”a* has aspiration\n\nSo *st”* should have aspiration → so *st”*\n\n→ So *qaqst”a*\n\nBut in *qucxst”psa*, the word is *qucxst”psa* — does it have a vowel between?\n\n*qucx* ends with *x* → then *st”* → then *psa*\n\nNo vowel between → so no issue.\n\nSo for *qaqst”a*, it should be: **qaqst”a**\n\nBut check if any example shows \"our1+2 cliff\" → no.\n\nBut logic: we pattern with:\n- *qucxst”psa* → from our1+2 lake too → possessive *st”* in place of \"our1+2\"\n- So for \"our1+2 cliff\", with no case → just possessive + noun → *qaqst”a*\n\nSo **4. qaqst”a**\n\n---\n\n**5. in your corner**\n\n- \"in your corner\"\n\n- We need the location \"in\" + \"your\" + \"corner\"\n\n- \"corner\" root: *chush* (his corner)\n\n- *chushp”a* → his corner → so root = *chush*\n\n- Possession: *t”a* = \"your\" → so *chusht”a*?\n\n- But need \"in\" → so case suffix -na?\n\n- Look: *aq”na* → in the cave → root *aq* + *na*\n\n- So *in* = -na\n\n- So for \"your corner\" → *chush* + *t”a* → *chusht”a* → but then add *-na*?\n\nBut *-na* consumes the vowel if it belongs to another suffix.\n\nSo is *-na* an oral or nasal suffix?\n\nGiven: oral suffixes consume the vowel if it belongs to another suffix.\n\nSo *-na* is oral → consumes vowel if vowel belongs to another.\n\nCurrent: *chush* → ends with *h* → so does not contain a vowel?\n\n*chush* = c-h-u-s-h → contains *u*\n\nSo vowel: *u* in *chush*\n\nNow, add *-t”a* → which may consume the vowel?\n\nLook at pattern:\n\n*chushp”a* → *chush* + *p”a* → no *-na*, so no issue\n\n*chushuntxi* → *chush* + *untxi* → *untxi* = ex: -t”a + -txi?\n\n*untxi* → *un* + *txi* → is the vowel *u* from *chush*?\n\nBut *-t”a* is a possessive → likely lacks vowel → so may eat the *u*?\n\nBut we don’t see *chusht”a* — only *chushp”a* and *chushuntxi*\n\nSo *chushuntxi* = is it in the corner? → includes *-txi* → so may have *-na* in combination?\n\nNo — *chushuntxi* = \"is it in the corner?\" — implied *-txi* = interrogative\n\nSo no explicit case.\n\nBut *aq”na* = in the cave → *aq* + *na*\n\nSo form: *root* + *-na* → \"in the root\"\n\nSo \"in your corner\" = *chush* + *t”a* + *na*? But vowel conflict.\n\nSo the sequence should be:\n\n- Root: *chush* (has vowel *u*)\n- Suffix: *-t”a* → possessive (your)\n- Then *-na* → locative (in)\n\nBut *-na* is oral → it consumes the vowel **if it belongs to another suffix**\n\nWho owns the vowel?\n\nIf *-t”a* owns the vowel (i.e., the *u*), then it doesn’t belong to root → so *-na* doesn’t consume it?\n\nBut *-t”a* has no vowel — it's *t”a* — ends with *a*\n\nSo the *u* is from root → so belongs to root.\n\nNow, *-na* is adding a suffix → if the vowel belongs to root, then *-na* consumes it?\n\nRule: oral suffixes consume the vowel if it belongs to another suffix → i.e., if the vowel is not in the suffix.\n\nSo: if the vowel is in the root → it belongs to root → so oral suffix *-na* consumes it?\n\nSo *chush* + *t”a* + *na* → the vowel *u* is consumed → becomes *chush* → *chusht”ana*?\n\nBut after consumption, what remains?\n\nPossibility: elimination of *u* → so *chush* → *chsh*? (but no such letter)\n\nWait: in *chushp”a*, no *u* consumption.\n\nBut *chush* → ends with *h*, and has *u* in middle.\n\nPossibly, in *t”a* case, the suffix *-t”a* (your) requires vowel — but it doesn't.\n\nBut in *utamt”a* → from your house → root *utam* → *utam* + *t”a* → so *utam* ends with *m*, no vowel → no issue.\n\n*utam* → u-t-a-m → has *u* and *a*\n\n→ *utam* + *t”a* → so vowel *a* → where?\n\nIn *utamt”a*, if *-t”a* comes after, the vowel *a* is in root.\n\nThen is *-t”a* consuming it?\n\nIn *utamt”a*, suffix is *-t”a* → so if *-t”a* consumes the vowel, then the *a* is gone?\n\nBut the word is *utamt”a* — so the vowel *a* is preserved → so likely, the suffix doesn't consume it if it has its own vowel?\n\nWait — rule is: oral suffixes consume the vowel if it belongs to another suffix.\n\nSo if the vowel is in root, and the suffix is oral, then it consumes it → so the vowel is gone.\n\nBut in *utamt”a*, we have *a* in root → and *t”a* → both have *a* → so the root has *a*, suffix has *a*, so the root’s vowel is now consumed?\n\nBut the word is *utamt”a* — so the *a* is still there.\n\nHypothesis: the rule may mean that the vowel is consumed **only if it is not part of the suffix itself**.\n\nSo *-na* consumes only if the vowel belongs to the root.\n\nIn *utamt”a*: root *utam* → vowel *u* and *a* → suffix *-t”a* → has its own *a* → so does it consume the *a* in root?\n\nBut the root already has *a* → so the suffix *-t”a* may take the *a*, so no consumption?\n\nBut no clear rule.\n\nAlternative: *-na* is meant to be attached directly to root, consuming vowel only if it doesn’t have one.\n\nBut in *aq”na* → *aq* + *na* → *aq* has *q*, so no vowel → no issue.\n\nBut *aq* — a-q, no vowel → so *aq”na* → forms *aq”na*\n\nNow, *chush* has a vowel *u* → so if *-na* is added after, and it consumes the vowel, then result is consonant + *na*?\n\nSo *chush* → *chush* → remove *u* → *chsh* → then *chsh* + *t”a* → *chsh t”a* → then *chsh t”a* + *na*?\n\nBut no such example.\n\nBack to *chushuntxi* → is it in the corner?\n\n→ Structure: *chush* + *untxi*\n\n→ *untxi* = likely *un* + *txi* → where *un* is from *chush*?\n\nSo the *u* is dropped?\n\nPossibly the *u* is consumed by *-t”a* or *-txi*?\n\nBut *-txi* is interrogative → oral suffix.\n\nIn *chushuntxi* → no possessive → just *chush* + *untxi* → the *u* is lost?\n\nSo when adding a suffix with a vowel, it may consume the root vowel.\n\nSo rule: oral suffixes consume the vowel if it belongs to root.\n\nTherefore, when adding *-na* or *-txi*, if root has a vowel, it gets consumed.\n\nSo for \"in your corner\" → we need:\n\n- Root: *chush* (has *u*)\n- Add *-t”a* (your) → possess", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10998.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 5. The word forms in the problem consist of a root and up to three suffixes. Each\nsuffix may cause the elision of the preceding vowel:\n\n possessor case\n -p”a -p”a -psa\n -sa -t”a -txi\n oral suffixes always consume the consume the vowel if it belongs to another\n vowel suffix, but leave it if it belongs to the root\n -nha, -ma -na\n nasal suffixes consume the vowel if they keep theirs, but\n leave it if they give up theirs\n\n Answers:\n\n (a) 1. utnhantxi — is it in my house?\n\n 2. yapp”psa — his field too\n\n 3. yapup”psa — through the field too\n\n (b) 4. our1+2 cliff— [TARGET ANSWER REDACTED]\n 5. in your corner — [TARGET ANSWER REDACTED]\n\n 6. in your corner too — [TARGET ANSWER REDACTED]\n\n 7. from your corner too — [TARGET ANSWER REDACTED]\n\n 8. is it from the cave? — [TARGET ANSWER REDACTED]\n\n 9. is it the house? — [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "redacted_solution_hint_mask6", + "sample_index": 0, + "output": "We are given a set of Inuktitut sentences with English translations and a set of linguistic rules. Our task is to translate six new sentences (13–18) into English using the patterns provided.\n\nLet’s first extract and analyze the grammatical rules from the problem:\n\n---\n\n**Core sentence structures**:\n\n1. **X-(q) V–** \n → \"X V (himself)\" — reflexive. When the subject is marked with -q and no object (or object is indefinite), the verb applies to reflexive meaning.\n\n2. **X-(q) Y-(r)mik V-si–** \n → \"X V a Y\" — transitive: X performs action on Y. \n - If Y is definite, it may get -q; if indefinite (indefinite object), it gets -r before -mik (e.g., nanu-q → nanu-r-mik; iluaqhaiji → iluaqhaiji-mik).\n\n3. **X-up Y-(q) V–** \n → \"X V the Y\" — definite object (Y) marked with -q; X marked with -up.\n\n**Key suffix rules**:\n\n- **Verb suffixes**:\n - -j after vowel, -t after consonant (this is likely the base verb morpheme).\n - Person marking:\n - In 1st/2nd schema: -u-tit (2nd person), -u-q (3rd person)\n - In 3rd schema: -a-it (2/3), -a-nga (3/3), -a-atit (3/2)\n\n- **Possessive markers**:\n - \"your\" → -(q) becomes -it, -(up) becomes -vit.\n\n- **Indefinite object**: if object is indefinite (e.g., \"a doctor\", \"a wolf\"), it gets -r before -mik.\n\n- **Definite object**: object has -q (e.g., \"the doctor\" → iluaqhaiji), or is marked with -q.\n\n- **Reflexive verb**: transitive verb with no object → interpreted as reflexive (speaker or subject acted on themselves).\n\n---\n\nNow, go sentence by sentence (13 to 18) and apply the rules.\n\n---\n\n**13. Amaruup angatkuit takujanga.**\n\nBreak down:\n- Amaruup → Amaru (hunter) + up → \"the hunter\"\n- angatkuit → angatkuq (came) + -it → 2nd person? But -it is likely possessed\n- takujanga → takujaatit (saw) + -anga → possibly person marking?\n\nWait — check known examples:\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga.\" → \"The hunter speared the wolf.\"\n\nSo: \n- Angunahuktiup → Angunahukti + up → \"the hunter\"\n- amaruq → amaru (wolf) + q → definite object\n- iputujanga → iputujait + -anga → 3rd person?\n\nWait — suffixes on verbs:\n\nFrom problem:\n- Verb gets:\n - -j after vowel, -t after consonant\n - person suffix:\n - in first two: -u-tit (2), -u-q (3)\n - in third: -a-it (2/3), -a-nga (3/3), -a-atit (3/2)\n\nIn sentence 9: Angunahuktiup amaruq iputujanga \n→ \"The hunter speared the wolf.\"\n\nSo verb: iputujanga — base: iputujait? (spear) → -a-nga? (3rd person)\n\nBut it ends in -anga → likely -a-nga.\n\nSo:\n- iputujait (base), + -a-nga → third person, definite object.\n\nSimilarly: angatkuit → verb form of \"come\"? Angatkuq → came → angatkuit → comes?\n\n\"angatkuit\" → \"come\" (in third person?)\n\nBut in 7: \"Nanuq qaijuq.\" → \"The polar bear came.\" — qaijuq → verb form with -q → a verb form of \"come\" → base qaiju → + q → definite?\n\nBut no person suffix — subject is nanuq → (polar bear) → defective?\n\nNo person suffix on verb → so perhaps only definite object or no object?\n\nWe see in 7: Nanuq qaijuq → \"The polar bear came\" — no object → so must be intransitive.\n\nThus, verb forms are:\n- Intransitive: verb + person suffix or not?\n- Transitive: verb + -si + object suffix\n\nBut verbs in the pattern are shown with -si only when object is present.\n\nSo: verb + -si indicates transitive.\n\nBut look at:\n\nSentence 1: Qingmivit takujaatit → \"Your dog saw you\" \n→ Qingmivit → qingmivit = (your) dog → qingmia + vit (your) → in vtip → verb “saw” → takujaatit → takujaat → saw? takujaatit = saw (3rd person)\n\nSo verb = takujaat? with -it = 3rd person.\n\nBut is that the same as takujanga? → similar form.\n\nBack to 13: Amaruup angatkuit takujanga.\n\n- Amaruup → the hunter (subject)\n- angatkuit → verb? \"came\" → form of \"come\"?\n- takujanga → takes the verb \"saw\"? → takujanga → takujait → with -anga?\n\nBut in #1: takujaatit → saw → -it → 3rd person\n\nIn #5: Qingmiq iputujait → \"you speared the dog\" → iputujait → verb\n\nBut #9: Angunahuktiup amaruq iputujanga → \"the hunter speared a wolf\" → iputujanga → verb with -anga → 3rd person?\n\nSo iputujanga → iputujait + a-nga → 3rd person?\n\nThen takujanga → takujait + a-nga?\n\nBut that would be \"he saw\", not \"saw\".\n\nBut \"angatkuit\" — is that a verb?\n\nIn sentence 7: Nanuq qaijuq → \"The polar bear came\" → qaijuq → verb of \"come\"\n\nSo angatkuq → came → angatkuit → comes? (3rd person)\n\nSo angatkuit → third person for \"come\"\n\nThus, amaruup angatkuit → \"the hunter came\"?\n\nBut takujanga → saw?\n\nSo then it’s: \"the hunter came saw\" — illogical.\n\nBut grammar: X-(q) V– meaning \"X V (himself)\"\n\nBut this is a transitive verb.\n\nWait — is \"angatkuit\" the verb meaning \"saw\"?\n\nNo — \"saw\" is takujaat → but in #1, \"your dog saw you\" → Qingmivit takujaatit\n\nSo takujaatit = saw (third person)\n\nSo takujanga → might be saw (but with -anga)\n\nBut in sentence 4: iluaqhaijiup aarqijaatit → \"the doctor cured you\" → aarqijaatit → cured (3rd person)\n\nSo verb ending with -it → 3rd person.\n\nSo takujanga → would be with -anga → not a 3rd person?\n\nBut in 3rd schema: X-up Y-(q) V– → X V the Y → not transitive.\n\nSo let's analyze the structure.\n\nLook at 13: Amaruup angatkuit takujanga\n\n- First noun: Amaruup → \"the hunter\" → uses -up → likely subject\n- Then: angatkuit → verb?\n- Then: takujanga → object? but no object marker?\n\nNo object — so perhaps this is reflexive?\n\nBut angle: are “angatkuit” and “takujanga” both verbs?\n\nBut there is no apparent subject-object link.\n\nWait — the structure is X-up Y V?\n\nNo, it’s Amaruup angatkuit takujanga.\n\nPossibility: this is X-up V Y?\n\nNo — V is the verb in middle.\n\nBetter: perhaps it’s X-up V-? Y?\n\nBut Y is takujanga?\n\nSo: amaruup → the hunter\n\nangatkuit → verb?\n\nBut what verb?\n\nWe have:\n- takujanga → could be \"saw\" → 3rd person? (takujatit → saw, takujanga → ?)\n\nBut in sentence 4: iluaqhaijiup aarqijaatit → doctor cured you → so “cured” is aarqijaatit → 3rd person.\n\nSo take the verb forms:\n\n- takujait → saw (with -it → 3rd person)\n- takujanga → maybe the same base with -anga → third person? but why not -it?\n\nBut in sentence 11: Ukiakhaqtutit → \"you fell\" → you → so -ut → 2nd person?\n\nBut ukiakhaqtutit → base ukiakhaqt → fell → -ut → 2nd person?\n\nSo person suffixes:\n\n- -u-tit → 2nd person (subject)\n- -u-q → 3rd person (subject or object)\n- -a-it → 2/3 (some)\n- -a-nga → 3/3\n- -a-atit → 3/2\n\nSo in 13: takujanga → possibly taking -anga → 3rd person\n\nBut angatkuit → what is this?\n\nCould it be the verb? But angatkuit → in 7: nanuq qaijuq → came → qaijuq → third person without suffix?\n\nBut qaijuq → no person suffix?\n\nSo maybe verbs can have either:\n\n- intransitive: no object → verb + person suffix (if applicable)\n\n- transitive: verb + -si + object (with object marked)\n\nBut in 13: no -si — so it must be intransitive.\n\nBut then we have two verbs: angatkuit and takujanga?\n\nNo — likely angatkuit is the verb, takujanga is object?\n\nBut takujanga has suffix -anga — object?\n\nLook at sentence 3: Aanniqtutit → \"you hurt yourself\"\n\nHere: aanniqtutit → \"you hurt yourself\" → reflexive → transitive verb with no object → interpreted as reflexive.\n\nSo aanniqtut → hurt → with -it → 3rd person?\n\nBut you → so 2nd person → so verb must have -u-tit?\n\nBut it has -ut → in aanniqtutit → ut → -u-tit → 2nd person?\n\nIn sentence 11: ukiakhaqtutit → you fell → ukiakhaqt → fell → ut → -u-tit → 2nd person.\n\nSo -ut → 2nd person for subject.\n\nSimilarly:\n\nIn sentence 1: Qingmivit takujaatit → your dog saw you → subject \"your dog\" → qingmivit → qingmiv → with -vit → your (you → your → -it → -vit)\n\nSo -vit → \"your\" → in subject.\n\nSo possessive replaces -q with -it or -vit.\n\nSo in 13: Amaruup → \"the hunter\" → has -up → is definite → so subject \"the hunter\"\n\nSubject marked with -up → makes it \"the hunter\"\n\nSo verb: angatkuit?\n\nBut angatkuit → what does it mean?\n\nAngatkuq → came → so angatkuit → comes?\n\nSo \"the hunter came\" — then what is takujanga?\n\nPossibly object? But object is missing marker.\n\nBut takujanga → -anga → likely object?\n\nFor non-definite object → object must have -r-mik\n\nBut here it ends with -anga — not -mik — so not indefinite.\n\nSo definite object?\n\nBut no definite object marked — unless takujanga is the object with -q?\n\nBut takujanga → -anga → not -q.\n\nSo only marking: -q for definite object or subject.\n\nSo for object to be definite — it should have -q; for indefinite — -r-mik.\n\nHere: takujanga → -anga — not -q → so not definite?\n\nAnd not -mik → so not indefinite?\n\nThus, contradiction.\n\nPerhaps angatkuit is the verb and takujanga is object with -anga — not possible.\n\nAlternative — is the verb takujanga?\n\n\"angatkuit\" → is a verb meaning \"came\"?\n\nIn sentence 7: Nanuq qaijuq → \"the polar bear came\"\n\nSo qaijuq — came → base qaiju → + q → definite?\n\nBut in that case, qaijuq → verb with no person marking? But it's a third person intransitive.\n\nIn sentence 2: Inuuhuktuup iluaqhaiji qukiqtanga → \"the boy shot the doctor\" → verb qukiqtanga → qukiqta + a-nga → 3rd person\n\nSo:\n\n- verbs after vowel → -j\n- after consonant → -t\n- person suffix: -u-tit (2), -u-q (3), -a-it (2/3), -a-nga (3/3), -a-atit (3/2)\n\nSo verb base → + suffix\n\nSo take takujanga → base takujait → with -anga → 3rd person → \"he saw\"\n\nSimilarly, angatkuit → base angatku → + it → 3rd person → \"he came\"\n\nBut so both verbs?\n\nNo — only one verb per sentence.\n\nSo likely the structure is:\n\nX-up Y V → but Y is a noun, V the verb.\n\nBut here: amaruup angatkuit takujanga\n\nStructure: subject X-up, then verb, then object?\n\nSo: the hunter (X-up) angatkuit (verb) takujanga (object)?\n\nBut no -si — and no -mik?\n\nBut in sentence 4: iluaqhaijiup aarqijaatit → doctor cured you → iluaqhaiji (the doctor) → up → definite → cured → aarqijaatit → with -it → 2nd person? — you.\n\nBut \"you\" is the object → so object is marked with -it → because \"you\" — not marked with -q?\n\nIn sentence 1: \"your dog saw you\" → saw you → \"you\" is object → so object is \"you\" → marked with -it (since it's \"you\")\n\nAh — important point:\n\nIn sentence 1: Qingmivit takujaatit → \"your dog saw you\" \n→ \"you\" is object → in English — \"saw you\" — so the object is \"you\", marked with -it.\n\nSimilarly, sentence 5: Qingmiq iputujait → \"you speared the dog\" → \"the dog\" is object → so marked with -q.\n\nSentence 6: Angatkuq iluaqhaijimik aarqisijuq → \"the shaman cured a doctor\" → cured a doctor → doctor is indefinite → marked with -mik.\n\nSo:\n\n- Object definite → marked with -q\n- Object indefinite → marked with -r-mik\n- Object = \"you\" → marked with -it (reflexive or personal)\n\nSo back to 13: Amaruup angatkuit takujanga\n\n- Subject: Amaruup → \"the hunter\" → marked with -up\n- Verb: angatkuit → comes? → 3rd person? → ? But no person suffix — but verb must have\n- Object: takujanga → with -anga → could be object?\n\nBut -anga is not -q or -r-mik → so not object marking.\n\nFor object:\n- definite → -q\n- indefinite → -r-mik\n- personal (you) → -it\n\nHere: takujanga → -anga → not any of these.\n\nSo not object.\n\nThus, only possibility: angatkuit is the verb, takujanga is object → but invalid suffix.\n\nUnless -anga is the person suffix.\n\nSo is \"angatkuit\" the verb with person suffix?\n\nangatku → consonant → so should end with -t? But it ends with -it.\n\n- it after consonant? no — rule says: -t after consonant.\n\nBut in 7: nanuq qaijuq → qaiju → after vowel? qai → q is consonant → qaiju → then + q → so qaijuq → qai (consonant) → + q → so no -t?\n\nRule: verb gets -j after vowel, -t after consonant.\n\nSo base verb: must end with vowel or consonant.\n\n- After vowel → -j\n- After consonant → -t\n\nSo verb base:\n- ends with vowel → add -j\n- ends with consonant → add -t\n\nSo takujait — ends with consonant (t) → so -t? But takujait ends with -it — which is -it, not -t?\n\nSo contradiction?\n\nWait — in sentence 1: takujaatit → takujaat → ends with t → consonant → so verb should add -t → so takujaat → +t → takujaatit\n\nYes — so verb base ends with consonant → -t suffix.\n\nSimilarly, in #4: aarqijaatit — base aarqijai? aarqija → ends with a → vowel → add -j → aarqija-j → aarqijaj? But it's aarqijaatit — no.\n\naarqijaatit → ends with -it — so must be base aarqij → vowel a → vowel → so -j → aarqija → then -it?\n\nBut -j is added after vowel — so aarqija → then -it?\n\nBut then why not aarqija + it?\n\nRule says: verb gets -j after vowel or -t after consonant — then optionally person suffix.\n\nSo the basic verb forms are with -j or -t.\n\nThen, after that, person suffix.\n\nSo:\n- takujaat → verb form with consonant end → so -t → takujaat → + it → takujaatit\n\n- aarqija → vowel ending → +j → aarqija → + it → aarqijaatit\n\nYes.\n\nSo verb base:\n- ends in vowel → add -j\n- ends in consonant → add -t\n\nThen person suffix added.\n\nSo takujanga → base takuj (consonant end) → so -", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12521.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "redacted_solution_hint_mask6", + "sample_index": 1, + "output": "We are given six reference sentences in Inuktitut and their English translations. We must analyze the grammatical structure to deduce the patterns of noun and verb morphology, specifically focusing on:\n\n- The role of suffixes on nouns (especially -q, -r, -mik)\n- The patterns of verb morphology (especially -j, -tit, -q, -ung, etc.)\n- Possessive markers: -it (your), -up (the), -vit (your), -up, -uq, -it, etc.\n\nWe are only solving part (a), translating six new sentences.\n\n---\n\nStep 1: Identify the structural patterns from the given examples.\n\nFrom the guidance:\n\n**Schema 1:** \nX-(q) V– → ‘X V (himself)’ \n→ Reflexive verb (no object), subject with -q → reflexive\n\n**Schema 2:** \nX-(q) Y-(r)mik V-si– → ‘X V a Y’ \n→ Transitive, indefinite object Y (with -mik), noun Y gets -r before -mik \n→ Example: iluaqhaiji-mik → iluaqhaiji-??-mik → iluaqhaiji (has -r before -mik)\n\n**Schema 3:** \nX-up Y-(q) V– → ‘X V the Y’ \n→ Definite object Y, marked with -q (independent of subject) \n→ Example: iluaqhaiji → iluaqhaiji in \"The doctor cured you\"\n\nAlso, possessive:\n- -(q) → replaced by -it in \"your\"\n- -up → replaced by -vit in \"your [object]\"\n\nVerb suffixes:\n- -j after vowel, -t after consonant\n- Person marking:\n - First two schemas: -utit = 2nd person, -uq = 3rd person\n - Third schema: -ait = 2/3, -anga = 3/3, -atit = 3/2\n\nAlso, a transitive verb without an object → interpreted as reflexive → X-(q) V– → reflexive\n\n---\n\nCompare sentences:\n\n1. Qingmivit takujaatit → \"Your dog saw you\"\n→ \"Your dog\" = Qingmi-it (Qingmi + -it), a subject with possessive\n→ \"saw\" = takujaatit → takuj- + aatit → at the end, aatit = 2nd person (since subject is \"your dog\", object is \"you\")\n→ So verb suffix -aatit = 2nd person (object), subject is 1st\n\nWait — but subject is \"your dog\", not \"you\". So object is \"you\".\n\nSo structure: X-up Y-(q) V– → “X V the Y” \n“Your dog” = Qingmi-it (possessive), and \"you\" = you → so Y-(q) → \"you\" = (you) with -q? But \"you\" is not marked by -q in the sentence.\n\nWait — “Qingmivit takujaatit” → the verb is takujaatit → likely -j + -a-tit\n\nFocus on verb morphology.\n\nAll verbs end in -j or -t (after vowel/consonant), and have person suffixes.\n\nLet’s identify verbs:\n\nSentence 1: takujaatit \n→ takuj- + aatit → in common forms, takujaatit = saw → -j before aatit\n\nSentence 2: iluaqhaiji qukiqtanga → “the boy shot the doctor” \n→ iluaqhaiji (the boy) → up → definite \n→ qukiqtanga → qukiqt- + aanga → aanga = 3rd person (object)\n\n→ So schema: X-up Y-(q) V– → Object marked by -q → “the doctor” → iluaqhaiji → iluaqhaiji is noun, as subject, object is \"the doctor\"\n\nSentence 3: Aanniqtutit → “You hurt yourself” \n→ no object → reflexive → schema 1 → X-(q) V– → X = you, -(q) → you → \"you hurt yourself\"\n\nSentence 4: Iluaqhaijiup aarqijaatit → “The doctor cured you” \n→ iluaqhaijiup = the doctor → object → cured you → verb aarqijaatit \n→ aarqij- + aatit → -atit → 2nd person \n→ object “you” → so -atit → 2nd person\n\nSentence 5: Qingmiq iputujait → “You speared the dog” \n→ subject “you” → you → subject with -q? No, verb is iputujait \n→ iputujait → iputuj- + ait → ait = 2/3? → in this context, subject is you → 1st person, so 2nd person object: dog?\n\nWait — “you speared the dog” → subject = you, object = the dog → schema: X-up Y-(q) V– → X = you, Y = dog?\n\nBut “you” is not marked with -up, and no direct -it?\n\nIn sentence 1: “your dog saw you” → “your dog” = Qingmivit → Qingmi + vit → vit = your (your dog), so subject\n\nSimilarly, sentence 5: “You speared the dog” → subject “you” → not marked with -it or -up → so it is marked by appropriate suffix\n\nVerb: iputujait → iputuj- + ait → ait = 2/3? But object is the dog → third person?\n\nWait — in sentence 4: aarqijaatit → aarqij- + aatit → 2nd person object\n\nBut in sentence 5: iputujait → ait → could be 2nd or 3rd?\n\nBut person suffixes:\n\nFrom guidance:\n- First two schemata: -utit = 2, -uq = 3\n- Third schema: -ait = 2/3, -anga = 3/3, -atit = 3/2\n\nSo in schema 3: X-up Y-(q) V– → verb suffix:\n- -ait = 2/3, -anga = 3/3, -atit = 3/2\n\nIn sentence 5: “You speared the dog” → subject = you (1st person), object = the dog (definite → marked with -q)\n\n→ So schema 3: X-up Y-(q) V– → “X V the Y”\n\n- X = you = you → is this “you” with up? Not in sentence → but “you” is subject → how is it marked?\n\nPossibility:\n- “you” → without -up → base form\n- In sentence 5: “You speared the dog” → so verb: iputujait → -ait\n\nIn sentence 4: “The doctor cured you” → iluaqhaijiup → the doctor, object “you” → verb aarqijaatit → -aatit → 2nd person\n\nSo for 2nd person object → -aatit\n\nIn sentence 3: “You hurt yourself” → reflexive → schema 1 → X-(q) V– → you (with -q?) → Aanniqtutit → Aanniqt- + utit → utit = 2nd person?\n\nBut “you” is 1st person → inconsistency?\n\nWait — sentence 3: Aanniqtutit → “You hurt yourself” → transitive verb without object → reflexive\n\nSo verb suffix is -utit → 2nd person?\n\nBut subject is “you” → first person.\n\nPossibility: in reflexive, the subject is marked implicitly, and verb takes -utit for second person? That seems wrong.\n\nWait — check other reflexive.\n\nOnly sentence 3 is reflexive.\n\nSentence 10: Qingmiup ilinniaqtitsijiit aanniqtanga → “The dog hurt your teacher” \n→ subject = the dog → ilinniaqtitsijiit → probably ilinniaqtitsiji + it? \n“your teacher” → teacher marked with -it? → aanniqtanga → aanniqt- + aanga → aanga = 3rd person?\n\nBut object is “your teacher” → so with -it?\n\nBut it ends in -anga — in sentence 4: aarqijaatit → aatit → 2nd person → so why here aanga?\n\nWait — in sentence 10: “The dog hurt your teacher” \n→ subject = the dog → ilinniaqtitsijiit → ilinniaqtitsij- + it → -it = your? → yes → so object is “your teacher”\n\nVerb: aanniqtanga → aanniqt- + aanga → aanga = 3rd person\n\nSo 3rd person object → aanga\n\nSimilarly, in sentence 4: aarqijaatit → aatit → 2nd person object → “you”\n\nIn sentence 2: qukiqtanga → qukiqt- + aanga → 3rd person object → “the doctor”\n\nSo:\n- 2nd person object → -aatit\n- 3rd person object → -anga\n\nIn schema 3: X-up Y-(q) V– → object suffix: -ait, -anga, -atit → but -it in object?\n\nGuide says:\n- Third schema: -ait = 2/3, -anga = 3/3, -atit = 3/2\n\nSo:\n- 2nd person object → -ait\n- 3rd person object → -anga\n- 3rd person subject → -atit\n\nWait — -atit = 3/2 → object?\n\nNo: -atit = 3/2 → meaning 3rd person subject, 2nd person object?\n\nThat seems off.\n\nLet’s tabulate:\n\n| Sentence | Subject | Object | Verb Suffix | Object marking |\n|---------|--------|--------|-------------|----------------|\n| 1 | your dog | you | takujaatit | -aatit (2nd) |\n| 2 | boy | doctor | qukiqtanga | -anga (3rd) |\n| 3 | you | yourself | aanniqtutit | reflexive → no object |\n| 4 | doctor | you | aarqijaatit | -aatit (2nd) |\n| 5 | you | dog | iputujait | -ait (2/3) → object \"the dog\" → 3rd person → contradiction |\n| 6 | shaman | doctor | angatkuq aarqisijuq | → perhaps two verbs? |\n\nWait sentence 6: Angatkuq iluaqhaijimik aarqisijuq → “The shaman cured a doctor”\n\n→ \"a doctor\" → definite? → iluaqhaijimik → iluaqhaiji (doctor) + mik → indefinite? But \"a doctor\" → indefinite → so -mik\n\n→ So schema 2: X-(q) Y-(r)mik V-si– → “X V a Y”\n\n→ X = the shaman → Angatkuq → Angatku- + q → q = 3rd person? But subject is third person → Angatkuq → -q → 3rd person subject?\n\nBut in guidance: \"in first two schemata: -utit ‘2’, -uq ‘3’\"\n\nSo verb endings:\n- -utit → 2nd person\n- -uq → 3rd person\n\nIn sentence 6: verb aarqisijuq → aarqisijuq → aarqisij- + uq → -uq → 3rd person\n\nSo verb suffix -uq → 3rd person\n\nBut object is “a doctor” → intransitive, so object is indefinite → marked with -mik → and the noun gets -r before -mik?\n\nYes: guid says \"Y-(r)mik\" → so doctor → iluaqhaijimik → iluaqhaiji + r + mik → iluaqhaiji has -r before -mik\n\nSo inference:\n- If object is indefinite (a X), then X has -r + mik\n- If object is definite (the X), then it has -q (e.g. the doctor)\n\nAlso:\n- Possessive: your → replaces -q with -it, -up with -vit\n\nSo now, in sentence 5: “You speared the dog”\n\n→ subject = you → not marked with -up or -it, so base\n→ object = “the dog” → definite → so should have -q → dog + q → but no -q in \"dog\"?\n\nWait — verb: iputujait → iputuj- + ait\n\nait = 2/3 → but object is “the dog” → 3rd person → should be -anga → contradiction?\n\nWait — look at sentence 4: “The doctor cured you” → aarqijaatit → aarqij- + aatit → -aatit → 2nd person\n\nSentence 2: “the boy shot the doctor” → qukiqtanga → -anga → 3rd person\n\nSo object person marking:\n- 2nd person → -aatit\n- 3rd person → -anga\n\nBut in sentence 5: iputujait → ait → not -anga → so not 3rd person?\n\nBut the dog is third person → should be -anga?\n\nPossibility — error in sentence 5 analysis.\n\nSentence 5: Qingmiq iputujait → “You speared the dog”\n\nSubject = you — 1st person → no marking.\n\nVerb: iputujait → \"speared\" → iputuj- + ait\n\nait → 2/3 → could be due to object being third person?\n\nBut in sentence 4: “The doctor cured you” — object “you” → 2nd person → -aatit → yes\n\nSentence 2: “the boy shot the doctor” → 3rd person → -anga → yes\n\nSo when object is 2nd person → -aatit \n3rd person → -anga\n\nSo in sentence 5, object = “the dog” → 3rd person → should be -anga\n\nBut verb is iputujait → -ait → not -anga\n\nSo is the object not the dog?\n\nNo — sentence says: “You speared the dog”\n\nUnless the object is not the dog? But that seems off.\n\nWait — is “the dog” marked with -q? In this sentence, is “dog” marked?\n\nIn sentence 1: “your dog” → Qingmivit → Qingmi + vit → vit = your → so noun “dog” is not marked by -q in “Qingmivit”\n\nBut “Qingmivit” = your dog → so noun “dog” is not marked independently.\n\nIn sentence 5: “You speared the dog” → “the dog” → so dog should have -q?\n\nBut “Qingmiq” → is that \"you\" or \"the dog\"?\n\n“Qingmiq” — cannot be “the dog” → because “the dog” would be “qingmi-?”, and “qingmiq” ends with q → so maybe “qingmiq” = the dog?\n\nPossibility: “q” at end is -q → indicative of definite object?\n\nSo “Qingmiq” = the dog?\n\nThen “you speared the dog” → “you” → subject → you → verb = iputujait → iputuj- + ait → ait = 2/3?\n\nBut if object is the dog → 3rd person → should be -anga\n\nBut -ait → could be 2/3 only?\n\nContradiction.\n\nWait — maybe ait is used for second person?\n\nBut no — sentence 4: object “you” → aarqijaatit → aatit → different\n\nSo object person suffix:\n- 2nd person → -aatit\n- 3rd person → -anga\n\nSo sentence 5: object is “the dog” → 3rd person → verb should have -anga\n\nBut verb is iputujait → -ait → not -anga → contradiction\n\nAlternative: “you speared the dog” → the dog is indefinite?\n\nBut it says “the dog” → definite → should have -q → but not marked?\n\nWait — in Inuktitut, definite objects get -q, indefinite get -mik with -r\n\nSo “a dog” → dog-mik → with -r\n\n“the dog” → dog-q\n\nIn sentence 5, if it's \"you speared the dog\" → object is definite → should be -q → so “dog” should be “qingmivit” or “qingmivit” — but here it's “Qingmiq” — ends in q — could be dog-q\n\nSo “Qingmiq” = the dog\n\nThen the verb should be iputujanga → -anga → but it is iputujait → -ait\n\nStill contradiction.\n\nUnless the suffix is not person-specific?\n\nNo — from sentence 2 and 4, we see:\n\n- Object = 2nd person → -aatit\n- Object = 3rd person → -anga\n\nSo only possibility: the object in sentence 5 is 2nd person? But “the dog” is not you.\n\nWait — perhaps “the dog” is a mistake.\n\nLooking at the structure: \"Qingmiq iputujait\"\n\n“Qingmiq” — if we assume “q” is suffix, then it's \"Qingmi-q\" = the dog\n\nBut maybe \"Qingmi\" is subject, \"q\" is suffix → so subject is \"you\" → but \"you\" should not have -q\n\nUnless -q is for object.\n\nSo perhaps the verb is iputujait → and “the dog” is marked with -q → so in the structure.\n\nBut still, verb suffix should be -anga.\n\nUnless the rule for person suffix is different.\n\nAnother possibility: the suffix -ait may be used for 2nd person, -anga for 3rd.\n\nBut sentence 4: “you” = object → aarqijaatit → aatit → 2nd person\n\nSentence 2: doctor = object → qukiqtanga → aanga → 3rd person\n\nSo same pattern.\n\nSentence 5 verb is iputujait — -ait — not -anga → only -ait appears here? In sentence 6, verb aarqisijuq → has -uq → 3rd person.\n\nIn", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12006.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "redacted_solution_hint_mask6", + "sample_index": 2, + "output": "First, analyze the structure and patterns from the given examples.\n\nGeneral sentence structures:\n\n1. X-(q) V– → 'X V (himself)' → reflexive\n2. X-(q) Y-(r)mik V-si– → 'X V a Y' → transitive, indefinite object with -mik\n3. X-up Y-(q) V– → 'X V the Y' → transitive, definite object\n - If object is definite, object gets -q; if indefinite, gets -r before -mik (e.g., nanuq → nanur-mik)\n - Subject marks: -it → \"your\", -up → \"your\", -vit → \"your\" for subject or object\n - Verb suffixes:\n - -j after vowel, -t after consonant\n - Person endings:\n - In 1,2: -u-tit (2nd), -u-q (3rd)\n - In 3: -a-it (2nd/3rd), -a-nga (3rd/3rd), -a-atit (3rd/2nd)\n\nNow, work on each sentence:\n\n13. Amaruup angatkuit takujanga \nBreak down:\n- Amaruup = Amaru (hunter) + -up → \"your hunter\"\n- angatkuit = angatkuq → \"came\" + -uit → verb form\n- takujanga = takujaatit → \"saw\" + -anga → object is \"you\" with object marking?\nWait: takujanga → base verb takuju → \"saw\" \nBut \"takujanga\" ends in -anga → likely -anga = object-marking or possession?\n\nBut the verb form: takujanga → if derived from takujaatit, which means \"your dog saw you\", we need to find the pattern.\n\nLook at sentence 1: Qingmivit takujaatit → \"Your dog saw you\" \n→ Qingmi = dog → Qingmivit = dog + -vit → \"your dog\" \ntakujat → saw → takujaatit → with -it → definite object (you)\n\nSo: when the verb has a definite object, object gets -it; when indefinite, gets -r-mik.\n\nNow in 13: \"Amaruup angatkuit takujanga\"\n\nAmaruup → Amaru (hunter) + up → \"your hunter\" \nangatkuit → probably angatkuq (came) + -uit → -uit = past tense, maybe from -uq \nin sentence 7: Nanuq qaijuq → \"polar bear came\" → so qaijuq → \"came\" \nin 12: Angunahukti nanurmik qukiqsijuq → \"hunter shot a polar bear\"\n\nIn sentence 12: Angunahukti nanurmik qukiqsijuq \n→ Angunahukti → hunter (subject) → \"shot\" \nnanurmik → nanuq (polar bear) + -r-mik → indefinite object → so nanurmik = \"a polar bear\"\n\nSo -r-mik = indefinite object → derived from -q → nanuq → nanur-mik\n\nSimilarly, in sentence 2: Inuuhuktuup iluaqhaiji qukiqtanga \nInuuhuktuup → inuuhuktuit → inuuhuktuup → \"the boy shot the doctor\"? \nNo: \"the boy shot the doctor\" → so subject is definite → inuuhuktuup → inuuhuktu → \"boy\" + -up → \"your boy\"? \nBut \"your boy\" → inuuhuktuup → but sentence says \"the boy\"\n\nWait: the rule says: \n\"if a noun gets the ending -q when it is either a definite object or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending -mik when it is an indefinite object\"\n\nSo: if object is definite → object ends in -q \nif object is indefinite → ends in -r-mik\n\nAlso: subject: if \"your\", -(q) → -it, -up → -vit\n\nNow sentence 3: Aanniqtutit → you hurt yourself → reflexive → \"you hurt (yourself)\"\n\nSo: Aanniqtutit → aanniqtu → hurt, -tut → reflexive\n\nNow sentence 4: Iluaqhaijiup aarqijaatit → \"the doctor cured you\" \n→ iluaqhaiji = doctor → iluaqhaijiup = the doctor → definite object → so doctor has -q → iluaqhaijiup \naarqijaatit → cure + -it → definite object (you) → so you → -it\n\nSentence 5: Qingmiq iputujait → you speared the dog \n→ Qingmiq = you + -q → \"you\" → \"you speared\" → but one verb suffix → \"putujait\" → \"speared\"\n\nBut in sentence 1: Qingmivit takujaatit → your dog saw you → so \"v\" is \"saw\"\n\nIn 5: Qingmiq iputujait → you speared the dog → base verb is \"putujait\"?\n\nNow look at 10: Qingmiup ilinniaqtitsijiit aanniqtanga → the dog hurt your teacher \n→ Qingmiup = the dog → \"dog\" + -up → \"the dog\" → but -up not for \"your\" \nThen ilinniaqtitsijiit → verb \"hurt\" → ilinniaqtis → hurt, with -it → \"you\" \naanniqtanga → \"your teacher\" → aanniqtanga → aanniqtu (hurt) + -anga → but no -q?\n\nWait: aanniqtanga → aanniqtutit → you hurt yourself → so aanniqtu → hurt \nso aanniqtanga → likely \"you\" with -anga → but only if in a particular context.\n\nBut sentence 10: \"the dog hurt your teacher\" \n→ ilinniaqtitsijiit → verb → \"hurt\" → past tense \n→ object: your teacher → not in -q? → but must have -q for definite object or with -it?\n\nBut teacher is definite? \"your teacher\" = definite.\n\nBut in the sentence, the object is \"your teacher\" → so should have -q or be marked?\n\nWait: \"your teacher\" → if it's a definite object → it gets -q → so aanniqtanga → aanniqtut → no.\n\nWait: sentence 17: Qaijutit → \"you fell\" → likely reflexive → qaijutit → \"you fell\"\n\nSimilarly, sentence 11: Ukiakhaqtutit → you fell → same.\n\nSo \"you fell\" is a reflexive.\n\nSo reflexive verbs have -t → -ut → -tut?\n\nNow back to 13: Amaruup angatkuit takujanga \n→ subject: Amaruup → \"your hunter\" (Amaru = hunter → -up → your) \n→ verb: angatkuit → angatkuq → \"came\" → -uit → past form \n→ object: takujanga → \"saw\" with -anga?\n\nBut \"takujanga\" → takujait → \"saw\" → with -anga?\n\nBut in sentence 1: \"your dog saw you\" → takujaatit → \"saw you\" → object \"you\" with -it\n\nIf object is \"you\", then -it → definite → takujaatit\n\nBut in 13: takujanga → -anga → not -it\n\nCould -anga be an object?\n\nBut then object would be indefinite? Or is it \"someone\"?\n\nBut the verb is \"takuj\" → to see → so \"your hunter saw [someone]\"\n\nSo object is not \"you\" → not reflexive → so not yourself\n\nSo object is indefinite → so should be marked with -r-mik?\n\nBut takujanga → ends with -anga, not -r-mik\n\nWait: pattern: for indefinite object, it gets -r before -mik → e.g., nanuq → nanur-mik\n\nBut takujanga → no -r → so may not be indefinite.\n\nBut verb: takujanga → from takuju → saw → with suffix?\n\nIn sentence 1: takujaatit → took -it → because object is definite (\"you\")\n\nIn sentence 13: takujanga → no -it, no -mik → so object is indefinite → must have -r-mik?\n\nBut it doesn't → unless \"-anga\" is derived from \"takuj\" + -a → but no.\n\nWait: perhaps the verb suffix is -j after vowel, -t after consonant.\n\nangatkuit → ends in -uit → after \"k\" (consonant) → -t → so -uit → possible?\n\nangatkuq → \"came\" → verb base \nangatkuit → past form? → maybe -uit = past tense suffix?\n\nBut sentence 7: Nanuq qaijuq → \"polar bear came\" → qaijuq → no -it → so definite object → object not marked with -it\n\nOnly when object is definite, the object gets -q.\n\nWhen object is indefinite, object gets -r-mik.\n\nVerb receives -j after vowel, -t after consonant.\n\nSo for verb form: suffix after base verb: -j (vowel), -t (consonant)\n\nIn sentence 1: Qingmivit takujaatit → verb is \"takuj\" + -a (end of word) → takujaatit → -a → after vowel? \"takuj\" ends in \"j\" → vowel? \"takuj\" → /takuːj/ → ends in consonant? j is consonant → so after consonant → -t → takujat → then -it → so -at → -t + -it → takujaatit → yes\n\nSo: after consonant → -t → so takuj → takujat → then -it → takujaatit\n\nSimilarly, in sentence 4: aarqijaatit → aarqij + -a + -it → \"cured\" → base verb aarqij → ends in j → consonant → so -t → aarqijat → then -it → aarqijaatit → yes\n\nIn sentence 2: iluaqhaiji qukiqtanga → iluaqhaiji → \"the doctor\" → definite object → so -q → iluaqhaiji → then qukiqtanga → \"shot\" → qukiq → + -t → qukiqt → then -anga → -a → added?\n\nqukiqtanga → base verb qukiqt → + -a → -anga?\n\nqukiqt → ends in t → consonant → so -t → qukiqt → then -anga? → no -t suffix?\n\nBut the rule says verb gets -j after vowel, -t after consonant.\n\nSo if the verb ends in consonant → suffix is -t → so \"qukiqt\" → ends in t → consonant → so -t → but already has -t? → qukiqtang → then -a?\n\nBut it's qukiqtanga → so might be -a → possession?\n\nPossibly, the -a is object marking.\n\nNow back to 13: Amaruup angatkuit takujanga\n\nSubject: Amaruup → \"your hunter\" → Amaru = hunter → -up → your → \"your hunter\"\n\nVerb: angatkuit → angatkuq → base verb → \"came\" → ends in q → vowel → so after vowel → verb gets -j → angatkuq → q → vowel → so -j → angatkuqj → then -uit? → but it's angatkuit → so -uit?\n\nAfter q → vowel → so should get -j → but angatkuit → ends in -uit → so perhaps -uit is a separate suffix?\n\nBut sentence 7: Nanuq qaijuq → \"came\" → base qaiju → ends in u → vowel → so should get -j → but it's qaijuq → qaiju + q? → so -q?\n\nWait: qaijuq → qaiju → ends in u → vowel → so -j → but qaijuq → ends in q → so -q?\n\nPossibly -q is the object marking.\n\nSo verb base → angatku → \"came\" → base → angatku → ends in u → vowel → so -j → angatku + j → angatkuj → then -uit? → no\n\nBut sentence 7: nanuq qaijuq → nanuq → \"polar bear\" → definite → so object gets -q → so it's not the verb.\n\nSo verb: qaijuq → base qaij → ends in j → consonant → so -t → qaijt → then? → qaijuq → so maybe -uq?\n\nPerhaps the verb is structured as verb + person + object.\n\nBut sentences:\n\n1: Qingmivit takujaatit → \"your dog saw you\" \n→ Qingmivit → subject: dog + vit → \"your dog\" \ntakuj + aat → takujaatit → verb with -it → object you → definite → so -it\n\n2: Inuuhuktuup iluaqhaiji qukiqtanga → the boy shot the doctor \n→ subject: inuuhuktuup → boy + up → \"your boy\"? but sentence says \"the boy\" \n→ but \"the boy\" → not marked with -it → so perhaps \"the\" is just definite → so object is definite → iluaqhaiji → doctor with -q → so -q \nqukiqtanga → verb \"shot\" → qukiq → base → ends in q → vowel → so -j → qukiqj → then -anga → object marking? or person?\n\nqukiqtanga → qukiq → + -t →? → qukiqt → then -anga → -a?\n\nBut -a → not a standard suffix.\n\nWait: in sentence 4: aarqijaatit → aarqij + aat → aarqijaatit → verb with -it → object \"you\"\n\nIn sentence 2: qukiqtanga → so likely qukiq → base → ends in q → vowel → so -j → qukiqj → then -anga → so -anga = object marking?\n\nBut the rule says \"the verb receives: -j after vowel, -t after consonant\" — so only one of these.\n\nSo if base verb ends in vowel → get -j → base + j → then + person + object?\n\nBut in 2: iluaqhaiji qukiqtanga → so object is definite → so object gets -q? → iluaqhaiji → yes\n\nAnd verb: qukiq → ends in q → vowel → so -j → qukiqj → then -anga → -anga = object marking? → or -a?\n\nIn 4: aarqijaatit → aarqij → ends in j → consonant → so -t → aarqijt → then -it → aarqijaatit → so -it is person?\n\nIn 1: takujaatit → takuj → ends in j → consonant → so -t → takujat → then -it → takujaatit\n\nSo verb structure:\n- base verb → if ends in vowel → add -j → if consonant → add -t\n- then add person suffix and object suffix (if any)\n\nPerson suffix:\n- in 1,2: -u-tit (2nd person), -u-q (3rd)\n- in 3: -a-it (2nd/3rd), -a-nga (3rd/3rd), -a-atit (3rd/2nd)\n\nBack to 13: Amaruup angatkuit takujanga\n\nSubject: Amaruup → your hunter → so hunter + -up → \"your\"\n\nVerb: angatkuit → base angatku → ends in u → vowel → so -j → angatkuj → then -uit? → but it's angatkuit → so -uit?\n\nPossibly -uit is a past tense suffix or person suffix?\n\nIn 7: Nanuq qaijuq → \"polar bear came\" → qaijuq → base qaij → ends in j → consonant → so -t → qaijt → then -uq? → but it's qaijuq → so perhaps the -uq is the person suffix?\n\nIn 7: no person marking → only \"the polar bear came\"\n\nBut in 1: Qingmivit takujaatit → subject \"your dog\" → -vit → 2nd person?\n\n- it → in pattern: -vit = \"your\" → in 1: Qingmivit → so \"your dog\"\n\nSo -vit = 2nd person → subject\n\nSimilarly, -up = 2nd person? But in 2: inuuhuktuup → \"your boy\" → but sentence says \"the boy\" → contradiction?\n\nWait: the problem says: \"To say ‘your’, -(q) is replaced by -it, -up by -vit\"\n\nSo:\n- if object is definite → object has -q\n- if object is indefinite → object has -r before -mik\n- subject: if \"your\", then -q → -it (if -q) or -up → -vit (if -up)\n\nSo:\n- -it in subject → \"your\"\n- -up → \"your\"\n- -vit → \"your\"\n\nIn sentence 1: Qingmivit → \"your dog\" → so -vit → 2nd person\n\nIn sentence 2: Inuuhuktuup → \"your boy\" → so -up → \"your boy\"\n\nBut sentence says \"the boy shot the doctor\" → so \"the boy\" — not \"your boy\"\n\nContradiction.\n\nWait: look at 8: Iluaqhaijivit inuuhuktuit aarqijanga → \"your doctor cured your boy\"\n\n→ iluaqhaijivit → doctor + -vit → \"your doctor\"\n→ inuuhuktuit → boy + -uit → \"your boy\"\n→ aarqijanga → cured\n\nSo -vit and -uit → both \"your\"\n\nSo in 2: Inuuhuktuup iluaqhaiji qukiqtanga → \"your boy shot the doctor\"\n\nBut the translation says \"the boy shot the doctor\" — contradiction?\n\nUnless the translation is wrong.\n\nThe problem says: \"2. Inuuhuktuup iluaqhai", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11899.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "redacted_solution_hint_mask6", + "sample_index": 3, + "output": "Step 1: Understand the grammatical patterns from the given examples.\n\nWe are given structure rules for Inuktitut:\n\n1. X-(q) V– → 'X V (himself)' (reflexive)\n2. X-(q) Y-(r)mik V-si– → 'X V a Y' (transitive, with indefinite object)\n3. X-up Y-(q) V– → 'X V the Y' (definite object)\n\nRules:\n- Noun endings:\n - When a noun is a definite object or subject without definite object → gets -q\n - When it’s an indefinite object → gets -r before -mik (e.g., nanu-q → nanu-r-mik)\n- -(q) becomes -it or -vit for \"your\"\n- -up becomes -vit for \"your\" (subject)\n- Verb suffixes:\n - -j after vowel, -t after consonant\n - Person marking:\n - Schemata 1, 2: -utit (2nd person), -uq (3rd person)\n - Schemata 3: -ait (2/3), -anga (3/3), -atit (3/2)\n\nAlso: A transitive verb without an object is interpreted as reflexive.\n\nStep 2: Analyze given sentences to reinforce patterns.\n\nExample 1: Qingmivit takujaatit → Your dog saw you.\n- \"Your dog\" = Qingmivit → Qingmi-(vit) → subject = Qingmivit (Qingmi + -vit)\n- saw = takujaatit → takuj (verb) + -aatit (3rd person singular) → \"saw\"\n- \"you\" is object → \"you\" = takujaatit → object = you → implied definite\n\nExample 2: Inuuhuktuup iluaqhaiji qukiqtanga → The boy shot the doctor.\n- \"The boy\" = Inuuhuktuup → Inuuhuktu (boy) + -up → definite subject\n- \"the doctor\" = iluaqhaiji → definite object → iluaqhaiji (no -mik)\n- verb = qukiqtanga → qukiq + -tanga → -t after consonant → -t at end → \"shot\"\n- no -mik → definite object → so no -r before -mik\n\nExample 3: Aanniqtutit → You hurt yourself.\n- \"You\" = Aanniqtutit → Aanniqt → verb = aanniqt + -utit → 2nd person\n- reflexive → no object → \"yourself\"\n\nExample 4: Iluaqhaijiup aarqijaatit → The doctor cured you.\n- Iluaqhaijiup → doctor (definite) → + up\n- aarqijaatit → verb \"cured\" + -a-it (2nd person) → cured you\n- object = you → definite → no -mik\n\nExample 5: Qingmiq iputujait → You speared the dog.\n- You = Qingmiq → Qingmi + -q → subject\n- speared → iputujait → verb ending: -j after vowel (u → j), -ait → 3rd person? Wait, subject is \"you\"\n- But \"you\" is 2nd person → should be -utit? But it's -ait?\n\nCheck structure: \"You speared the dog\" → subject = you, object = the dog → fits schema 3?\n\nSchema 3: X-up Y-(q) V– → X-up Y-(q) + V → \"X V the Y\"\n\nBut here \"you\" is subject → not \"X-up\" → unless \"X-up\" is not used.\n\nWait: in example 5: Qingmiq iputujait → You speared the dog.\n\nBut has no -up → so is subject \"you\"?\n\nBut \"you\" is not marked with -up. So this may be schema 1.\n\nSchema 1: X-(q) V– → X-(q) = you? → yes → Qingmiq → you → \"you speared\", so reflexive?\n\nBut it says \"the dog\" → so object. Thus not reflexive.\n\nWait, contradiction.\n\nBut the rule says: \"A transitive verb without an object is interpreted as reflexive.\"\n\nSo if object missing → reflexive.\n\nBut here: object is \"the dog\" → present → transitive.\n\nThus schema: X-(q) Y-(q) V–? Not directly.\n\nWait — \"Qingmiq\" = \"you\" → not -up → subject\n\n\"iputujait\" → verb: -j after vowel (u), and -ait → person marking?\n\nLooking at examples:\n\nExample 6: Angatkuq iluaqhaijimik aarqisijuq → The shaman cured a doctor.\n- Angatkuq → the shaman → definite → -q\n- iluaqhaijimik → iluaqhaiji (doctor) + -mik → indefinite object → object is \"a doctor\"\n- aarqisijuq → cured → -si + -jua + -uq → so \"cured a doctor\" → transitive with indefinite object\n\nSo from example 6:\n- indefinite object → marked with -mik → after -r → nanu-q → nanu-r-mik\n- so iluaqhaiji → iluaqhaijimik → indefinite\n\nExample 7: Nanuq qaijuq → The polar bear came.\n→ subject: Nanuq (definite) → no object → \"came\"\n\nExample 8: Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy.\n→ \"Your doctor\" = Iluaqhaijivit → iluaqhaiji + -vit (your)\n→ \"your boy\" = inuuhuktuit → inuuhuktu + -vit\n→ object = your boy → definite → so object has -vit\n→ verb = aarqijanga → cured + -janga → -janga = how?\n\nWait: in example 4: aarqijaatit → cured you → -a-it → 2nd person\nIn example 8: aarqijanga → cured your boy → object is \"your boy\" → which is defined → so must be 3rd person?\n\nBut \"your boy\" is not 3rd person — context says \"your boy\" → so subject is \"your doctor\", object is \"your boy\"\n\nSo verb is \"cured\" → aarqijanga → -janga → probably 3rd person\n\nWait: in example 4: \"aariqijaatit\" → cured you → \"you\" is 2nd person → -it\n\nSo person suffix: \n- if object is definite → the object is definite → so has -q or -vit → and verb ending reflects object person?\n\nBut in schema 3: X-up Y-(q) V– → \"X V the Y\" → Y is object\n\nThen person marking on verb:\n- first two schemata: -utit (2), -uq (3)\n- third: -ait (2/3), -anga (3/3), -atit (3/2)\n\nIn example 8: \"Your doctor cured your boy\" → verb = aarqijanga → likely -anga → 3rd person (object is in 3rd person)\n\nSo -anga → 3rd person → object is 3rd person → so \"your boy\" is treated as 3rd person?\n\nBut \"your boy\" is not 3rd person — but in Inuktitut, object case may shift.\n\nBut the rule says: in schema 3 → verb ending reflects object person.\n\nSo in schema 3: X-up Y-(q) V– → verb ending = -ait (2/3), -anga (3/3), -atit (3/2)\n\nSo if object is 2nd person → -ait; if 3rd → -anga; if 2nd person subject → -atit?\n\nIn example 8:\n- subject: your doctor → Iluaqhaijivit → your + doctor → subject is 2nd person (your)\n- object: your boy → 2nd person (your boy)\n- verb = aarqijanga → -anga? → 3rd person?\n\nBut your boy is 2nd person → so why -anga?\n\nWait — \"your boy\" is not \"the boy\", but \"your\" → so how is it marked?\n\nLook at example 2: Inuuhuktuup iluaqhaiji qukiqtanga → \"The boy shot the doctor\"\n- subject: boy (definite) → 3rd person → so verb is -uq → qukiqtanga → -tanga → -t at end → but -t after consonant → qukiqt → qukiqt → q → consonant → +t → qukiqtanga → likely -tanga → verb suffix: -t → after consonant → so -t\n\nBut person: -uq → 3rd person → matches object: doctor → 3rd person\n\nIn example 8: subject = your doctor → 2nd person, object = your boy → 2nd person → verb ending should be -ait (2/3)\n\nBut aarqijanga → -anga? → no.\n\nWait — example 8: verb is aarqijanga → is that -anga?\n\n\"aarqijanga\" → aarqij + aanga → likely -anga → which is 3rd person\n\nBut object is \"your boy\" → 2nd person → should be -ait?\n\nContradiction.\n\nWait — review original:\n\n8. Iluaqhaijivit inuuhuktuit aarqijanga → Your doctor cured your boy.\n\naariqijaatit → cured you → -it → 2nd person\n\naarqijanga → cured → likely -anga → 3rd person\n\nBut \"your boy\" is 2nd person → so unless \"your\" is not marking person — or is it?\n\nIn example 4: aarqijaatit → cured you → \"you\" → 2nd person → -it\n\nIn example 8: \"your boy\" → object → 2nd person → should be -ait?\n\nBut \"aarqijanga\" has -anga → 3rd person?\n\nWait — perhaps the suffix is for object person in schema 3:\n\nSchema 3: X-up Y-(q) V– → verb = -ait (2/3), -anga (3/3), -atit (3/2)\n\nSo if object is 2nd person → -ait\n\nIf object is 3rd person → -anga\n\nIf object is 2nd person, subject is 3rd → -atit\n\nBut here:\n- object = \"your boy\" → 2nd person → so should be -ait → aarqijait?\n\nBut it's aarqijanga → so -anga → 3rd person?\n\nBut \"your boy\" is 2nd person → contradiction?\n\nWait — is \"your boy\" treated as 3rd person?\n\nNo — \"your\" is possessive — so object is \"the boy\" → definite → and \"your\" is attached to the noun.\n\nBut in Inuktitut, possessive may not affect case marking.\n\nBut example 4: aarqijaatit → cured you → \"you\" → 2nd person → -it\n\nSo structure: verb ending = person of the object.\n\nThus in 8:\n- object = your boy → 2nd person → verb should be -ait → aarqijait\n\nBut it's aarqijanga → so not matching.\n\nWait — perhaps typo or misreading.\n\nWait — example 4: iluaqhaiji aarqijaatit → cured you → object = you → 2nd person → -it\n\nExample 8: iluaqhaijivit (your doctor) + inuuhuktuit (your boy) + aarqijanga\n\n→ aarqijanga → suffix -anga → 3rd person\n\nSo object is 3rd person → so \"your boy\" is treated as 3rd person? But \"your\" is possessive.\n\nBut \"boy\" is not a third person pronoun — so it should be 2nd person.\n\nAlternative: in Inuktitut, \"your\" → -it in subject / -vit in object → so object is \"your boy\" → marked with -vit → not with person?\n\nBut the verb should mirror object.\n\nPerhaps the pattern in schema 3 is:\n\nVerb ending = -ait (2/3), -anga (3/3), -atit (3/2)\n\nSo if object is 2nd person → -ait\n\n3rd person → -anga\n\n2nd person (subject) and object 3rd → -atit\n\nIn example 8:\n- subject = your doctor → 2nd person\n- object = your boy → 2nd person → so object is 2nd person → verb should be -ait → aarqijait\n\nBut given is aarqijanga → -anga → 3rd person → inconsistency?\n\nWait — original text says: \"Iluaqhaijivit inuuhuktuit aarqijanga\"\n\nIs that a typo?\n\nPossibly — maybe it's aarqijaatit? But no, it's aarqijanga.\n\naariqijanga → likely -anga → 3rd person object.\n\nSo perhaps \"your boy\" is treated as 3rd person?\n\n→ Only if \"your\" is not marking person — or if \"boy\" is 3rd person.\n\nBut no evidence.\n\nAlternative: perhaps the suffix is for the subject.\n\nCheck schema 3: subject is X-up → person marking?\n\nExample 3: Aanniqtutit → you hurt yourself → reflexive → subject = you → person = 2nd → verb = -utit → -utit → 2nd person\n\nExample 5: Qingmiq iputujait → you speared the dog → subject = you → 2nd person → verb = -j + -ait? → iputujait → -jait → -j after u → vowel → then -ait → 2nd person?\n\nBut -ait can be 2nd or 3rd.\n\nBut in example 8: subject = your doctor → 2nd person → so should be -ait or -atit?\n\nX-up → if X is subject → person suffix on verb?\n\nBut in schema 3: verb ends with -ait, -anga, -atit → so probably person-based.\n\nIn example 8: subject = your doctor → 2nd person → so verb should reflect subject person?\n\nBut example 4: subject = doctor → 3rd person → verb = aarqijaatit → -it → which is 2nd person? No.\n\nExample 4: aarqijaatit → cured you → object = you → so person on verb is 2nd.\n\nIn example 8: object = your boy → 2nd person → so verb = -ait → aarqijait\n\nBut given is aarqijanga → so likely a typo or misprint.\n\nAlternatively, perhaps the suffix -anga is used when object is 3rd person.\n\nSo if object is not 2nd person, use -anga.\n\n\"Your boy\" → may be treated as 3rd person?\n\nUnlikely.\n\nAlternatively, \"your\" may be attached via -it, but the word \"boy\" is not marked with person.\n\nBut in example 2: \"the boy\" → boy is 3rd person → verb is -uq → shot → 3rd person\n\nIn example 8: \"your boy\" → possessive → so when object is specified with \"your\", is it 2nd or 3rd?\n\nPossessive may mark person.\n\nBut in example 13, we have: Amaruup angatkuit takujanga → or target: 13. Amaruup angatkuit takujanga\n\nBreak it down.\n\nSentence 13: Amaruup angatkuit takujanga\n\n- Amaruup → \"the hunter\" → definite subject → -up\n- angatkuit → angatku + -it → \"you\" (object, 2nd person)\n- takujanga → verb \"saw\" + -anga → -anga (third person)\n\nBut object is \"you\" → 2nd person → should be -ait?\n\nBut -anga → 3rd person → contradiction?\n\nWait — if the object is \"you\", it should be -it (reflexive or 2nd person)\n\nBut \"takujanga\" → takuj + aanga → word ending -anga → 3rd person\n\nBut object = you → 2nd person → so verb should be -ait\n\nThus likely error — or pattern applies only when object is definite.\n\nBut in example 3: Aanniqtutit → you hurt yourself → reflexive → no object → so verb = -utit → 2nd person\n\nExample 5: Qingmiq iputujait → you speared the dog → not reflexive → object = dog → definite → so verb should mark 3rd person?\n\n\"iputujait\" → -jait → -j after vowel (u) → -ait → 2nd person?\n\nBut subject = you → 2nd person → so if \"-ait\" is for 2nd person, then could be.\n\nBut \"the dog\" is 3rd person → should be verbal marking for 3rd person?\n\nNo rule says that.\n\nPattern: verb suffix depends on object in schema 2 and 3.\n\nIn schema 2: X-(q) Y-(r)mik V-si– → \"X V a Y\" → object = Y → indefinite → marked with -mik → and verb has -si + suffix\n\nIn example 6: Angatkuq iluaqhaijimik aarqisijuq → \"the shaman cured a doctor\"\n\n- object = a doctor → indefinite → -mik → so iluaqhaijimik → -mik\n- verb = aarqisijuq → \"cured\" + -si + -jua + -uq → -uq → 3rd person\n- object is \"a doctor\" → 3rd person → so -uq makes sense\n\nIn example 4: aarqijaatit → cured you → you is 2nd person → -it → 2nd person\n\nIn example 8: aarqijanga → cured your boy → your boy is 2nd person → should be -ait → but is -anga → contradiction\n\nUnless \"your\" is not marking person — or the object is 3rd person.\n\nBut \"your boy\" is not \"the", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12144.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem #5. The Inuktitut sentences have the following general structure:\n X-(q) V– ‘X V (himself).’\n X-(q) Y-(r)mik V-si– ‘X V a Y.’\n X-up Y-(q) V– ‘X V the Y.’\nwhere X and Y are nouns and V is the verb. If a noun gets the ending -q when it is either a definite\nobject or a subject of a sentence that doesn’t have a definite object, it also gets -r before the ending\n-mik when it is an indefinite object (nanu-q — nanu-r-mik; iluaqhaiji — iluaqhaiji-mik).\nTo say ‘your’, -(q) is replaced by -it, -up by -vit.\n The verb receives the following suffixes:\n • -j following a vowel or -t following a consonant;\n • an ending for the persons of the subject and the definite object, if there is one:\n – in the first two schemata: -u-tit ‘2’, -u-q ‘3’;\n – in the third schema: -a-it ‘2/3’, -a-nga ‘3/3’, -a-atit ‘3/2’.\n\nA transitive verb without an object is interpreted as reflexive.\n\n (a) 13. [TARGET ANSWER REDACTED]\n 14. [TARGET ANSWER REDACTED]\n 15. [TARGET ANSWER REDACTED]\n 16. [TARGET ANSWER REDACTED]\n 17. [TARGET ANSWER REDACTED]\n 18. [TARGET ANSWER REDACTED]\n\n (b) 19. Angatkuup aanniqtaatit.\n 20. Ilinniaqtitsijiup inuuhuktuq takujanga.\n 21. Amaruit ukiakhaqtuq.\n 22. Qingmirmik qukiqsijutit.\n 23. Qingmiit ilinniaqtitsijimik aanniqsijuq.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "redacted_solution_hint_mask2", + "sample_index": 0, + "output": "We are given a set of equations in Nahuatl and Arammba, and a mapping of numerical values to linguistic forms based on positional and structural rules.\n\nWe are to write **42** and **494** in Nahuatl.\n\n---\n\n### Step 1: Understand the Nahuatl numeral system from the guidance\n\nFrom the problem's guidance:\n\n- Units:\n - 1: cë\n - 2: öme\n - 3: ëyi\n - 4: nähui\n - 5: mäcuïlli\n - 10: pöhualli\n - 20: cem (used in multiplication)\n - 400: tzontli\n - 8000: xiquipilli\n\nWait — correction: From the table:\n\n> α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: \n> - 1: ceM (i.e., cem) \n> - 2: öm \n> - 3: yë \n> - 4: näuh \n> - 5: mäcuïl\n\nBut actually, this seems to define the **multipliers** in base-20 numeration:\n\nSo, the numerals are based on powers:\n\n- 20¹ = 20 \n- 20² = 400 \n- 20³ = 8000 \n\nSo we can represent numbers as:\n\n> α × 20β + δ, where δ is a remainder less than 20β\n\nEach digit α (1–5) corresponds to a base-20 digit, and is mapped to a specific word:\n\n| α | word |\n|---|-------------|\n| 1 | cem |\n| 2 | öm |\n| 3 | yë |\n| 4 | näuh |\n| 5 | mäcuïl |\n\nNote: In equation (13): \n> yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nBut this may be a compound form for 1296.\n\nFrom guidance:\n\n- 64 = 1296 → 4 × 6³ → ndamno \n→ 6³ = 216 → tarumba \n→ 6⁴ = 1296 → ndamno \n\nBut in Nahuatl, digits are in base-20. So let's focus on the base-20 system:\n\nWe have:\n\n- 1 × 20¹ = 20 → cem \n- 2 × 20¹ = 40 → öm \n- 3 × 20¹ = 60 → yë \n- 4 × 20¹ = 80 → näuh \n- 5 × 20¹ = 100 → mäcuïl \n\nBut in the equations:\n\n(3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nThis may suggest composition.\n\nBut more usefully, from the guidance:\n\n> 42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\n\nSo:\n\n42 = 2 × 20 + 2\n\nThat is:\n\n- α = 2 → word = öm \n- β = 1 (20¹) \n- δ = 2\n\nNow, the rule for forming numerals:\n\nFrom guidance:\n\n> α × 20β, 1 ≤α ≤5, 1 ≤β ≤3 \n> γ + δ, γ = α × 20β, 1 ≤δ < 20β \n> M = m before m, p, or vowel; n otherwise.\n\nWait — it says:\n\n> M = \n> m before m, p, or a vowel; \n> n otherwise.\n\nBut this seems to be a rule for the **morpheme** or **syllable** fusional rule — likely for applying prefixes or suffixes.\n\nBut to form the expression:\n\n**α × 20^β + δ**\n\nThis is composed as:\n\n- α × 20^β produces a stem \n- δ (the remainder) produces a suffix derived from components with known values.\n\nBut for the remainder, we must map δ:\n\nWe know that in the examples:\n\n- 1: cë \n- 2: öme \n- 3: ëyi \n- 4: nähui \n\nThese appear to be the **smaller values**, so:\n\n- δ = 1 → cë \n- δ = 2 → öme \n- δ = 3 → ëyi \n- δ = 4 → nähui \n\nYes, from equation (3): \n> yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n\nThis suggests that:\n\nA number expressed as (α × 20^β) + δ is built as:\n\n> [α] + [δ] in form: (α-stem) + (δ-stem) with specific structure like \"on-cë\", etc. \n\nBut from the base structure:\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (1 × 20) + 1 × (1 × 20) = 2×20 +1 = 41? Not matching.\n\nBut regardless, from the guidance:\n\n> 42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\n\nSo we have:\n\n42 = 2×20 + 2\n\nSo:\n\n- 20² = 400 → too big \n- 20¹ = 20 → 2×20 = 40 \n- 42 - 40 = 2 → remainder 2\n\nSo β = 1 → word for 2×20 is **öm**\n\nRemainder = 2 → δ = 2 → word = **öme**\n\nNow, how is it built?\n\nFrom equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli → this might be multiplication.\n\nBut from equation (3):\n\nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n(“yë-pöhualli” → possibly 3×20? “3×20 = 60”) \n+ “mahtlactli-on-nähui” → mahtlactli = 1×20? on-nähui = 4? → 20 + 4 = 24? \nBut 60 + 24 = 84, not matching.\n\nAlternatively, look at equation (4): \nmäcuïlli + öme = chicöme → 5×20 + 2 = 102? \n→ 5×20 = 100, + 2 → 102 = chicöme\n\nSimilarly, equation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nThis suggests that multiplication forms a larger compound.\n\nBut from (4): \nmäcuïlli + öme = chicöme → (5×20) + 2 = 102 → chicöme\n\nSo addition seems to be formed by combining two numerals with an \"on\" infix.\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nNow, if yë-pöhualli is (3×20) = 60\n\nmahtlactli-on-nähui = 1×20 + 4 = 24 → 60+24 = 84\n\nnäuh-pöhualli-on-cë → 4×20 + 1 = 81 → not matching.\n\nAlternatively, perhaps the \"on\" infix is structural.\n\nBut from the guidance, we see that:\n\n> 42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\n\nSo it must be formed from:\n\n- 2 × 20 → öm \n- + 2 → öme\n\nAnd since it's a sum, likely structured as: \n**öm-pöhualli-on-öme**?\n\nBut from (4): mäcuïlli + öme = chicöme → seems like the addition rule is \"A + B = C\" where A and B are stored in specific forms.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nThis suggests that the form is: (A) + (B) = (result) with a structure using \"on\" infix.\n\nLook at the structure:\n\n\"yë-pöhualli-on-chicöme\" — is \"yë-pöhualli\" (3×20) and \"on-chicöme\" — i.e., \"on\" + \"chicöme\" (which may be 5×20 + 2 = 102?)\n\nThen \"mahtlactli-on-nähui\" → 1×20 + 4 → 24\n\nThen result is \"näuh-pöhualli-on-cë\" → 4×20 + 1 = 81\n\nNot matching.\n\nWait — perhaps the additives are combined differently.\n\nAlternatively, the form for a number is:\n\n> (α × 20^β) + δ → written as (α-stem) + (δ-stem) with \"on\" between?\n\nBut from (4): mäcuïlli + öme = chicöme → direct addition.\n\nSo it seems that **addition** is written as **A + B = C**, with no explicit \"on\", but only when both are large?\n\nBut in (3), it is written with \"on\" — so structure includes \"on\".\n\nPossibility: The compound is formed as **A-on-B**, meaning A + B?\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui → derived as näuh-pöhualli-on-cë\n\nSo the entire expression is complex.\n\nBut from the guidance:\n\n> 42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\n\nAnd from arithmetic:\n\n42 = 2×20 + 2\n\nSo:\n\n- α = 2 → stem = öm \n- β = 1 → 20¹ = 20 \n- δ = 2 → stem = öme\n\nAnd from equation (4): mäcuïlli + öme = chicöme → seems to be addition of a 20-multiple and a unit\n\nThus, likely the form is **öm-pöhualli-on-öme**\n\nBut why \"pöhualli\"?\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n→ multiplication of 1×20 +1 × 1×20 = 2×20 +1 = 41 → result is mäcuïl-pöhualli-om-mahtlactli\n\nIs that the case?\n\n1×20 +1 = 21 → but 21×20? No.\n\nWait — mahtlactli = 1×20? → so 1×20 on cë → 21?\n\nThen × mahtlactli (21 × 20) = 420?\n\nBut result is mäcuïl-pöhualli-om-mahtlactli — too big.\n\nAlternatively, the multiplication is component-wise.\n\nFrom (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nmahtlactli-om-ëyi = 1×20 + 3 = 23? \n× ëyi = 3 → 23×3 = 69\n\nResult: cem-pöhualli-on-caxtölli-on-nähui — 1×20 + 1 = 21? No.\n\nNot helping.\n\nBut from guidance:\n\n> 42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\n\n> 494 = 1×400 + 4×20 + 10 + 4 → [TARGET ANSWER REDACTED]\n\nNow, 400 = 20² → so β = 2\n\nSo 1 × 400 = 400\n\n4×20 = 80 → total = 480\n\n10+4 = 14 → total = 494\n\nSo components:\n\n- 1 → tzontli \n- 4 → näuh \n- 10 → pöhualli \n- 4 → nähui \n\nWait — what’s the value of each?\n\nFrom guidance:\n\n- 1: cë \n- 2: öme \n- 3: ëyi \n- 4: nähui \n→ δ values\n\nSo remainder components: \n- 10 → ? \n- 10 is not in the list.\n\nBut in equation (15): \ncen-tzontli = 400 → so 400 = tzontli\n\nIn (13): 3×400 + 4×20 + (15+1) = 1296 → 3×400 = 1200, 4×20=80 → 1280, +16 → 1296 → matches.\n\nSo:\n\n- 400 = tzontli \n- 20 = pöhualli → wait, earlier we thought 20 = cem\n\nBut in equation (6): mäcuïlli × ëyi = caxtölli → 5×20 = 100 × 3 → 300 = caxtölli?\n\nNot helpful.\n\nBut from (13): 3×400 + 4×20 + (15+1) = 1296\n\nSo:\n\n- 400 = tzontli \n- 20 = ? → 20 is printed in \"tzontli-on-phhualli\" → possibly \"pöhualli\" = 20\n\nYes — in (15): 1×400 = 400 → so tzontli = 400\n\nIn (14): 1×400 + 1×20 + (10+2) = 432 \n→ 400 + 20 = 420 → +12 → 432\n\nSo:\n\n- 20 = pöhualli \n- 10 = ? → it appears in (14): 10+2 → so 10 is part of remainder\n\nStill, no clear form.\n\nBut from guidance:\n\n> α × 20β + δ \n> with δ ∈ {1,2,3,4} → mapped to cë, öme, ëyi, nähui\n\nBut 10 is not in that set.\n\nWait — in (14): 1×400 + 1×20 + (10+2) → remainder = 12\n\nBut 10+2 = 12 — not 10.\n\nSimilarly, in (13): 3×400 + 4×20 + (15+1) = 1296\n\n15+1 = 16 → 3×400 = 1200, 4×20 = 80 → 1280 → +16 = 1296\n\nSo remainder is 16.\n\nBut 15+1 → 15 is a value? 15 is not in δ.\n\nWait — in the table:\n\n> γ ∈{10,15}, 1 ≤δ ≤4\n\nAnd:\n\n> γ + δ → γ -oM- δ \n\nSo:\n\n- γ = α × 20β \n- δ ≤4\n\nAnd γ + δ → is written as γ -oM- δ\n\nSo for example:\n\n- γ = 10 → 10 + δ → 10 -oM- δ \n- γ = 15 → 15 + δ → 15 -oM- δ\n\nNow, γ = α × 20β\n\nSo 20¹ = 20 → so α=1 → 1×20 = 20 \nα=2 → 40 \nα=3 → 60 \nα=4 → 80 \nα=5 → 100\n\n20² = 400 → α=1 → 400 \nα=2 → 800 \nα=3 → 1200 \nα=4 → 1600 \nα=5 → 2000\n\nSo γ = 10 or 15 → only possible if these values are not multiple of 20 → contradiction.\n\nSo must be that γ = 10 or 15 is not a 20-multiple.\n\nTherefore, perhaps the mapping is not in base-20, or particular values are special.\n\nBut earlier we saw that 42 = 2×20 + 2 → so 40 + 2 = 42\n\nSo we need to write it as:\n\n- α = 2 → 2×20 \n- δ = 2 → 2\n\nSo form: (2-stem) + (2-stem)\n\nFrom (4): mäcuïlli + öme = chicöme → 5×20 + 2 = 102\n\nSo addition: A + B = C → occurs as direct combination.\n\nSo likely, 42 is written as **öm-pöhualli-on-öme**\n\nBecause:\n\n- Each component: \n - 2×20 = öm-pöhualli \n - 2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9204.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "redacted_solution_hint_mask2", + "sample_index": 1, + "output": "We are to write out the Nahuatl expressions for the numbers 42 and 494, based on the provided linguistic rules and examples.\n\n---\n\n### Step 1: Understand the base units and their values\n\nFrom the guidance:\n\n- 1: cë → value 1 \n- 2: öme → value 20 \n- 3: ëyi → value 400 \n- 4: nähui → value 8000 \n\nAlso, the numbers are constructed using combinations of:\n- Multiples of 20: 20, 40, 60, ..., up to 100 (20×5)\n- Multiples of 400: 400, 800, 1200, etc.\n- Multiples of 8000: 8000, etc.\n\nThe structure from the guidance:\n\n- α × 20β, where 1 ≤ α ≤ 5, 1 ≤ β ≤ 3 (β = 1 → 20, β = 2 → 400, β = 3 → 8000)\n- Then, additional values are added as δ (remainder), where δ < 20β\n\nAlso, in the addition rule:\n\n- γ + δ → γ -oM- δ \n- M is determined: \n - if m appears before m, p, or a vowel → m \n - otherwise → n \n\nBut we are not being asked to spell the full morpheme (just write it), only to reconstruct valid Nahuatl expressions.\n\nAlso note:\n\n- The construction is additive: \n total = m × (20^β) + remainder\n\n---\n\n### Step 2: Break down 42\n\nWe are told:\n\n> 42 = 2 × 20 + 2\n\nSo:\n\n- 2 × 20 → 2 × 20 = 40 \n- remainder = 2 → which corresponds to öme? Wait: 2 is labeled as öme (value 20) — but 2 is not 20.\n\nWait — check the values again.\n\nFrom the guidance:\n\n- 1: cë → value 1 \n- 2: öme → value 20 \n- 3: ëyi → value 400 \n- 4: nähui → value 8000 \n\nSo:\n\n- 1 is value 1 \n- 20 is value 20 \n- 400 is value 400 \n- 8000 is value 8000 \n\nNow, 42 = 2×20 + 2 → 40 + 2 → so we need to represent 2.\n\nBut 2 is not a base value.\n\nWait — look at the training examples:\n\nEquation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ suggests multiplication, but perhaps more importantly:\n\nEquation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ suggests addition\n\nEquation (4): \nmäcuïlli + öme = chicöme \n→ mäcuïlli + öme = chicöme → may suggest value of mäcuïlli = 1? or something else?\n\nBut critical point: the values are held in the guidance.\n\nFrom the inputs:\n\n- Values:\n - cë = 1\n - öme = 20\n - ëyi = 400\n - nähui = 8000\n\nBut equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ if it were multiplication, and cë = 1, then we have a unit × something → may suggest cë as 1.\n\nAlso, equation (4): mäcuïlli + öme = chicöme \nSo mäcuïlli + öme = chicöme — perhaps mäcuïlli = 1, öme = 20 → chicöme = 21?\n\nBut not necessarily.\n\nInstead, go to the redacted line:\n\n> (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\nThis tells us that 42 = 2×20 + 2 → 40 + 2\n\nSo we need to express:\n- 2×20 → 2 × öme → \"öme\" repeated twice?\n- Then +2 → which must be a value of 2 → but base units are 1, 20, 400, 8000.\n\nWe have cë = 1 → so 2 = cë + cë\n\nSo 42 = 2 × öme + 2 × cë → (öme + cë) × 2? Or 2×öme + 2×cë?\n\nBut how is addition structured?\n\nFrom equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nThis is addition of terms: A + B = C\n\nSo likely: base units form additive combinations.\n\nAlso, the form is: (X -oM- Y) — meaning X with a morpheme -oM- Y\n\nFrom the guidance: \nγ + δ → γ -oM- δ \nwhere M is m if m is before m, p, or vowel; otherwise n.\n\nBut what are the units?\n\nWe must deduce the morphemes for values:\n\n- 1 → cë\n- 2 → 2×cë? or is 2 a single unit?\n\nBut in the guidance, value 20 is öme → so öme = 20\n\nvalue 1 = cë\n\nSo 2 = cë + cë\n\nSo 42 = 2×20 + 2 = (2×öme) + (2×cë)\n\nNow how is that expressed?\n\nIn Nahuatl, addition is via -oM- (with M as m or n)\n\nFrom equation (4): mäcuïlli + öme = chicöme → suggests a structure: A + B = C\n\nSo likely, the form is: (base) -oM- (base)\n\nSo we write: \nöme + öme → öme-om-öme? or maybe öme-on-öme?\n\nBut look at (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ so it's (A-on-B) + (C-on-D) = (E-on-F)\n\nBut in (1), multiplication is similar.\n\nHowever, in the guidance, we have:\n\n> γ + δ → γ -oM- δ\n\nSo γ and δ are values.\n\nAlso, from (13) and (14): \n(3 × 400 + 4 × 20 + (15 + 1)) = 1296 \n→ so 1200 + 80 + 16 = 1296\n\nSo 400 → value 400 \n20 → value 20 \n1 → cë \n\nSo any number is expressed as: \n(α × 400) + (β × 20) + (γ × 1), where α, β, γ are integers, with constraints.\n\nNow, in the redacted part, it says:\n\n> 42 = 2 × 20 + 2 → 2 × öme + 2 × cë\n\nSo total: 40 + 2\n\nSo the expression should be:\n\n2×öme + 2×cë\n\nBut how is addition formed?\n\nFrom rule: γ + δ → γ -oM- δ\n\nSo likely, we write: \nöme -om- öme -om- cë -om- cë\n\nBut what about the \"m\" or \"n\"?\n\nFrom the rule: \nM = \n- m if m before m, p, or vowel \n- otherwise n\n\nBut what are the units?\n\nWe have:\n- öme → starts with 'ö' → vowel\n- cë → starts with 'c' → consonant\n\nSo in γ + δ → γ -oM- δ\n\nIf γ and δ are units with consonant prefixes or vowels?\n\nTypically, in such systems, if the first component ends with a consonant, and next begins with a vowel, we get -om- or -on-.\n\nBut in (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n→ written as a sum, with “on” connecting.\n\nSo the structure is: A-on-B + C-on-D → A-on-B-on-C-on-D? Or A-on-B-on-C-on-D?\n\nBut the result is on-cë — so ends with -cë.\n\nNote: the first term is yë-pöhualli-on-chicöme \nsecond: mahtlactli-on-nähui \nsum: näuh-pöhualli-on-cë\n\nNo clear morpheme combination.\n\nBut equation (4): \nmäcuïlli + öme = chicöme \n→ suggests that öme is added to mäcuïlli → gives chicöme\n\nSo likely: mäcuïlli -oM- öme = chicöme\n\nNow, what is the morpheme in between?\n\nIt may be -on- or -om-\n\nBut in the guidance: γ + δ → γ -oM- δ\n\nSo the form is γ -oM- δ\n\nAnd M is determined by whether the first unit has a consonant before the second.\n\nBut what do we have for the units?\n\n- cë → c — consonant \n- öme → ö — vowel \n- ëyi → ë — vowel \n- nähui → n — consonant \n\nSo:\n\n- cë (consonant) + öme (vowel) → c - oM - ö → since c is consonant and ö is vowel → would call M = m? \n Rule: “m before m, p, or a vowel” — but the prefix is m? \n The structure is: γ -oM- δ → so the “oM” is inserted.\n\nBut “m” appears before “m, p, or vowel”?\n\nLet's re-read:\n\n> m before m, p, or a vowel\n\nSo if the unit γ starts with a consonant that is m, p, or a vowel? No — the rule says: \n“m” appears — if m is before m, p, or a vowel → m\n\nBut “m” is the morpheme.\n\nThe rule for M is applied when combining two units.\n\nBut only when a consonant precedes a vowel.\n\nLet’s simplify.\n\nFrom the examples and the system, likely:\n\n- When adding two units, we write A -on- B → if A ends with consonant or B starts with vowel → but not clearly.\n\nBut look at equation (4): mäcuïlli + öme = chicöme\n\nNo “on” or “om” in the result — chicöme.\n\nBut we don’t know the derivation.\n\nBut in equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nWe see “on” used.\n\nLikely, addition inserts “on” between the two units — or between their components.\n\nBut in (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe see structure: A-on-B-on-C-on-D\n\nSo likely, the expression is built as:\n\n(α × value) -on- (β × value) -on- ... etc.\n\nValues:\n- cë = 1 \n- öme = 20 \n- ëyi = 400 \n- nähui = 8000\n\nSo 42 = 2×20 + 2×1 = 40 + 2 = 42\n\nSo expression: (2×öme) + (2×cë)\n\nSo: öme + öme + cë + cë → in order\n\nWith the morpheme “on” between.\n\nSo: öme-on-öme-on-cë-on-cë\n\nBut is that correct?\n\nCheck if any rule uses “on” or “om”.\n\nIn equation (3): A-on-B + C-on-D = result → so likely the “on” is used in the addition, between the two terms.\n\nIn equation (4): mäcuïlli + öme = chicöme → so likely a different morpheme — doesn't have “on”.\n\nBut in (3): we have “on” in both terms.\n\nFrom the guidance: γ + δ → γ -oM- δ\n\nSo perhaps the addition uses -oM- with M determined.\n\nBut in (13), 1296 = 3×400 + 4×20 + (15+1) → structured as: \n3×400 + 4×20 + 16 \n→ which is 1200 + 80 + 16 = 1296\n\nAnd written as: 3×400 + 4×20 + (15 + 1) → so 15 and 1 are values.\n\nBut what is 15? 15 = 1×20 + 1×1? No — values are 1,20,400,8000.\n\nBut 15 = 1×20 + 1×15? Not present.\n\nWait — earlier guidance says: \nγ = α × 20^β → and γ + δ → γ -oM- δ\n\nSo the values are additive.\n\nNow for 42:\n\n42 = 2×20 + 2×1 = 2×öme + 2×cë\n\nSo we need to write: \nöme -oM- öme -oM- cë -oM- cë\n\nWith M in each case.\n\nNow determine M.\n\nRule:\n- If m in γ or before a vowel in δ → m \n- Otherwise → n\n\nBut what is “m” in the units?\n\nUnits:\n- cë → starts with c → consonant → not m \n- öme → starts with ö → vowel → so vowel\n\nIn γ -oM- δ:\n\n- γ = öme → starts with vowel → so the base is vowel \n- δ = öme → also vowel \n- So no consonant before vowel → so M = n?\n\nBut rule says: “m before m, p, or a vowel” — this is ambiguous.\n\nBut “m” appears as a letter? Or as a morpheme?\n\nThe rule says: \"m before m, p, or a vowel\" → meaning if the second unit starts with a vowel or m or p, then M = m?\n\nBut γ and δ are units: öme, cë.\n\nöme starts with vowel → so δ starts with vowel → so M = m?\n\nNo — the rule says “m before m, p, or a vowel” → “before” likely means in the word.\n\nSo if γ ends with m, p, or a vowel → then M = m?\n\nOr if γ starts with m, p, or vowel → M = m?\n\nInterpret:\n\nIf the first component has a consonant that is m, p, or a vowel → then M = m \nBut vowel is not consonant.\n\nLikely: if the first component has a consonant and it is m or p, then M = m \nElse, if first ends in consonant that is not m/p → M = n?\n\nBut the units:\n\n- cë → c → consonant, not m or p → so M = n \n- öme → ö → vowel → so not a consonant → so no consonant to check → M = n?\n\nBut the rule says: “m before m, p, or a vowel” → might mean that if the first word ends with a consonant that is m or p or the next begins with vowel → then M = m\n\nBut this is ambiguous.\n\nBut look at the guidance: in (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nWe see “on” — which is likely used when adding units.\n\nAlso, in (4): mäcuïlli + öme = chicöme \n→ no “on”, so perhaps only when units are of certain type?\n\nAnother idea: the morpheme is “on” in all additions, and the “om” in the guidance is a typo or refers to “on”.\n\nBut the problem says “-oM-”, and M is m or n.\n\nBut in (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSo clearly “on” is used.\n\nLikely, in all additions of units, we use “on” between them.\n\nSo for 42 = 2×20 + 2×1 → we have:\n\nöme-on-öme-on-cë-on-cë\n\nBut is that valid?\n\nBut 494 = 1×400 + 4×20 + 10 + 4 → from guidance\n\nWait, guidance says: \n494 = 1×400 + 4×20 + 10 + 4\n\nBut 400 + 80 = 480 +10+4=494 → yes.\n\nNow what is 10?\n\n10 = 1×20 + 1×10 → but 10 not a base value.\n\nBut earlier values: cë =1, öme=20 → so 10 = 0×20 + 10×1 → not directly.\n\nBut in the redacted line: \n494 = 1×400 + 4×20 + 10 + 4\n\nSo 10 and 4 → must be in terms of cë.\n\ncë =1 → so 10×cë, 4×cë\n\nSo 494 = 1×400 + 4×20 + 10×cë + 4×cë", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10571.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "redacted_solution_hint_mask2", + "sample_index": 2, + "output": "We are asked to write out in Nahuatl: 42 and 494.\n\nFrom the guidance:\n\nIn Nahuatl, numbers are built using a base-20 system.\n\nThe breakdown of number components is given as:\n\n- 1: cë \n- 2: öme \n- 3: ëyi \n- 4: nähui \n\nAlso:\n\n- 20β: pöhualli for β=1; 400 (20²) for β=2; 8000 (20³) for β=3 \n- α × 20β: represented as α followed by 20β \n- γ + δ: γ -oM- δ \n- M (modifier): if m comes before m, p, or a vowel → m; otherwise → n \n\nThe number 42:\n\nWe break 42 into base-20:\n\n42 = 2 × 20 + 2 \n→ 2 × 20 + 2 → \"2\" (öme) + \"2\" (öme) → but need the structure with \"on\"\n\nFrom the examples:\n\n- mahtlactli-on-cë: 20×1 + 1 → \"mahtlactli-on-cë\" \n- mahtlactli × öme = mäcuïl-pöhualli-om-mahtlactli → shows multiplication, but we are looking at addition.\n\nBut rule from guidance:\n\nγ + δ → γ -oM- δ\n\nAlso, in example (3):\n\nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n→ suggests additive structure: A-on-B + C-on-D = result\n\nSo in general: (α × 20β) + δ → (α × 20β) -oM- δ\n\nAnd the \"M\" determines the form: m before m, p, vowel → m; otherwise → n\n\nBut we are only doing 42 = 2×20 + 2\n\nSo:\n\n2 × 20 = 40 → represented as \"mahtlactli\" for 20? Wait: in (1): mahtlactli-on-cë → 20×1 + 1\n\nIn (4): mäcuïlli + öme = chicöme → multiplication\n\nBut observation: in example (2): cem-pöhualli × öme = öm-pöhualli → multiplication\n\nBut we are building additively.\n\nFrom guidance:\n\n42 = 2 × 20 + 2 → this is exactly 2×20 + 2\n\nSo the form is: (2 × 20) + 2 → should be written as: \"öme\" (for 2) + \"on\" + \"öme\" (for 2)? Or with \"on\"?\n\nWe see that 2×20 + 2 → in Nahuatl: forms like \"mahtlactli-on-cë\" → 20×1 + 1\n\nSimilarly, 3×20 + 4 → would be \"ëyi-on-nähui\" or something?\n\nBut look at (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo additive: (yë-pöhualli-on-chicöme) + (mahtlactli-on-nähui) = näuh-pöhualli-on-cë\n\n→ So base-20 units: pöhualli = 20 → yë-pöhualli → 1×20 + 1 → yë = 1, so 1×20 + 1 → yë-pöhualli\n\n→ So the number α×20 + β is written as α + \"pöhualli\" (or similar) + β?\n\nBut pöhualli is 20 → so in (3):\n\n\"yë-pöhualli-on-chicöme\" → so yë (1) ×20 + chicöme? But chicöme is from (4): mäcuïlli + öme = chicöme → 1×20 + 1?\n\nWait — need to find what 1×20 + 1 is.\n\nIn (1): mahtlactli-on-cë → 20×1 + 1 → cë = 1\n\nSo 20×1 + 1 = mahtlactli-on-cë\n\nSimilarly, 20×2 + 1 → should be \"mahtlactli-on-cë\" → but with α=2?\n\nFrom (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui → multiplication\n\nBut in (4): mäcuïlli + öme = chicöme → multiplication\n\nBut look at (6): mäcuïlli × ëyi = caxtölli → multiplication\n\nNo additive examples with 2×20.\n\nBut (1): mahtlactli-on-cë = 20×1 + 1 → written as \"mahtlactli-on-cë\"\n\nSo general form: (α × 20) + β → α × 20 is written as α “pöhualli”? But pöhualli is 20.\n\nIn (2): cem-pöhualli × öme = öm-pöhualli → shows cem = 3, pöhualli = 20, so cem-pöhualli = 3×20 + 0? But then multiplied by öme.\n\nBut in (1): mahtlactli-on-cë → 20×1 + 1 → so \"mahtlactli\" = 20, \"on\" + \"cë\" = +1\n\nSo likely: α × 20 + β → α + pöhualli + on + β\n\nBut α is written with the numeral for α.\n\nFrom the list:\n\n1: cë \n2: öme \n3: ëyi \n4: nähui \n\nSo:\n\n- 1×20 + 1 = mahtlactli-on-cë \n- 2×20 + 2 → α=2, β=2 → should be \"öme-pöhualli-on-öme\"? \n\nBut in (3): yë-pöhualli-on-chicöme → so it's structured as α + pöhualli + on + β\n\nSo 2×20 + 2 → öme-pöhualli-on-öme\n\nHowever, we need to check the \"M\" rule.\n\nRule: m before m, p, or vowel → use m, otherwise n\n\nSo in \"öme-pöhualli-on-öme\", the syllables:\n\n- öme → m? \"öme\" has m? No — \"öme\" ends with \"e\", so \"m\" is at start — \"ö\" is vowel, so m not before vowel? → m conditional.\n\n\"m\" appears in \"mahtlactli\" — mahtlactli starts with \"ma\", so \"m\" before \"a\" → vowel? a is vowel → so m before vowel → use m.\n\n\"öme\" has no \"m\" — it starts with \"ö\" → vowel → so no m.\n\nBut the rule says: \"m before m, p, or a vowel\" → so only for syllables that start with m?\n\nThe rule is about applying \"M\" as a modifier in the additive form: γ -oM- δ\n\nSo when adding γ + δ, you write γ -oM- δ\n\nAnd the \"M\" is determined by whether the initial of γ or δ has m before m, p, or vowel?\n\nNo — the rule is:\n\nM = \n- m if m comes before m, p, or a vowel; \n- n otherwise.\n\nSo in the example of 2×20 + 2 → γ = 40 = 2×20 → what is its form?\n\nIn (1): 1×20 + 1 → mahtlactli-on-cë\n\n→ so 1×20 = mahtlactli\n\nSo 2×20 = ? → likely mahtlactli-pöhualli? But no such example.\n\nBut (2): cem-pöhualli × öme = öm-pöhualli → shows that multiplication is involved.\n\nWe have an additive rule in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo:\n\nFirst term: yë-pöhualli-on-chicöme → yë = 1 → 1×20 + chicöme? But chicöme = mäcuïlli + öme = 1×20 + 1 = 21?\n\nBut 1×20 + 1 = 21 → how is it represented?\n\nFrom (1): 1×20 + 1 = mahtlactli-on-cë\n\nSo chicöme? Not equal.\n\nWait — in (4): mäcuïlli + öme = chicöme → so multiplication?\n\nBut in (3), it's addition.\n\nSo the only additive constructions are in (3) and (1) and (2) are multiplicative.\n\nBut (3) has two addends: one with pöhualli, one with nähui?\n\n\"mahtlactli-on-nähui\" → 1×20 + 4 → nähui = 4 → so 20 + 4 = 24\n\nAnd \"yë-pöhualli-on-chicöme\" → yë = 1 → 20 + something\n\n\"chicöme\" — from (4): mäcuïlli + öme = chicöme → so 20×1 + 1 = 21?\n\nSo \"yë-pöhualli-on-chicöme\" = 1×20 + (21) = 41?\n\nThen add to 24 → 41 + 24 = 65?\n\nBut result is \"näuh-pöhualli-on-cë\" → 4×20 + 1 = 81?\n\nNo.\n\nMistake.\n\nSo perhaps \"pöhualli\" is not 20.\n\nFrom the guidance:\n\n• α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: \n1: ceM (cë?) — likely typo — it's \"cë\" \n2: öm (öme) \n3: yë \n4: näuh \n5: mäcuïl \n\nAnd then:\n\n20β: \nβ=1 → 20 \nβ=2 → 400 \nβ=3 → 8000\n\nSo in (1): mahtlactli-on-cë = 20×1 + 1 → so mahtlactli = 20\n\nSimilarly, in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n\"yë-pöhualli-on-chicöme\" → yë = 1 → 1×20 + chicöme \n\"mahtlactli-on-nähui\" → 1×20 + 4 \nSum → 2×20 + (chicöme + 4)\n\nBut result: näuh-pöhualli-on-cë → 4×20 + 1 = 81\n\nSo 40 + 1 = 81 → so 2×20 + (chicöme + 4) = 81 → 40 + (chicöme + 4) = 81 → chicöme = 37\n\nBut from (4): mäcuïlli + öme = chicöme → so multiplication?\n\nWait — (4): mäcuïlli + öme = chicöme\n\nSo \"mäcuïlli\" and \"öme\" — are they numbers?\n\nFrom guidance: \n\"γ ∈{10,15}, 1 ≤δ ≤4\" \nγ + δ → γ -oM- δ\n\nγ = α×20β, 1 ≤δ < 20β\n\nBut γ=10,15 → 10=5×20, 15=3×5? Not clear.\n\nWait: 10 and 15 — what is 10?\n\n20×1 = 20 → so 10 is not 20.\n\nWait — may be the values are not base 20.\n\nBut (13): 1296 = 3×400 + 4×20 + (15 + 1) → 1200 + 80 + 16 = 1296 → 3×400 = 1200 → 400 = 20² → so 20β with β=2 → 400\n\nSimilarly, 400 = 20² → so 20β, β=2 → 400\n\nβ=3 → 8000\n\n3×400 = 1200 → 1296 - 1200 = 96 → 4×20 = 80, 15+1=16 → 80+16=96 → yes.\n\nSo 42 = 2×20 + 2\n\nWe need the form.\n\nFrom the guidance: 42 = 2×20 + 2 → [TARGET ANSWER REDACTED]\n\nSimilarly, 494 = 1×400 + 4×20 + 10 + 4 → 400 + 80 + 14 = 494\n\nSo base-20 with 400 = 20² → β=2, so 20²\n\nSo general form:\n\nα × 20β + δ → (α × 20β) -oM- δ\n\nAnd δ is a small number, 1–19.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nHere:\n\n- yë-pöhualli-on-chicöme → 1×20 + x \n- mahtlactli-on-nähui → 1×20 + 4 \n- Sum → 2×20 + (x + 4) \n- Result: näuh-pöhualli-on-cë → 4×20 + 1\n\nSo 2×20 + (x+4) = 80 + 1 = 81 → x+4 = 41 → x = 37\n\nBut from (4): mäcuïlli + öme = chicöme → so multiplication → 1×20 + 1 = 21? Not 37.\n\nSo the additive part is not simply α×20 + β.\n\nAnother possibility: the additive structure is with \"on\" for addition.\n\nIn the form: (α × 20β) + δ → written as (α's name) + (20β) + on + (δ)\n\nFor δ=1: cë \nδ=2: öme \nδ=3: ëyi \nδ=4: nähui\n\nIn (1): mahtlactli-on-cë = 1×20 + 1 → so \"mahtlactli\" = 20 → so α = 1 → \"mahtlactli\" is for 20\n\nSo:\n\nα×20β → written as (α's numeral) + (20β)\n\nBut 20β is represented by a word:\n\nβ=1: pöhualli \nβ=2: 400 → but not a word — pöhualli is 20 \nβ=3: 8000 → not named\n\nBut in (3): yë-pöhualli-on-chicöme — so \"pöhualli\" is used for 20\n\nSo likely:\n\n- 20^0 = 1 → numbers 1–19 → cë, öme, ëyi, nähui \n- 20^1 = 20 → pöhualli \n- 20^2 = 400 → ? \n- 20^3 = 8000 → ?\n\nIn (13): 1296 = 3×400 + 4×20 + (15+1) → 3×400 = 1200 → 4×20 = 80 → 15+1=16 → total 1296\n\nAnd (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSo \"yë\" = 1 → at start, so 1×20? But 1×20 = 20 → not 1296.\n\nWait — the value 1296 is composed of 3×400 + 4×20 + 16\n\nSo likely β=2 for 400\n\nSo the base-20 digits are:\n\n- 400: 400 = 20² \n- 20: 20^1 \n- 1: 1\n\nSo the number is written as:\n\nα × 400 + β × 20 + γ → written as α (name) + pöhualli + on + β (name) + on + γ (name)\n\nBut with M rule for combining the units.\n\nFor 42 = 2×20 + 2 → so α = 2, β = 20, γ = 2\n\nSo form: \"öme\" + \"pöhualli\" + \"on\" + \"öme\"\n\nBut the M rule: if m comes before m, p, or a vowel → use m, else n\n\nCheck the syllables:\n\n\"öme\" → starts with \"ö\" — vowel → so \"m\" not before vowel → no m \n\"pöhualli\" → starts with \"p\" — p is in \"m, p, or vowel\" — so \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8706.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "redacted_solution_hint_mask2", + "sample_index": 3, + "output": "We are given a system of equations in two languages — Nahuatl and Arammba — and are to solve part (b): write 42 and 494 in Nahuatl.\n\nWe are also given a guidance table that maps numerical values to linguistic components in Nahuatl, using a positional system based on powers of 20 and 400, 8000, etc.\n\nFrom the guidance:\n\nIn Nahuatl:\n- 1: cë\n- 2: öme\n- 3: ëyi\n- 4: nähui\n- 5: mäcuïlli\n- 10: chicöme\n- 20β: pöhualli for β=1, 20; 400: tzontli; 8000: xiquipilli\n- α × 20β: written as α × 20β\n- γ + δ: γ -oM- δ\n- M = m if before m, p, or a vowel; otherwise n\n\nWe are told that:\n- Values are built from components corresponding to powers of 20:\n - 1 = cë\n - 20 = pöhualli\n - 400 = tzontli\n - 8000 = xiquipilli\n- Also, 20 × 20 = 400 → tzontli\n- 20 × 400 = 8000 → xiquipilli\n\nWe see the pattern from example (13):\n- 1296 = 3 × 400 + 4 × 20 + (15 + 1) → 3 tzontli, 4 pöhualli, 16 (15+1) → so 15+1 is probably a compound.\n\nBut 1296 = 6⁴ → and in Arammba, 6⁴ = ndamno \nSimilarly, 6³ = 216 = tarumba, 6² = 36 = fete\n\nSo the numbers are being constructed from combinations of:\n- tzontli = 400\n- pöhualli = 20\n- xiquipilli = 8000\n- cë, öme, etc. → units of 1\n\nBut the key is the representation in the equations.\n\nLook at the pattern from (13): \n\"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\" \nThis is 1296 = 3×400 + 4×20 + (15 + 1)\n\nWait — 15 is a multiple of 3×5? 15 = 3×5? But 5 corresponds to mäcuïlli.\n\nBut 15 is not directly a base unit.\n\nAlternative: use the given mapping:\n\nFrom guidance:\n- α × 20β → built as α × 20β\n- γ + δ → γ -oM- δ\n- γ = α × 20β, 1 ≤ δ < 20β; so for δ < 20β\n\nAlso, M = m if before m, p, or vowel; otherwise n.\n\nNow consider target 42:\n\nBreak 42 into base 20:\n\n- 42 = 2 × 20 + 2\n- So α = 2, β = 1 → 2 × 20 = 40, remainder 2\n\nFrom guidance:\n- 2 × 20 = 2 × pöhualli = \"pöhualli\" with multiplier\n- But how is “2 × 20” written?\n\nFrom equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nNot clearly helpful.\n\nBut from the guidance: \n\"42 = 2 × 20 + 2 → [TARGET ANSWER REDACTED]\" \nSo we need to write 2×20 + 2 in Nahuatl.\n\nWe have:\n- 20 → pöhualli\n- So 2 × 20 → \"mäcuïlli-pöhualli\"? \nWait — from (4): mäcuïlli + öme = chicöme → suggests mäcuïlli is 1×20 → mäcuïlli = 20?\n\nYes: from (4): mäcuïlli + öme = chicöme → if mäcuïlli is 20, then 20 + 2 = 22 ≠ 20 → not quite.\n\nWait: (4): mäcuïlli + öme = chicöme → suggests mäcuïlli = 20 → because öme = 2? \nBut earlier: 1 = cë; 2 = öme\n\nSo maybe:\n- 1 = cë\n- 2 = öme\n- 20 = pöhualli\n- 400 = tzontli\n\nSo 20 = pöhualli → 2 × 20 = two pöhualli → pöhualli-on-pöhualli?\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ Perhaps multiplication. mahtlactli × mahtlactli → mäcuïl-pöhualli-om-mahtlactli\n\nBut 20×20 = 400 → which should be tzontli.\n\nAlso (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n→ suggesting multiplication influences form\n\nBut from (6): mäcuïlli × ëyi = caxtölli → suggests mäcuïlli × ëyi = caxtölli \nIf ëyi = 3, then 3 × mäcuïlli = caxtölli → mäcuïlli = 3? Not matching.\n\nWait — perhaps the components are units, and multiplication is a form of addition.\n\nBut guidance says: \nγ + δ → γ -oM- δ \nwith M = m if before m, p, or vowel; else n.\n\nSo addition is written with -oM- \nif γ and δ are equal, maybe it’s just repeated.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSo addition: left + right → compound with -on- and then -oM-?\n\n\"yë-pöhualli-on-chicöme\" + \"mahtlactli-on-nähui\" → \"näuh-pöhualli-on-cë\"\n\nNot clearly additive.\n\nBut look at (13): \n\"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\" \nWhich is 1296 = 3×400 + 4×20 + (15+1)\n\nSo 3 tzontli (3×400), 4 pöhualli (4×20), and (15+1) = 16?\n\nWait — 15 is 3×5? 5 is mäcuïlli → mäcuïlli = 5?\n\nFrom (4): mäcuïlli + öme = chicöme \nSo if mäcuïlli = 5, öme = 2 → 5+2 = 7 → but chicöme is not 7.\n\nBut in (3): yë-pöhualli-on-chicöme → if chicöme = 15?\n\nWait — 15 = 3×5 → may be 3×mäcuïlli?\n\nWait: \"mäcuïlli\" might be 5 → 1×5 = 5\n\n(4): mäcuïlli + öme = chicöme → 5 + 2 = 7 → not 15\n\nSo not matching.\n\nWait — equation (13) has \"15 + 1\" → 16\n\nBut 15 and 1 → 15 could be 3×5 → 3 mäcuïlli?\n\nBut 3×5 = 15\n\nSo maybe mäcuïlli = 5\n\nThen 3×mäcuïlli = 15\n\nThen (15 + 1) = 16 → written as \"mäcuïlli-on-cë\" with 3 copies?\n\nWait — in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ suggests mahtlactli × mahtlactli → mäcuïl-pöhualli-om-mahtlactli → but product is 400 → 20×20\n\nBut 20×20 = 400 = tzontli → 400\n\nSo if 20×20 → tzontli → so 400 = tzontli\n\nSo the units:\n- 1 = cë\n- 2 = öme\n- 20 = pöhualli\n- 400 = tzontli\n- 8000 = xiquipilli\n\nSo 42 = 2×20 + 2 → 2 pöhualli and 2 units\n\nSo 2×20 → written as \"pöhualli-on-pöhualli\" or something?\n\nBut how?\n\nIn (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nBut also (6): mäcuïlli × ëyi = caxtölli → if ëyi = 3, then mäcuïlli × 3 = caxtölli → so mäcuïlli = 3?\n\nBut from (4): mäcuïlli + öme = chicöme → 3 + 2 = 5 → not matching.\n\nWait — maybe mäcuïlli = 5, and ëyi = 3 → 5×3 = 15 → caxtölli?\n\ncaxtölli might be 15?\n\nThen 2×20 = 40\n\nSo 42 = 40 + 2 → 40 = 2×20, 2 = öme\n\nSo 2×20 → written as \"pöhualli-on-pöhualli\" \nAddition → \"pöhualli-on-pöhualli-on-öme\"\n\nBut is there a pattern of \"a-on-b\" for addition?\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nLeft: yë-pöhualli-on-chicöme \nRight: mahtlactli-on-nähui \nResult: näuh-pöhualli-on-cë\n\nNot obviously additive.\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ maybe × means something like addition of units?\n\nBut multiplication of 1×1 → gives something base.\n\nBut 1×1 = 1 → cë?\n\nBut result is mäcuïl-pöhualli-om-mahtlactli — not 1.\n\nSo not.\n\nAnother idea: the numbers are built with:\n- tzontli = 400\n- pöhualli = 20\n- units = 1 (cë, öme, etc.)\n\nAnd any value between 1 and 199 (or so) is written as:\n- α × 20 + β → α pöhualli + β\n\nWith β written as a unit.\n\nSo 42 = 2 × 20 + 2 → 2 pöhualli + 2\n\nSo written as \"pöhualli-on-pöhualli-on-öme\" ?\n\nBut how are the multiples formed?\n\nIn (8): ngámbi + asàr → tambaroy → additive, but not clear form.\n\nIn Nahuatl, the form for \"a + b\" seems to be: a-on-b, and the connector \"on\" may indicate addition.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui → näuh-pöhualli-on-cë\n\nSo a + b = result → so left and right are connected with on?\n\nBut it becomes näuh-pöhualli-on-cë → which is simpler.\n\nSo not preserved.\n\nBut in (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \nThis is 432 → 1×400 + 1×20 + (10+2)\n\nSo 432 = 1×400 + 1×20 + 12 → which is 1 tzontli + 1 pöhualli + 12?\n\nBut 12 = 2×6? 6 not present.\n\nBut in guidance: for γ + δ → γ -oM- δ\n\nFor 2×20 + 2 → 2 pöhualli + 2 → written as (2 pöhualli) -oM- (2)\n\nNow, what is the form of the unit 2?\n\n2 = öme\n\nSo 2×20 = 40 → written as \"pöhualli-on-pöhualli\"?\n\nBut multiplication in Nahuatl might be symmetric.\n\nIn (6): mäcuïlli × ëyi = caxtölli → so multiplication gives a new unit.\n\nBut for addition, we have \"a-on-b\"\n\nIn (1): mahtlactli-on-cë × mahtlactli → produces a compound.\n\nBut in guidance, it says: \nγ + δ → γ -oM- δ\n\nSo addition = γ -oM- δ\n\nWith M = m if before m, p, or vowel; else n.\n\nSo we need to write 2×20 + 2 = 42 → as (2×20) -oM- 2\n\n2×20 → how to write?\n\n\"2 × 20\" → if 20 is pöhualli, then 2×20 = 2 pöhualli → written as \"pöhualli-on-pöhualli\"?\n\nBut how to form 2 pöhualli?\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nThis is 1×1 = 1 → not matching.\n\nWait — perhaps multiplication of a × b gives a + b?\n\nNo.\n\nAlternative: the base units are:\n- 1 = cë\n- 2 = öme\n- 20 = pöhualli\n\nSo 42 = 2×20 + 2 → written as \"pöhualli-on-pöhualli-on-öme\"\n\nBut we need to check the M rule.\n\nFor \"a-on-b\", if b is a vowel or p or m, then M = m; else n.\n\nöme → has 'e' (vowel), so if \"öme\" is after, and before a consonant, then M = m?\n\nBut in (13): \n\"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\"\n\nThe structure is: yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\n\nSo it's a chain: A-on-B-on-C-on-D\n\nSo likely, for numbers, it's multiple components linked by \"on\".\n\nEach component is a digit in a base-20 system.\n\nSo 42 = 2×20 + 2 → so:\n- 2 in 20s place → 2 × pöhualli\n- 2 in units → 2 × cë or öme?\n\nBut in (4): mäcuïlli + öme = chicöme → if öme = 2, then 2 units → öme\n\nSo units = öme for 2\n\nThus 42 = pöhualli-on-pöhualli-on-öme\n\nBut is this written with \"on\" between?\n\nYes.\n\nNow, is the multiplier formed by repetition?\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nIf mahtlactli = 1, then 1×1 = 1 → but result is not cë.\n\nBut 1×1 → mäcuïl-pöhualli-om-mahtlactli → 400 → tzontli?\n\nNo.\n\nWait — (4): mäcuïlli + öme = chicöme → so 5+2 = 7 → chicöme?\n\nBut in (13): 3×400 + 4×20 + (15+1) = 1296\n\n1296 = 1296 → in base 6: 6⁴ = 1296\n\nAnd in arammba, 6⁴ = ndamno, 6³ = tarumba, 6² = fete, 6¹ = asàr\n\nSo size of numbers in arammba is based on 6.\n\nIn Nahuatl, it's base 20.\n\nSo decomposition of 42:\n\n42 ÷ 20 = 2 R2\n\nSo 2 in 20s, 2 in units.\n\nNow, 20s: 2 × 20 → written as \"pöhualli-on-pöhualli\"\n\nUnits: 2 → \"öme\"\n\nSo full: \"pöhualli-on-pöhualli-on-öme\"\n\nBut is this correct?\n\nBut in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9147.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: [TARGET ANSWER REDACTED];\n\n • 494 = 1×400+4×20+10+4: [TARGET ANSWER REDACTED]\n\n (c) • 43 = 36 + 6 + 1: fete nimbo ngámbi;\n\n • 569 = 2×216+3×36+4×6+5: yànparo tarumba yenówe fete asàr tàxwo tambaroy.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "redacted_solution_hint_mask2", + "sample_index": 0, + "output": "We are given a system of equations in Nahuatl and Arammba, and we need to decode how numbers are represented in Arammba, specifically for 43 and 569.\n\nFrom the guidance, we observe:\n\nIn Arammba:\n- Powers of 6 are:\n - 6² = 36 → fete\n - 6³ = 216 → tarumba\n - 6⁴ = 1296 → ndamno\n - 6⁵ = 7776 → weremeke\n\n- A number of the form α × 6β is represented as α × 6β.\n- A number of the form α × 6β + δ, where 0 < δ < 6β, is represented as α × 6β δ.\n\nWe are to write 43 and 569 in Arammba using this system.\n\n---\n\n**Step 1: Represent 43**\n\nWe know:\n6² = 36 \n6³ = 216 → too big\n\nSo consider 43 = 36 + 6 + 1\n\nBreak down:\n- 36 → fete\n- 6 → ? (from earlier, 6 = 6¹ → 6)\n\nBut what is the unit for 6?\n\nGuidance says: α × 6, 2 ≤ α ≤ 5 → α tàxwo\n\n→ When α = 1? Not covered in \"2 ≤ α ≤ 5\"\n\nBut in the equations:\n\n- Equation (7): ngámbi + ngámbi = ngámbi × yànparo → suggests multiplication\n- Equation (8): ngámbi + asàr = tambaroy\n- (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nAlso, 6² = 36 → fete \n6¹ = 6 → is this \"6\" a separate unit?\n\nLook at equation (11): nimbo × fete = tarumba → tarumba = 216, so fete = 36\n\nThen equation (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ implies that 6 is tied to \"tàxwo\"\n\nFrom guidance: α × 6, 2 ≤ α ≤ 5 → α tàxwo\n\nSo 2 tàxwo = 12 \n3 tàxwo = 18 \n4 tàxwo = 24 \n5 tàxwo = 30\n\nSo these are multiples of 6 (α×6).\n\nBut what about 6 itself? Is there a unit for 1×6?\n\nNo such entry, but we see that δ < 6β is used in addition.\n\nIn general, α × 6β + δ → α × 6β δ\n\nSo 43 = 36 + 6 + 1\n\nWe have:\n- 36 = fete\n- 6 = 1 × 6 → we may denote as 1×6, but if \"6\" is 1×6, then we need to know how to write that.\n\nBut look at equation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\n→ 6² = 36 → fete\n\nSo forms like \"fete\" are for 6² = 36\n\nThus, 6 is the base.\n\nNow, 43 = 36 + 6 + 1\n\nWe write:\n- 36 → fete\n- 6 → from α × 6β, β=1, α=1 → 1×6 → what unit?\n\nBut in the system, only α ≥2 has α tàxwo, so 1×6 is not explicitly given.\n\nBut in the addition rule: α × 6β + δ with 0 < δ < 6β → represents α × 6β δ\n\nSo 36 + 6 + 1 = 36 + (6 + 1) = 36 + 7 → which is 36 + 6 + 1\n\nSo: 36 + 6 is 42, then +1 → 43\n\nSo 43 = 36 + 6 + 1\n\nBut how is 6 written?\n\nWe see in guidance: 6² = 36 → fete\n\nAnd 6¹ = 6 → seems to be \"6\" as a unit, but not labeled.\n\nWe see in equation (8): ngámbi + asàr = tambaroy → 1+1=2? Not matching.\n\nBut in list: α × 6β, 2 ≤ α ≤ 5 → α tàxwo\n\nSo 2 tàxwo = 12, etc.\n\nBut for α = 1, we need to build via addition.\n\nSo perhaps 6 is not a standalone word; instead, we must represent numbers using base 6, with digits.\n\nSo 43 in base 6:\n\nDivide 43 by 6:\n\n43 ÷ 6 = 7 remainder 1 \n7 ÷ 6 = 1 remainder 1 \n1 ÷ 6 = 0 remainder 1\n\nSo 43 = 1×6² + 1×6¹ + 1×6⁰ → 1,1,1 → 111 in base 6\n\nSo:\n- 6² → fete\n- 6¹ → ?\n- 6⁰ → ?\n\nBut 6² = 36 → fete \n6¹ = 6 → not labeled \n6⁰ = 1 → not labeled\n\nWait — guidance says:\n\n6² = 36 → fete \n6³ = 216 → tarumba \n6⁴ = 1296 → ndamno \n6⁵ = 7776 → weremeke\n\nSo powers:\n\n- 6¹ = 6 — not represented directly, but must be in terms of \"6\"\n\nNow possible that the digits are:\n- 6¹ is not a base unit, but embedded in \"α tàxwo\" for α≥2\n\nBut in equation (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\n→ 20 + 36 = 56? → 20×6 = 120, 36 = 36 → 156? Not matching.\n\nWait — the guidance has numbers:\n\nFor (9): 3×20 + (5+2) → 60 + 7 = 67 → 3×20 + 7 → but 20 is not 6.\n\nWait — another idea: perhaps the indexing is based on a different system.\n\nLook at the given equations in guidance for (13) to (16):\n\n(13): 1296 = 3×400 + 4×20 + (15+1) → 3×400 = 1200, 4×20=80, 16 → total 1296 \n(14): 432 = 1×400 + 1×20 + (10+2) → 400+20+12=432 \n(15): 400 = 1×400 → 400 \n(16): 8000 = 1×8000 → 8000\n\nSo units are:\n- 400 → tzontli \n- 20 → 20? \n- 10 → 10? \n- 15 → 15?\n\nAnd from (13): \n3×400 + 4×20 + (15+1) = 1296 → 1200 + 80 + 16 = 1296\n\nAlso, 6³ = 216 → tarumba → so 216 is tarumba\n\nBut 1296 = 6⁴ → ndamno → so 1296 → ndamno\n\nNow, 43: from guidance: 36 + 6 + 1\n\nWe know:\n- 36 = fete\n- 6 = ?\n- 1 = ?\n\nWe can try to find what 6 corresponds to.\n\nIn Arammba, numbers are built using:\n\n- α × 6β → written as α × 6β\n- α × 6β + δ, with 0 < δ < 6β → written as α × 6β δ\n\nSo 43 = 36 + 6 + 1 = 36 + 7\n\nNow 36 + 7 = 36 + 6 + 1\n\nSince 6 < 36, we can write:\n\n→ fete + 6 + 1\n\nBut what is the word for 6 and 1?\n\nBut in the system, the form α × 6β with α ≥2 is given as α tàxwo\n\nSo α=2,3,4,5 → 2,3,4,5 tàxwo\n\nSo:\n- 2 tàxwo = 12\n- 3 tàxwo = 18\n- 4 tàxwo = 24\n- 5 tàxwo = 30\n\nSo 6 is not a multiple of 6 with α≥2.\n\nBut 6 = 1×6 → not represented as α tàxwo, since α=1 not in range.\n\nSo must represent \"1×6\" via addition or digit.\n\nSo we suppose that 1×6 is just \"6\", and 1×6⁰ = \"1\"\n\nBut what are the values?\n\nWe have:\n\n- 6² = 36 → fete\n- 6¹ = 6 → we need a unit for that\n- 6⁰ = 1\n\nBut no unit named.\n\nBut in guidance, they write: \n43 = 36 + 6 + 1 → so likely: fete + 6 + 1\n\nNow, what is the unit for 6? Note that in the list:\n\n\"α × 6, 2 ≤ α ≤ 5: α tàxwo\"\n\n→ so 2,3,4,5 are in unit \"tàxwo\"\n\nBut 1×6 is not given.\n\nSo perhaps in the expression α × 6β δ, when α=1, β=1, δ = 1, it is written as 1×6 1\n\nBut we need to know what 6 is.\n\nAlternatively, use base 6 representation.\n\nWe already did: 43 = 1×36 + 1×6 + 1×1 → 1,1,1 in base 6\n\nNow, if:\n- 6² → fete\n- 6¹ → ? → we denote as \"6\" → but is there a word?\n\nBut in the list, we see:\n- 6² = 36 → fete\n- 6³ = 216 → tarumba\n- etc.\n\nNow in the addition rule: α × 6β + δ → α × 6β δ\n\nSo for example, 1×36 + 1 = 37 → 36 + 1 → written as 36 1\n\nSimilarly, 1×36 + 6 = 42 → 36 + 6 → written as 36 6\n\nSo the digit components are:\n- For each position, the value is added as a separate term\n\nSo we have:\n\n- 36 → fete\n- 6 → ? → we must find a unit\n\nBut from the list, only units are:\n- fete (36)\n- tarumba (216)\n- ndamno (1296)\n- weremeke (7776)\n\nSo the digits must be formed from the building blocks.\n\nNotice that 6 = 1×6 → not listed, but 6 is a base unit.\n\nIn the equations:\n\nEquation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\n→ let’s interpret:\n\nLeft: (yenówe) × (yenówe tàxwo)\n\nyenówe is a number. If we assume yenówe is 6, then:\n\n6 × (6 tàxwo) = 6 × 12 = 72 → right: fete yenówe tàxwo = 36 + 6 tàxwo = 36 + 12 = 48 → no\n\nWait: 6 × 12 = 72 ≠ 48\n\nFalse.\n\nEquation (8): ngámbi + asàr = tambaroy → not helpful\n\nEquation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nSuppose: nimbo = 6, yànparo = 2 → yànparo tàxwo = 2×6 = 12 → nimbo + yànparo tàxwo = 6 + 12 = 18\n\nRight: yenówe tàxwo = 3×6 = 18 → yes\n\nSo if nimbo = 6, then:\n\nnimbo = 6 \nyànparo = 2? Then 2 tàxwo = 12 → 6 + 12 = 18 = 3 tàxwo → yenówe = 3\n\nSo yenówe = 3 → so 3 = 3\n\nBut then yenówe = 3 → not 6.\n\nBut in the expression \"yenówe tàxwo\" → 3×6 = 18\n\nSo yenówe = 3\n\nSimilarly, in equation (10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nLeft: 3 × (3×6) = 3×18 = 54\n\nRight: fete yenówe tàxwo = 36 + 3×6 = 36 + 18 = 54 → matches\n\nSo: yenówe = 3\n\nSo the number \"3\" is yenówe\n\nSimilarly, nimbo = 6 (from above)\n\nIn equation (12): nimbo + yànparo tàxwo = yenówe tàxwo → 6 + (2×6) = 18 = 3×6 → true\n\nSo nimbo = 6\n\nSo unit for 6 is nimbo\n\nNow, what about 1?\n\n6⁰ = 1 → is there a unit?\n\nWe have:\n- ngámbi → 1?\n\nBut in equation (7): ngámbi + ngámbi = ngámbi × yànparo\n\nIf ngámbi = 1 → 1+1 = 2 → right: 1 × yànparo → 1×yànparo = 2 → so yànparo = 2\n\nCheck equation (8): ngámbi + asàr = tambaroy\n\n1 + a = b → must be something\n\nBut if asàr = 1, then 1+1=2 → tambaroy = 2 → but not known\n\nBut from (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have: 6 + (2×6) = 18 → 3×6 → holds\n\nSo yànparo = 2\n\nNow, is there a unit for 1?\n\nPossibly, the base digits are:\n- 1 → ?\n- 2 → yànparo\n- 3 → yenówe\n- 4 → ?\n- 5 → ?\n- 6 → nimbo\n\nBut we need 1.\n\nIn addition: α × 6β + δ → α × 6β δ\n\nFor δ=1, we write \"1\"\n\nSo 1 is a unit.\n\nFrom the list, what units are available?\n\nWe have:\n- fete → 36\n- tarumba → 216\n- ndamno → 1296\n- weremeke → 7776\n\nAnd from the construction:\n- α tàxwo → for α=2,3,4,5 → α×6 → so 12,18,24,30 → these are \"2 tàxwo\", \"3 tàxwo\", etc.\n\nAnd addition: α × 6β δ → so for example, 1×36 + 1 → \"36 1\"\n\nNow back to 43:\n\n43 = 36 + 6 + 1 = fete + nimbo + 1\n\nSo we write: fete nimbo 1\n\nBut units:\n- fete = 36\n- nimbo = 6\n- 1 = 1\n\nSo expression: fete nimbo 1\n\nBut is \"1\" a separate word?\n\nYes — from rule: α × 6β + δ, 0 < δ < 6β → written as α × 6β δ\n\nSo δ = 1 → represents 1\n\nSo the word for 1 is just the digit.\n\nSo in Arammba, 43 = 36 + 6 + 1 → fete + nimbo + 1 → fete nimbo 1\n\nNow check size:\n\n36 + 6 + 1 = 43 → correct.\n\nNow 569.\n\n569 in base 6:\n\n6⁴ = 1296 → too big → so max 6³ = 216\n\n569 ÷ 216 = 2.63 → 2 × 216 = 432\n\n569 − 432 = 137\n\n137 ÷ 36 = 3.8 → 3 × 36 = 108\n\n137 − 108 = 29\n\n29 ÷ 6 = 4.83 → 4 × 6 = 24\n\n29 − 24 = 5\n\nSo remainder 5\n\nSo 569 = 2×216 + 3×36 + 4×6 + 5×1\n\nThus:\n- 2×216 → 2 tarumba\n- 3×36 → 3 fete\n- 4×6 → 4 nimbo\n- 5×1 → 5\n\nNow, 5", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8645.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "redacted_solution_hint_mask2", + "sample_index": 1, + "output": "We are given a system of equations in Nahuatl and Arammba, with mappings between numbers and expressions. The goal is to write **43** and **569** in Arammba, based on the provided linguistic rules.\n\n---\n\n### Step 1: Understand the Arammba numeral system\n\nFrom the guidance:\n\n- Arammba uses base **6**.\n- Powers of 6:\n - 6¹ = 6 → **fete**\n - 6² = 36 → **tarumba**\n - 6³ = 216 → **ndamno**\n - 6⁴ = 1296 → **weremeke**\n\nThis is key. The numbers are represented in base 6, with special forms for each power.\n\nAlso:\n\n- **α × 6β** → written as **α 6β** \n- **α × 6β + δ** where 0 < δ < 6β → written as **α × 6β δ**\n\nValues:\n- 6¹ = 6 → fete\n- 6² = 36 → tarumba\n- 6³ = 216 → ndamno\n- 6⁴ = 1296 → weremeke\n\nSo, numbers are formed by:\n- Base-6 digits: units, sixes, thirty-sixes, etc.\n- When adding a smaller number (δ) to a multiple of 6β, it is written as \"α × 6β δ\"\n\n---\n\n### Step 2: Convert 43 to base 6\n\nWe find the base-6 representation of 43.\n\n- 6² = 36\n- 43 ÷ 36 = 1 → remainder 7\n- 7 ÷ 6 = 1 → remainder 1\n- So: 43 = 1×36 + 1×6 + 1 → (1,1,1) in base-6\n\nThus: \n43 = 1×6² + 1×6¹ + 1×6⁰ \n= **1 × 36 + 1 × 6 + 1**\n\nUsing the rule: \nα × 6β + δ → α × 6β δ \nBut here we have multiple terms. We must group as:\n\n- 1×36 → \"1 tarumba\"\n- 1×6 → \"1 fete\"\n- 1 → \"1\" but not a standard unit\n\nWe must check if the \"1\" is a separate digit.\n\nIn the system:\n- 6⁰ = 1 (not explicitly named, but implied)\n- But in equations, small additives are written in the last position.\n\nLook at equation (13): \n\"1296 = 1296\" → 3×400 + 4×20 + (15 + 1) → 3×400 + 4×20 + 16 \nBut in Arammba, this is not directly mapped.\n\nInstead, from guidance:\n\n> 43 = 36 + 6 + 1 → so in Arammba: **tarumba fete 1**\n\nBut what is \"1\"?\n\nIn the example (8): \nngámbi + asàr = tambaroy → not helpful\n\nEquation (7): \nngámbi + ngámbi = ngámbi × yànparo \n→ ngámbi × 2 = ngámbi × yànparo → maybe multiplication is idempotent?\n\nBut more helpful: we see that:\n- 6¹ = fete\n- 6² = tarumba\n- 6³ = ndamno\n\nSo, in base 6:\n- 43 = 1×36 + 1×6 + 1 = **1 tarumba 1 fete 1**\n\nBut the representation rule says:\n> α × 6β + δ → α × 6β δ\n\nThis implies that δ (the additive part) is written after.\n\nSo: \n43 = 1×36 + 6 + 1 = (1 × 36) + (6 + 1)\n\nNow, (6 + 1) = 7 → is this written as \"fete 1\"?\n\nYes — because 6 is fete, and 1 is just a unit.\n\nLook at (13): \n3×400 + 4×20 + (15 + 1) = 1296 → shows additive expression: (15 + 1)\n\nSo the additive part is written as (a + b)\n\nThus, 43 = 1×36 + (6 + 1) = **1 tarumba (fete 1)**\n\nBut in the form: **α × 6β δ** → but δ is a value less than 6β\n\nHere, β = 2 → 6² = 36 → δ = 7 → which is > 6²? No, 7 < 36 → ok.\n\nSo 43 = 1 × 36 + 7 → δ = 7 → written as \"fete 1\"? Because 7 = 1×6 + 1\n\nIn the structure, we can write:\n- 1×tarumba + (1×fete + 1×unit)\n\nIn Arammba: \n**tarumba fete 1**\n\nBut let's confirm from (14):\n\n432 = 1×400 + 1×20 + (10 + 2) → 400 + 20 + 12 = 432 → so unit is written as \"20 + 10 + 2\"? Not exactly.\n\nWait: (14): \n1×400 + 1×20 + (10 + 2) = 432\n\nNote: 400 → tzontli (from guidance: 400 → tzontli)\n\nSo 1×tzontli + 1×20 + (10 + 2)\n\nNow: 400 → tzontli \n20 → ? → in guidance: 20 → pöhualli? But not named.\n\nWait — guidance says:\n\n> 10 + 1 → 110 \n> 1×20 → 20 \n> 2×20 → 40 \n> 1×20 → 20 \n> 3×20 → 60\n\nAh — 20 → pöhualli? \nAnd 10 → öme? \nBut in Arammba, we have:\n\n- fete → 6 \n- tarumba → 36 \n- ndamno → 216 \n- weremeke → 1296\n\nAlso, 10 is not a power of 6. So no direct mapping.\n\nBut in the system, we have:\n\n- 43 = 36 + 6 + 1 → **tarumba fete 1**\n\nSimilarly, 36 + 6 = 42 → then 43 = 42 + 1 → so \"tarumba fete 1\"\n\nSo we write: **tarumba fete 1**\n\nBut check: is \"1\" a valid unit? In Arammba, is the number 1 written?\n\nNo explicit symbol, but additive parts use the unit.\n\nFrom (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ seems like addition of units.\n\nSo likely, the base-6 digits are:\n- Units: 1\n- 6: fete\n- 36: tarumba\n- 216: ndamno\n\nSo yes: 43 = 1×36 + 1×6 + 1×1 = **tarumba fete 1**\n\nThus: \n**c.1: tarumba fete 1**\n\n---\n\n### Step 3: Convert 569 to base 6\n\nWe break down 569 in base 6.\n\nPowers of 6:\n- 6⁰ = 1 \n- 6¹ = 6 \n- 6² = 36 \n- 6³ = 216 \n- 6⁴ = 1296 → too big\n\nSo:\n\n- 569 ÷ 216 = 2 → remainder 569 - 432 = 137 \n- 137 ÷ 36 = 3 → 3×36 = 108 → remainder 137 - 108 = 29 \n- 29 ÷ 6 = 4 → 4×6 = 24 → remainder 5 \n- So: 569 = 2×216 + 3×36 + 4×6 + 5×1\n\nSo in base-6: (2,3,4,5)\n\nNow, using the rule: \nα × 6β + δ → written as α × 6β δ\n\nWe break into terms:\n- 2×216 = 2×6³ → 2 **ndamno**\n- Then 3×36 = 3×6² → 3 **tarumba**\n- 4×6 = 4×6¹ → 4 **fete**\n- 5×1 → 5 → written as \"5\"\n\nBut here we have multiple components. How to write them?\n\nLook at guidance: \nEquation (3): \n67 + 14 = 81 → written as 3×6² + 3×6 + 3 = 36+18+3=57? No.\n\nEquation (10): \nyenówe × yenówe tàxwo = fete yenówe tàxwo → not helpful.\n\nBut equation (11): \nnimbo × fete = tarumba → so tarumba = nimbo × fete\n\nThat implies multiplication: but we are doing addition.\n\nInstead, from the form: \nIn base 6, we write digits from highest to lowest, and for values greater than 1, we write them with the base units.\n\nBut the rule is:\n> α × 6β + δ → α × 6β δ \nwhere δ is the remainder less than 6β.\n\nSo for 569:\n\n569 = 2×216 + (3×36 + 4×6 + 5) = 2×6³ + (3×6² + 4×6 + 5)\n\nNow, (3×36 + 4×6 + 5) = 108 + 24 + 5 = 137 → 137 < 216 → ok.\n\nSo we write: \n2 × ndamno (2×6³) + (3 tarumba 4 fete 5)\n\nBut is the additive part written as \"3 tarumba 4 fete 5\"?\n\nYes — because in the system:\n- α × 6β + δ, with δ < 6β → written as α × 6β δ \nbut δ is a sum of smaller parts.\n\nIn guidance (13): \n(3×400 + 4×20 + (15+1)) → added value\n\nSo for 569 = 2×216 + (3×36 + 4×6 + 5), we can write:\n\n**2 ndamno 3 tarumba 4 fete 5**\n\nBut check: is this consistent?\n\nWe have 2×216 = 432 \n3×36 = 108 → 432+108 = 540 \n4×6 = 24 → 564 \n5 → 569 → correct.\n\nSo yes — valid.\n\nIn Arammba:\n- 216 → ndamno \n- 36 → tarumba \n- 6 → fete \n- 1 → unit\n\nSo 569 = 2×ndamno + 3×tarumba + 4×fete + 5×1 → written as:\n\n**2 ndamno 3 tarumba 4 fete 5**\n\nNow, is there any constraint on units?\n\nFrom (8): ngámbi + asàr = tambaroy — not about units.\n\nAll base digits are allowed.\n\nTherefore, the answer is:\n\n**c.1: tarumba fete 1** \n**c.2: 2 ndamno 3 tarumba 4 fete 5**\n\n\\boxed{c.1: tarumba fete 1; c.2: 2 ndamno 3 tarumba 4 fete 5}", + "generated_tokens": 2802, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: tarumba fete 1; c.2: 2 ndamno 3 tarumba 4 fete 5", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 6158.0, + "ioling_final_answer_chars": 53.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "redacted_solution_hint_mask2", + "sample_index": 2, + "output": "We are to solve (c): write out in Arammba: 43; 569.\n\nFrom the guidance:\n\nIn Arammba:\n- 6² = 36 → fete\n- 6³ = 216 → tarumba\n- 6⁴ = 1296 → ndamno\n- 6⁵ = 7776 → weremeke\n\nAlso:\n- α × 6β → represents α × 6β\n- α × 6β + δ (0 < δ < 6β) → α × 6β δ\n\nSo, we break down 43 and 569 into base 6, then apply the formation rules.\n\n---\n\n**Step 1: Represent 43 in base 6**\n\nDivide 43 by 6:\n- 43 ÷ 6 = 7 remainder 1\n- 7 ÷ 6 = 1 remainder 1\n- 1 ÷ 6 = 0 remainder 1\n\nSo 43 = 1×6² + 1×6¹ + 1×6⁰ = 1×36 + 1×6 + 1 = 43\n\nThis is 111₆ → α = 1, β = 2, and δ = 1, 1, 1.\n\nBut according to the format:\n- α × 6β = 1 × 6² = 36\n- Then add δ values where δ < 6β\n\nBut since we have several digits, we must process from right.\n\nWe have:\n- 43 = 36 + 6 + 1 = 1×36 + 1×6 + 1×1\n\nNow, in the system:\n- α × 6β is written as α × 6β\n- Then any remainder δ (0 < δ < 6β) is written as δ (but only if less than 6β)\n\nBut in the examples:\n- 3 × 20 + (5 + 2) → 3×20 + 7 → written as 3×20 + 7 in the derivation\n- 67 + 14 = 81 → written as 2×6² + 3×6 + 3 = 72 + 18 + 3 = 93? Wait — inconsistent.\n\nWait — look at example (9):\n- yànparo tàxwo + fete asàr tàxwo = yànparo fete\n→ interpreted as: 20 × 2 = 40, 2 × 6 = 12, 4 × 6 = 24 → 3 × 20 + (5 + 2) = 60 + 7 = 67 → but 3×20 + 7 → written as 3×20 + (5+2)\n\nAlso seen:\n- 3 × 6 + 4 = 22 → written as 3×6 + 4\n- (10): 3 × 6² = 108 → 3×36 = 108 → but example says 2×6 + 3×6 = 12 + 18 = 30 — no.\n\nWait, the guidance says:\n\nγ + δ where γ = α × 20β, and δ < 20β → γ -oM- δ\n\nBut in Arammba it's different.\n\nWait — in Arammba, the structure is clearly base-6:\n\n- 6¹ = 6 → fete (from 6² = 36 → fete)\nWait — contradiction.\n\nWait — guidance says:\n- 6² = 36 → fete\n- 6³ = 216 → tarumba\n- 6⁴ = 1296 → ndamno\n- 6⁵ = 7776 → weremeke\n\nSo:\n- 6² → fete\n- 6³ → tarumba\n- etc.\n\nSo base 6, powers:\n- 6¹ → ??? not given, but in (11): 6 × 36 = 216 → tarumba → 6³\n- In (8): ngámbi + asàr → tambaroy → 6²?\n- In (11): nimbo × fete = tarumba → implies fete = 6²?\n\nLet’s re-check guidance:\n\n- 6² = 36 → fete\n- 6³ = 216 → tarumba\n- 6⁴ = 1296 → ndamno\n- 6⁵ = 7776 → weremeke\n\nSo:\n- fete = 36 = 6²\n- tarumba = 216 = 6³\n- ndamno = 1296 = 6⁴\n- weremeke = 7776 = 6⁵\n\nSo powers of 6, starting at 2.\n\nNow, how to represent a number?\n\nThe rule:\n- α × 6β → α × 6β\n- α × 6β + δ, 0 < δ < 6β → α × 6β δ\n\nNote: δ must be less than 6β\n\nSo for example:\n- 36 + 4 = 40 → 1×6² + 4 → written as 1×6² 4 → since 4 < 6² = 36\n\nSimilarly, 36 + 6 = 42 → 1×6² 6 → but 6 < 36 → valid → written as 1×6² 6\n\nBut 6 is 6¹ → so the \"δ\" part is a number less than 6β.\n\n---\n\nNow for 43:\n\n43 in base-6:\n43 ÷ 6 = 7 rem 1\n7 ÷ 6 = 1 rem 1\n1 ÷ 6 = 0 rem 1 → so 1×36 + 1×6 + 1 → 111₆\n\nSo:\n- 1×6² + 1×6¹ + 1×6⁰\n\nBut the system breaks numbers as α × 6β + δ, where δ < 6β\n\nWe can interpret this as:\n- Start with α × 6β\n- Then add δ with δ < 6β\n\nSo for 43:\n- α × 6² = 1×36 = 36\n- δ = 7 → but 7 < 36 → yes → so 36 + 7 = 43\n\nNow, 7 = 1×6 + 1 → so written as 1×6 + 1\n\nBut how to write it in the language?\n\nThe example (14): 432 = 432 → 1×400 + 1×20 + (10 + 2) → 400 + 20 + 12 = 432\n\nBut 400 = 1×400, 400 = 20×20? Wait — 20×20 = 400?\n\nEarlier guidance says:\n- 1 × 400 = 400 → → so 400 is 20² → tzontli = 400\n- 20×3 = 60 → etc.\n\nWait — the references in guidance:\n\n- α × 20β → α × 20β\n- where 20¹ = 20, 20² = 400, 20³ = 8000 → tzontli = 400, xiquipilli = 8000\n\nSo:\n- 20¹ = 20 → but not explicitly used\n- 20² = 400 → tzontli\n- 20³ = 8000 → xiquipilli\n\nSimilarly, 6² = 36 → fete, 6³ = 216 → tarumba\n\nSo in Arammba:\n- Numbers are formed in base-6\n- Each \"digit\" is a multiplier of 6ᵏ\n- The symbol for k ≥ 2: fete (6²), tarumba (6³), etc.\n- Then, when there's a remainder δ < 6^β, it is written as δ\n\nBut δ is a number less than 6β.\n\nSo for 43:\n- 43 = 1×36 + 7 → 7 < 36 → so 1×6² 7\n\nNow, what is 7 written as?\n7 = 6 + 1 → so 6 + 1 → fete is 6², not 6¹ → no direct entry\n\nBut in the compounds, we see:\n(8): ngámbi + asàr → tambaroy → 36 + 4 = 40? No — 36 = 6², 4 = 4 → 36 + 4 = 40?\n\nBut not given.\n\nWait — look at (14): 432 = 1×400 + 1×20 + (10 + 2)\n\n→ 400 + 20 + 12 = 432\n\nSo the unresolved part (10 + 2) → makes sense as a sum.\n\nSo δ is written as a sum of terms.\n\nSo in (14): 1×400 + 1×20 + (10 + 2)\n\n10 and 2 are not base-6, but numbers.\n\nWait — in the mathematical examples, we have:\n- (9): 3×20 + (5+2) = 60 + 7 = 67 → written as 3×20 + (5+2)\n\nSo (5+2) = 7\n\nSimilarly, (3): 3×18 = 54 → 18 = 3×6 → so 3×18 = 3×(3×6) = 9×6 = 54 → but 18 = 3×6\n\nSo terms like 5+2 are just numbers.\n\nTherefore, in the representation:\nα × 6β + δ → written as α × 6β δ, and δ is written as a sum of numbers.\n\nSo for 43:\n43 = 1×6² + 7 → 7 = 6 + 1 → so written as 1×6² 6 + 1\n\nBut since 6 is not a base symbol, is 6 added as a number?\n\nBut in (8): ngámbi + asàr → 36 + 4 = 40 → tambaroy? No.\n\nIn (11): nimbo × fete = tarumba → so fete = 36 → tarumba = 216 → 6³\n\nSo base-6 digits:\n\nDigit positions: 6⁰, 6¹, 6², etc.\n\nSo:\n6⁰ = 1\n6¹ = 6\n6² = 36 → fete\n6³ = 216 → tarumba\n6⁴ = 1296 → ndamno\n\nNow, in (14): 432 = 1×400 + 1×20 + (10 + 2)\n→ 400 = 20×20 = 400 → so 20² → tzontli = 400\n→ 20 = 20¹ → not labeled in table\n→ (10+2) → where 10 and 2 are just numbers\n\nSo δ is written not as a number, but as a sum.\n\nTherefore, for 43:\n- α × 6² + δ → α = 1, β = 2, δ = 7\n- δ = 7 = 6 + 1 → write as 6+1\n\nSo the term is: 1×6² (6+1)\n\nBut what is 6? In the language, 6 is not a word — it's 6¹\n\nBut in (12): nimbo + yànparo tàxwo = yenówe tàxwo → 2×6² = 72 → no\n\nWait — in (12): nimbo + yànparo tàxwo → 2×6² = 72 → 2×36 = 72\n\nNo — (11): nimbo × fete = tarumba → nimbo × 36 = 216 → nimbo = 6\n\nSo nimbo = 6\n\nSo nimbo = 6¹\n\nSimilarly, asàr = 4? (8): ngámbi + asàr = tambaroy → 36 + 4 = 40 → tambaroy\n\nSo asàr = 4\n\nBut 6 = nimbo → so 6 is a word: nimbo\n\n1 = ? — not given, but 1×6⁰ = 1\n\nSo in the representation:\n\n- For a number α × 6β + δ, with δ < 6β, the number is written as:\n α × 6β (δ) → where δ is expressed as a sum of numbers, with components like:\n\n- base-6 digits: values 1 to 5\n- but in the form, δ is a sum of numbers (like 5+2, 10+2) — could be any numbers\n\nBut in (9): 3×20 + (5+2) = 67 → so 5+2 = 7 written as such\n\nSimilarly, in (14): 1×400 + 1×20 + (10+2) → 432\n\nSo it’s written with numbers, not base symbols.\n\nSo δ is written as a sum of numbers.\n\nFor 43:\n43 = 1×36 + 7 → so 1×6² (7) → and 7 = 6 + 1\n\nSince 6 = nimbo, 1 = ???\n\nIs there a word for 1?\n\nLook at (7): ngámbi + ngámbi = ngámbi × yànparo → 2×36 = 72 → not 43\n\nBut in (15): cen-xiquipilli = weremeke tarumba nimbo yànparo → 8000 = 7776 + 216 + 6 + 2 → 8000 = 6⁵ + 6³ + 6¹ + 2 → 7776 + 216 + 6 + 2 = 8000\n\nSo 2 is present — so 2 is a number.\n\nSimilarly, in (14): 432 = 1×400 + 1×20 + (10+2)\n\nSo numbers like 10, 2 are used.\n\nThus, 7 = 6 + 1 → analogously, 43 = 1×6² (6+1)\n\nSo the word is: 1×6² (6+1)\n\nBut 6 = nimbo\n\nSo (6+1) = nimbo + 1\n\nBut 1 is not defined.\n\nWait — in (15): 8000 = 7776 + 216 + 6 + 2 → so 6 and 2 are used.\n\nIs there a word for 1?\n\nNot explicitly, but perhaps 1 is just used as a number in the expression.\n\nIn (14): 432 = 1×400 + 1×20 + (10+2)\n\nThe 1×20 — 20 is not a base unit, but in (10): 3×6² = 108? 3×36 = 108 → no\n\nWait — (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → 6×6 = 36 → fete → so yenówe = 6\n\nSo yenówe = 6\n\nAnd (10): (6) × (6 tàxwo) = fete (6²) → 6 × 6 = 36 → yes\n\nSo yenówe = 6\n\nThus:\n- 1 = 1 (implied)\n- 2 = 2\n- 6 = nimbo\n- 36 = fete\n\nSo 7 = 6 + 1 → so nimbo + 1\n\nTherefore, 43 = 1×fete (nimbo + 1)\n\nBut in (14): 432 = 1×tzontli + 1×yànparo + (10+2)\n\nSo the pattern is: α × 6β + δ → written as α × 6β δ (with δ written as sum)\n\nSo for 43:\n- 43 = 1×36 + 7\n- δ = 7 = 6 + 1 → so 6+1 → nimbo + 1\n\nTherefore, 43 is: 1×fete (nimbo + 1)\n\nBut what is the symbol for 1?\n\nIt’s not named — but in the compound, it's expressed as a number.\n\nSo we use \"1\" as a number.\n\nThus: fete (nimbo + 1)\n\nBut to follow the pattern, it's written with the multiplier.\n\nSo: 1 × fete (nimbo + 1)\n\nBut in (14): 432 = 1×tzontli + 1×yànparo + (10+2) → so multiple terms\n\nSo for 43: only one term with addition.\n\nThus: 1×fete (nimbo + 1)\n\nBut the word \"1\" is not given — is there a standard?\n\nIn (15): 8000 = 7776 + 216 + 6 + 2 → so numbers 6 and 2 are used.\n\nSimilarly, in (14): (10+2) → so 10 and 2\n\nSo numbers like 1, 2, 6, 10 are just numbers.\n\nSo 1 is used.\n\nThus, 43 → 1×fete (nimbo + 1)\n\nNow for 5", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8158.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "redacted_solution_hint_mask2", + "sample_index": 3, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to translate the numbers **43** and **569** into Arammba, using the provided linguistic rules and patterns.\n\n---\n\n### Step 1: Understand the numbering system in Arammba\n\nFrom the guidance:\n\n- The base is **6**, with powers:\n - $6^1 = 6$\n - $6^2 = 36$\n - $6^3 = 216$\n - $6^4 = 1296$\n\n- The special values:\n - $6^2 = 36$: **fete**\n - $6^3 = 216$: **tarumba**\n - $6^4 = 1296$: **ndamno**\n - $6^5 = 7776$: **weremeke**\n\n- The structure of numbers:\n - $ \\alpha \\times 6^{\\beta} $: written as $ \\alpha \\times 6^{\\beta} $, or in Arammba as $ \\alpha \\times 6^{\\beta} $\n - $ \\alpha \\times 6^{\\beta} + \\delta $, where $0 < \\delta < 6^{\\beta}$: written as $ \\alpha \\times 6^{\\beta} \\ \\delta $\n\n- Specific forms:\n - $ \\alpha \\times 6^{\\beta} \\ \\delta $ means $ \\alpha \\times 6^{\\beta} $ plus a smaller number $ \\delta $\n - The addition is written as $ A \\ \\delta $, with $ \\delta $ in simpler terms (like in (8), (9), etc.)\n\n---\n\n### Step 2: Express 43 in base 6\n\nWe compute base-6 expansion:\n\n- $6^3 = 216$ → too big\n- $6^2 = 36$\n\n$43 \\div 36 = 1$ remainder $7$\n\n$7 \\div 6 = 1$ remainder $1$\n\nSo: $43 = 1 \\times 36 + 1 \\times 6 + 1$\n\nThis is: $1 \\times 6^2 + 1 \\times 6^1 + 1 \\times 6^0$\n\nThus, in base 6: $43 = 111_6$\n\nBut our system uses:\n- $6^2 = 36$ → **fete**\n- $6^1 = 6$ → $1 \\times 6$ → not named directly, but in rules, we see $ \\alpha \\times 6^{\\beta} + \\delta $\n- The small parts are added as $ \\alpha \\times 6^{\\beta} \\ \\delta $\n\nIn the given equations:\n\n- (3): $3 \\times 20 + (5 + 2) = 10 + 4 = 14$ → written as $3 \\times 20 \\ 14$, but 20 is not base 6.\n\nWait — we must match the form used in the examples.\n\nLook at equation (9): \n$ yànparo tàxwo + fete asàr tàxwo = yànparo fete $ \n→ suggests that “fete” is a unit, and “tàxwo” is a marker for multiplication by 6?\n\nFrom guidance:\n- $ \\alpha \\times 6 $, $2 \\le \\alpha \\le 5$: $ \\alpha \\ tàxwo $\n\nSo:\n- $2 \\ tàxwo = 2 \\times 6$\n- $3 \\ tàxwo = 3 \\times 6 = 18$\n- $4 \\ tàxwo = 24$\n- $5 \\ tàxwo = 30$\n\nThus, “tàxwo” = ×6\n\nThen:\n- $ \\alpha \\times 6^{\\beta} \\ \\delta $: $ \\alpha \\times 6^{\\beta} $ + $ \\delta $\n\nFrom (10): $ yenówe × yenówe tàxwo = fete yenówe tàxwo $ \n→ $ y^2 \\times 6 = fete \\times y $ → not directly useful\n\nFrom (8): $ ngámbi + asàr = tambaroy $ → sum\n\nFrom (9): $ yànparo tàxwo + fete asàr tàxwo = yànparo fete $ \n→ $ (yànparo \\times 6) + (fete \\times 6) = yànparo fete $? No, seems inconsistent.\n\nWait — actually equation (9): \n$ yànparo tàxwo + fete asàr tàxwo = yànparo fete $ \n→ meaning: \n$ (yànparo \\times 6) + (fete \\times asàr \\times 6) = yànparo fete $\n\nBut that doesn’t match.\n\nAlternatively, perhaps **tara** and **täxwo** are positional markers.\n\nBut from guidance:\n\n> • α × 6, 2 ≤α ≤5: α tàxwo\n\nSo:\n- 2 tàxwo = 2×6 = 12\n- 3 tàxwo = 18\n- 4 tàxwo = 24\n- 5 tàxwo = 30\n\nBut no explicit value for 1 × 6.\n\nImportant: from (14): \n$ 432 = 1 \\times 400 + 1 \\times 20 + (10 + 2) $ → $400 = 10^2$?\n\nWait — go back to the **explanation** of the system:\n\nIn the guidance, it says:\n\n> 3 × 400 + 4 × 20 + (15 + 1) = 1296 → 1296 = 6^4 → **ndamno**\n\n> 1 × 400 + 1 × 20 + (10 + 2) = 432 → 432 = 432\n\n> 1 × 400 = 400\n\n> 1 × 8000 = 8000\n\nSo we see that:\n- 400 = 100 × 4? But 100 × 4 = 400\n- 400 = 10² × 4?\n- 8000 = 1000 × 8?\n\nBut 1000 = 8 × 125?\n\nWait — better:\n\nFrom earlier:\n- 400 = 10² × 4 = 100 × 4 = 400\n- 400 → corresponds to **tzontli** (from 400: tzontli)\n\nFrom guidance:\n> α × 20β, 1 ≤α ≤5, 1 ≤β ≤3 \n> 1: ceM → 20 \n> 2: öm → 20 \n> 3: yë → 400 \n> 4: näuh → 8000 \n> 5: mäcuïl → ?\n\nAnd:\n- 20 → pöhualli \n- 400 → tzontli \n- 8000 → xiquipilli\n\nSo:\n- 20 = 20\n- 400 = 4 × 100 = 4 × 10²\n- 8000 = 8 × 1000 = 8 × 10³\n\nSimilarly in Arammba, we have:\n- 36 = 6² → fete\n- 216 = 6³ → tarumba\n- 1296 = 6⁴ → ndamno\n- 7776 = 6⁵ → weremeke\n\nAnd the number system uses:\n- $ \\alpha \\times 6^{\\beta} + \\delta $ → written as $ \\alpha \\times 6^{\\beta} \\ \\delta $\n\nSo for 43:\n\n$43 = 36 + 6 + 1 = 1 \\times 36 + 1 \\times 6 + 1$\n\nSo:\n- $1 \\times 36$ → **fete**\n- $1 \\times 6$ → not a named unit directly, but from (9): $ yànparo tàxwo = yànparo × 6 $\n- So $1 \\times 6$ is $1 \\ tàxwo$\n\nBut is \"1\" a valid multiplier?\n\nGuidance says: α × 6, 2 ≤ α ≤ 5 → so only 2–5, not 1.\n\nSo $1 \\ tàxwo$ is not defined.\n\nBut in equation (8): $ ngámbi + asàr = tambaroy $ → sum\n\nIn (10): $ yenówe × yenówe tàxwo = fete yenówe tàxwo $ → perhaps multiplication?\n\nBut from (9): \n$ yànparo tàxwo + fete asàr tàxwo = yànparo fete $\n\nSo:\nLeft: $ yànparo \\times 6 + fete \\times asàr \\times 6 = yànparo fete $? \nBut right is $ yànparo fete $\n\nThat would suggest that $ (A \\times 6) + (B \\times C \\times 6) = A \\times B $? Doesn't make sense.\n\nWait — re-read (9):\n\n> yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo it's not multiplication of the entire term. It may mean:\n\n- \"yànparo with tàxwo\" + \"fete with asàr with tàxwo\" = \"yànparo fete\"\n\nBut in terms of composition, this may indicate that:\n- $ A + B = C $, where A and B are composed with modifiers\n\nBut more importantly, in the **solving of (c)**, the clue says:\n\n> 43 = 36 + 6 + 1 → [TARGET ANSWER REDACTED]\n\nSo clearly, 43 = 36 + 6 + 1\n\nSo:\n- 36 → **fete**\n- 6 → **1 tàxwo**? But only 2–5 are given.\n\nBut 1 × 6 is just \"1\" × 6, so perhaps “1” is written as “1” or implied?\n\nWait — check equation (15):\n\n> 400 = 1 × 400 → written as “400”\n\nBut 400 → tzontli\n\nIn (14): \n$432 = 1 \\times 400 + 1 \\times 20 + (10 + 2)$ \n→ 1 × 400 = 400 \n→ 1 × 20 = 20 \n→ (10 + 2) = 12\n\nSo 400 + 20 + 12 = 432\n\nSo the form is: \n$ \\alpha \\times 400 $ or $ \\alpha \\times 20 $ or $ \\alpha \\times 10 $\n\nSo in Arammba:\n- 400 → tzontli\n- 20 → pöhualli\n- 10 → ?\n\nBut from (2): $ cem-pöhualli × öme = öm-pöhualli $\n\n(?) 10 might be from decomposition.\n\nBut back to 43.\n\n43 = 36 + 6 + 1 \n- 36 → fete \n- 6 → ? \n- 1 → ?\n\nFrom (10): $ yenówe × yenówe tàxwo = fete yenówe tàxwo $\n\nSo $ y^2 \\times 6 = fete \\times y \\times 6 $? → no.\n\nBut from earlier, we have:\n- $ \\alpha \\times 6^{\\beta} + \\delta $ → $ \\alpha \\times 6^{\\beta} \\ \\delta $\n\nSo for 43:\n\n43 = 1 × 36 + 1 × 6 + 1 = 1 × 36 + 7\n\nSo $ 1 \\times 36 $ + 7\n\nBut 7 = 6 + 1 → so we write $ 1 \\times 36 \\ 7 $ → and 7 is written as “6 + 1”?\n\nBut in base 6, 7 = 1×6 + 1 → so 1×6 + 1\n\nBut the system seems to write additive parts in full.\n\nLook at (3): \n$3 × 20 + (5 + 2) = 10 + 4 = 14$ → written as $3 × 20 \\ 14$ → but 14 is written as “5+2”, not in base 6.\n\nSimilarly, (13): \n$3 × 400 + 4 × 20 + (15 + 1) = 1296$ → so addition of terms with known units\n\nBut in Arammba, the **only named units** are:\n- 36: fete\n- 216: tarumba\n- 1296: ndamno\n- 1×6, 2×6, ..., 5×6 → α tàxwo\n\nSo:\n- 1×6 = 1 tàxwo → is this allowed?\n\nGuidance says: α × 6, 2 ≤ α ≤ 5 → so only 2–5.\n\nThus, 1×6 is **not** a standard unit.\n\nBut in (15): $400 = 1 × 400$ → valid \n(16): $8000 = 1 × 8000$ → valid\n\nSo small additions like 1 or 6 can still be used as addends.\n\nFrom (9): $ yànparo tàxwo + fete asàr tàxwo = yànparo fete $\n\n→ This implies that “asàr” is a unit that can be added, with “tàxwo” as a multiplier.\n\nBut more importantly, in the derivation of (c), the hint says:\n\n> 43 = 36 + 6 + 1 → [TARGET ANSWER REDACTED]\n\nTherefore, we interpret:\n- 36 → fete\n- 6 → 1 tàxwo\n- 1 → separate value\n\nBut is there a name for 1?\n\nNo. So likely, we write:\n- fete + 1 tàxwo + 1\n\nBut is “1” a word?\n\nFrom (8): ngámbi + asàr = tambaroy → sum\n\nSo additive components are allowed.\n\nBut in equation (10): $ yenówe × yenówe tàxwo = fete yenówe tàxwo $\n\n→ perhaps multiplication and addition mixed.\n\nBut in equation (9): sum of two terms equals a simpler compound.\n\nSo in (c), for 43 = 36 + 6 + 1:\n- 36 → fete\n- 6 → 1 tàxwo\n- 1 → 1 (as unit)\n\nBut is “1” a unit? Possibly.\n\nAlternatively, in (14): $432 = 1 × 400 + 1 × 20 + (10 + 2)$\n\nSo:\n- 1 × 400 → tzontli\n- 1 × 20 → pöhualli\n- (10 + 2) → named as a sum\n\nSimilarly, for 43 = 1 × 36 + 1 × 6 + 1 → we may write:\n- 1 × fete + 1 × 6 + 1\n\nBut 1 × 6 = 1 tàxwo\n\nSo:\n- fete 1 tàxwo 1\n\nBut from example (11): $ nimbo × fete = tarumba $\n\nNo additive units.\n\nBut in (12): $ nimbo + yànparo tàxwo = yenówe tàxwo $\n\n→ sum is valid.\n\nTherefore, addition is used.\n\nSo likely, 43 = fete + 1 tàxwo + 1\n\nBut is “1” a word?\n\nWe have no unit for 1, but in the decomposition, it appears as an addend in sum.\n\nGiven that in (14): “1 × 400 + 1 × 20 + (10 + 2)” → the “1” is used as multiplier.\n\nSo in 43 = 1×36 + 1×6 + 1 → the \"1\" may be a standalone numeral.\n\nBut perhaps the structure is:\n\nWhenever the remainder is small, it is written in base 6 factoring.\n\nBut 43 = 36 + 6 + 1 → 1×36 + 1×6 + 1\n\nIn Arammba, the form is:\n- $ \\alpha \\times 6^{\\beta} \\ \\delta $, where $ \\delta $ is a small number, written in reduced form.\n\nBut in (3): $3 \\times 20 + (5+2) = 10 + 4 = 14$ → “(5+2)” used\n\nIn (5): $5 + 2 = 7$ → written as “5+2”\n\nSo small additions are written with “+”\n\nThus, 6 + 1 → “6 + 1”\n\nBut what is “6”? It is 1 × 6 → so written as “1 tàxwo”?\n\nBut 1 tàxwo is not listed in the standard forms.\n\nGuidance says: α × 6, 2 ≤ α ≤5 → so 2–5 only.\n\nThus, “1 tàxwo” is **not** valid.\n\nAlternative: perhaps 6 is a unit?\n\nNo — only 36, 216, etc.\n\nSo only units are:\n- fete = 36\n- tarumba = 216\n- ndamno = 1296\n\nBut 6 must be broken.\n\nWait — in (10): $ yenówe × yenówe tàxwo = fete yenówe tàxwo $\n\n→ $ y^2 \\times 6 = fete \\times", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9206.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 1. Nahuatl:\n\n • 1: cë, 2: öme, 3: ëyi, 4: nähui;\n\n • 5: mäcuïlli, 10: mahtlactli, 15: caxtölli;\n\n α\n 1: ceM 20β\n 2: öm 20: pöhualli\n • α × 20β, 1 ≤α ≤5, 1 ≤β ≤3: - ;\n 3: yë 400: tzontli\n 4: näuh 8000: xiquipilli\n 5: mäcuïl\n\n • 7: chicöme;\n { }\n γ ∈{10, 15}, 1 ≤δ ≤4\n • γ + δ, : γ -oM- δ ,\n γ = α × 20β, 1 ≤δ < 20β\n {\n m before m, p, or a vowel;\n M =\n n otherwise.\n\n Arammba:\n\n • 1: ngámbi, 2: yànparo, 3: yenówe, 4: asàr, 5: tambaroy, 6: nimbo;\n\n • α × 6, 2 ≤α ≤5: α tàxwo;\n\n • 62 = 36: fete, 63 = 216: tarumba, 64 = 1296: ndamno, 65 = 7776: weremeke;\n\n • α × 6β, 2 ≤β: α 6β ;\n\n • α × 6β + δ, 0 < δ < 6β: α × 6β δ .\n\n 10 + 1 5 × 20 + 10\n 11 × 10 = 110 (1) 1 + 1 = 1 × 2 (7)\n 1 × 20 2 × 20 1 + 4 = 5 (8) 20 × 2 = 40 (2)\n 2 × 6 36 + 4 × 6 2 × 36\n 3 × 20 + (5 + 2) 10 + 4 4 × 20 + 1 12 + 60 = 72 (9) (a) 67 + 14 = 81 (3)\n 3 × 6 36 + 3 × 6\n 5 + 2 = 7 (4) 3 × 18 = 54 (10)\n 10 + 3 1 × 20 + (15 + 4) 6 × 36 = 216 (11)\n 13 × 3 = 39 (5) 2 × 6 3 × 6\n 5 × 3 = 15 (6) 6 + 12 = 18 (12)\n\nThirteenth International Olympiad in Linguistics (2015). 2\nIndividual Contest Solutions\n\n 3 × 400 + 4 × 20 + (15 + 1)\n 1296 = 1296 (13)\n\n 1 × 400 + 1 × 20 + (10 + 2) 2 × 216\n 432 = 432 (14)\n\n 1 × 400 216 + 5 × 36 + 4\n 400 = 400 (15)\n\n 1 × 8000 7776 + 216 + 6 + 2\n 8000 = 8000 (16)\n\n (b) • 42 = 2 × 20 + 2: öm-pöhualli-om-öme;\n\n • 494 = 1×400+4×20+10+4: cen-tzontli-on-näuh-pöhualli-om-mahtlactli-on-nähui.\n\n (c) • 43 = 36 + 6 + 1: [TARGET ANSWER REDACTED];\n\n • 569 = 2×216+3×36+4×6+5: [TARGET ANSWER REDACTED].", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "redacted_solution_hint_mask5", + "sample_index": 0, + "output": "Step 1: Understand the word order pattern. \nThe rule states: S (O′) O V → Subject, then indirect object (if any), then direct object, then verb. \nThis matches the standard order seen in the examples.\n\nStep 2: Analyze noun case marking. \nCase marking depends on position and consonant type: \n- S (subject): no case marker (-∅) \n- O′ (indirect object): -gi after sonorant consonants, -ki after obstruents \n- O (direct object): -gi after sonorant, -ki after obstruent \n\nNote: In examples, singular nouns have no suffix; plural means -ːcci after a vowel.\n\nStep 3: Identify verb structure. \n- Tense: present/future = -r, past = -s \n- For “to give”: \n - to first person: deːn \n - to second/third person: tir \n- Object marking: \n - If O′ exists, O′ gets -ccir (plural) or ∅ (singular), if no O′, then O gets -ir (plural) \n- Subject: \n - 1st person sg: -i \n - 1st person pl / 3rd person sg: -u \n - 3rd person pl: -a \n\nStep 4: Analyze the given examples to confirm patterns.\n\nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu \nar = subject (3rd person sg → -u, but ar is used; likely ar = \"we\" or \"the people\"? Wait — \"we\" is \"kamiːg\"?) \nWait: \"ar\" is likely \"they\" or \"we\"? \n\"ar kanarriːcciːg kamiːg\" → \"we bought the camels\" \nSo \"ar\" = subject → 1st person pl → should be -u → ar matches. \n\"kanarriːcciːg\" = verb \"buy\" + past tense (-s?) but it's -ciːg → indicates past tense and -ciːg includes -i for singular? \nWait — verb base: root is likely \"kanarri\" — \"to buy\" \n\"kanarriːcciːg\" → -ciːg → suggests past tense and plural for object? \nWait: direct object is \"kamiːg\" → camels → plural → ends with -ːcci → yes → plural noun \nSo object is plural → needs -ːcci (after vowel) → yes \n\"kanarriːcciːg\" likely = \"bought\" + object (camels) → object marked with -ciːg → mark on object. \nBut how is it derived?\n\nWait — verb structure: \n\"kanarri\" → root \"to buy\" \n\"kanarriːcciːg\" = base + past tense + object → object is camels → plural → must have -ciːg → suffix after vowel \n\"ciːg\" — must be the object marker? \nBut the verb form seems to attach a suffix to the object.\n\nWait — rule says: for \"to give\", object is marked with -ccir (plural), or ∅ (singular), and if no indirect object, then O gets -ir (plural). \nFor \"to buy\" — not explicitly given. \nBut in example 5: ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces\" \n\"ay\" = 1st person sg → subject \n\"befyyeːcciːg\" = verb \"buy\"? \n\"beyyeːcciːg\" → -ciːg → likely past or present? But tense: present/future = -r, past = -s \nHere: \"beyyeːcciːg\" → ends with -ciːg → not -r → suggests past? \nBut \"I am buying\" is present → contradiction?\n\nWait: \"beyyeːcciːg\" — is it present or past?\n\nWait — example 1: ar kanarriːcciːg kamiːg → past (we bought) → has -ciːg → which may be past tense (-s?) — but not marked with -s? \nIn rule: past = -s, present/future = -r (r > d | n)\n\nSo \"kanarriːcciːg\" → has no -s → should be present? \nBut \"we bought\" is past → contradiction?\n\nWait — perhaps the verb inflection is on the verb root.\n\nIn example 1: ar kanarriːcciːg kamiːg → \"we bought\" \n\"kanarri\" base → with suffix? \n\"ciːg\" appears — not -s for past — puzzle.\n\nWait — in example 5: ay beyyeːcciːg ajaːnirri → \"I am buying\" → present tense → should have -r \nBut \"beyyeːcciːg\" → ends with -ciːg → that’s not -r → contradiction.\n\nWait — unless -r is not visible. \nLook at root: beyyeː → might be derived from \"buy\", but \"beyye\" with -ciːg?\n\nPerhaps -ciːg is not tense — or the tense suffix is lost in transcriptions?\n\nWait — in rule: \"tense: past -s, present/future -r (r > d | n)\" \nSo — if present/future → -r \nSo verb root + -r = present/future \nIf -s = past\n\nBut in example 5: ay beyyeːcciːg → should be present → should have -r → but is -ciːg → lacks -r \nUnless -r is absorbed or merged?\n\nWait — beyyeːcciːg → perhaps it’s beyyeːc-ir or something.\n\nWait — perhaps the verb form is: root + tense suffix + object suffix \nBut in example 5: ajaːnirri → object: necklaces → plural → must have -ir? \n\"ira\" → -ir → plural → yes → so object ends in -ir → indicates plural \nSimilarly, example 1: kamiːg → camels → plural → should have -ciːg → yes → it has -ciːg at end.\n\nBut verb \"kanarriːcciːg\" — where is the tense?\n\nIf it's past, should be -s → but not → so perhaps there's a mistake.\n\nWait — example 2: tirt kadeːg allesu → \"the owner repaired the dress\" \n\"tirt\" → verb → for “repair” → likely from “tirt” root → and \"tirt\" → to another → “repair” \n\"tirt\" — likely a verb → first person? \nSubject: \"the owner\" → not clearly inflected → but \"tirt\" → if second person → ? \nBut \"kadeːg\" → dress → singular → ends in -g → so not -ciːg → so singular → so no plural object? \nThen object is singular → so no -ccir \nThen object marked with -g → after obstruent? \n\"kadeːg\" → after obstruent (d) → so -g → correct \nSo object is marked with -g → after obstruent → valid. \nVerb: \"tirt\" → tense? → present → no -r? → but present/future should have -r → so tirt → present? \n\nBut if present, should have -r → unless tirt is root + r? \nWait — tirt is likely root + r — but not visible. \n\nPossibility: The tense suffix is in the verb root, and if absent, it's past? \nWait — rule: \"tense: past -s, present/future -r\" \nSo: present/future = -r → must be present or future \nSo verbs with -r = present/future \nVerbs without -r = past?\n\nBut in example 2: \"tirt\" — no -r — so past? \nBut \"repaired\" is past → okay.\n\nIn example 1: \"kanarriːcciːg\" — ends in -ciːg → does it have -r? \n\"kanarri\" → root → \"kanarri\" + \"ciːg\" → if ciːg includes -r → possibility? \nBut -r only appears in \"beyyeːcciːg\" → no -r → only in beyye → but beyye has -e → no -r.\n\nWait — in example 5: \"ay beyyeːcciːg\" → no -r → but it's present? Contradiction.\n\nUnless the -r is not visible in transcription — or the verb root includes the -r.\n\nWait — in the verb rule, \"tense: present/future -r\" — it's a suffix. \nSo verb must end with -r for present/future.\n\nBut in all examples: \n1. kanarriːcciːg → ends with -ciːg → no -r \n2. tirt → no -r \n3. biticcirra → ends with -ra → possibly -ir → object? \n\"biticcirra\" → direct object → \"chicken\" → plural → should have -ccir → yes → -ccir at end → plural \nSo -ccir → marks object \nAnd no -r → so past tense? \nYes — \"will give\" → future → should have -r → contradiction?\n\nExample 3: jahali waliːg darbadki biticcirra \n\"will give the chicken to the dogs\" → future → should have -r — but \"biticcirra\" ends with -ra → not -r → so verb doesn't have -r? \n\"biticcirra\" — could it be object? \nYes — \"biticcirra\" → chicken → plural → has -ccir → so object is plural → marked properly \nBut verb: \"jahali\" → subject → young men → plural → so 1st person pl → -u? \nBut \"jahali\" → -i? \nIn example 4: man jahalgi kadeːcciːg maːgtirsu → \"he stole\" → subject \"man\" → 3rd person sg → should be -u? But man = singular → 3rd person sg → so -u → but \"man\" is not -u → unless \"man\" is root? \nWait — \"man\" → subject → 3rd person sg → so should be marked with -u → but not → contradiction.\n\nWait — perhaps the subject marker is only on verb. \nIn example 4: man jahalgi kadeːcciːg maːgtirsu \n\"man\" = subject → 3rd person sg → should have -u → but doesn't → so maybe \"man\" is not the subject? \n\"man\" → could be indirect object? \n\"jahalgi\" → verb → to steal? \n\"jahalgi\" → past tense (no -r) → past → so \"stole\" → yes \n\"man\" → object? → \"stole the dresses for the young man\" → so \"man\" is indirect object → so O′ → must be marked with -gi or -ki \n\"man\" → ends in -n → obstruent → so should be marked with -ki → but no -ki → so contradiction.\n\nWait — rule: O′, O: -gi after sonorant, -ki after obstruent \nSo if O′ → after obstruent → -ki \n\"man\" ends in -n → obstruent → so should have -ki → but not → so not marked → so not O′ → so not indirect object → so must be direct object → but \"stole the dresses for the young man\" → dresses = direct object → man = indirect object → contradiction.\n\nUnless the marking is not on the noun but on the verb form.\n\nWait — re-read rule: \n\"for somebody: ‘to give’ (to the first person: deːn, to the second or third person: tir)\" \nSo for “give” — the verb root is changed based on recipient.\n\nBut in example 3: jahali waliːg darbadki biticcirra → \"young men will give the chicken to the dogs\" \n\"will\" → future → should have -r → but not visible in verb? \nVerb: \"darbadki\" → is this the verb? \n\"darbadki\" → ends with -ki → after obstruent → likely object marking? \nd → obstruent → so -ki → object suffix → so object is marked → object is \"biticcirra\" → chicken → plural → -ccir → valid → so direct object → so no indirect object?\n\nBut it says “to the dogs” → so dogs = indirect object → should be marked with -gi or -ki.\n\n\"to the dogs\" → so dogs = indirect object.\n\n\"waliːg\" → after -g → after sonorant? w → sonorant → so -g → so -gi after sonorant → valid → so waliːg = indirect object → marked properly.\n\nYes — so \"waliːg\" → indirect object → after sonorant (w) → -gi → valid.\n\nSo the marking on the noun is for its case.\n\nTherefore, for indirect object: noun + -gi (if after sonorant), -ki (if after obstruent)\n\nFor direct object: -gi (sonorant), -ki (obstruent)\n\nFor subject: no marking\n\nFor tense: past = -s, present/future = -r\n\nIn examples:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu \n\"we bought the camels\" \n\"ar\" → subject → 1st person pl → should be -u → but \"ar\" is used → possibly \"ar\" is \"we\" → so not marked — okay \n\"kanarriːcciːg\" → verb — \"buy\" root → has -ciːg? \n- ciːg → might be -r + -g? \nBut -r not visible → if present, should be -r \n\"kanarri\" + \"r\" → \"kanarriːr\" → but written as \"kanarriːcciːg\" → ends in -ciːg → so likely -r is merged? \nWait — perhaps the -r is part of the object marking? \nBut object is \"kamiːg\" → camels → plural → -ciːg → so -ciːg = plural mark → so perhaps -r is lost.\n\nContradiction — must resolve.\n\nIn example 5: ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces\" \n\"ay\" = 1st person sg → should be marked with -i → yes \n\"beyyeːcciːg\" → verb → \"buy\" → should have present/future -r → but not visible → unless the -r is attached to \"beyye\" → beyye + r = beyyer? \nBut it's beyyeːcciːg → so -r missing.\n\nIn example 6: wal aygi baːbiːg eldeːnsu → \"the dog found the doors for me\" \n\"wal\" = subject → \"dog\" → third person sg → should be -u → not → so \"wal\" = subject? \n\"wal\" → no -u → but should have -u → contradiction.\n\nWait — \"wal\" → may be \"the dog\" — not inflected → but in rule, subject → should have -u or -i → only if first person.\n\nSo if subject is third person → should be -a → but \"wal\" → not → so not directly marked.\n\nPossibility: the subject marker is only for the verb, not the noun.\n\nBut the rule says: \"subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\"\n\nSo the subject of the sentence has a marker that is attached to the verb.\n\nFor example: in example 3, \"jahali\" → subject → young men → plural → so should have -u → but not marked → so perhaps \"jahali\" = root with -u?\n\nIn example 4: man jahalgi kadeːcciːg maːgtirsu \n\"man\" = subject → 3rd person sg → should have -u → but now \"man\" is subject → so verb should have -u?\n\nBut verb is \"jahalgi\" → does it have -u? It doesn't.\n\nSo likely: the subject marker is on the verb.\n\n\"jahalgi\" → verb root → with subject marker?\n\n\"jahalgi\" → if past → -s → not visible → past?\n\nBut \"stole\" → past → so -s → in transcription, absent.\n\nSimilarly, in example 5: \"beyyeːcciːg\" → \"buying\" → present → should have -r → but not visible.\n\nBut in example 1: \"kanarriːcciːg\" → past → should have -s → not visible.\n\nSo likely: the tense suffix -s or -r is omitted in transcription, or part of the object marking.\n\nBut in example 2: tirt kadeːg allesu → \"repaired\" → past → should have -s → not visible.\n\nIn example 3: darbadki → future → should have -r → not visible.\n\nSo perhaps the tense is not visible — or the rules are compressed.\n\nFor the purpose of translation, we must infer from structure.\n\nNow, let's apply to the target items.\n\n11. magasi argi ajomirra.\n\nBreak down: \n\"magasi\" — likely subject? \n\"argi\" — likely indirect object or verb? \n\"ajomirra\" — direct object?\n\nStructure: S (O′) O V\n\nSo likely: \n[subject] [indirect object] [direct object] [verb]\n\nSo: magasi → subject → what is \"magasi\"? \n- \"ma\" → obstruent → if followed by -g → then -gi or -ki \n\"magasi\" — ends in -i → after vowel? \"a\" → vowel → so -i after vowel → so \"magas\" + i → could be S: subject → -i after vowel → yes → so subject = magas (root) + -i → 1st person sg? → yes — \"I\" → so \"magasi\" = I\n\nThen \"argi\" → could be indirect object → \"argi\" — after \"g\" → g is obstruent → so -ki after obstruent? But \"argi\" ends in -i — not -ki → unless -i is the case marker", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12596.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "redacted_solution_hint_mask5", + "sample_index": 1, + "output": "Step 1: Understand the word order pattern \nThe given structure is S (O′) O V — subject, indirect object, direct object, verb. \nThis means the verb comes at the end, and the object (direct or indirect) is specified before it.\n\nStep 2: Analyze case markers \n- Noun case: \n - Subject (S): no case marker \n - Indirect object (O′): -gi after a sonorant consonant, -ki after an obstruent consonant \n - Direct object (O): -gi after a sonorant, -ki after an obstruent \n- Plural marking: \n - -ːcci after a vowel (singular → plural) \n - -i after a consonant (in singular, if preceded by consonant)\n\nStep 3: Verb structure \n- Tense: \n - Past: ends in -s \n - Present/future: ends in -r (with r > d | n) \n- “Give” verb: \n - To the first person: deːn \n - To second/third person: tir \n- Object marking: \n - If O′ exists: O′ has no marker, O has -ccir (plural) or -ir (singular) \n - For plural O: -ccir (after consonant > ∅ → -ccir) \n - For singular O: -ir \n\nStep 4: Subject markers \n- 1st person singular: -i \n- 1st person plural / 3rd person singular: -u \n- 3rd person plural: -a \n\nStep 5: Identify patterns from given sentences\n\nExample 1: \n“ar kanarriːcciːg kamiːg jaːnticcirsu” \n→ We bought the camels for the neighbours \n“ar” = subject (1st person plural) \n“kanarriːcciːg” = object (camels) — plural marker -ːcci after vowel \n“kamiːg” = indirect object (neighbours) — case: -gi (after vowel, sonorant → -gi) \n“jaːnticcirsu” = verb: “bought” (past), -s suffix, root “jaːnti” → “buy” → past = “jaːnts” → but gets -s in past? Wait — “jaːnticcirsu” → past tense. \nBut root is “jaːnti” → buy → past = “jaːnts” → after root “jaːnti” → -ts → but here it's “jaːnticcirsu” → so likely: “jaːntic” + “cirsu” → perhaps a compound verb? \nWait — it says: verb has past -s, present/future -r \nSo past → -s, present → -r \nHere: jaːnticcirsu → ends in -s → past \nRoot is “jaːnti” → buy → so verb root is “jaːnti” → past → “jaːnti” + “s” → “jaːnts”? Wait — but it's “jaːnticcirsu” → has -ccir→ marks plural? \nAh — direct object “kamiːg” — camels → plural → -ːcci → so -ːcci after vowel → yes \nBut the verb is “jaːnticcirsu” → ends in -s → past verb \nWhat about the verb form: \n“jaːnti” + “c” + “cirsu” — seems like “cirsu” may be “s” with a modification? \nBut the rule says: past tense → -s, present/future → -r \nSo “jaːnti” + “s” = “jaːntis” → but here it's “jaːnticcirsu” → seems like irregular? \nWait — look at sentence 5: “ay beyyeːcciːg ajaːnirri” → I am buying the necklaces \n“ay” = 1st person singular subject \n“beyyeːcciːg” = necklaces → plural → -ːcci after vowel \n“ajaːnirri” = verb “buying” → present → -r → “beyyeːc” + “irri” → “beyyeːc” + “ir” → since object singular or plural? \nObject is “necks” → plural → so should have -ccir? \nBut here it's “ajanni” → root → “ajat” → buy → present → “ajani” + “r” → “ajani” → but written as “ajaːnirri” → “rri” → so -ir → for singular? \nWait — verb: \n- if there is indirect object → no object marking \n- otherwise, O (direct object) → singular → -ir, plural → -ccir \n\nSo in sentence 5: \n“ay beyyeːcciːg ajaːnirri” \n→ “ay” → 1st person singular \n→ “beyyeːcciːg” → necklaces → plural → -ːcci \n→ “ajaːnirri” → verb → present → -r → root “ajat” → “ajani” → but root is “aja” → buy → so “aja” + “nir” → “ajaːnirri” → ending in -ir → for singular object? \nBut object is plural → necklaces → so should have -ccir → contradiction? \nWait — direct object is \"the necklaces\" — plural → should be -ccir → but verb is -ir? \nAh — unless the noun is marked for case? \nWait — the verb form does not mark the number — it depends on whether there is an O′ or not. \nRule: \n- if O′ exists → O (direct) → -ccir (plural) or -ir (singular) \n- if no O′ → O directly → -ir (singular) or -ccir (plural)\n\nIn sentence 5: no O′ → only direct object → “necks” → plural → so must be -ccir \nBut verb is “ajaːnirri” → ends in -ir → contradiction?\n\nWait — may be a typo in parsing.\n\nWait — sentence 5: “ay beyyeːcciːg ajaːnirri” \n“beyyeːcciːg” → necklaces → plural → so marked with -ːcci \n“ajaːnirri” → verb → root “ajat” → present → -r → but ends in -ir → so perhaps -ir is suffix for singular?\n\nBut the object is plural → should be -ccir → so why -ir?\n\nUnless the noun “necks” is not being treated as direct object? \nWait — in “ay beyyeːcciːg ajaːnirri” → “beyyeːcciːg” is the direct object → so translation: “I am buying the necklaces” → direct object = necklaces → plural → should trigger -ccir in verb? \nBut verb is -ir → so what's going on?\n\nCheck sentence 2: “tirt kadeːg allesu” → The owner repaired the dress \n“tirt” → to second person or third → “to repair” → “tirt” = giver → so verb root is “tirt” → to give → for third person → “tirt” + “kadeːg” → kadeːg = dress → singular → object → no O′ → so object → singular → -ir? \nBut “allesu” → verb → present → -r? \nBut it ends in -s → “allesu” → ends in -s → so past tense? \nBut “repaired” → past → past → -s → so verb → past tense → -s → yes \nSo verb root “al” → repair → past → al + s → al+s → “al” → but written “al” → “allesu” → so yes → root = “al” → past → -s → “al” → “al” + “es” → “allesu” → yes \nSo verb ending: past → -s → so “al” + “s” → “al” → not “al” → “al” + “es” → “al” → misspelled? \n“allesu” → likely “al” + “es” → root “al” → past → -s → yes \nSo verb: past → -s → present/future → -r \n\nSo in sentence 5: “ay beyyeːcciːg ajaːnirri” \n“ay” → 1st person subject → present → verb → must be -r \nSo verb should end in -r → “ajaːnirri” → ends in -ir → so -r, not -s → so present → yes \nBut for plural direct object → should have -ccir → but current form is -ir → contradiction?\n\nWait — verb forms: \nIf O′ exists → direct object → -ccir (plural), -ir (singular) \nIf no O′ → direct object → -ir (singular), -ccir (plural)\n\nSo in sentence 5: no O′ → direct object → so plural → must have -ccir → so verb must be “ajaːnccirri” → but it is “ajaːnirri” → so maybe object is singular?\n\nBut \"the necklaces\" → plural \nUnless “necklaces” is plural → but marked with -ːcci → yes → so object is plural → verb must be -ccir → so why -ir?\n\nContradiction.\n\nWait — perhaps verb marking is only on the direct object? \nNo — the rule says: \n- if O′ exists → O (direct) → -ccir or -ir \n- otherwise O → -ir or -ccir\n\nSo for no O′ → O → singular → -ir, plural → -ccir\n\nSo for plural direct object → must be -ccir\n\nBut in 5: “ay beyyeːcciːg ajaːnirri” → object \"necklaces\" → plural → verb must end in -ccir → but ends in -ir → so contradiction?\n\nUnless the -ccir is on the noun → not on the verb.\n\nAh! The rule says: verb: \n- object: \n - O′: -∅ or -ccir (plural) \n - otherwise O: -∅ or -ir (singular) → and also -ccir in plural?\n\nBut no — it says: \n\"object: singular → -∅, plural → -ccir\"\n\nBut only in context of object marking → for direct object when no O′ → it says: \"otherwise O → -∅ or -ir\" — but never -ccir?\n\nWait — original:\n\n\"object: singular plural \nO′, if there is one -∅ -ccir (-C > ∅ | -ccir) \notherwise O -∅ -ir\"\n\nWait — it doesn’t say -ccir for otherwise O → says -ir → so for direct object when no O′ → only -ir → singular \nBut in plural, it implies no marking for direct object then?\n\nBut that contradicts the example.\n\nLook at sentence 10: “wali sarkaːygi darbadiːg eltirsa” \n→ \"The dogs found the chickens for the coward\" \nSo: \n- wali = subject → plural → ωal → dogs \n- sarkaːygi = indirect object? → for the coward → so O′ \n- darbadiːg = object (chickens) → direct object \n- eltirsa = verb → “found” → past → -s → so past tense → -s → yes \nSo verb: past → -s → root “el” → found → “el” + “tir” → “eltir” → with -s → “eltirsa” \nNow, direct object: \"chickens\" → plural → should have case? \n\"darbadiːg\" → ends in -gi → after obstruent (d → likely) → so case → for direct object → after obstruent → -ki → so should be -ki → but it's -gi → contradiction?\n\nAh! Case marking on the object: \n- O′ and O: \n - if after sonorant → -gi \n - if after obstruent → -ki \n\nSo \"darbadiːg\" → ends in -gi → after obstruent? d → obstruent → so should be -ki → but it's -gi → contradiction?\n\nBut \"darbadiːg\" → d is obstruent → so should have -ki → but it has -gi → so error?\n\nWait — spelling: “darbadiːg” — d is consonant, but after \"i\"? \n\"darbadiːg\" → “d” → obstruent → yes → so after obstruent → should be -ki → so should be -ki → not -gi → so why -gi?\n\nUnless the noun is after a vowel? \n- \"dari\" → d after vowel? no — \"darbadi\" → after \"i\" — \"di\" → i is vowel → so d after vowel → so d is after vowel → so after vowel → after sonorant? \nVowel → d is after vowel → so consonant after vowel → so after vowel → so for case: after a vowel → case marker is -gi → yes → so \"d\" after vowel → so -gi → correct → the consonant is after a vowel → so -gi → yes → so case is -gi → rules apply by position of consonant.\n\nSo: \n- Case marker attached after a consonant → \n - if consonant is after a vowel → -gi (if sonorant) → or -ki (if obstruent) \nBut the rule says: \n- O′, O: \n - after sonorant → -gi \n - after obstruent → -ki \n\nSo only based on the consonant type, not whether it's after vowel.\n\nSo d is obstruent → after vowel → so should be -ki → not -gi → but it is -gi → contradiction?\n\nUnless d is not the consonant being followed — the word is \"darbadiːg\" → ends in -gi → the consonant is d → which is after i → vowel → so d after vowel → d is obstruent → so should be -ki → but it is -gi → so error?\n\nWait — the noun is \"chickens\" → in Kunuz Nubian → \"darbad\" → so \"darbad\" + \"ki\" → but form is \"darbadiːg\" → ends in -gi → so perhaps -gi is the case marker.\n\nAh — the case marker is -gi or -ki → so the word has a consonant (d) and then -gi or -ki → so the case is attached to the end.\n\nBut the rule says: case marker applies after a consonant → and depends on the consonant:\n\n- if after a sonorant → -gi \n- if after an obstruent → -ki \n\nSo for \"darbadiːg\" → last syllable: \"diːg\" → d is after vowel i → d is obstruent → so should be -ki → but it is -gi → contradiction.\n\nUnless the d is not the consonant — it's part of a consonant cluster? \n\"darbadi\" → d, a, r, b, a, d, i → so d before i → so before vowel → so not after vowel — so when we say \"after a consonant\", it's the position of the consonant relative to vowel.\n\nRule: case marker after a consonant → so if the noun ends with a consonant → the case marker is added after that consonant.\n\nSo in \"darbadiːg\", the syllable is \"diːg\" → so the consonant is d → and it is preceded by i (vowel) → so d is after vowel → so d is after vowel → so whether it's sonorant or obstruent → we look at the consonant itself.\n\nd is obstruent → so after vowel → → case marker should be -ki → so word should be \"darbadki\" → not \"darbadiːg\"\n\nBut in sentence 10: \"wali sarkaːygi darbadiːg eltirsa\" → given as \"darbadiːg\" → so likely typo or interpretation error.\n\nPerhaps \"darbadki\" is intended — but written as \"darbadiːg\" due to transcription mistake.\n\nSimilarly, in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" \n→ jahali = subject → young men → plural \n→ waliːg = indirect object → to the dogs → so O′ \n→ darbadki = direct object → chicken → singular → so should be -ki → after obstruent (d) → yes → -ki → correct \n→ biticcirra = verb → future → -r? → \"biticcirra\" → ends in -ra → so -r → yes → future-tense verb → affix -r\n\nSo verb: \"biticcirra\" → root \"biti\" → give → future → -r → yes\n\nSo case marking is correct: \n- only when after consonant → \n - if that consonant is obstruent → -ki \n - if sonorant → -gi \n\nBack to sentence 5: \"ay beyyeːcciːg ajaːnirri\" \n→ \"ay\" = 1st person singular \n→ \"beyyeːcciːg\" = necklaces → plural → -ːcci after vowel \n→ \"ajaːnirri\" = verb → present → -r (ends in -r? -ir → ends in -ir → not -r)\n\n“ajaːnirri” ends in -ir → -i → so likely -ir → but present tense should be -r\n\nAh — rule: present/future → -r (r > d | n) \nSo verb must end in -r → but “ir” → so likely a typo or misreading.\n\nPossibly it is “ajaːnirri” → root “ajat” → present → “ajani” → with -r → so should be “ajaːnirri” → but “ir” is not -r → so perhaps -r is not pronounced as -r?\n\nCheck sentence 6: “wal aygi baːbiːg eldeːnsu” \n→ \"The dog found the doors for me\" \n→ \"wal\" = dog → subject \n→ \"ay", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12216.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "redacted_solution_hint_mask5", + "sample_index": 2, + "output": "We are given a set of Kunuz Nubian sentences with English translations, and we must translate five new ones using the provided linguistic rules.\n\nStep 1: Understand the syntax pattern.\n\nWord order: S (O′) O V → Subject, then indirect object (if present), then direct object, then verb.\n\nStep 2: Analyze the noun morphology.\n\n- Root form: no change.\n- Number:\n - Singular: no suffix (or -i after consonant)\n - Plural: -ːcci after vowel\n- Case:\n - Subject (S): -∅ or -i after consonant\n - Indirect object (O′) and direct object (O):\n - After sonorant consonant: -gi\n - After obstruent consonant: -ki\n\nStep 3: Verb structure.\n\n- Tense:\n - Past: -s\n - Present/future: -r (r > d | n, so perhaps -r becomes -d or -n in some cases, but we’ll check context)\n- \"To give\":\n - To first person: deːn\n - To second/third person: tir\n- Object:\n - If O′ present: O′ has -ccir (plural) or ∅ (singular), only if after vowel (C > ∅ | -ccir)\n - If no O′: O has -ir (plural), or ∅ (singular)\n- Subject:\n - 1st person singular: -i\n - 1st person plural / 3rd person singular: -u\n - 3rd person plural: -a\n\nStep 4: Identify patterns in known examples.\n\nExample 1: ar kanarriːcciːg kamiːg jaːnticcirsu \nWe bought the camels for the neighbours. \n→ ar = we (1st person pl, -u? but ar → subject → must be -u, but ar is not -u) → perhaps ar is root with -a? \nWait: \"We\" → 1st person plural → should be -u → so likely ar is root + -u? But ar is not spelled that. \nBut look at sentence 4: man jahalgi kadeːcciːg maːgtirsu → He stole the dresses for the young man. \nman = he? → 3rd person singular → so -a or -u? But man is the subject. \nBut \"He\" = 3rd person singular → should be -a? \nBut in sentence 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces. \nay = I → 1st person singular → -i → correct. \nThus, subject markers:\n- 1st person singular: -i → ay = I \n- 1st person plural / 3rd person singular: -u → ar = we, or a person? In 1, ar = we → so -u? But ar → no -u → contradiction? \nWait: sentence 1: ar → we bought → ar must be 1st person plural → so ar = root + -u → perhaps ar is just short form? \nBut sentence 8: iːdi magaski kamiːg tirsa → The men gave the camels to the thief. \niːdi = men (3rd person plural → -a?) → iːdi → could be i: root, -di → perhaps di = -a? \nBut -a is for 3rd plural → iːdi → likely root i + -di → di → -a? \nLikely: subjects:\n- 1st sg: -i (ay)\n- 1st pl / 3rd sg: -u (ar, ay is 1st sg, ar is 1st pl → 1st pl = ar → so ar = root + -u → but ar has no -u → perhaps ar is root? Not satisfying)\n\nWait: sentence 6: wal aygi baːbiːg eldeːnsu → The dog found the doors for me. \nwal → dog → 3rd person singular → should be -a? But wal → no suffix → so is wal = root, -a not marked? \nBut sentence 13: hanu tirtiːg elirsu → I will strike the donkey. \nhanu → I (1st person → -i?) → hanu → likely root + -u → so -u for 1st pl/3rd sg → hanu → 1st person? \nhanu → 1st person → -u → correct.\n\nSimilarly, sentence 2: tirt kadeːg allesu → The owner repaired the dress. \ntirt → to someone → \"to give\" is deːn or tir → tirt → likely \"to give\" to second/third person → so tirt = verb \"to give\" to someone → so tirt = verb morpheme for \"to give to\" → so tirt = [to give to], and object → kadeːg → dress → singular → root → kadeːg? \nThen allesu → the dress? → alle → dress, su → case? The dress → object → O → must be -gi or -ki? \nkadeːg → dress → vowel followed → so -gi? No → kadeːg → root + g → g is sonorant → after vowel → so -gi → kadeːg → so object is dress (O) → with -gi? \nBut in sentence 2: tirt kadeːg allesu → The owner repaired the dress. \nBut “repaired” is not “to give” → contradiction. \n\nWait: the verb rules say \"for somebody: ‘to give’ (to the first person: deːn, to the second or third person: tir)\" → so only for \"to give\" → but sentence 2 is \"repaired\" → so must be different verb.\n\nBut in sentence 2: tirt kadeːg allesu → \"The owner repaired the dress\" → so tirt can't be “to give”. \nSo perhaps “tirt” is not “to give” → maybe “tirt” is a verb meaning “to repair”?\n\nBut the rule says: “for somebody: to give” → so perhaps “tirt” means “to give” only for second/third person → but here it's \"repaired\" → contradiction.\n\nWait: sentence 8: iːdi magaski kamiːg tirsa → The men gave the camels to the thief. \niːdi → men (3rd person plural → -a) \nmagaski → camels (plural → -ːcci?) → maga → root, ski → -ki → after obstruent? \nk → obstruent → after k → -ki → so magaski → plural → yes \nkamiːg → camels → kami → root, -i after consonant? k → not after vowel → so not -i? \nkami → after k → consonant → so after consonant → -i → so kami → root + i → singular? \nBut it's plural → so must be -ːcci after vowel → but kami → vowel after k? → ami → after k → k is consonant → so -i after consonant → singular? \nBut camels → plural → so must have -ːcci → so kamiːg → has -g → after vowel? → after i → i is vowel → so -gi? \nBut -gi after sonorant → g is sonorant → so -gi → so kamiːg → kam + i + g? → kam → root, i → after consonant → k → consonant → so -i → so kami → kam -i → singular → then -g? → is -g case suffix? \nYes: O or O′ → -gi after sonorant, -ki after obstruent. \nSo kamiːg → kam + i → i after consonant → singular → then g → after vowel? → after i → vowel → so -gi → but -gi is case → so object? \nkamiːg is the direct object (camels) → so object → must have case suffix → so yes → -gi after sonorant (g) → so kam → root, i after consonant (k), then g → case suffix → so object is camels → plural? → but -i after consonant is singular → contradiction.\n\nWait: maybe the \"number\" rule is:\n- singular: -∅ or -i after consonant\n- plural: -ːcci after vowel\n\nSo kam → root → if plural → must have -ːcci after vowel → but kamiːg → after i → vowel → so -ːcci? → but it's -gi → not -ccir? \nSo not matching.\n\nBut in sentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu \nWe bought the camels for the neighbours. \nar → we (1st pl) → should be -u → ar → not -u → unless ar is root with -u → but no. \nBut in sentence 13: hanu tirtiːg elirsu → I will strike the donkey. \nhanu → I → 1st person singular → should be -i → but hanu → -u → so likely -u for 1st pl / 3rd sg → so I → 1st sg → usage of -u? \nWait: in sentence 5: ay beyyeːcciːg ajaːnirri → I am buying the necklaces → ay → I → 1st sg → -i → correct. \nSo 1st sg → -i → ay \n1st pl → ? → ar → must be -u → so ar → root + -u → but written as ar → so perhaps in spelling, -u is omitted? \nBut in sentence 4: man jahalgi kadeːcciːg maːgtirsu → He stole the dresses for the young man. \nman → he → 3rd person singular → should be -a → so man → root + -a? → man → no -a → only if -a is suffix → m → consonant → after m → -a → so man = m + a → so -a → yes → so 3rd sg → -a \nSimilarly, sentence 7: The young man bought the dog for us → jahal argi walgi jaːndeːccirsu \njahal → young man → 3rd person singular → -a → jahal = jah + a → yes. \nSo:\n\nSubject marks:\n- 1st sg: -i → ay\n- 1st pl / 3rd sg: -u → ar, hanu → hanu is “I” → but hanu → -u → so how? \nWait: hanu → I → but \"I\" is 1st sg → should be -i → so maybe hanu is 1st pl? → but \"I will strike\" → first person singular.\n\nUnless the marking is:\n- 1st person singular: -i (ay)\n- 1st person plural or 3rd person singular: -u (ar, hanu?) → but hanu is in sentence 13: \"I will strike\" → contradiction.\n\nUnless \"hanu\" is not 1st singular.\n\nLook at sentence 9: ay hanuːg bijomri → I will strike the donkey → ay = I → 1st sg → mark -i → correct → hanuːg → \"the donkey\" → object → hanu → root? \nBut in sentence 13: hanu tirtiːg elirsu → hanu tirtiːg elirsu → \"I will strike the donkey\" → so hanu → subject → I → must be 1st sg → so should be -i → but it's -u? \nhanu → -u → unless the subject marker is -u for 1st pl or 3rd sg → so perhaps \"I\" is marked as -u here? \nBut in sentence 5: ay = I → -i → so why different?\n\nWait: sentence 10: The dogs found the chickens for the coward → wali sarkaːygi darbadiːg eltirsa \nwali → dogs → plural → so 3rd person plural → -a → wali → likely root + -a? → but wali → no -a → wali → perhaps wali is root → and for plural → -a not added? \nBut sentence 8: iːdi → men → plural → must be -a → iːdi → i + di → di → -a → yes. \nSo plural = -a for 3rd person plural? \nBut in sentence 2: tirt kadeːg allesu → owner → 3rd person singular → should be -a → tirt is verb → kadeːg → dress → object → allesu → the dress → so allesu is object → case? \nallesu → after vowel? → e → vowel → so -gi after sonorant? → l → sonorant → so -gi → so allesu = al + le + su → su = -gi? \nal → root, le → after l → l is consonant → so -i → then su → after e → vowel → -gi → so yes → object → case suffix -gi → after sonorant.\n\nThus, case suffix:\n- O and O′: -gi after sonorant (l, m, n, r, w, y), -ki after obstruent (p, t, k, s, b, d, g)\n\nNow, verbs:\n- \"to give\" to first person: deːn\n- to second/third person: tir\n- tense: past -s, present/future -r (r > d|n → so when r after vowel, becomes d or n? e.g., r → d or n in some cases)\n\nBut verb roots:\n- example 1: kanarriːcciːg → \"bought\" → present/future → so -r? → but has -r → and -ci at end → -ci is plural? \nkanarriːcciːg → root kanar? + -r → past tense → -s? → has -r → so present/future → but \"bought\" is past → contradiction.\n\nBut in sentence 1: \"We bought the camels for the neighbours\" → \"bought\" is past → so should have -s → but word is kanarriːcciːg → has -r → and -ci → plural? \n-riːcci → after vowel → -ːcci → plural → so kanarriːcciːg → after vowel → -ːcci → so plural → and -r → but -r is present/future → not past.\n\nSo perhaps tense marking is:\n- past: -s\n- present/future: -r\n\nBut \"bought\" is past → so must have -s → so kanarriːcciːg → has -r → contradiction.\n\nUnless \"kanarriːcciːg\" has -s → but it's -r → perhaps spelling error? \nLook at sentence 2: tirt kadeːg allesu → \"repaired\" → not \"gave\" → so tirt is not “to give” → so must be different verb.\n\nBut in sentence 8: iːdi magaski kamiːg tirsa → gave → so tir → verb “to give” to third person.\n\nSo in example 1: \"We bought\" → verb = kanarriːcciːg → likely “bought” → past → so should have -s → but it has -r → contradiction.\n\nUnless the -r is future → \"will buy\" → but the English says \"we bought\" → past.\n\nBut sentence 5: ay beyyeːcciːg ajaːnirri → \"I am buying\" → present/future → -r → yes → has -r.\n\nSo perhaps only if used with present/future.\n\nBut sentence 1 is past → so must have -s → but kanarriːcciːg has no -s → only -r.\n\nUnless the root is different.\n\nAnother possibility: \"kanarriːcciːg\" has a past suffix.\n\nBut the rules say: past -s, present/future -r.\n\nSo if \"bought\" is past → should be -s → not -r.\n\nWait, look at sentence 4: man jahalgi kadeːcciːg maːgtirsu → He stole the dresses for the young man → man → he → 3rd person → -a → kadeːcciːg → stole → past → should have -s → but has -r? → kadeːcciːg → has -r → still.\n\nSo all verbs have -r → not -s? But sentence 1 is past.\n\nUnless tense is not marked by -s/-r.\n\nPerhaps the rules are mistated, or the examples are inconsistent.\n\nWait: sentence 1: ar kanarriːcciːg kamiːg jaːnticcirsu → we bought the camels for the neighbours → bought → past → so must have past marker → no -s → only -r → so likely the -r is future → but \"bought\" is past.\n\nContradiction.\n\nUnless the \"past\" marker is not -s → or it's absent.\n\nBut in sentence 8: iːdi magaski kamiːg tirsa → gave → present → because \"gave\" is present → past is not given.\n\nNo sentence has past -s → all have -r.\n\nSo perhaps tense is:\n- present/future: -r (which may be pronounced as -d or -n in some cases)\n- past: no -s → or the verb root is different\n\nBut sentence 9: ay hanuːg bijomri → I will strike the donkey → future → -r → yes.\n\nSentence 10: wali sarkaːygi darbadiːg eltirsa → The dogs found the chickens for the coward → found → past? → but \"eltirsa\" → -sa → could be -s? → but not -s → likely -r → so present/future?\n\n\"found\" is past → so should be -s → but verb is eltirsa → -sa → perhaps s is suffix → s after root? → so -s is suffix.\n\nIn sentence 10: eltirsa → e + l + t + i + r + s a → so -s at end → so likely past tense.\n\nIn sentence 2: tirt kadeːg allesu → repaired → past → no -s? → tirt → no -s → kadeːg → no -s → allesu → no -s → no past marker.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12073.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "redacted_solution_hint_mask5", + "sample_index": 3, + "output": "We are given a set of Kunuz Nubian sentences with translations and linguistic rules. Our goal is to translate five new sentences (11–15) into English, using the provided rules.\n\n---\n\n**Step 1: Understand the word order**\n\nThe rule says: \n**S (O′) O V** \n→ Subject, then indirect object (if any), then direct object, then verb.\n\nSo the structure is: \n[Subject] [Indirect Object (optional)] [Direct Object] [Verb]\n\n---\n\n**Step 2: Analyze noun inflection**\n\nNoun morphology:\n\n- **Root**: base form\n- **Number**:\n - singular: no mark\n - plural: suffix **-ːcci** after a vowel\n- **Case**:\n - Subject (S): -∅ (no case)\n - Indirect object (O′) and direct object (O):\n - After a **sonorant consonant** (like /l/, /m/, /n/, /r/, /j/, /w/): **-gi**\n - After an **obstruent consonant** (like /p/, /t/, /k/, /s/, /f/, /θ/, /ʃ/): **-ki**\n\nNote: the case suffix is only added to O’ or O, depending on the consonant before.\n\n---\n\n**Step 3: Verb morphology**\n\n- **Tense**:\n - past: ends in **-s**\n - present/future: ends in **-r** (note: r > d | n → if r is followed by d or n, it becomes d or n; likely a phonetic change)\n- **Subject**:\n - 1st person singular: -i\n - 1st person plural / 3rd person singular: -u\n - 3rd person plural: -a\n- **Verb root**:\n - “to give” → to the first person: **deːn**, to second/third: **tir**\n- **Object marking**:\n - If there is an indirect object (O′), no object suffix on O (but the O′ has case)\n - If no O′, then:\n - direct object is marked:\n - singular: -∅\n - plural: -ccir (if object is plural, replaces -C → ∅)\n - If there is no direct object (O), then:\n - object suffix: -ir (plural) or -∅ (singular), but only if no O′\n - Actually: if no O′, and O exists, then:\n - singular: -∅\n - plural: -ir\n\nWait — let's re-check the rule:\n\n> object: \n> - singular: -∅ \n> - plural: -ccir (-C > ∅ | -ccir) \n> (only if O′ is present)\n\nWait — the rule says:\n\n> O′, if there is one → -∅ for singular, -ccir for plural \n> otherwise O → -∅ for singular, -ir for plural\n\nSo:\n- If there is an indirect object (O′), then:\n - direct object (O) is marked with -ccir in plural, not -ir\n- If no O′, then:\n - direct object is marked with -ir in plural, -∅ in singular\n\nBut note: the suffix appears after the noun, and the rule says \"after a consonant\", so applies based on consonant before.\n\nWait — actually, the case suffix applies to the object, depending on what comes before it.\n\nLet’s interpret carefully.\n\n---\n\nWe’ll go sentence by sentence, using pattern recognition from the examples.\n\n---\n\n**Sentence 1**: *ar kanarriːcciːg kamiːg jaːnticcirsu* \n→ \"We bought the camels for the neighbours.\" \nBreak it down:\n- ar = we → 1st person plural → subject (S)\n- kanarriːcciːg = bought → verb root kanarriːc → past tense (ends in -s), so past\n - kanarriːc → original root + -r for present/future, but -s → past\n- kamiːg = camels → direct object\n - kamiːg → root is \"kami\", + -g → case: after vowel, so -g for object?\n - After \"i\", vowel → \"kami\" → after vowel → case is -gi? But here it's -g?\n - Root: kami → but → kamgi? Wait, it's \"kamiːg\"\n - Pattern: if after vowel → use -gi? But here -g?\n\nWait: case rule:\n\n> O′, O: after sonorant → -gi; after obstruent → -ki\n\n\"ma\" is a vowel → followed by \"k\" (obstruent), so case suffix should be -ki → but here it's -g?\n\nWait — \"kamiːg\" — \"kami\" → k after vowel → is k an obstruent? Yes. So case suffix should be -ki.\n\nBut we have -g → contradiction?\n\nWait — perhaps the case suffix is not applied to all nouns at the end.\n\nLook at sentence 2:\n\n2. tirt kadeːg allesu. → \"The owner repaired the dress.\"\n\n- tirt = repaired → verb “tir” (to repair), present tense? → “tirt” → tirt → tense: -r → so present (present/future)\n- kadeːg = dress → direct object\n- allesu = (to) the owner? → indirect object?\n\nNo: \"the owner repaired the dress\" → so “the owner” is subject, “the dress” is direct object.\n\nBut structure is S O V → so S = owner, O = dress, V = repaired\n\nBut in the sentence: “tirt kadeːg allesu” → subject is tirt (owner) → so “tirt” is subject?\n\nWait — no! “tirt” is likely the verb.\n\nSo “tirt” is verb (present), “kadeːg” is object (dress), “allessu” → possibly “to the owner”? But that's after.\n\nWait — “allessu” — al → a, lessu → ? Could be “to the owner”?\n\nBut “tirt” = repaired, so \"the owner repaired the dress\" → subject = owner → so tirt is not the subject.\n\nBut the verb is “tirt” → so subject must come before.\n\nSo: “tirt kadeːg allesu” → tirt = verb, kadeːg = direct object, allesu = indirect object?\n\nBut the structure is S (O′) O V → so S first.\n\nSo if it's “tirt [O′] [O]”, then tirt is not S.\n\nContradiction.\n\nUnless tirt is subject.\n\nBut “tirt” = “to repair” → belongs to the verb.\n\nSo “tirt” is the verb.\n\nSo the sentence is: [subject] [O′] [O] [verb]\n\nSo: (subject) (O′) (O) (verb)\n\nIn “tirt kadeːg allesu” → kadeːg is likely O, allesu is O′?\n\nBut kadeːg has suffix -g → after vowel? k after vowel → k is obstruent → should be -ki → not -g.\n\nUnless the noun is only marked if it has a following object.\n\nWait — in the rule:\n\n> O′, if there is one → -∅ (singular) or -ccir (plural)\n\n> otherwise O → -∅ or -ir (plural)\n\nAnd case suffix is only added depending on the consonant immediately before.\n\nSo apply case marking only to O or O′ when needed.\n\nIn sentence 2: tirt kadeːg allesu\n\nWe interpret:\n\n- subject: “tirt” — but tirt is verb (to repair), so not subject.\n\nNo.\n\nPerhaps “tirt” is the subject.\n\nBut “tirt” is root of “to repair” — so it cannot be subject.\n\nWait — look at sentence 3:\n\n3. jahali waliːg darbadki biticcirra.\n\n→ The young men will give the chicken to the dogs.\n\n“jahali” = young men (subject)\n\n“waliːg” = to the dogs (O′)\n\n“darbadki” = chicken (direct object)\n\n“biticcirra” = verb — future? (b- + t)\n\n\"biticcirra\" → b (future) + t (root) → future → \"will give\"\n\nSo: S = jahali (young men) — 1st person plural or 3rd? → \"young men\" → 3rd person plural\n\n→ so subject = jahali → plural → -a? → but jahali ends with -i → no.\n\n“jahali” → jahal + i → root jahal → i at end? In the rules, only 1st person singular uses -i.\n\nBut “jahali” is not -i → so not 1st person.\n\nSo jahali = noun → root jahal → plural → -ːcci? But no -ːcci → so singular?\n\nBut \"young men\" is plural.\n\nContradiction.\n\nWait — perhaps “jahali” is root → full form: jahal (young) + -i → stems from root jahal, with -i suffix for plural?\n\nBut the rule says:\n\n- singular: -∅\n- plural: -ːcci after vowel\n\nSo “jahali” has -i → not -ːcci → so not plural.\n\nSo is “jahali” singular?\n\nBut “young men” is plural.\n\nLook at sentence 4: man jahalgi kadeːcciːg maːgtirsu \n→ He stole the dresses for the young man.\n\n\"man\" → he → 3rd person singular → subject\n\n\"jahalgi\" → to the young man? → so O′ = young man → “jahal” root → case: after \"l\" (sonorant), so -gi → yes → jahalgi\n\n\"kadeːcciːg\" → stole the dresses? “kade” → dress, then -cciːg → ends with -g → case?\n\nkade → k after vowel → k is obstruent → should be -ki → but ends in -g?\n\nWait — this is confusing.\n\nPerhaps the case suffix is only applied to objects, and only if they are not root.\n\nLet’s go back to the rule for case:\n\n> S: -∅ \n> O′, O: after sonorant consonant: -gi; after obstruent: -ki\n\nSo in “kadeːcciːg” — kade → k is obstruent → after vowel → so should be -ki → but it has -g?\n\nWait — “kadeːcciːg” — ends in -g → not -ki.\n\nUnless the -g is from another marker.\n\nWait — look at sentence 8: iːdi magaski kamiːg tirsa \n→ The men gave the camels to the thief.\n\n“iːdi” → men → plural → in root → iːdi → i is not present in root, but ends with -i → 1st person singular? No.\n\n\"iːdi\" — perhaps root \"i\" + -di? — no.\n\nBut \"iːdi\" → likely subject.\n\n\"magaski\" → to the thief → O′ → so \"magas\" root → case: after “s” (sonorant) → -gi → yes — \"magaski\"\n\n\"kamiːg\" → the camels → O → \"kami\" root → after “i” (vowel) → k is obstruent → should be -ki → but it is -g?\n\nStill -g — contradiction.\n\nUnless the rule is misread.\n\nWait — perhaps the \"g\" is not the case suffix.\n\nIn sentence 1: \"kamiːg\" — in \"kamgi\" form? But here it's \"kamiːg\"\n\nBut in the verb, we have \"jaːnticcirsu\" — jaːn + ticcir + su\n\n\"jaːnticcir\" — likely \"to buy\" → root \"jant\", with -s for past tense?\n\nBut \"kanarriːcciːg\" → kanarri + cci + ig?\n\n\"kana\" + \"ri\" → but complex.\n\nAlternative: perhaps the case suffix is only added to object, and the form depends on the noun.\n\nPerhaps the suffix -g is a marker for object (O), and only appears after vowel.\n\nBut rule says:\n- for O′ and O: after sonorant → -gi, after obstruent → -ki\n\nSo in \"kamiːg\": \"kami\" → k after vowel → k is obstruent → should be -ki → but it's -g.\n\nBut -g vs -ki — different.\n\nUnless \"g\" is a typo or a different form.\n\nWait — in sentence 10: wali sarkaːygi darbadiːg eltirsa \n→ \"The dogs found the chickens for the coward.\"\n\nwali = dogs → subject \nsarkaːygi = to the coward — O′ → sarka → s is sonorant → so -gi → yes \ndarbadiːg = chickens → direct object → \"darba\" root → after “d” (obstruent) → so should be -ki → but it's -g?\n\nAgain, -g.\n\nSo it seems that in all cases, objects marked with -g, not -ki or -gi.\n\nSo perhaps the rule is misstated.\n\nAlternatively, perhaps \"g\" is the standard form for object case in this language.\n\nOr perhaps the case suffix is not -gi or -ki, but rather a different system.\n\nWait — look at sentence 4: jahalgi kadeːcciːg maːgtirsu \n\"jahalgi\" = to the young man — O′ \n\"kadeːcciːg\" = the dresses — O \n\"maːgtirsu\" = stole → verb \n\n\"kadeːcciːg\" — has -g at end — k after vowel → after obstruent → should be -ki → but it's -g.\n\nPerhaps it's a reduction or fixed form.\n\nMaybe the case suffix is simply -g for object when after vowel.\n\nBut rule says after sonorant → -gi, after obstruent → -ki.\n\nBut all examples show -g at end.\n\nIn sentence 8: \"kamiːg\" — same.\n\nIn sentence 3: \"biticcirra\" — verb ending — not object.\n\nPerhaps the case suffix is only applied to the object, and in the examples, due to phonetic reduction, it's written as -g.\n\nBut it doesn't match the rule.\n\nWait — maybe the rule was written in a different way.\n\nAnother possibility: the \"g\" is not case suffix, but part of the root.\n\nBut in \"kami\" → k is after vowel, so vowel to k → obstruent → should be -ki.\n\nBut all examples have -g.\n\nUnless the language has a fixed object case marker -g.\n\nGiven that, perhaps we should ignore the detailed case rule and just look at word forms.\n\nLet’s extract patterns from known translations.\n\n---\n\nFrom known sentences:\n\n1. ar kanarriːcciːg kamiːg jaːnticcirsu \n→ \"We bought the camels for the neighbours.\" \n- \"ar\" = we (1st person plural) \n- \"kanarriːcciːg\" = bought → verb root kanarri → with -r for present/future, -s for past? But here it's -ciːg → ends in -g, not -s.\n\nWait — \"kanarriːcciːg\" — seems to have -r, -c, -i, -g.\n\nBut \"jaːnticcirsu\" → \"jaːnti\" + \"ccir\" + \"su\" → \"to buy\" — past tense?\n\n\"jaːnti\" → root → with -t + -ccir suffix? No.\n\nNote: \"jaːnticcirsu\" → likely \"buy\" with past suffix -s.\n\nBut -s is at end.\n\nIn sentence 5: ay beyyeːcciːg ajaːnirri → \"I am buying the necklaces.\"\n\n\"ay\" = I (1st person singular) \n\"beyyeːcciːg\" → buying → root \"beyy\" + -c → present/future? \n\"ajaːnirri\" → the necklaces → direct object.\n\n\"beyyeːcciːg\" — ends with -g → possible object case.\n\n\"ajaːnirri\" — ends with -ri → after \"n\" (obstruent) → should be -ki → but is -ri?\n\nWait — in sentence 5: \"ajaːnirri\" — \"n\" is obstruent → after vowel → should be -ki → but it's -ri.\n\n-ri vs -ki.\n\nAgain, not matching.\n\nBut perhaps the suffix is -ir for plural, and -g for object.\n\nIn sentence 5: \"beyyeːcciːg\" — verb? \"beyye\" root → \"be\" + \"yye\" → \"buy\" → with -r for present/future → \"beyyeːr\" → but here it's \"beyyeːcciːg\" — has -g.\n\nNot matching.\n\nPossibly the verb is \"beyy\" + \"e\" + \"c\" + \"i\" + \"g\" — not.\n\nI think the morphological rules given may be either approximate or simplified.\n\nBut the structure is clear.\n\nWe can use the known patterns to infer meaning of words.\n\n---\n\n**Step 4: Identify and group nouns**\n\nFrom known sentences:\n\n- kanarriː (camel) → used in \"camels\"\n- kadeː (dress)\n- waliː (dog)\n- jahal (young man)\n- magas (thief)\n- tirt (to repair, to give)\n- el (door)\n- bijomri (to strike)\n- baːbiːg (to find)\n- deːn (to give to first person)\n- tir (to give to others)\n\nSubject markers:\n\n- ar = we (1st person plural)\n- ay = I (1st person singular)\n- man = he (3rd person singular)\n- hanu = I will (future) — \"hanu\" → future, with \"tirt\" or \"hanu\"\n- iːdi = the men (3rd person plural)\n- wal = the dog (3rd person singular)\n- sarkaːy = coward\n\nObject markers:\n\n- -g after vowel → object (O)\n- -gi after sonorant → O'\n- -ki after obstruent → O'\n\nBut", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12506.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n [TARGET ANSWER REDACTED]\n 2. ay kanarriːg baːbki alletirsi.\n [TARGET ANSWER REDACTED]\n 3. hanu tirtiːg elirsu.\n [TARGET ANSWER REDACTED]\n 4. tirti argi kamgi deːccirsa.\n [TARGET ANSWER REDACTED]\n 5. ay darbadki bijaːndi.\n [TARGET ANSWER REDACTED]\n\n (b) 6. The neighbours are giving the necklace to the owner.\n kanarriːcci tirtki beyyeːg atirra.\n 7. The young man bought the dog for us.\n jahal argi walgi jaːndeːccirsu.\n 8. We will steal him.\n ar mangi bimaːgru.\n 9. The owners struck the thieves.\n tirti magasiːg jomirsa.\n 10. The dogs found the chickens for the coward.\n wali sarkaːygi darbadiːg eltirsa.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 0, + "output": "We are given a set of English sentences and their translations into Kunuz Nubian, along with grammatical rules for structure and morphophonology. Our task is to translate five new sentences into Kunuz Nubian using the rules provided.\n\nWe analyze each sentence step by step using the given structure and morphological patterns.\n\n---\n\n**Rule summary:**\n\n- Word order: **S (O′) O V** \n → Subject, then indirect object (if any), then direct object, then verb.\n\n- Noun morphology:\n - Singular: bare root; if after consonant: add **-i**\n - Plural: add **-ːcci** after a vowel\n - Case:\n - Subject (S): bare → **-∅**\n - Indirect object (O′) or direct object (O): \n - After **sonorant consonant**: **-gi** \n - After **obstruent consonant**: **-ki**\n\n- Verb:\n - Tense:\n - Past: **-s**\n - Present/future: **-r** (and r > d | n → e.g., r → d or n if preceded by certain sounds)\n - Root:\n - \"to give\" → to first person: **deːn**, to second/third person: **tir**\n - \"to buy\" → **kanaːrriːg** (from example 1), root appears to be **kanaːrri** → extended to **kanaːrriːg**\n - \"to steal\" → **man** (example 4: \"man jahalgi kadeːcciːg\" → \"he stole the dresses for the young man\")\n - \"to strike\" → **hanuːg** (example 9: \"I will strike the donkey\")\n - \"to find\" → **tirt** (example 2, 6: \"tirt kadeːg\", \"tirti argi kamgi\")\n - Object marking:\n - If O′ exists (indirect object), add:\n - singular: -∅\n - plural: -ccir (C > ∅ or -ccir if consonant > obstruent)\n - Otherwise, direct object: singular -∅, plural -ir\n\n- Subject markers:\n - 1st sg: **-i**\n - 1st pl / 3rd sg: **-u**\n - 3rd pl: **-a**\n\n---\n\n### 16. The neighbours are giving the necklace to the owner.\n\n- Subject: \"the neighbours\" → plural → root + -ːcci \n → root: *neighbour* likely from \"kanarri\" or similar → likely \"kamiːg\" (from sentence 1: \"we bought the camels for the neighbours\") → \"neighbour\" is *jaːnticcirsu*? Wait, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \n → So \"kamiːg\" = camels (plural), \"jaːnticcirsu\" = neighbours? \n → But \"kamiːg\" is singular or plural? In sentence 1, \"kanarriːcciːg\" = bought the camels → \"kanarriːcciːg\" has -ːcci → camels is plural → so \"the camels\" = plural \n → \"kamiːg\" = camels? But in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"kamiːg\" is direct object \n → So \"kamiːg\" = camels (plural) → likely a noun root meaning camels\n\nBack to \"neighbours\" → in sentence 1: \"jaːnticcirsu\" → \"for the neighbours\" → so \"jaːnticcirsu\" contains -ːcci → plural → so root: *jaːnti*? → so \"jaːnti\" = neighbour (singular), \"jaːnticcirsu\" = neighbours (plural)\n\nSo: Subject: \"neighbours\" → **jaːnticcir**? Wait, -ːcci after vowel → jaːnti + -ːcci → jaːnticcir? But in sentence 1 it's \"jaːnticcirsu\" → ends in -su → perhaps vowel + -ːcci → so \"jaːnti\" + -ːcci → \"jaːnticcir\"? But full form has -su → maybe /s/ is devoicing?\n\nWait: in sentence 1: \"jaːnticcirsu\" → seems like \"jaːnticci\" + \"rsu\"? But perhaps the -ːcci is part of plural marker → so neighbour (plural): **jaːnticcir** → but last part is -rsu? Actually, check: \"jaːnticcirsu\" → perhaps it's \"jaːnticci\" + \"rsu\", but maybe \"rsu\" is not a suffix.\n\nAlternatively, focus on the verb.\n\nVerb: \"are giving\" → present tense → root: \"to give\" → for third person, it's **tir** (see example 2: \"tirt kadeːg\" → past; \"tirti argi kamgi\" → present → \"tirt\" is base verb)\n\n→ \"are giving\" = present → **tir** + present -> **tirr** (because -r after present)\n\nBut in sentence 4: \"tirti argi kamgi deːccirsa\" → \"the owners gave us the camel\" → \"tirti\" = present tense → so verb: **tir** + present → **tirr**?\n\nWait → examples show:\n- S1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → verb: \"kanarriːcciːg\" → has -ːcci → plural object? → \"kanarri\" root → \"buy\" → \"kanarri\" + -ːcci → plural?\n\nBut \"buy\" is not marked as personal, so likely root is **kanaːrri** → \"kanarri\" → with -ːcci for plural → \"kanaːrriːcci\"?\n\nHowever, in sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → \"beyyeːcciːg\" → \"I am buying\", with -ːcci → so \"necklaces\" = plural → so \"beyyeːcci\" = necklaces?\n\nThus, noun plural marker: -ːcci → after vowel → root + -ːcci\n\nSo: \"necklace\" → root: *beyye* → plural: *beyyeːcci*\n\n\"owner\" → from sentence 2: \"the owner repaired the dress\" → \"tirt kadeːg allesu\" → \"tirt\" = repaired → root: \"tirt\" → meaning \"to repair\"\n\nBut in sentence 16: \"giving the necklace to the owner\"\n\n→ verb: \"giving\" → root: \"tir\" → present → **tirr**\n\n→ subject: \"the neighbours\" → plural → root: *jaːnti* → plural: **jaːnticcir** (since vowel → -ːcci)\n\n→ indirect object: \"to the owner\" → so O′ = owner → owner is noun → plural? no → singular → so mark with -gi or -ki?\n\n→ owner: root? → likely \"eldeːnsu\" → in sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = doors → not owner\n\nBut in sentence 2: \"the owner repaired the dress\" → \"tirt kadeːg allesu\" → \"allesu\" = dress → \"elde\" root?\n\n→ \"owner\" not seen → but in sentence 16: \"to the owner\" → object is \"owner\" → must be noun\n\nWe infer: \"owner\" → root: *ale*? or *elde*? We don’t know.\n\nBut in sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = doors → so \"elde\" root → might \"elde\" = door or owner?\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" → verb: \"tir\" + -s → past → so \"tir\" = give\n\nTherefore, the verb \"to give\" is **tir** (for 2nd/3rd person), present/future → with **-r**\n\nSo \"are giving\" = **tirr**\n\nStructure: S (O′) O V → Subject (neighbours) → O′ (to the owner) → O (necklace) → V (tirr)\n\nSo:\n- S: \"neighbours\" (plural) → **jaːnticcir**\n- O′: \"to the owner\" → owner is singular → case: after consonant? → root? → assume root: *al* or *ale* → possibly *ale* → after obstruent? → need to mark with -ki if after obstruent; but \"ale\" starts with /l/ → sonorant → so -gi?\n → Rule: O′/O after **sonorant** → -gi; after **obstruent** → -ki\n\n→ \"owner\" → assume root *ale* → begins with /l/ → sonorant → so **alegi**\n\n→ O: \"necklace\" → plural → root *beyye* → + -ːcci → **beyyeːcci**\n\n→ V: present → **tirr**\n\nSo full sentence: \n**jaːnticcir alegi beyyeːcci tirr**\n\nBut check grammar:\n\n- Word order: S (O′) O V → jaːnticcir (S) alegi (O') beyyeːcci (O) tirr (V) → correct\n\n- Case for O′: owner → after sonorant → -gi → correct\n\n- Plural mark on necklace → beyyeːcci → correct\n\n- Present tense → tirr → yes\n\n→ This matches pattern.\n\n✅ So **16 → jaːnticcir alegi beyyeːcci tirr**\n\n---\n\n### 17. The young man bought the dog for us.\n\n- Subject: \"the young man\" → singular → \"young man\" ≈ \"jahali\" (sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men\") → plural → \"jahali\" + -ːcci → \"jahalgi\" → then \"waliːg\" = young men? → \"waliːg\" = young → \"waliːg\" → so \"young man\" → possibly root \"jahali\" (singular), but only used in plural\n\n→ But in sentence 3: \"jahali waliːg\" → \"the young men\" → \"jahali\" is subject → so singular form not given → but \"waliːg\" might be the root?\n\nWait: sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → so \"jahali\" = subject (pl), \"waliːg\" = part of \"young men\"? → likely \"waliːg\" = young man → perhaps root \"wali\" → \"wali\" + -i after consonant → \"waliːg\"? → \"wali\" → sonorant → so after vowel → -gi?\n\nWait: the noun rule says: after vowel → -ːcci for plural → after sonorant → -gi → for object\n\nBut for subject: singular → no marker → unless root ends with consonant → after consonant → add -i\n\n→ So \"young man\" → root: \"wali\"? → consonant → add -i → \"waliːi\"? → but no example\n\nAlternative: in sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"man\" = he → subject, singular → \"man\" → is \"he\"?\n\nSo \"young man\" → appears as argument → \"for the young man\" → what is \"young man\" form?\n\nIn sentence 3: \"the young men\" → \"jahali waliːg\" → so \"waliːg\" = young man (pl)? → maybe \"wali\" → root → so singular → \"wali\" → but with -i? → perhaps \"wali\" → ends with /i/ → already vowel → so no -i → so root is \"wali\"\n\n→ So subject: \"the young man\" → singular → root: \"wali\" → after consonant? → no — ends with vowel → so bare → but in plural → \"waliːg\"?\n\nWait: plural → after vowel → -ːcci → so \"waliːg\" → has -ːcci → but this is in plural → so \"young men\" = waliːg → so \"young man\" = wali?\n\n→ But in sentence 4: \"for the young man\" → \"for man\" → so \"man\" is used as noun\n\nTherefore, \"young man\" → root: *wali* → singular → no marker → just *wali*\n\n→ So subject: **wali**\n\n- Verb: \"bought\" → past tense → root: \"kanaːrri\" → verb \"buy\"\n\nIn sentence 1: \"ar kanarriːcciːg kamiːg...\" → \"we bought\" → \"kanarriːcciːg\"\n\n→ Buy → root: \"kanarri\" → plural object marked with -ːcci → in \"kanarriːcciːg\" → so past tense → ends with -s → \"kanarriːcciːg\" → ends with -g? → not -s\n\nWait: sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\n→ \"beyyeːcciːg\" → has -ːcci → plural object → verb is present → ends with -r → \"beyyeːcciːg\" + \"ajaːnirri\" → verb is \"beyyeːcciːg\" → wait, not matching\n\nIn sentence 1: \"ar kanarriːcciːg kamiːg...\" → \"we bought\" → so verb \"kanarriːcciːg\" → ends with -g\n\nIn sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\" → \"beyyeːcciːg\" → present → ends with -g → and \"ajaːnirri\" → object (necklace) → singular → \"ajaːnirri\" → ends in -i → could be indirect?\n\nWait, no — in word order: S (O') O V → so after O is V.\n\nSo sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\n→ Verb: \"beyyeːcciːg\" → morphologically: root + -ːcci + -g → past? → but \"beyyeːcciːg\" → ends with -g → and \"beyyeːcci\" → plural → so likely means \"am buying\" → but \"beyye\" is root → so \"am buying\" → present → but not marked with -r?\n\nProblem: verb tense?\n\nRule: tense:\n- past: -s\n- present/future: -r (r > d | n)\n\nSo why isn't \"beyyeːcciːg\" ending in -r?\n\nBut \"beyyeːcciːg\" → after -ːcci → ends with -g → so perhaps it's a different root?\n\nAlternatively, in sentence 1: \"ar kanarriːcciːg kamiːg\" → \"we bought\" → has -ːcci → plural object → verb ends in -g → and \"kamiːg\" is direct object → so the verb must be in past → with -s?\n\nBut no -s → rather -g → possibly a phonological shift?\n\nNote: rule says: r > d | n → so if r, it turns to d or n → but here we have g → so perhaps the verb root is \"kanaːrri\" → past → -s → not -g\n\nWait — sentence 1: \"ar kanarriːcciːg kamiːg...\" → \"we bought\" → so verb is in past → should end with -s → but ends with -g → unless \"-g\" is a spelling error? Or phonetic?\n\nBut in sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\" → present → should end with -r → but ends with -g → contradiction?\n\nUnless the root is different.\n\nWait: sentence 5: \"ay beyyeːcciːg ajaːnirri\" → if \"beyyeːcciːg\" is \"beyye\" + -ːcci + -g → but -g is not -r → so likely a typo or misreading.\n\nBut in sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"kadeːcciːg\" → verb → \"stole\" → past → ends with -g? → \"kadeːcciːg\" → after -ːcci → ends with -g → so past tense → verb ends with -g → but rule says past → -s → contradiction?\n\nWait — rule says: tense:\n- past: -s\n- present/future: -r (r > d | n)\n\nBut examples have -g → so perhaps the -g is the past marker? → and -r for present?\n\nBut in sentence 5: \"ay beyyeːcciːg ajaːnirri\" → present → should be -r → but has -g → so not matching\n\nPossible explanation: the verb form **-r** may be contracted or altered — or the root is modified.\n\nBut look at sentence 6: \"wal aygi baːbiːg eldeː", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11542.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 1, + "output": "We are given a translation task from English to Kunuz Nubian, with rules for word order, noun morphology, and verb conjugation.\n\nWe will go through each sentence step by step, applying the provided linguistic rules.\n\n---\n\n**Rule summary:**\n\n- Word order: **S (O′) O V** \n (Subject, indirect object, direct object, verb)\n\n- Noun:\n - Singular: no suffix\n - Plural: **-ːcci** after vowel\n - Case:\n - Subject: **-∅**\n - Indirect object or direct object: \n - After **sonorant** consonant → **-gi** \n - After **obstruent** consonant → **-ki**\n\n- Verb:\n - Tense:\n - Past: **-s**\n - Present/future: **-r** (r > d | n)\n - Root: \n - \"to give\" → to first person: **deːn**, to second/third: **tir**\n - Object:\n - If O′ (indirect object) exists: \n - Singular: **-∅** \n - Plural: **-ccir** (C > ∅ | -ccir)\n - Else (only O): \n - Singular: **-∅** \n - Plural: **-ir**\n\n- Subject person:\n - 1st sg: **-i**\n - 1st pl / 3rd sg: **-u**\n - 3rd pl: **-a**\n\n---\n\n### 16. The neighbours are giving the necklace to the owner.\n\n- Subject: \"the neighbours\" → plural → **kanarriːg** (from \"ar kanarriːcciːg\" → \"ar\" = subject, \"kanarriːcciːg\" = plural \"neighbours\", ending in -ːcci)\n- Verb: \"are giving\" → present tense → **-r**\n- \"to give\" to third person (owner) → verb root **tir** (for 2nd/3rd)\n- Direct object: \"the necklace\" → singular → **beyyeːcci** (from \"beyyeːcciːg\" in example 5: \"I am buying the necklaces\" → singular and plural use -i at end)\n- Indirect object: \"to the owner\" → owner is third person → **-ki** (because \"owner\" starts with obstruent \"w\" → after obstruent → -ki)\n\nWord order: S (O′) O V\n\nSo:\n- Subject: kanarriːg\n- O′: owner → owner is 3rd person → **waliːg** → but in case: after obstruent → **-ki**\n → So **waliːgki** (waliːg + ki)\n- O: necklace → singular → **beyyeːcci** (no case; but root with -i for singular noun ending)\n- Verb: **tir** + r (present) → **tirr**\n\nThus: **kanarriːg waliːgki beyyeːcci tirr**\n\nBut wait — in example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → subject (ar), O′ (kamiːg), O (jaːnticcirsu), V (jaːnticcirsu)\n\nSo subject is S, then O′, then O.\n\nSo we use: \nS: kanarriːg \nO′: waliːgki \nO: beyyeːcci \nV: tirr\n\nBut is \"necklace\" singular? Yes. In sentence 5: \"I am buying the necklaces\" → plural → so also has -ːcci.\n\nSo singular → beyyeːcci → no -ːcci.\n\nBut \"beyyeːcci\" → is that singular?\n\nLook at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → so singular has beyyeːcci?\n\nBut root: \"beyyeːcci\" — in the inflection, it's \"beyyeːcciːg\" → after vowel → ends with -gi → because \"necklace\" ends with vowel?\n\nWait: rule says:\n- O′, O: \n - After sonorant → -gi \n - After obstruent → -ki\n\nSo \"necklace\" → is it a sonorant or obstruent? The word is \"beyyeːcci\" → likely ends with consonant.\n\nBut \"beyyeːcci\" — has consonant 'c'\n\n- \"beyyeːcci\" → ends in consonant \"c\", so if it's a noun, and it's used as O, it needs case.\n\nBut the rule says:\n- For object (O): after vowel → -gi; after obstruent → -ki\n\nSo for direct object, if the noun ends in obstruent consonant → add -ki\n\n\"beyyeːcci\" → ends in consonant 'c' → obstruent → so O → beyyeːcciki?\n\nWait — but in example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\n\"beyyeːcciːg\" → has -gi → after vowel? Last vowel is 'e', then 'c' — so after consonant (c) → gets -gi?\n\nBut if the noun is a vowel-ended word, maybe.\n\nPerhaps the noun itself has a base.\n\nBut in 5: \"beyyeːcciːg\" → this is the full word, and \"beyyeːcci\" might be singular base.\n\nBut the example shows \"beyyeːcciːg\" with -gi → so if the word ends in consonant, it gets -gi?\n\nWait — rule says:\n- After **sonorant** consonant → -gi \n- After **obstruent** → -ki\n\nObstruents: p, t, k, b, d, g, s, f, etc.\n\nSonorants: m, n, l, r, w, j, ʔ\n\nSo 'c' → is it obstruent? Yes → so after obstruent → -ki\n\nThus, if direct object is \"necklace\", which ends with consonant (c), then O → beyyeːcciki\n\nBut in example 5: \"beyyeːcciːg\" — is this the base or the inflected?\n\n\"ay beyyeːcciːg ajaːnirri\" → subject (ay), O (beyyeːcciːg), verb\n\nO is \"the necklaces\" → plural → so plural suffix -ːcci added → \"beyyeːcciːg\"\n\nSo in singular, it would be \"beyyeːcci\" (with no -ːcci), and if it ends in obstruent 'c', then case → -ki\n\nBut it's used as O → so we add -ki → beyyeːcciki\n\nThus, for O: beyyeːcciki\n\nBut the rule says: for object, after vowel → -gi; after obstruent → -ki\n\nSo yes.\n\nSo for 16:\n- S: neighbours → plural → **kanarriːg** (base, with -ːcci in plural) → but in example 1: \"ar kanarriːcciːg\" → so \"kanarriːcciːg\" is full form → has -ːcci after vowel → so yes, \"kanarriːg\" → no, \"kanarriːg\" is root; full is \"kanarriːcciːg\"\n\nSo S: **kanarriːcciːg**\n\nWait — in example 1: \"ar kanarriːcciːg\" → so kanarriːcciːg is the plural form of neighbours.\n\nThus, in 16, S: **kanarriːcciːg** (neighbours, plural)\n\nO′: owner → third person → root \"waliːg\" → after obstruent → -ki → **waliːgki**\n\nO: necklace → singular → root \"beyyeːcci\" → ends in obstruent 'c' → so object case → **beyyeːcciki**\n\nVerb: \"are giving\" → present → **tirr** (tir + r)\n\nSo full sentence: **kanarriːcciːg waliːgki beyyeːcciki tirr**\n\nBut let’s verify if that fits pattern.\n\nNow, look at example 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\"\n\nS: iːdi (men → plural) \nO′: kamiːg (to the camels?) — no — \"kamiːg\" is direct object? Wait — \"magaski kamiːg tirsa\" → \"gave the camels to the thief\"\n\nSo S: iːdi \nO′: thief → trem → or \"tirsa\" → is verb?\n\nVerb: tirsa → past tense → -s\n\nSo \"tir\" → past = -s → \"tirsa\"\n\nSo \"gave\" → to third person → \"tir\"\n\nSo O′: to thief → \"tir\" root → for third person → \"tir\"\n\nIn this case, O′ = thief → so inflected: \"tir\" → but here it's part of verb?\n\nNo — verb is \"tirsa\"\n\nBut in example 16: \"giving\" → present → so verb root = \"tir\" + r = \"tirr\"\n\nNow O′: to owner → third person → so \"waliːgki\"\n\nYes.\n\nSo final: **kanarriːcciːg waliːgki beyyeːcciki tirr**\n\nBut in example 5: \"I am buying\" → \"beyyeːcciːg\" → so \"beyyeːcci\" is root → with -ːcci for plural → but singular should be without.\n\nSo in 16, \"necklace\" is singular → so base is \"beyyeːcci\" → with case -ki → beyyeːcciki\n\nYes.\n\nSo 16 → **kanarriːcciːg waliːgki beyyeːcciki tirr**\n\n---\n\n### 17. The young man bought the dog for us.\n\n- Subject: \"the young man\" → third person singular → \"jahali\" → singular → so no -ːcci → jahali\n- Verb: \"bought\" → past tense → root \"kadeː\" → \"kadeːg\" → in example 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\" → so \"kadeːg\" is root \"kadeː\" → verb \"to repair\"\n\nBut verb root for \"buy\" — in example 5: \"beyyeːcciːg\" → buying → so \"beyyeːcci\" → \"buy\"\n\nWait — in example 5: \"I am buying the necklaces\" → \"ajaːnirri\" → which is \"to buy\"\n\nSo root for \"buy\" = \"ajaːn\"\n\nIn 5: \"ay beyyeːcciːg ajaːnirri\" → \"beyyeːcci\" is direct object, \"ajaːnirri\" is verb → so verb root is \"ajaːn\"\n\nBut in 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → stole → root \"kadeː\" → \"kadeːcciːg\" → past — so \"kadeː\" is root for \"steal\"\n\nSimilarly, \"buy\" — is it \"ajaːn\"?\n\nYes: example 5 uses \"ajaːnirri\" → \"buying\"\n\nSo buy → root \"ajaːn\"\n\nPast → -s → \"ajaːns\"\n\nBut in example 5: \"ay beyyeːcciːg ajaːnirri\" → present → \"ajaːnirri\" → future? \"ir\" for present/future?\n\nRule: tense — present/future → -r → past → -s\n\nSo present/future: -r \nPast: -s\n\n\"bought\" → past → so verb = ajaːns\n\n- Indirect object: \"for us\" → \"us\" → first person plural → \"we\" → so \"to us\" → first person plural → verb root: \"deːn\" (to first person)\n\nSo for indirect object: to us → → use root \"deːn\"\n\nBut the verb is \"to buy\" → so verb should be: \"ajaːns\" with object → now, we have O′ = us (first person plural)\n\nSo in word order: S (O′) O V\n\n- S: jahali (young man)\n- O′: us → first person plural → \"aːu\" → but what form?\n\nO′: indirect object → \"us\" → first person plural → root? Not given.\n\nBut in example 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → \"for me\" → to me → first person singular → verb root \"deːn\"\n\nSo for first person → \"deːn\"\n\nFor second/third → \"tir\"\n\nFor plural → \"tir\" also? Example 8: \"tirsa\" → third person past.\n\nSo to us → first person plural → likely \"deːn\" → same as first person? But in example 6: \"for me\" → \"deːn\"\n\nSo \"for us\" → \"deːn\" ? But is it plural?\n\nThe rule does not specify, but given that \"for me\" uses \"deːn\", \"for us\" likely uses \"deːn\" too — perhaps the root is the same for first person.\n\nBut in sentence 5: \"I am buying the necklaces\" → no indirect object → so we don't have \"for\".\n\nIn sentence 10: \"The cowards are giving me the necklaces\" → \"for me\" → me → first person singular → so verb root = deːn\n\nSo likely, for any \"for [first person]\" → deːn\n\nThus, O′: us → \"deːn\"\n\nBut what form? The object is defined by the verb — for indirect object, the root is \"deːn\" for first person.\n\nSo verb becomes: ajaːns + deːn? → No.\n\nThe verb base is \"ajaːn\" with tense → \"ajaːns\" (past)\n\nBut the \"for\" is expressed by the root → so the verb itself is modified.\n\nIn the verb, the meaning \"to give to X\" is expressed via the root, so when \"to us\", we use \"deːn\" as the root of the verb.\n\nSo verb = ajaːns → but with \"to us\" → so the verb root changes to \"deːn\" → so \"deːns\"?\n\nBut in example 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → verb root \"baːbiːg\" → \"eldeːnsu\" → \"eldeːn\" + \"s\"\n\n\"eldeːn\" → root → \"found\" → so \"eldeːn\" is root → for \"for me\" → uses deːn → \"eldeːn\" → but the verb root is \"eldeː\" → not changed.\n\nWait — in that example: \"wal aygi baːbiːg eldeːnsu\" → \"found\" → root \"eldeː\" → past → eldeːnsu\n\nSo \"to me\" is not changing the verb root — but showing up in the argument?\n\nNo — the root is \"eldeː\" — not deːn.\n\nBut in example 8: \"iːdi magaski kamiːg tirsa\" → \"gave\" → \"tir\" → to third person → \"tir\" → so for third person → \"tir\" → for first person → \"deːn\"\n\nBut in \"found for me\" — the verb root is still \"eldeː\"\n\nSo perhaps \"to\" is expressed via the object case?\n\nWait — the rule says:\n\n- for somebody: ‘to give’ (to the first person: deːn, to the second or third person: tir)\n\nSo in verb, the indirect object is expressed via the root.\n\nSo:\n\n- to first person → verb root = deːn \n- to second/third → tir\n\nThus, verb becomes:\n\n- \"bought for us\" → us → first person plural → so root = deːn → so verb = deːns (past)\n\nBut in example 6: \"for me\" → me → first person singular → verb root = deːn → \"eldeːnsu\" → eldeːn → so yes.\n\nSo for \"us\" → first person plural → verb root = deːn → so past → deːns\n\nBut in sentence 5: \"I am buying\" → no \"for\", so verb root is \"ajaːn\"\n\nSo here, verb is \"bought for us\" → so verb root = deːn → past → deːns\n\nBut root \"ajaːn\" is for \"buy\", not \"give\".\n\nImportant: the verb root for \"buy\" is not \"deːn\" — \"give\" is.\n\nSo is \"bought\" a \"buy\" verb with separate root?\n\nIn example 5: \"I am buying the necklaces\" → ajaːnirri → so \"buy\" root = \"ajaːn\"\n\nIn example 4: \"He stole\" → kadeːcciːg → root \"kadeː\" → steal\n\nSo \"buy\" is a distinct root.\n\nThe rule says: for \"to give\" → roots deːn, tir\n\nSo \"buy\" is not \"to give\" — it is a different verb.\n\nSo how is \"for us\" expressed?\n\nIn example 6: \"the dog found the doors for me\" → verb root \"baːbiːg\" → \"found\", and \"for me\" → uses deːn root?\n\nNo — verb is \"eldeːnsu\" — base \"eldeː\", which is \"found\"\n\nSo not changed.\n\nIn example 10: \"The cowards are giving me the necklaces\" → \"giving me\" → so verb is \"tirr\" or \"tir\" → but in English \"giving me\" → so indirect object = me → first person", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11396.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 2, + "output": "We are given a set of English sentences and their translations into Kunuz Nubian, along with grammatical rules. We are to translate five new sentences into Kunuz Nubian, using the pattern observed in the examples.\n\nStep-by-step derivation:\n\nFirst, understand the word order: \n**S (O′) O V** \n→ Subject, then indirect object (if any), then direct object, then verb.\n\nNow, noun morphology:\n\n- **Number**:\n - singular: no suffix\n - plural: -ːcci after vowel (not after consonant)\n\n- **Case**:\n - Subject (S): -∅\n - Indirect object (O′): -gi after sonorant consonant; -ki after obstruent consonant\n - Direct object (O): -gi after sonorant; -ki after obstruent\n\nVerb morphology:\n\n- Tense:\n - past: -s\n - present/future: -r (with r > d | n → so r becomes d or n in some cases? See note)\n\n- Verb root:\n - \"to give\": to first person → deːn; to second/third → tir\n - \"to buy\": root appears in \"kanarriːg\" → \"kanar\" (buy) + object markers\n - \"to steal\": root appears in \"man jahalgi kadeːcciːg\" → \"kadeːcciːg\" = stole (the dress), so \"kade\" root?\n - \"to strike\": \"hanuːg bijomri\" → \"hanu\" = strike, \"bijomri\" = donkey\n\n- Object marking:\n - If there is an O′ (indirect object): -∅ (for O′), -ccir (plural O′), or -C > ∅ | -ccir\n - If no O′, then O marked with -∅ (singular) or -ir (plural)\n\n- Subject marking:\n - 1st sg: -i\n - 1st pl / 3rd sg: -u\n - 3rd pl: -a\n\nLet’s now go sentence by sentence.\n\n---\n\n**16. The neighbours are giving the necklace to the owner.**\n\n- Subject: \"The neighbours\" → plural → \"kanarriːg\" → base is kanar? But \"kanarriːg\" = bought, not neighbours.\n\nWait. From sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\"\n\n\"ar\" = we; \"kanarriːcciːg\" = bought (with 'i' conditional?); \"kamiːg\" = camels; \"jaːnticcirsu\" = for the neighbours.\n\n\"neighbours\" is O′ → in sentence 1, \"jaːnticcirsu\" = for the neighbours → so \"jaːnti\" → base \"jaːnt\" for \"neighbour\"?\n\nTry to reconstruct.\n\nLook at sentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\"\n\n\"tirt\" = repaired; \"kadeːg\" = dress?\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\"\n\n\"beyyeːcciːg\" = buying? → \"beyye\" → necklaces.\n\nSo \"beyye\" = necklace.\n\nSo: \n- \"necklace\" = beyye \n- \"neighbour\" = jaːnt? (sentence 1: for the neighbours → jaːnticcirsu)\n\n\"jaːnticcirsu\" → \"jaːnt\" + \"c\" → after vowel, plural → -ːcci? But \"jaːnt\" + \"c\" → jiːnt? Not matching.\n\nIn sentence 1: \"jaːnticcirsu\" → \"for the neighbours\" → verb is \"jaːnticcirsu\"? But verb is \"kanarriːcciːg\" (bought), so \"jaːnticcirsu\" is a noun phrase.\n\nThus, \"neighbour\" = jaːnt?\n\nBut what about case?\n\nIn sentence 1: \"for the neighbours\" = \"jaːnticcirsu\" → the O′ (indirect object). \n\"O′\" is marked with -gi or -ki based on consonant.\n\n\"jaːnt\" → ends in 't' (obstruent) → so -ki → so \"jaːntki\"? But it's \"jaːnticcirsu\".\n\nWait: \"jaːnticcirsu\" — has \"c\" after vowel → so after vowel → -ːcci → so it's plural.\n\nSo: \"neighbour\" = \"jaːnt\" → plural → \"jaːntːcci\" → but written as \"jaːnticcirsu\"?\n\nWait: \"jaːnticcirsu\" → fits: \"jaːnt\" (neighbour) → plural → -ːcci → jaːntːcci → but written as \"jaːnticcirsu\"? → perhaps \"jaːnt\" + \"c\" + \"ci\" → typo or transcription?\n\nMore likely: \"jaːnt\" is base, followed by -ci for plural → so \"jaːntci\"? But it's \"jaːnticcirsu\" → \"c\" and \"ci\" — likely \"jaːntiːcci\"? Or the truncation is in writing.\n\nFrom sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\"\n\n\"iːdi\" = men, plural → subject \n\"magaski\" = camels (O)? \"magas\" = camel → \"magas\" + -ki? After 's' (obstruent) → -ki → yes → so \"magas\" → \"magaski\" → so \"camel\" is \"magas\", plural → \"magaski\"\n\nSimilarly: in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\"\n\n\"jahali\" = young men → plural \n\"waliːg\" = dogs → O′? \n\"darbadki\" = chicken → \"darbad\" = chicken? \n\"biticcirra\" = to the dogs — object with -ccir?\n\nBut \"biticcirra\" → ends with -ra → likely verb: \"bitir\" → give? → \"bit\" → so \"bit\" for give.\n\n\"biticcirra\" → \"bit\" + \"ic\" + \"cirra\"? Why \"cirra\"?\n\nWait: \"bit\" + \"ic\" → is \"biti\" (indirect object)? But \"biticcirra\" — perhaps \"biti\" (to) + \"ccir\" (for)?\n\nBut in sentence 8: \"tirsa\" → \"gave\" — root \"tir\"\n\nSo \"to give\" = \"tir\"\n\nThus: verb is \"tir\" with object markers.\n\nObject markers:\n- if O′ → -∅ (singular) or -ccir (plural)\n- if no O′ → -ir (for O)\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → subject \"iːdi\" (men), then \"magaski\" (camels → O), then \"kamiːg\" (to the thief → O′)\n\nSo: O′ after thief → \"kamiːg\" → case: after 'm' (obstruent) → -ki → \"kamiːg\"\n\nYes — matches rule.\n\nBack to sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" \nSubject: \"ar\" = we \n\"kanarriːcciːg\" = bought (present tense, root kanar, with -r, and -ci after vowel → plural) \n\"mamiːg\" = for the neighbours? → \"kamiːg\" → present? But no direct object word.\n\nWait: \"kamiːg\" is for the neighbours — so O′ → noun: \"neighbours\" = \"jaːnt\" → plural → \"jaːntːcci\" → \"jaːnticcirsu\" → \"jaːnticcirsu\" → likely \"jaːnt\" + \"iːcci\" → after vowel → -ːcci → so \"jaːnt\" → \"jaːntːcci\" → but written as \"jaːnticcirsu\"?\n\nPerhaps \"jaːnt\" + \"ci\" → \"jaːntci\" → no.\n\nBut \"jaːnticcirsu\" → likely \"jaːnt\" (neighbour) + \"ic\" (plural) + \"ci\" (verb suffix)? No.\n\nWait: the verb is \"kanarriːcciːg\" — root \"kanar\" + -r (present) + -ci (plural)? In sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → \"beyyeːcciːg\" → \"beyye\" + \"ci\" → so \"necklaces\" → plural → -ːcci after vowel.\n\nSo such marked noun = plural.\n\n\"jaːnticcirsu\" → if \"jaːnt\" is base, then \"jaːnt\" + \"c\" → \"jaːntci\" → but it's \"jaːnticcirsu\" → maybe \"jaːnt\" + \"ic\" → \"jaːntic\" → or marking for plural.\n\nBut observe: \"jaːnt\" → ends in obstruent → so if it's not plural, it would be -ki — so \"jaːntki\" (neighbour)? But it's not.\n\n\"jaːnticcirsu\" — has \"c\" after vowel → after vowel → -ːcci → so it's plural → \"jaːnt\" → plural → \"jaːntːcci\"\n\nSo \"neighbours\" = \"jaːnt\" → plural → \"jaːntːcci\" → but written as \"jaːnticcirsu\"?\n\nPossibly a transcription error or reduction — we take the stem as \"jaːnt\"\n\nSimilarly: \"kamiːg\" = camels → \"kami\" = camel → obstruent → so -ki → \"kamiːg\"\n\nYes.\n\nSo in sentence 1: \n\"ar\" (we) = subject \n\"kanarriːcciːg\" = bought (present, plural object) — verb \n\"kamiːg\" = for the camels → O′ → noun: \"camels\" → \"kami\" → plural → -ki → \"kamiːg\"\n\nWait — \"kamiːg\" is the object? But in sentence: \"bought the camels for the neighbours\" → so direct object: camels, indirect: neighbours.\n\nIn the sentence: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" \n→ We bought (camels) for (neighbours)\n\nSo: \n- Subject: ar \n- O: kamiːg → camels → plural → \"kami\" → after obstruent → -ki → \"kamiːg\" \n- O′: jaːnticcirsu → neighbours → \"jaːnt\" → plural → after vowel → -ːcci → so \"jaːntːcci\", but written \"jaːnticcirsu\" — likely typo; the \"c\" is the marker.\n\nThus, object marker for O′ is -gi or -ki → \"jaːnt\" → ends with 't' (obstruent) → so -ki → \"jaːntki\"? But it's \"jaːnticcirsu\" — not matching.\n\nConflict.\n\nWait: \"jaːnticcirsu\" — perhaps suffix \"cirsu\" is verb? No.\n\nAll evidence: \"c\" after vowel → so plural → \"jaːnt\" → becomes \"jaːntːcci\"\n\nSo base \"neighbour\" = \"jaːnt\"\n\nSimilarly, \"dog\" = ? In sentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress\" → so \"dress\" = \"allegesu\"? \"kadeːg\" = dress?\n\nNo: \"tirt\" = repaired? \"kadeːg\" = dress?\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\"\n\n\"wal\" = dog → subject \n\"aygi\" = for me → O′ \n\"baːbiːg\" = doors → O \n\"eldeːnsu\" = found\n\nSo \"baːbiːg\" = doors → plural → after vowel → -ːcci → so \"baːbi\" → plural → \"baːbiːcci\"? But written as \"baːbiːg\"?\n\n\"baːbiːg\" → after consonant? 'b' is obstruent → so O → mark via case → -gi or -ki → 'b' is sonorant? B is obstruent → so -ki → \"baːbiːg\"? Yes.\n\n\"baːbi\" → doors → plural → -ːcci → so \"baːbiːcci\" → but written as \"baːbiːg\"? Probably a typo — perhaps \"baːbi\" is base, and \"g\" is case suffix?\n\nBut rule says: O → -gi after sonorant, -ki after obstruent.\n\n'b' is obstruent → so -ki → so \"baːbiːg\" → matches.\n\nSimilarly, in sentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\"\n\n\"tirt\" = repaired → verb \n\"kadeːg\" = dress → singular? → no marker → so singular\n\n\"kadeːg\" → ends in 'g' → obstruent → so if it were O → should be -ki → but it's not.\n\nBut it's direct object — so no case marking in word order? Wait — word order is S (O′) O V → so if only one object, it is O.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → no O′ → so only direct object → so O marked with -∅ (singular) — so no case suffix.\n\nSo \"kadeːg\" = dress (singular)\n\nSimilarly, \"allegesu\" — already the verb?\n\nSentence 2: \"tirt kadeːg allesu\" — \"tirt\" = verb, \"kadeːg\" = object, \"allegesu\" = something?\n\nNo — likely \"allegesu\" is verb suffix.\n\nBut verb is \"tirt\" = repaired → with present → -r? But it's not marked.\n\nThe verb \"tirt\" — \"tirt\" → if present, it should have -r? In sentence 1: \"kanarriːcciːg\" → has -r → so past? No, \"bought\" → present → present has -r.\n\n\"kanarriːcciːg\" → has -r → present → yes.\n\nIn sentence 2: \"tirt kadeːg allesu\" → \"tirt\" — no -r? But \"tirt\" = repaired → past tense → so -s? So should be \"tirts\"?\n\nBut it's \"tirt\" — no -s? So maybe past is -s, present is -r.\n\nSo \"tirt\" = past tense → \"tirts\" → but written as \"tirt\" → likely omission or error.\n\nIn sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying\" → present → has -r → \"beyyeːcciːg\" → has -r.\n\nSo present → -r, past → -s.\n\nIn sentence 2: \"tirt\" → may be past → with -s → but no -s → possibly typo.\n\nAssume that \"tirt\" is past — so past tense → -s → missing.\n\nProceed.\n\nBack to translation.\n\n**16. The neighbours are giving the necklace to the owner.**\n\n- Subject: the neighbours → plural → \"jaːnt\" → plural → -ːcci → \"jaːntːcci\"\n- Verb: \"are giving\" → present → so -r → root \"tir\" → \"tirr\"\n- Direct object: \"the necklace\" → singular → \"beyye\" → no suffix → \"beyye\"\n- Indirect object: \"to the owner\" → \"owner\" = ? → in sentence 2: \"the owner repaired the dress\" → \"owner\" = \"tirt\" owner?\n\n\"tirt\" = repaired → owner is subject → so \"owner\" is \"tirt\"? No.\n\nSentence 2: \"The owner\" → subject → so \"tirt\" is verb.\n\nSo \"owner\" → what is the word?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnt\"\n\nIn sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\"\n\n\"maːgtirsu\" = for the young man → O′ → \"maːgt\" = man → ends in 't' → obstruent → so -ki → \"maːgtki\"? But it's \"maːgtirsu\"\n\n\"maːgtiri\" → ? → likely \"maːgt\" + \"i\" → for the man.\n\nBut verb: \"kadeːcciːg\" → stole — past tense → -s → \"kadeːcciːg\" → has -s? No — \"kadeːcciːg\" → ends with 'g' → not -s.\n\nWait: sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\"\n\n\"man\" = he \n\"jahalgi\" = stole? No → \"kadeːcciːg\" = stole → root \"kade\" → past → should have -s → but \"kadeːcciːg\" → ends with 'g' → maybe -g is case or something.\n\nBut \"kadeːg\" → from sentence 2: dress → singular → \"kadeːg\" → base.\n\n\"kadeːcciːg\" → plural? -ːcci after vowel → so plural → \"dresses\"\n\nSo \"kade\" root → past → -s → should be \"kades\"? But not.\n\nAlternatively, the marker is in object — \"kadeːcciːg\" → base \"kade\" → plural → -ːcci → and past → -s? But missing.\n\nPossibly \"kade\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11090.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 3, + "output": "We are given a set of English sentences and their Kunuz Nubian translations, along with grammatical rules for Kunuz Nubian. Our task is to translate five new sentences into Kunuz Nubian, using the given rules and patterns.\n\n---\n\n### Step 1: Understand the Word Order\nThe word order is: **S (O′) O V** \n- S = subject \n- O′ = indirect object \n- O = direct object \n- V = verb (predicate)\n\n---\n\n### Step 2: Noun Inflection Patterns\n\n#### Number:\n- Singular: no suffix \n- Plural: **-ːcci** (after a vowel)\n\n#### Case:\n- Subject (S): \n - singular: -∅ \n - plural: **-u** (in 1st plural and 3rd sg, but this varies) \n- Object (O′, O): \n - after sonorant consonant: **-gi** \n - after obstruent consonant: **-ki**\n\nNote: \"after a vowel\" is not explicitly defined. But based on examples:\n- The suffix -gi or -ki comes on the noun after a consonant, depending on type.\n\nYet, from examples:\n- \"kamiːg\" = \"camels\" (plural), so plural marked with -ːcci → \"kamiːg\" → kam + iː + g + ci? Wait: \"kamiːg\" – likely \"kam\" + \"iːg\" + \"ci\"? But \"kamiːg\" has -i after consonant → suggests vowel-consonant boundary.\n\nLet’s analyze one example:\n- (1) ar kanarriːcciːg kamiːg jaːnticcirsu \n = \"We bought the camels for the neighbours.\"\n\nBreak down:\n- \"ar\" = we = subject (1st plural) → in S, 1st pl → indicates **-u**? But \"ar\" is given. \n But in the rules: \n - 1st person sg: -i \n - 1st person pl / 3rd sg: -u \n → So \"ar\" = \"we\" = 1st plural → → -u? But \"ar\" may just be root.\n\nWait — in (5): \"ay\" = I → 1st person sg → matches -i in rules.\n\nIn (4): \"man\" → \"he\" → 3rd person sg → subject → should be -u? But \"man\" is used as subject → so grammar uses root or stem.\n\nBut in (1): subject is \"ar\" = \"we\" → 1st pl → in rule: 1st pl/3rd sg → -u → so \"ar\" might be built from root + -u?\n\nBut \"ar\" is not clearly -u.\n\nIn (8): \"iːdi\" → \"the men\" → plural → so \"iːdi\" → \"men\" → with -i? Or -u?\n\nWait — (8): \"iːdi magaski kamiːg tirsa\" \n= \"The men gave the camels to the thief\"\n\n\"iːdi\" → \"men\" — subject → plural → so should be plural form.\n\nFrom rules: *S: -∅ or -u* \nPossibly:\n- 1st pl: -u \n- 3rd sg: -u? \n- 3rd pl: -a?\n\nRule says:\n- 1st person sg: -i \n- 1st person pl / 3rd person sg: -u \n- 3rd person pl: -a\n\nSo:\n- 1st person: \n - sg: -i → \"ay\" = I \n - pl: -u → \"ar\" = we \n- 3rd person: \n - sg: -u → \"man\" = he? But \"man\" not modified — so \"man\" is root? \n - pl: -a → e.g., \"the owners\" → might be \"maːgtirsu\" → \"maːgti\" + \"rsu\"? Wait.\n\nIn (2): \"tirt kadeːg allesu\" → \"The owner repaired the dress\" \n→ \"tirt\" = repaired (verb) \n→ \"kadeːg\" = the dress (object) \n→ \"allesu\" = owner (subject) → 3rd sg → so \"als\" or \"al\", with -u? → \"allesu\"\n\nSo “allesu” → \"al\" + \"lesu\"? \nPossibly “al” is the root, \"lesu\" with -u at end.\n\n\"tirt\" = verb, past tense → past form → -s or -r? \nRule: past -s, present/future -r \nBut \"tirt\" → past → so tense marked.\n\nVerbs:\n- present/future: -r \n- past: -s\n\nSo “tirt” = “repair” → verb → past → -s\n\nFuture: bi- → e.g., \"bi...\" → future\n\nPresent: -r → e.g., \"kanarriːg\" → \"buy\" → present → has -r → so base verb + -r\n\nThus:\n- S: determines the subject marking: \n - 1st sg: -i → \"ay\" \n - 1st pl / 3rd sg: -u → \"ar\", \"man\" (he) → so \"man\" = \"man\" + u? \n But in (4): \"man jahalgi kadeːcciːg maːgtirsu\" \n → \"man\" + \"jahalgi\" (young man) → \"man\" is \"he\"\n\nBut he is third person singular → so subject = -u → so \"man\" → possibly root + u? But not marked — so maybe \"man\" is root and we just accept it.\n\nBut in (9): \"ay hanuːg bijomri\" → \"I will strike the donkey\" \n→ \"ay\" = I → 1st sg → -i \n→ \"hanuːg\" = strike → verb? \n→ But \"hanuːg\" → word with -u → but verb?\n\nWait — \"hanuːg\" — likely verb: strike → future? \nRule: future → \"bi\" + verb root?\n\nBut here: \"ay hanuːg bijomri\" → \"I will strike the donkey\"\n\n\"hanuːg\" → strike → verb? \n\"bijomri\" → object → \"the donkey\" → object → marked with -gi or -ki?\n\n\"donkey\" = \"hau\" or \"hanu\"? \"hanuːg\" → likely \"hanu\" + \"g\" → verb root?\n\nBut verb structure: tense + root?\n\nIn (5): \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\"\n\n\"ay\" = I \n\"beyyeːcciːg\" = buying → root \"beyy\" → + -eːc → for \"necklace\"? \nBut \"beyyeːcciːg\" → has plural marker -ːcci → plural → necklaces → so plural\n\nAnd \"ajaːnirri\" → \"the necklaces\" → object → \"aj\" + \"aːn\" + \"irri\"? → \"ir\" at end → so object with -ir?\n\nRule: object:\n- O′ (indirect): -∅ or -ccir (when after consonant) \n- O (direct): singular → -∅, plural → -ir\n\nSo in (5): \"ajaːnirri\" → object → plural → so -ir → so object form is -ir\n\nThus, in (5): object = \"ajaːnirri\" → \"necklaces\" (plural) → marked with -ir\n\nSo O → -ir in plural\n\nSimilarly, in (1): \"kamiːg\" → \"camels\" → plural → marked with -ːcci? \n\"kamiːg\" → kam + iː + g → k + a + m → after vowel? — \"kam\" → consonants → then vowel → then \"iːg\"? \nBut \"kam\" → consonant → then vowel → then \"iːg\" → so after vowel → -gi?\n\nWait rule: \n- for object (O′, O): \n - after sonorant consonant → -gi \n - after obstruent → -ki \n\nSonorants: [l, m, n, r, w, j] \nObstruents: [p, t, k, b, d, g, f, s, š, θ, ɣ]\n\nSo in \"kamiːg\": \n\"kam\" → consonant cluster → ends with m → m is sonorant → so after sonorant → object → so -gi → hence \"kamiːg\"\n\nYes. So after sonorant → -gi; after obstruent → -ki.\n\nSo \"kamiːg\" → noun \"camels\" → plural → -ːcci? Wait — no?\n\nWait — rule says:\n- plural: -ːcci **after a vowel**\n\nBut \"kamiːg\" ends with -g → no -ːcci?\n\nWait — conflict.\n\nIn (1): \"ar kanarriːcciːg kamiːg jaːnticcirsu\"\n\n\"kanarriːcciːg\" → verb → \"buy\" → root \"kanar\" + -riːcciːg → where is -ːcci?\n\n\"kanarriːcciːg\" — has \"riːcciːg\" → so contains -ːcci at end → but is this the verb or object?\n\nThe verb is \"kanarriːcciːg\" → \"we bought\"\n\nStructure: S O V \nBut S is \"ar\" (“we”) → S → 1st pl → so verb should be present → with -r → and \"kanar\" → root?\n\n\"kanar\" → buy → so \"kanar\" + -r → present → \"kanarri\" → then why -ːcciːg?\n\nPossibly the verb root has -ːcci embedded?\n\nWait — no, the verb has tense and object.\n\nLook at (3): \"jahali waliːg darbadki biticcirra\" \n= \"The young men will give the chicken to the dogs\"\n\n\"jahali\" = young men → plural → so subject \n\"waliːg\" = give → verb? \n\"darbadki\" = chicken → object? \n\"biticcirra\" = to the dogs → indirect object?\n\n\"biticcirra\" → \"to the dogs\" → indirect object → so O′ → so should get case marker.\n\n\"biticcirra\" → \"bit\" + \"iccirra\" → has -iccir → plural? → so plural → plural object → -ccir?\n\nRule: object O′, if exists → singular: -∅, plural: -ccir (after consonant)\n\nSo \"biticcirra\" → plural → -ccir\n\nIn (8): \"iːdi magaski kamiːg tirsa\" \n= \"The men gave the camels to the thief\"\n\n\"iːdi\" → men → subject \n\"magaski\" → camels → object → so O → \"kamiːg\" → so we need to mark with -gi or -ki?\n\n-kamiːg → after vowel? \"kam\" → consonant → then vowel \"iː\" → so after vowel → so -gi → yes → \"kamiːg\"\n\nBut in (1): \"kamiːg\" — object → so -gi → yes.\n\nBut what about plural? \n\"kamiːg\" → does it have plural marker?\n\nIn (1): \"kamiːg\" = camels → plural → but how marked?\n\n\"kamiːg\" → contains \"iːg\" — not -ːcci.\n\nBut in (3): \"darbadki\" = chicken — singular → \"darbad\" → root → \"ki\" → object? \n\"ki\" after obstruent \"d\" → d is obstruent → so after obstruent → -ki → so \"darbadki\"\n\nSimilarly, \"biticcirra\" = to dogs → dogs plural → -ccir → after consonant (b)\n\nSo object -ccir → plural → after consonant.\n\nSo the plural marker for object is -ccir (when after consonant), not -ːcci.\n\nPlural marker for nouns: -ːcci after vowel — but not applied to object? Wait.\n\nBut in (4): \"man jahalgi kadeːcciːg maːgtirsu\" \n= \"He stole the dresses for the young man\"\n\n\"man\" = he → subject \n\"jahalgi\" = young man → indirect object? \n\"kadeːcciːg\" = dresses → object? \n\"maːgtirsu\" = young man → so \"maːgtir\" + \"su\"?\n\n\"kadeːcciːg\" → dresses → plural → has -ːcci → so here -ːcci appears → after vowel \"eː\" → so after vowel → so must be a noun marked with plural -ːcci.\n\nSo kadeːcciːg → root \"kade\" + -ːcci → after vowel → so yes → monthly, has -ːcci.\n\nSimilarly, \"kamiːg\" → \"camels\" → has -iːg → but not -ːcci → so no?\n\nWait — \"kamiːg\" — is \"kam\" consonant → vowel \"iː\" → so after vowel → so -gi → yes → but no -ːcci → so why not plural?\n\nBut camels is plural → so where is -ːcci?\n\nIn (1): \"kamiːg\" — here it is → \"kamiːg\" — but does it have -ːcci?\n\n\"kanarriːcciːg\" is separate — the verb — with -ːcci?\n\nThe verb \"kanarriːcciːg\" — likely contains the object suffix?\n\nWait — the verb form is \"kanarriːcciːg\" — root \"kanar\" + -r → present → then -ːcciːg → which is object?\n\nBut object is “camels” → which should be in object case.\n\nIn English: \"We bought the camels for the neighbours\" → object is camels → then \"for the neighbours\" → indirect object.\n\nIn the sentence: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" \n→ \"ar\" = we \n\"kanarriːcciːg\" = verb — past (s)? or present? \n\"kanar\" = buy → past? \n\"kanar\" → root; \"riːcciːg\" → object suffix?\n\nBut \"riːcciːg\" → where is -ːcci?\n\n- \"riːcci\" = after vowel? \"iː\" → vowel → so after vowel → so should be -gi? \nBut \"riːcci\" — has -ːcci → so ends with -ːcci → after vowel → so applies to noun?\n\nBut \"kamiːg\" is the noun — \"camels\"\n\nSo if \"kamiːg\" is object → it should have -gi → it does → \"kamiːg\"\n\nBut why is \"kamiːg\" not marked with -ːcci?\n\nBecause the rule says: plural = -ːcci **after a vowel**\n\n\"kamiːg\" → after vowel → there is \"iːg\" — after \"m\", not after vowel? \n\"m\" is consonant → so the -gi is after consonant → not after vowel.\n\nWait — rule says: for object, after sonorant → -gi; after obstruent → -ki.\n\nSo the case suffix is on the noun, not the number.\n\nBut number marking (plural) is: -ːcci after vowel.\n\nSo a noun like \"camels\" → k + a + m + iː + g → \"kamiːg\" → vowel \"iː\" → after consonant \"m\" → so we don't apply -ːcci there.\n\nSo where is plural marking?\n\nIn \"kamiːg\" — no -ːcci — so is it singular?\n\nNo: \"camels\" → plural.\n\nBut in (1): \"kamiːg\" — is marked only with -gi → so the plural marker -ːcci is missing?\n\nBut in (4): \"kadeːcciːg\" → \"dresses\" — has -ːcci → after \"eː\" → vowel → so yes → marked with -ːcci → plural.\n\nSimilarly, in (3): \"biticcirra\" → \"to dogs\" → has -ccir → plural → object suffix.\n\nSo both noun plural and object plural are marked.\n\nBut in (1): \"kamiːg\" → not marked with -ːcci → so why?\n\nUnless \"kamiːg\" is not the noun — maybe it's already in object form.\n\nWait — sentence: \"ar kanarriːcciːg kamiːg jaːnticcirsu\"\n\n\"jaːnticcirsu\" = for the neighbours → indirect object → so O′\n\n\"jaːnticcirsu\" → has -iccirsu → -ccir → plural → object → so O′ → -ccir\n\n\"kamiːg\" → no -ːcci → so not plural?\n\nBut \"camels\" is plural.\n\nPossibility: the -ːcci is part of the verb.\n\n\"kanarriːcciːg\" → \"kanar\" + \"riːcci\" → so the -riːcci is object suffix?\n\nBut \"riːcci\" → after vowel → so for object → after vowel → so -gi?\n\n\"riːcci\" → after vowel → \"iː\" → so after vowel → object → -gi → so should be -gi, not -ːcci.\n\nBut \"riːcci\" ends with -ci → so not -gi.\n\nUnless the verb takes object case directly.\n\nBut in (3): \"waliːg\" → verb — \"give\" → present → root \"wali\" → with -g → so \"waliːg\"\n\nThen \"darbadki\" = direct object → “chicken” → singular → so -ki? \n\"dar\" → obstruent d → after d → -ki → \"darbadki\"\n\nThen \"biticcirra\" = indirect object → “to dogs” → plural → so -ccir → \"biticcirra\"\n\nSimilarly, in (5): \"beyyeːcciːg\" → verb = \"buy\" → present → with -r → \"beyy\" → \"beyyeːcciːg\" → but has -ːcci — could be object?\n\n\"agaːnirri\" = object → “necklaces” → plural → so -ir → so object marked with -", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11264.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3. Rules:\n\n • Word order: S (O′) O V\n (S = subject, O′ = indirect object, O = direct object, V = predicate).\n\n • noun:\n\n – \n\n – number:\n\n * singular: -∅\n {\n -i after a consonant\n * plural:\n -ːcci after a vowel\n – case:\n\n * S: -∅ \n  -ːg after a vowel\n * O′, O: -gi after a sonorant consonant\n  -ki after an obstruent consonant\n\n • verb:\n\n – tense (present a-, future bi-)\n\n – \n\n – for somebody: ‘to give’ (to the first person: deːn, to the second or third person:\n tir)\n\n –\n object: singular plural\n O′, if there is one -∅ -ccir (-C > ∅| -ccir)\n otherwise O -∅ -ir\n\n – tense: past -s, present/future -r (r > d | n )\n\n – subject: 1st person sg -i, 1st person pl/3rd person sg -u, 3rd person pl -a\n\nFourteenth International Linguistics Olympiad (2016). 4\nIndividual Contest Solutions\n\n (a) 1. magasi argi ajomirra.\n The thieves are striking us.\n 2. ay kanarriːg baːbki alletirsi.\n I repaired the door for the neighbour.\n 3. hanu tirtiːg elirsu.\n The donkey found the owners.\n 4. tirti argi kamgi deːccirsa.\n The owners gave us the camel.\n 5. ay darbadki bijaːndi.\n I will buy the chicken.\n\n (b) 6. The neighbours are giving the necklace to the owner.\n [TARGET ANSWER REDACTED]\n 7. The young man bought the dog for us.\n [TARGET ANSWER REDACTED]\n 8. We will steal him.\n [TARGET ANSWER REDACTED]\n 9. The owners struck the thieves.\n [TARGET ANSWER REDACTED]\n 10. The dogs found the chickens for the coward.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 0, + "output": "Step 1: Analyze the structure and components of the provided English-Kilivila pairs.\n\nKey observations:\n\n- Verb forms:\n - \"le-\" = past\n - \"bi-\" = future\n - \"-si\" = plural subject (e.g., \"givesi\" = plural of \"gives\")\n\n- Nouns:\n - man → tau / tauwau (plural)\n - child → gwadi / gugwadi (plural)\n - chief → guyau / gweguyau (plural)\n - old woman → namwaya / nunumwaya (plural)\n - canoe → ke- (no plural form; used as is)\n - thing/stone → kwe-\n\n- Class prefixes:\n - men: te- (before quantity), to-\n - women/animals: na-\n - children: gudi-\n - canoes: ke-\n - things: kwe-\n\n- Demonstratives:\n - (a-)ma-Cl(-si)(-we)-na → \"ma-tau\" → \"mtona\" (in 2: \"mtona\" = this)\n - \"ma-na\" → \"mina\" (as in \"minasina\")\n - \"ma-to\" → \"mto-\", as in \"mtona\"\n\n- Quantity:\n - \"vila\" = how many?\n - \"tala\" = one\n - \"yu\" = two\n - \"vasi\" = four\n\n- Interrogative markers:\n - \"Am-\" = which?\n - \"Navila\" = how many?\n - \"Bik-\" = will (future) + subject?\n - \"Legi-\" = see, past\n - \"Tevila\" = how many?\n\nStep 2: Derive each sentence, using structure and patterns.\n\nSentence 14: Navila vivila biyamata tomwaya mtona?\n\n- Navila = How many?\n- vivila = will see\n- biyamata = will see (bi- + ya-mata) → “will see” (but also \"bi\" + object?)\n- tomwaya = man (tomwaya = man, \"ma-tau\" → mtona)\n- mtona = this\n\nSo: How many [men] will see this man?\n\nBut is it \"How many men will see this man?\" or \"How many men will this man see?\"\n\nCheck core pattern: In sentence 17, there's ambiguity:\n- Tevila tauwau bigisesi gugwadi gudigasisi?\n- Which version is ambiguous?\n- The example says two possible translations: \n - How many men will see the wild children?\n - How many men will the wild children see?\n\nThis pattern appears when the verb is passive or the subject-object is reversed due to word order or Pro (pronominal) movement.\n\nIn 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n- Tevila = how many?\n- tauwau = men (plural)\n- bigisesi = plural of \"see\" (bi- + see + -si)\n- gugwadi = children (plural)\n- gudigasisi = wild children?\n\nBut “gudigasisi” = wild children? → \"gudi\" = child; \"gasi\" = wild?\n\nSo: \"gugwadi gudigasisi\" = wild children?\n\nThus: \"How many men will see the wild children?\" vs \"How many men will the wild children see?\"\n\nThis is a classic ambiguity: the verb \"see\" can be passive (subject sees object) or active (object sees subject).\n\nThus, 17 is ambiguous.\n\nNow, check 14: Navila vivila biyamata tomwaya mtona?\n\n- Navila = how many?\n- vivila = will see\n- biyamata → \"bi\" + \"yamata\" → see?\n- tomwaya = man\n- mtona = this\n\nSo: Who sees what?\n\nPossibility:\n- How many men will see this man? → subject = men, object = man\n- How many men will this man see? → subject = man, object = men\n\nThis seems similar. But is the word order indicating direction?\n\nIn 18: Legisesi ketala waga vivila minasiwena.\n\n- Legisesi = saw (past)\n- ketala = the (demonstrative? or object?)\n- waga = (a-?) → \"waga\" = a canoes?\n- vivila = see\n- minasiwena = something?\n\nWait: “minasiwena” likely = these things?\n\nCompare with sentence 10:\n- Legisi dakuna makwena gwadi magudiwena gudimanabweta\n- \"that beautiful child saw this stone\"\n\nSo “gudimanabweta” = this stone?\n\n\"minasiwena\" → \"these things\"?\n\nIn 18: Legisesi ketala waga vivila minasiwena\n\n→ \"saw (the) canoes, will see things\"?\n\nBut word order: \"waga vivila\" → \"canoes see\"?\n\nBut \"vivila\" = see — is it transitive?\n\nIn 10: \"gudimanabweta\" = stone; \"gwadi magudiwena\" = that child\n\nIn 18: \"waga\" = canoes (ke-?) → but \"waga\" appears in “waga makesiwena” → \"waga\" = canoes\n\nSo \"waga\" = canoes\n\n\"vivila\" = will see\n\n\"minasiwena\" = things\n\nSo: \"Canoes will see things?\"\n\nBut \"legisesi\" = saw → past?\n\n\"Legisesi ketala waga vivila minasiwena\" → past?\n\nBut word order: \"legisesi\" + \"ketala\" + \"waga\" + \"vivila\" + \"minasiwena\"\n\nIt’s likely: “The canoes saw [something]” → but \"waga\" is object?\n\nWait: in 4: \"legisi waga makesiwena namwaya minana\" → “the woman saw those canoes”\n\nStructure: Legisi (saw) + waga (those canoes) → object = canoes\n\nSo in 18: Legisesi ketala waga vivila minasiwena?\n\n→ \"saw the canoes, will see things\"?\n\nBut \"vivila\" is not present in past form.\n\nWait — \"legisesi\" = past (le-), so past tense.\n\nBut does “waga” follow \"ketala\"? Is \"waga\" the object?\n\nYes — so: “The canoes saw [something]” → object = canoes?\n\nBut \"waga\" is noun (canos), so likely: \"The canoes saw the things\" — but \"vivila\" is not transitive.\n\nAlternative parsing:\n\n\"Legisesi ketala waga\" → \"saw the canoes\"?\n\n\"vivila minasiwena\" → \"will see things\"\n\nBut no verb for \"will see\" — \"vivila\" is a verb.\n\nSo likely: \"The canoes saw the things, will see things\"?\n\nThat doesn't make sense.\n\nWait — perhaps \"vivila\" is embedded.\n\nAnother possibility: \"vivila\" is in object position, like in \"legisesi waga makesiwena\" → \"saw the canoes\" → \"waga\" is object.\n\nIn 18: \"waga vivila minasiwena\" → first, \"waga\" is subject?\n\nBut in 4: \"legisi waga makesiwena\" → \"the woman saw the canoes\" → waga = object.\n\nSo \"waga\" is object in a verb-stative.\n\nThus: \"legisesi [object] vivila\" → vivila = verb?\n\nNo — \"vivila\" is not a verb in that position.\n\nWait: only verb is \"legisesi\" — past tense.\n\nTherefore: \"Legisesi ketala waga vivila minasiwena\" → \"saw the canoes, will see things\"?\n\nBut that is two verbs.\n\nUnlikely.\n\nAlternative parsing:\n\n\"Legisesi\" = past, so see (past)\n\n\"ketala\" = the (demonstrative?) → \"the\"\n\n\"waga\" = canoes\n\n\"vivila minasiwena\" = will see things?\n\nBut vivila = verb?\n\nSo: \"Saw the canoes, will see things?\"\n\nBut no marker of future.\n\nAlternatively, is vivila a different verb?\n\nNo — vivila appears in 14 and 15 as future (bi-), but here it's in past?\n\n\"vivila\" = see, used as future in \"biyamata\", in 14.\n\nIn 14: \"vivila biyamata\" → will see?\n\nPossibility: \"vivila\" is future only when preceded by \"bi-\", otherwise past?\n\nBut in 18, no \"bi\", so past?\n\n\"Legisesi\" = past → verb used.\n\nSo likely: \"The canoes saw the things\" → but \"waga\" is subject?\n\nBut in 4: \"waga\" is object.\n\nConsistency: in 4 → \"legisi waga makesiwena\" → \"the woman saw the canoes\"\n\nSo waga = object.\n\nSo in 18: \"legisesi ketala waga\" → saw the canoes?\n\nThen \"vivila minasiwena\" = separate clause?\n\nBut that violates tense.\n\nPossibility: \"Legisesi ketala waga\" = saw the canoes\n\n\"vivila minasiwena\" = will see things\n\nBut unclear.\n\nBut no clear future marker.\n\nWait — perhaps the verb is \"vivila\" and \"legisesi\" is misread?\n\n\"legisesi\" is past — le-.\n\n\"vivila\" is likely present/future.\n\nBut no \"bi\" — so future?\n\nIn 3: \"Bikota gwadi magudiwena\" → \"that child will arrive\" → \"bi\" + \"kota\" → future.\n\nSo \"vivila\" without \"bi\" → past?\n\nSo only future if \"bi\" is present.\n\nThus, in 18: \"vivila\" → past?\n\nThen \"legisesi\" is also past → redundant?\n\nNo — \"legisesi\" = past, \"vivila\" = past.\n\nBut in the sentence, \"vivila\" comes after \"waga\", so \"waga vivila\" = canoes see?\n\nBut \"waga\" is noun.\n\nSo: \"The canoes will see things\" → future?\n\nBut no \"bi\".\n\nThus, likely: \"The canoes will see things\" — but \"bi\" missing.\n\nWait — no \"bi\" → so not future.\n\nOnly patterns:\n\n- \"bi\" = future\n- \"le\" = past\n\nSo unless \"bi\" is present, no future.\n\nThus in 18: \"vivila\" without bi → past → \"will see\" = not there.\n\nBut the sentence is \"Legisesi ketala waga vivila minasiwena\" → two verbs?\n\nUnlikely.\n\nAlternative: \"vivila\" is a noun?\n\nNo — in 14: \"vivila minasina\" = will see things.\n\nSo vivila = verb meaning \"see\".\n\nThus, only future with \"bi\".\n\nSo \"vivila\" without \"bi\" must be past.\n\nBut \"legisesi\" is already past.\n\nSo contradiction.\n\nThus, likely typo or wrong parsing.\n\nWait — in 18: \"Legisesi ketala waga vivila minasiwena\" — possibly:\n\n\"Legisesi\" = saw\n\n\"ketala\" = the\n\n\"waga\" = canoes\n\n\"vivila minasiwena\" = things\n\nSyntax: verb + demonstrative + object + verb?\n\nBut no.\n\nPerhaps: \"the canoes (waga) will see the things (minasiwena)\" → so \"waga\" is subject → but in earlier sentences, \"waga\" is object.\n\nIn 4: \"legisi waga makesiwena namwaya minana\" → woman saw canoes → waga = object.\n\nIn 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → child saw this stone → \"dakuna\" = saw, \"makwena\" = this, \"gwadi\" = child, \"gudimanabweta\" = stone → so \"gwadi\" = subject.\n\nSo in 4: strong evidence that \"waga\" is object.\n\nThus in 18, if \"waga\" is object, then the verb is \"legisesi\" and object = waga.\n\nSo \"saw the canoes\"?\n\nThen \"vivila minasiwena\" → separate?\n\nBut no marker.\n\nTherefore, likely: the sentence is \"The canoes saw the things\" — but \"waga\" is object?\n\nNo — \"see\" takes object.\n\nSo: \"The canoes saw the things\" → waga = subject?\n\nBut in 4, waga = object.\n\nContradiction.\n\nUnless \"waga\" is a demonstrative.\n\n\"Waga\" appears as object — e.g., \"makesiwena waga\" → saw canoes.\n\nSo \"waga\" = canoes → object.\n\nThus, in 18: \"legisesi ketala waga\" = saw the canoes\n\nThen \"vivila minasiwena\" = separate?\n\nBut no verbal agreement.\n\nAlternatively, \"vivila\" is the verb, and \"waga\" is object — so \"the canoes will see things\" — but \"waga\" = canoes → subject?\n\nBut earlier pattern shows waga as object.\n\nOnly in 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" → child saw stone.\n\nSo subject is \"gwadi\" → child.\n\n\"makwena\" = this stone → object.\n\nSo verb is \"dakuna\" = saw.\n\nSo when waga is in stem, it's object.\n\nThus, in 18, if \"waga\" is object, then only one object.\n\nSo \"legisesi ketala waga\" = saw the canoes.\n\n\"vivila minasiwena\" = separate — no verb for \"will\"?\n\nNo.\n\nConclusion: likely a misplacement — possibly \"Legisesi ketala waga vivila minasiwena\" = \"The canoes saw the things\" → waga = subject — so must be possible.\n\nThus, the word \"waga\" is subject in this case — so it has to be moved or parsed differently.\n\nBut that breaks pattern.\n\nAlternatively, \"vivila\" is future with no \"bi\"?\n\nNo.\n\nWe must accept that in some sentences, the verb is ambiguous in direction.\n\nBack to 14: Navila vivila biyamata tomwaya mtona?\n\n- Navila = how many\n- vivila = will see\n- biyamata = (bi + see)? → bi- + yamata → see?\n- tomwaya = man\n- mtona = this\n\nSo: \"How many men will see this man?\"\n\nBut also: \"How many men will this man see?\"\n\nThis is a common ambiguity in reciprocal or reflexive constructions.\n\nSimilarly, 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n- Tevila = how many\n- tauwau = men\n- bigisesi = will see (bi + see + -si)\n- gugwadi = children\n- gudigasisi = wild children?\n\nSo: \"How many men will see the wild children?\"\n\nvs. \"How many men will the wild children see?\"\n\nThis is symmetric — only one sentence has two possibilities — and the solution says 17 does.\n\nTherefore, 14 may also have ambiguity.\n\nCheck 14: \"Navila vivila biyamata tomwaya mtona?\"\n\nSubject: men (tauwau implied) — \"navila vivila\" = how many men will see?\n\nObject: \"tomwaya mtona\" = this man\n\nSo: \"How many men will see this man?\" or \"How many men will this man see?\"\n\nIs the word order suggesting direction of see?\n\nIn passive constructions, \"be seen\" or \"see someone\" may be ambiguous.\n\nSimilarly, in 15: Bikamkwamsi kweyu vivila minasina.\n\n- Bikamkwamsi = will eat\n- kweyu = two\n- vivila = see\n- minasina = things\n\nSo: \"Two men will see things\" — likely only one reading.\n\n16: Amagudina gwadi lekota?\n\n- Amagudina = which woman?\n- gwadi = child\n- lekota = this\n\nSo: \"Which child is this?\" → \"Which child is this?\" — singular, no ambiguity.\n\n18: Legisesi ketala waga vivila minasiwena?\n\n- Legisesi = saw\n- ketala = the\n- waga = canoes\n- vivila = see → but no bi — so past?\n- minasiwena = things\n\nSo: \"The canoes saw the things\" — one reading.\n\nBut where is the ambiguity?\n\nOnly 17 is explicitly stated to have two translations.\n\nIn 14, the structure is similar — \"how many men will see this man?\"\n\nCould be \"how many men will see this man?\" or \"how many men will this man see?\"\n\nSo likely ambiguity.\n\nBut the problem says: \"One of these sentences has two possible translations.\"\n\nAnd in the official solution, it is 17.\n\nTherefore, only 17 has ambiguity.\n\nThus, for 14 to 18, only 17 is ambiguous.\n\nSo 14,15,16,18 have only one translation.\n\nNow derive:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n- Navila = how many?\n- vivila = will see\n- biyamata = (bi + see) → will see\n- tomwaya = man\n- mtona = this\n\n→ \"How many men will see this man?\"\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n- Bikamkwamsi = will eat\n- kweyu = two\n- vivila = see\n- minasina = things\n\n→ \"Two men will see things.\"\n\n16. Amagudina gwadi lekota?\n\n- Amagudina = which woman?\n- gwadi = child\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12254.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 1, + "output": "Step 1: Identify the verb structure and word order patterns from the examples.\n\nAll sentences follow a V(O)S or QVX word order. Interrogatives start with QVX (e.g., \"Amtona\", \"Navila\"). \nVerbs:\n- le- = past\n- bi- = future \n- -si suffix = plural subject (e.g., bigisi → \"that clever woman will see\"; gugesi → plural of \"child\")\n\nNouns:\n- man → tau (singular), tauwau (plural)\n- child → gwadi (singular), gugwadi (plural)\n- chief → guyau (singular), gweguyau (plural)\n- old woman → namwaya (singular), nunumwaya (plural)\n- canoes → ke-\n- things (e.g., stones) → kwe-\n\nDemonstratives:\n- ma- + Cl → mto- (man), mina- (woman)\n- ma-to- → mto-; ma-na- → mina-; ma-gudi- → makwena (child)\n\nQuantifiers:\n- vila = how many?\n- yu = 2\n- tala = 1\n- vasi = 4\n\nClass prefixes:\n- men: te- (before Qt), to- (in other uses)\n- women/animals: na-\n- children: gudi-\n- canoes: ke-\n- things: kwe-\n\nStep 2: Analyze each sentence from 1–13 to find mapping logic.\n\nExample 1:\n\"one man will catch these four fish\" → Bibani navasi yena minasina tetala tau. \n\"navasi\" = special interrogative? \"yena\" = demonstrative (\"these\") → yena → minasina (fish) \n\"tetala\" → 1 → tetala tau → one fish, but \"tau\" is man → possibly \"one man\" \nWait: \"navasi\" → interrogative? But \"navasi\" might be \"how many\"? → \"Navila\" in 14 → likely \"how many\"\n\n\"navasi\" = \"how many\" → Navila → how many?\n\nIn 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\n\"vivila\" = \"how many\"? So \"Navila\" = Q-vila = how many?\n\nIn 14: Navila vivila biyamata tomwaya mtona?\n\n\"Navila\" → how many \n\"vivila\" → how many (possibly redundant?) \n\"biyamata\" → future? \"bi\" + \"yamata\"? \n\"bityama\" → no, \"bityama\" not in examples \nWait: \"bi\" = future; \"yamata\" → ? \nWhat is \"tomwaya\"? → \"tomwaya\" → man (tom = man?)\n\n\"tomwaya\" → man (singular), so tomwaya = man? \n\"mtona\" → this? → demonstrative?\n\n\"ma-to-\" → mto- → \"mtona\" = this man?\n\nSo: \"how many [men] will see this man?\"\n\n\"Navila vivila biyamata tomwaya mtona?\" \nStructure: how many [men] will see this man?\n\n\"biyamata\" → verb: future + \"yamata\"? \n\nLook at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n\"Amtona\" = which man? → QVX \n\"tau\" = man \n\"lekalimati\" = killed \n\"nayu\" = 2 → quantity \n\"bunukwa\" = pig\n\nSo \"lekalimati\" = killed\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\n\"leyamatasi\" → looked after? \n\"teyu\" = 2 → because \"teyu\" = 2 \n\"tauwau\" = men (plural)\n\nSo \"teyu\" = 2 \n\"vila\" = how many? \n\"yuan\" = 1 → \"tala\" → \"tetala\" = 1 \n\"yukwamsi\" → \"kwe\" → thing \n\"minasiwena\" → stone?\n\nSentence 10: \"That beautiful child saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"Legisi\" → past \n\"dakuna\" → saw \n\"makwena\" → child (child) \n\"gwadi\" → that \n\"magudiwena\" → beautiful child (gudi + adjective) \n\"gudimanabweta\" → this stone (gudima → stone; \"gudimanabweta\" = this stone)\n\nSo \"gudimanabweta\" = this stone → stone (kwe) with demonstrative.\n\nSentence 18: \"Legisesi ketala waga vivila minasiwena.\" \n\"Legisesi\" → past verb → saw \n\"ketala\" → what? \n\"ketala\" → \"keta\" → object? \"waga\" = with? \n\"vivila\" → how many? \n\"minasiwena\" → what? → mina (woman)? mina + si → minasina (woman)? \n\"minasiwena\" → what?\n\nWait: \"minasina\" → fish \n\"minasina\" → fish \n\"vivila\" → how many?\n\nSo \"Legisesi ketala waga vivila minasiwena\" → \"the woman saw [what?] with how many things?\"\n\nBut \"ketala\" = object? \n\"ketala\" → perhaps \"what\" or \"the\"?\n\nCompare: in 10, \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"saw the child who is beautiful, this stone\"\n\n\"ketala\" → similar to \"waga\" = \"with\"? \n\"ketala\" → \"keta\" → a reference to an object.\n\nLook at 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n\"Tevila\" → how many? \n\"tauwau\" → men \n\"bigisesi\" → plural of \"bigisi\" → \"that clever woman\" → subject → \"that clever women will see\" → future? \n\"bigisesi\" = plural → so \"women\"?\n\n\"bigisesi\" → subject (plural) \n\"bigisesi\" = women (pl) \n\"bigisesi gugwadi\" = \"the women\" and \"children\"? \n\"gugwadi\" = child (pl) \n\"gudigasisi\" = wild children?\n\n\"gudigasisi\" → wild child (gudi + gasi → wild) → like \"gudigasisi\" = wild child?\n\nSo \"bigisesi gugwadi gudigasisi\" → \"the wild children\"?\n\nSo \"Tevila tauwau bigisesi gugwadi gudigasisi?\" → \"How many men will the wild children see?\"\n\nBut the problem says one has two translations.\n\nSentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\nStructure: \n- Tevila = how many \n- tauwau = men \n- bigisesi gugwadi gudigasisi → \"the women and wild children\" → but \"gugwadi gudigasisi\" → can be ambiguous?\n\n\"bigisesi\" is subject → \"the women\" \n\"bigisesi gugwadi\" = \"the women and children\"? \n\"bigisesi gugwadi\" → women and children → but \"gudigasisi\" → wild children → so object?\n\nSo could be:\n- How many men will the wild children see?\n- How many men will the women see?\n\nBut \"bigisesi gugwadi gudigasisi\" → if \"gugwadi gudigasisi\" is object, → \"the wild children\"?\n\n\"bigisesi\" → subject → \"the women\"\n\nSo \"how many men will the women see?\" — \"bigisesi\" → subject → \"women\"\n\nBut \"gugwadi gudigasisi\" → only appears with \"bigisesi\" → \"gugwadi\" after \"bigisesi\" → but \"gugwadi\" is child, and \"gudigasisi\" is wild child → so a compound?\n\nPossibility: “bigisesi” = women, “gugwadi” = children → but “gudigasisi” = wild children → is “gugwadi” modified?\n\n“gudigasisi” = wild child → so “gugwadi gudigasisi” = children and wild children? Unlikely.\n\nAlternatively, “bigisesi gugwadi” → \"the women who are children\" → doesn't make sense.\n\n\"bigisesi\" → the women, \"gugwadi\" → child → ambiguous.\n\nBut in sentence 7: \"That clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"bigisi\" → clever woman (singular) \n\"kwetala\" → see \n\"vivila\" → something \n\"minawena\" → thing (kwe + na?) → thing \n\"nakabitam\" → something\n\n\"vivila\" = something → thing\n\nSo “vivila” → something → object\n\nNow sentence 18: \"Legisesi ketala waga vivila minasiwena.\"\n\n\"Legisesi\" → saw \n\"ketala\" → ? \n\"waga\" → with \n\"vivila\" → how many \n\"minasiwena\" → fish?\n\n\"minasiwena\" → fish → from earlier, \"minasina\" = fish\n\nSo “saw with how many fish?” → doesn’t make sense.\n\n\"ketala\" → object?\n\nCompare to sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"the child saw the beautiful child and this stone\"\n\nSo “ketala” → object?\n\nIn sentence 18: “saw with how many things?” → but “vivila” is before “minasiwena”\n\nPossibility: “ketala” is object, “vivila” is quantity, “minasiwena” is noun?\n\nSo “saw with [something] — how many things?”\n\nBut that would be \"how many things did they see with?\" — awkward.\n\nAlternative: \"vivila\" = object, \"minasiwena\" = \"how many things\"?\n\nNo.\n\nStructure: “Legisesi ketala waga vivila minasiwena”\n\nMaybe it's: \"the one who saw [ketala] with [vivila minasiwena]\"?\n\nUnlikely.\n\nAnother look: sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → saw beautiful child and this stone\n\n\"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = beautiful child; \"gudimanabweta\" = this stone\n\nSo \"dakuna\" = saw; object = \"makwena gwadi magudiwena gudimanabweta\"\n\nSo in 18: \"Legisesi ketala waga vivila minasiwena\"\n\n“ketala” → object? \n\"waga\" → with → likely “with [X]” \n\"vivila minasiwena\" → how many fish?\n\nSo “saw with how many fish?”\n\nThat is awkward.\n\nWait — “minasiwena” could be “this child”?\n\nBut “minasina” = fish — only fish.\n\nSo “minasiwena” = fish?\n\nSo must be “with how many fish”?\n\nUnnatural.\n\nAlternative: “vivila” is a quantity phrase, and “minasiwena” is a noun, so “how many minasiwena” → how many fish?\n\nSo: “the woman saw with how many fish?”\n\nStill awkward.\n\nBut consider: in 14: \"Navila vivila biyamata tomwaya mtona?\"\n\n“Navila” → how many \n“vivila” → redundant? \n“biyamata” → future? \n“tomwaya” → man (singular) \n“mtona” → this man?\n\n“biyamata” → not in examples.\n\nBut look at sentence 15: “Bikamkwamsi kweyu vivila minasina.”\n\n“Bikamkwamsi” → future verb? “bi” → future; “kamkwamsi” → eat? \n“kweyu” → 2 → two \n“vivila” → how many? \n“minasina” → fish\n\nSo “two (how many) fish?” → how many fish?\n\nBut “kweyu” is 2 → “vila” is how many → so “two fish”?\n\n“kweyu” = 2 → quantity → so “two fish”\n\nSo “the two fish”?\n\nSo “two fish” → “kweyu minasina”\n\nBut sentence says: “Bikamkwamsi kweyu vivila minasina” → how many?\n\nPossibly: “the two fish will eat” → but “will eat” → future → bikamkwamsi\n\nSo: “the two fish will eat how many?” → doesn’t make sense.\n\n“kweyu vila minasina” → how many fish? → “two how many fish?”\n\nBut “kweyu” is quantity → 2 → so “two fish”?\n\nSo likely: “How many fish will the two eat?”\n\nSo structure: “How many [nouns] will [Q] eat?”\n\nIn 15: “Bikamkwamsi kweyu vivila minasina” → \"The two (how many) fish will eat?\"\n\nNo — the verb is with “kweyu” → so “the two fish” → “will eat how many?”\n\nSo \"How many fish will the two eat?\" → that's possible.\n\nBut “vila” is not explicitly a quantity — “kweyu” is quantity.\n\nSo: quantities: \n- vila → how many? \n- yu → two \n- tala → one \n- vasi → four \n\nSo in 15: “kweyu” = 2 \n“vila” = how many? \n“minasina” = fish \n\nSo “two fish → how many” → “how many fish will the two eat?”\n\nYes.\n\nSentence 16: “Amagudina gwadi lekota?” \n“Amagudina” → which? (interrogative) \n“gwadi” → child \n“lekota” → this? → demonstrative → “lekota” = this (child)\n\n“Amagudina” → which child? → “which child saw this?” \n\nBut sentence is “Amagudina gwadi lekota?” → “Which child did this?” — “did what?”\n\n“gudina” = verb? → \"gudina\" → see? → but in sentence 10: “dakuna” → saw\n\n“gudina” → not in examples.\n\nIn 14: “Navila vivila biyamata tomwaya mtona?”\n\n“Navila” = how many \n“vivila” = how many (redundant?) \n“biyamata” = future → will \n“tomwaya” = man \n“mtona” = this man\n\nSo “how many men will see this man?”\n\n“Yes — natural.”\n\nSo sentence 14: how many men will see this man?\n\n15: Bikamkwamsi kweyu vivila minasina → “how many fish will the two (fish) eat?” \n→ Better: “How many fish will the two eat?” \nBut “vila” is redundant?\n\nPossibly: “How many fish will the two eat?” → “kweyu vila minasina” → how many fish?\n\nBut “kweyu” is quantity → “the two fish” → so “the two fish eat how many?”\n\nSo: “how many fish will the two eat?” — yes.\n\n16: Amagudina gwadi lekota? → “Which child saw this?” → “which child did this (see)?”\n\nBut “gudina” = verb → see?\n\nIn 10: “dakuna” → saw → so “gudina” → not matching.\n\nIn 10: “dakuna” → saw → “dakuna”\n\nIn 14: “biyamata” → future\n\nIn 16: “amagudina” → could be “which child will see” → but no verb?\n\n“gudina” → may be a verb.\n\nBut in examples: \n1. “catch” → “navasi” → verb? not stated \n2. “arrived” → “mtona” → verb? All verbs seem to be in root form.\n\nIn 2: “This white man arrived” → “Lekota dimdim mtona” → “lekota” = this, “dimdim” = white, “mtona” = man → “arrived” is not there.\n\nSo likely the verb is missing?\n\nWait — no.\n\nSentence 10: “that child saw this stone” → “Legisi dakuna makwena gwadi magudiwena gudimanabweta”\n\n“Legisi” = saw (past) \n“dakuna” = verb → saw\n\nSo “dakuna” = saw\n\nSo “gudina” → may not be saw?\n\n“gudina” → might be a form of “see” or “saw”\n\nLikely not.\n\nIn sentence 16: “Amagudina gwadi lekota?” → “which child did [what]?”\n\nPossibility: “which child did this (something)?” — but no object.\n\nBetter: “which child saw this?” → if “gudina” = saw → then yes.\n\nIn 17: “Tevila tauwau bigisesi gugwadi gudigasisi?”\n\n→ “how many men will the wild children see?” or “how many men will the women see?”\n\nNow, “bigisesi” = women (subject), “gugwadi gudigasisi” → children or wild children?\n\n“gugwadi” = children, “gudigasisi”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11488.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 2, + "output": "Step 1: Identify core grammatical components from the given examples.\n\nWord order: V(O)S, QVX, (which | Qt)N(D)(A) \nVerbs: \n- le- = past \n- bi- = future \n- -si = plural subject (e.g., -gisi-si → -gisesi)\n\nNouns: \n- man → tau / tauwau (singular/plural) \n- child → gwadi / gugwadi \n- chief → guyau / gweguyau \n- old woman → namwaya / nunumwaya \n- canoes → ke- (no plural form shown, but \"ke-\" is used) \n- things/stones → kwe- \nSpecial: \"wild\" → appears with \"bunukwa\" (pig), \"gudigasisi\" (wild children) \n\nDemonstratives: \n- (a-)ma-Cl(-si)(-we)-na → mto- (man), mna- (woman), mina- (child), minasina (child plural) \n- ma-to- → mto- \n- ma-na- → mna- → mina- \n\nQuantities: \n- vila = how many? \n- yu = two \n- tala = one \n- vas-i = four \n\nClass prefixes: \n- men: te- (before Qt), to- \n- women/animals: na- \n- children: gudi- \n- canoes: ke- \n- things: kwe- \n\nStep 2: Analyze known examples for structure.\n\nExample 1: \n\"One man will catch these four fish.\" \n→ \"Bibani navasi yena minasina tetala tau.\" \n\"Bi\" → future; \"navasi\" → \"one man\"? \"navasi\" = \"one\" + \"man\"? \n\"yena\" = \"these\" → demonstrative \n\"minasina\" = \"four fish\" (minasi = fish; -na → plural) \n\"tetala\" = \"four\" → quantity \n\"tau\" = man, so \"minasina tetala tau\" = \"four fish of one man\"? \nWait: \"one man will catch these four fish\" → subject is man, object fish.\n\nRebuild: \n\"Bibani\" = future → \"bi\" + \"ban\" → \"bi\" verb, \"ban\" = \"catch\"? \n\"navasi\" → \"one\" + \"man\"? → \"navasi\" = subject \n\"yena\" = \"these\" → demonstrative (ma-+to? → mto? but yena = these) \n\"minasina\" = four fish? \"minasina\" = \"minasi\" (fish) + \"na\" (plural)? → fish plural \n\"tetala\" = \"four\" → quantity \n→ \"one man will catch these four fish\" → fits.\n\nSo: \n\"bi\" = future \n\"navasi\" = \"one man\" \n\"yena\" = these → demonstrates \"minasina\" (fish) \n\"tetala\" → quantity (four) → \"tetala tau\" = \"four fish\"\n\nSimilarly, Example 2: \n\"This white man arrived.\" \n\"Lekota dimdim mtona.\" \n\"le\" = past \n\"ekota\" = this? \n\"dimdim\" = white \n\"mtona\" = man? \"ma-to-\" → \"mtona\" → man \nSo: \"this white man\" → \"lekota dimdim mtona\"\n\nExample 3: \n\"That child will arrive.\" \n\"Bikota gwadi magudiwena.\" \n\"bi\" → future \n\"bikota\" → \"that\" + \"child\"? \"bi\" + \"kota\" → \"that\" + subject? \n\"gwadi\" = child → subject \n\"magudiwena\" = arrive? \"m\" + \"gudi\" → \"gudi\" = child → \"magudi\" → arrive? \n→ \"that child will arrive\" → fits.\n\nExample 4: \n\"This old woman saw those canoes.\" \n\"Legisi waga makesiwena namwaya minana.\" \n\"le\" = past \n\"legisi\" = saw \n\"waga\" = those? → demonstrative \n\"makesiwena\" = canoes? \"make\" → canoes? \"ke\" (canoe) → possibly \"mak\" is root? \n\"namwaya\" = old woman → subject \n\"minana\" = those? → mina- (child?) → no — mina → male? \nWait: \"minana\" → woman? → \"ma-na\" → \"mina\" → \"minana\"? \nBut \"namwaya\" = old woman → subject \n\"waga\" = those → → object \n\"makesiwena\" → \"canoes\" → ke + si? \"ke\" = canoe → \"make\" = ke? \n\"makesi\" = canoes? → seems like \"mak\" = canoe? \n\"makesiwena\" → \"saw canoes\" → yes.\n\nSo: \"waga\" = demonstrative (those) + object \n\"makesiwena\" = canoes \n\"namwaya\" = old woman → subject\n\nStructure: \n[le] + verb + [demonstrative] + object + subject \nBut in all cases, subject comes before object? Or after? \nExample 4: \"Legisi waga makesiwena namwaya minana\" \n→ saw those canoes (object) → \"waga makesiwena\", then \"namwaya minana\" → old woman \nSo: subject = \"namwaya minana\"? → \"namwaya\" = old woman; \"minana\" = those? \nConflict.\n\nWait: \"namwaya\" = old woman \n\"minana\" = those? \"ma-na\" → \"mina\" → \"minana\"? → female? → possible. \nBut \"namwaya\" is already woman. \nPossibly \"minana\" = those → \"minana\" = demonstrative → \"those\" \nSo \"namwaya minana\" = \"old woman, those\" → not subject.\n\nStructure: verb + object + subject \n\"legisi waga makesiwena\" → saw canoes \n\"namwaya minana\" → old woman (subject) \nBut word order: verb-object-subject → not V(O)S → V(O)S = verb, object, subject \nYes: V(O)S → here: legisi (V), waga (O), makesiwena (S)? no → makesiwena is \"canoe\"? \n\"makesiwena\" = canoes — can't be subject.\n\nAlternative: \"waga\" = demonstrative, \"makesiwena\" = canoes → object \n\"namwaya minana\" = subject \nSo structure: V + O + S → \"legisi waga makesiwena namwaya minana\"\n\nYes → fits V(O)S.\n\nSimilarly, Example 5: \n\"Which man killed two pigs?\" \n\"Amtona tau lekalimati nayu bunukwa?\" \n\"amtona\" = which man? \n\"tau\" = man \n\"lekalimati\" = killed \n\"nayu\" = two → quantity \n\"bunukwa\" = pig → \"bunukwa\" = wild pig → \"pig\" \n→ \"which man killed two pigs\" → fits.\n\nKey: \"am\" = interrogative \"which\" \n\"tona\" = man → but \"tona\" = man? \"tau\" = man → \"tona\" = same? \n\"amtona tau\" → \"which man\" \n\"lekalimati\" = past tense verb: \"kill\" \n\"nayu\" → two \n\"bunukwa\" → pig \nSo: \"which man killed two pigs?\"\n\nNow, translation pattern:\n\n- Interrogative: starts with \"am\" + noun → \"amtona\" = which man \n- Quantity: \"nayu\" = two \n- Object: \"bunukwa\" = pigs\n\nReconstructing structure:\n\nGeneral form:\n\n- [am] + [Qt] + [Cl] → interrogative \n- Qt: vila = how many, yu = two, tala = one, vas-i = four \n- Cl: man = tau, child = gwadi, chief = guyau, etc.\n\nVerb:\n- le- = past \n- bi- = future \n- -si = plural subject\n\nNoun Phrases:\n- nominals: Cl-vila, Cl-tala, Cl-yu, Cl-vasi → quantity markers \n- Cl preceded by te- for men (te- + Qt), to- for others? \n- Demonstratives: (a-)ma-Cl → mto- (man), mina- (child), mtona (man), mna- (woman), mna-naya →?\n\nBut: \"ma-to\" → mto- → \"that man\"? \n\"ma-na\" → mna- → \"that woman\"? \nIn example 4: \"waga makesiwena namwaya minana\" → \"those canoes\" → \"waga\" = those? \n\"minana\" → not man.\n\nWait: in example 4: \"waga\" = \"those\" → demonstrative \n\"makesiwena\" = canoes \n\"namwaya minana\" = old woman? \"minana\" = soil? possibly not.\n\nBut \"minana\" appears in:\n\"minasina\" → fish \n\"minana\" → in sentence 4 → \"namwaya minana\" → may be \"old woman\" in specific sense? \nIn sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"makwena\" = stone? \"kwe\" → \"kwe\" + \"wena\" → stone? \n\"gwadi\" = child \n\"gudimanabweta\" = beautiful? \n\"makwena\" = stone → so \"kwe\" = things\n\nSo:\n- things: kwe \n- animals: na \n- children: gudi \n- men: te or to \n- canoes: ke \n\nBack to interjections.\n\nSentence 7: \n\"That clever woman will see something.\" \n\"Bigisi kwetala vivila minawena nakabitam.\" \n\"bigisi\" → future? \"bi\" + \"gisi\" → \"that\" + \"woman\"? \n\"gwisi\" = woman? → \"gisi\" → woman? \n\"kwetala\" = clever? → \"kwe-tala\" → \"clever\" → tala = one? \n\"vivila\" = something? \"vi\" + \"vila\" = \"something\"? \n\"minawena\" = what? → \"mina\" + \"wena\"? \"wena\" → may be \"be\" → \"minawena\" = some thing? \n\"nakabitam\" = see? → \"naka\" + \"bitam\" \n\"vivila minawena\" → \"something\" → \"vivila\" = something → \"minawena\" = something? \n→ \"that clever woman will see something\" → fits.\n\nSo:\n- \"bigisi\" = future + woman \n- \"kwetala\" = clever → tala = one → adjectival \n- \"vivila\" = something \n- \"minawena\" = what? → possibly \"mina\" + \"wena\" → \"this\" or \"that\"? \n- \"nakabitam\" = see \n\nSo verb + subject + quantity/adj + object?\n\nBut object \"vivila\" → \"something\", \"minawena\" → possibly object?\n\nWait, \"vivila minawena\" → \"something\" → might be object \n\"nakabitam\" = see → verb \nSo: \"bigisi\" = subject? → woman \n\"kwetala\" = adjective \n\"vivila minawena\" = object? \n\"nakabitam\" = verb \nSo: subject + adj + object + verb → non-V(O)S.\n\nWait → primary V(O)S: may be verb at end.\n\nExample 5: \"which man killed two pigs?\" → \"amtona tau lekalimati nayu bunukwa?\" \n→ \"amtona tau\" = which man? \n\"lekalimati\" = killed \n\"nayu bunukwa\" = two pigs → object \nSo: interrogative → [am+]Qt+Cl → object → verb\n\nThus pattern: \n[am] + [Qt] + [Cl] + [verb] + [object] \nOr: [am] + [Qt] + [Cl] + [verb] + [Qt] + [N]\n\nNow Interrogatives in 14–18:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n\"navila\" → how many? → quantity \n\"vivila\" → something \n\"bi\" → future \n\"yamata\" → ??? \n\"tomwaya\" → man? tomwaya → tom = man? to- → man? \n\"mtona\" → man \n\n\"navila\" = how many? → QVX \n\"vivila\" = something → object \n\"bi\" = future → verb prefix \n\"yamata\" = ??? \n\"tomwaya\" → tom = man, waya = ?? → \"tomwaya\" → \"man\"? \n\"mtona\" = man → so \"tomwaya\" = man? \n\n\"biyamata\" = \"will see\"? \n\"bi\" + \"yamata\" → \"will see\"? \nIn sentence 7: \"nakabitam\" = see → so \"biyamata\" = will see? \nYes → \"bi\" + \"yamata\" = future + \"see\" \n\"tomwaya\" = man → subject? \n\"mtona\" = man → perhaps redundant? \n\n\"Navila vivila biyamata tomwaya mtona?\" \n→ \"How many things will the men see?\" → \"how many\" + \"things\" + \"will see\" + \"men\" (subject)? \nBut \"tomwaya\" = man → subject \n\"mtona\" = man → redundant?\n\nBut word order: QVX → \"navila\" = how many → at start \nThen \"vivila\" = something → object \nThen \"biyamata\" = will see (verb) \nThen \"tomwaya\" → man → subject? \nThen \"mtona\"? — repeated?\n\nNo: \"tomwaya mtona\" → man? \nMtona = man → is that a demonstrative? \n\"ma-to\" → mto- → man → \"mtona\" = that man? \n\nBut \"tomwaya\" → not standard. \nPossibly \"tomwaya\" = man (from \"to\" + \"mwa\")? → mwa? not found. \n\nAlternative: \"yamata\" = \"see\" → \"biyamata\" = will see \n\"tomwaya\" = man → subject \n\"mtona\" = that man → demonstrative? \nSo: \"how many things will the man see?\" → but \"tomwaya mtona\" = man that man? \n\nOr: \"how many men will see these things?\" \nBut \"vivila\" = things → object \n\"tomwaya\" = men → subject? \n\nSo: \"How many things will the men see?\" → \"Navila vivila biyamata tomwaya?\" → \"how many things will men see?\" \n\"mtona\" — probably just \"that man\"? → or error?\n\nBut in sentence 7: \"vivila minawena\" → something \n\"minawena\" → not \"things\" → \"vivila\" = something \n\nSo \"vivila\" = object → \"things\" → in English, \"something\" = things? \n\nConclusion: \n\"Navila vivila biyamata tomwaya mtona?\" = How many things will men see? (with \"mtona\" = that men?) \nBut \"tomwaya\" = men? → yes → \"tomwaya\" = men \n\"mtona\" = that? → perhaps redundant or emphasized \n\nAlternatively: \"how many men will see these things?\" → but \"vivila\" = things (object) \nIn V(O)S: verb after object → \"see\" after \"things\" → but here \"see\" is before \"men\"? \nNo: \"biyamata tomwaya mtona\" → \"will see men\"? → not logical.\n\nSo must be: \"how many things will men see?\" → object = \"things\", subject = \"men\" → object comes before subject?\n\nBut typical V(O)S: verb + object + subject → but here: \n\"navila vivila\" → how many things \n\"biyamata\" → will see \n\"tomwaya mtona\" → men → subject \n\nSo: [Q] + [O] + [V] + [S] → structure? \nQ = navila (how many) \nO = vivila (things) \nV = biyamata (see) \nS = tomwaya mtona (men)\n\nYes → V(O)S with Q at start → matches problem rule: QVX → interrogative with quantity and noun.\n\nSo: \"How many things will men see?\"\n\n15. Bikamkwamsi kweyu vivila minasina.\n\n\"bikamkwamsi\" = future? \"bi\" + \"kamkwamsi\"? \n\"bikamkwamsi\" → will eat? \n\"kweyu\" = two? → quantity → yu = two \n\"vivila\" = something \n\"minasina\" = fish? → minasi = fish, -na = plural → fish \n\nSo: \"will eat two things\"? or \"two fish\"? \n\"minasina\" → fish → object? \n\"kweyu\" = two → quantity \n\"vivila\" → something? \n\"minasina\" → fish? \n\nSo: \"those (fish) will eat two things\"? \nBut subject is missing.\n\n\"bikamkwamsi\" → subject or verb? \n\"bikamkwamsi\" = future verb → \"will eat\" \n\"vivila minasina\" = two fish → object? \nBut \"vivila\" = something → object \n\"minasina\" = fish → could be noun \n\nSo: [bi-kamkwamsi] = verb (will eat) \n[entity?] missing → likely subject is implied or in structure.\n\nBut in all examples, subject appears after object or before.\n\nWait: example 11: \n\"How", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11335.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "redacted_solution_hint_mask4", + "sample_index": 3, + "output": "Step 1: Identify key linguistic components from given examples.\n\nWord order: V(O)S, QVX, (which/Qt)N(D)(A) \nVerbs: \n- le- = past \n- bi- = future \n- -si = plural (e.g., gisi-si → gisesi)\n\nNouns: \n- man → tau (sing), tauwau (pl) \n- child → gwadi (sing), gugwadi (pl) \n- chief → guyau (sing), gweguyau (pl) \n- old woman → namwaya (sing), nunumwaya (pl) \n- singular and plural forms often overlap; no strict marking for number in all cases\n\nClass markers (Cl): \n- men: te- (before Qt), to- \n- women/animals: na- \n- children: gudi- \n- canoes: ke- \n- things (e.g., stones): kwe- \n\nDemonstratives: \n- (a-)ma-Cl(-si)(-we)-na → ma-to- → mto-, ma-na- → mina- \nE.g., \"this\" = mtona, \"that\" = bikota, not directly in all instances \n\nQuantities: \n- vila = how many? \n- tala = 1 \n- yu = 2 \n- vasi = 4 \n\nStep 2: Analyze sentence 17: \n\"17. Tevila tauwau bigisesi gugwadi gudigasisi?\" \nStructure: \n- Tevila → how many men (te- + vila → men's quantity) \n- tauwau → plural of man (subject) \n- bigisesi → plural form of \"see\" (bi- + gisi-si → gisesi, but here it's \"bigisesi\") \n → verb \"see\" is in future? bi- in front → \"will see\" \n- gugwadi → plural of child \n- gudigasisi → \"wild children\" → gudi- (child), gasisi → \"wild\"? \n → gudigasisi = \"wild children\" \n\nSo: \"How many men will see the wild children?\" \nAlternative: Could the object be the \"wild children\" seeing the men? \nBut word order is V(O)S — verb, object, subject \nSo: \"will see\" → verb, object, subject → so object is \"wild children\", subject is \"men\" \nSo primary reading: men see wild children \nBut is there a reversal? \nOnly if object is interpreted as subject or vice versa. \n\nBut in standard V(O)S, object comes before subject. \nSo: \"how many men will see the wild children?\" \nAlternative: \"how many men will the wild children see?\" \nThis would require object (wild children) to be the subject → not V(O)S in order.\n\nBut the language may allow reanalysis due to ambiguity in referent.\n\nIndeed, the official solution says: \n\"one possible translation: How many men will see the wild children?; \nother: How many men will the wild children see?\"\n\nSo the ambiguity arises from lack of clear subject-object direction in word order. \nIn V(O)S, object comes before subject — so it's \"men see children\". \nBut in questions like this, the question \"how many A will B do?\" may be structurally similar, and the object may be interpreted as agent.\n\nThus, the sentence allows two readings: \n1. How many men will see the wild children? \n2. How many men will the wild children see?\n\nThis is due to potential confusion in semantic role between agent and patient in \"see\".\n\nSo sentence 17 has two possible translations.\n\nNow test others for ambiguity.\n\nSentence 14: \"Navila vivila biyamata tomwaya mtona?\" \n- Navila → how many (quantity) \n- vivila → \"things\" (because kwe- is for things; vivila = things?) \n- biyamata → bi- future, ya-? \n → biyamata = will catch? \n- tomwaya → man (tomwaya = man) \n- mtona → this (demonstrative)\n\nSo: How many things will catch this man? \nOr: How many things will this man catch? \n\nCheck grammar: \n\"how many things will (somebody) catch\" → object of \"catch\" is \"things\" → so \"things\" are the object. \n\"will catch this man\" → man is object → then \"things\" are acting on man → not plausible. \nSo must be \"this man (subject) will catch things (object)\" → so \"how many things will this man catch?\"\n\nThus, only one reading makes sense: \nHow many things will this man catch?\n\nSo not ambiguous.\n\nSentence 15: \"Bikamkwamsi kweyu vivila minasina.\" \n- Bikamkwamsi → will eat? (bi- + kamkwamsi → eat?) \n- kweyu → quantity: 2 \n- vivila → things? \n- minasina → \"these\" + \"fish\"? \nBut minasina → from \"mina\" (this) + \"na\" (things)? Example 1: \"minasina tetala tau\" → \"those four fish\" → minasina + tetala (4) → \"those four fish\" \nSo minasina = \"these fish\"\n\nSo: \"Will two things (things) eat these fish?\" \nOr \"Will two things eat these fish?\" \n\"vivila\" → things? In context: things are eaten → so things are object → so subject is \"two things\"? \n\nBut \"two things eat these fish\" — plausible. \nCould it be \"two things will these fish eat\"? \nNo — pluralization not aligned. \n\"Events\" or \"subjects\" acting? \nNo structure for passive. \nSo only reading: two things will eat these fish → reasonable.\n\nNo ambiguity.\n\nSentence 16: \"Amagudina gwadi lekota?\" \n- Amagudina → \"which child\"? (am- → which; gudina → child?) \n- gwadi → child \n- lekota → this? \n→ \"Which child (is) this?\" \n→ \"Which child is this?\" \nOnly one reading.\n\nSentence 18: \"Legisesi ketala waga vivila minasiwena.\" \n- Legisesi → past tense \"see\" → verb \n- ketala → \"that\" + \"man\"? ketala → \"that man\"? \n- waga → \"those\" (demonstrative) \n- vivila → things? \n- minasiwena → \"these\" + \"things\" (minasina → these)?\n\nSo: \"That man saw those things (which are these things)?\"\n\nBut \"vivila minasiwena\" → things (these) \nSo: \"That man saw those things which are these?\"\n\nBut that's redundant. Possibly: \"That man saw those things\" → these are those?\n\nBut \"minasiwena\" = these, \"waga\" = those → conflict in demonstratives?\n\nBut no known rule for \"waga\" vs \"minasiwena\" — both demonstratives.\n\nPossibility: \"waga\" = those (in a group), \"minasiwena\" = these (near) → so \"those things which are these\"?\n\nBut unlikely. More likely: \"The man saw these things\" — but \"waga\" and \"minasiwena\" both used?\n\nCheck examples: \nExample 1: \"One man will catch these four fish.\" → \"these four fish\" → minasina + tetala → so \"these\" with quantity \nExample 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → dogs = ka’ukwa → canoes? no — ka’ukwa = dogs?\n\nFrom example 8: \"Navila ka’ukwa lekotasi?\" → How many dogs arrived?\n\nSo ka’ukwa → dogs \nSo \"ka’ukwa\" = dogs — a class noun.\n\nSo vivila = things (general)\n\nNow in 18: \"Legisesi ketala waga vivila minasiwena\" \n\"ketala\" = that man? or that things? \n\"ketal\" = not defined — only \"lekota\" = this, \"bikota\" = that — so \"ketala\" may be \"that man\" → similar to \"lekota\"\n\nSo \"that man (subject) saw those things (waga) which are these (minasiwena)?\"\n\nBut that is clunky.\n\nAlternatively: \"that man saw these\" → \"things\"?\n\nBut \"waga vivila\" = those things? → objects\n\nSo if verb is \"saw\", object is \"those things\", subject is \"man\"\n\nSo: \"That man saw those things\"\n\n\"minasiwena\" → these → may modify \"things\"? \nSo \"those things (that are these)\" — redundant.\n\nAlternatively: is it \"the man saw these things\"?\n\nBut \"waga\" = those → opposite of \"these\" — seems inconsistent.\n\nBut in other examples, e.g., 10: \"that beautiful child saw this stone\" → \"gwadi magudiwena gudimanabweta\" → child + stone\n\nHere: \"waga\" → those, \"minasiwena\" → these → conflict.\n\nBut no evidence of contradiction.\n\nNo ambiguity.\n\nOnly sentence 17 has a real ambiguity — between agent and patient in \"see\".\n\nThus, the one sentence with two translations is sentence 17.\n\nFinal translations:\n\n14. How many things will this man catch? \n15. Two things will eat these fish. \n16. Which child is this? \n17. How many men will see the wild children?; How many men will the wild children see? \n18. That man saw those things (which are these things)? → but simplify to: That man saw those things.\n\nBut in context, only 17 has ambiguity.\n\nSo answer:\n\na.1: How many things will this man catch? \na.2: Two things will eat these fish. \na.3: Which child is this? \na.4: How many men will see the wild children?; How many men will the wild children see? \na.5: That man saw those things.\n\n\\boxed{a.1: How many things will this man catch?; a.2: Two things will eat these fish.; a.3: Which child is this?; a.4: How many men will see the wild children?; How many men will the wild children see?; a.5: That man saw those things.}", + "generated_tokens": 2335, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: How many things will this man catch?; a.2: Two things will eat these fish.; a.3: Which child is this?; a.4: How many men will see the wild children?; How many men will the wild children see?; a.5: That man saw those things.", + "score_fraction": 0.2, + "exact": 0.0, + "matched_units": [ + "a.4" + ], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.2, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 1.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.2, + "ioling_strict_substring_reward": 0.2, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7714.0, + "ioling_final_answer_chars": 228.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n [TARGET ANSWER REDACTED]\n 15. Bikamkwamsi kweyu vivila minasina.\n [TARGET ANSWER REDACTED]\n 16. Amagudina gwadi lekota?\n [TARGET ANSWER REDACTED]\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n [TARGET ANSWER REDACTED]\n\n (b) 19. How many canoes did those old women see?\n Kevila waga legisesi nunumwaya minasiwena?\n 20. These four white men will look after this clever child.\n Biyamatasi gwadi magudina gudikabitam tevasi dimdim mtosina.\n 21. How many children will eat these pigs?\n Gudivila gugwadi bikamkwamsi bunukwa minasina?\n 22. Which woman caught those beautiful fish?\n Aminana vivila lebani yena minasiwena namanabweta?\n 23. Two wild dogs saw that old man.\n Legisesi tomwaya mtowena nayu ka’ukwa nagasisi.", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 0, + "output": "Step 1: Identify the core pattern from given translations.\n\nThe language uses V(O)S word order. Interrogatives use QVX structure (Q = interrogative, V = verb, X = object or other). Quantities are marked with Cl-vila (how many) or Cl-tala (1), Cl-yu (2), Cl-vasi (4). Demonstratives are in (a-)ma-Cl(-si)(-we)-na form; e.g., mto- for \"this\", mina- for \"that\", mtona for \"this man\".\n\nNouns have class-specific prefixes:\n- men: te- (before quantity), to- (in object)\n- women/animals: na-\n- children: gudi-\n- canoes: ke-\n- things: kwe-\n\nSubject marking:\n- -si for plural subject (e.g., tauwau → tauwau-si)\n- verb: bi- = future, le- = past\n\nNow analyze each target:\n\n19. How many canoes did those old women see?\n\n- \"How many\" → vila (quantifier)\n- \"canoes\" → ke- (class) → kevila\n- \"those old women\" → old woman = namwaya (singular); plural = nunumwaya\n- \"did see\" → past tense verb → le- + verb (see → makesi or makwena? From ex.4: \"saw those canoes\" → makesiwena, so verb = makesi → le-makesi)\n- \"those\" = demonstrative: ma-na- → mina- (for \"those\" with women → mina-namwaya)\n\nStructure: QVX → vila kevila le-makesi? → must place subject before verb.\n\nBut in English: \"how many canoes did those old women see?\" → goes into QVX: vila kevila le-makesi mina-nunumwaya\n\nNote: in ex.4: \"Legisi waga makesiwena namwaya minana\" → \"That woman saw those canoes\" → waga (demonstrative for woman?) → waga → probably \"those\" = \"waga\" (in ex.4, \"waga\" = \"those\")\n\nBut ex.4: \"Legisi waga makesiwena namwaya minana\" → that woman saw those canoes → so \"waga\" = those, \"namwaya\" = woman, \"minana\" = those?\n\nIn ex.4: \"namwaya\" → woman → \"minana\" = those → so demonstrative is separate from noun.\n\nSo in 19: subject is \"those old women\" → \"mina-nunumwaya\"\n\nVerb: past → le-makesi\n\nQuantifier: vila kevila → \"how many canoes\"\n\nQB: vila kevila le-makesi mina-nunumwaya?\n\nBut order must be QVX → quantifier first → vila kevila le-makesi mina-nunumwaya\n\nCheck if \"kevila\" applies correctly → yes, canoes → ke-\n\nSo 19: vila kevila le-makesi mina-nunumwaya\n\nBut in ex.4: \"Legisi waga makesiwena namwaya minana\" → \"that woman saw those canoes\" → subject is \"legisi\" (that), object \"namwaya\", but the demonstrative is used after.\n\nWait: structure is V(O)S → verb in middle, object after, subject at end?\n\nNo: ex.4: \"Legisi waga makesiwena namwaya minana\"\n\n- Legisi = that woman (subject)\n- waga = those (demonstrative)\n- makesiwena = saw canoes (verb + object)\n- namwaya minana → woman + those?\n\nNo, only one noun phrase.\n\nBetter: waga → demonstrative for object → object is \"waga\"? But \"waga\" is a noun.\n\nIn ex.4: \"saw those canoes\" → so \"waga\" = those canoes? Or \"waga makesiwena\" = saw → waga = object?\n\nBut \"makesiwena\" = saw + canoes → so waga = object?\n\nThen \"namwaya\" = subject?\n\nNo: \"Legisi waga makesiwena namwaya minana\" → subject = legisi (that woman), object = waga (those), verb = makesiwena?\n\nBut \"makesiwena\" must include object → makesiwena → so \"waga\" is object → then what is \"namwaya minana\"?\n\nAlternative: \"namwaya\" = woman, \"minana\" = those → so subject = \"legisi\" (that woman), object = \"waga\" (those canoes)\n\nBut \"waga\" is a word; is it a demonstrative for canoes?\n\nIn ex.8: \"How many dogs arrived?\" → Navila ka’ukwa lekotasi?\n\n\"ka’ukwa\" is a demonstrative for dogs?\n\nNo: ex.8: \"how many dogs arrived?\" → Navila ka’ukwa lekotasi?\n\n\"ka’ukwa\" → likely interrogative for quantity.\n\nIn ex.5: \"which man killed two pigs?\" → Amtona tau lekalimati nayu bunukwa?\n\n\"Amtona\" → interrogative for \"which\", \"tau\" = man, \"lekalimati\" = killed, \"nayu\" = two, \"bunukwa\" = pigs\n\nSo \"nayu\" = quantity for pigs → Cl-yu = 2\n\nSo quantity words: Cl-vila = how many, Cl-tala = 1, Cl-yu = 2, Cl-vasi = 4\n\nSo \"kevila\" = how many canoes\n\n\"those old women\" → women → na- prefix → plural = nunumwaya → demonstrative \"those\" → \"mina-\"\n\nSo: vila kevila le-makesi mina-nunumwaya\n\nBut in ex.4: \"Legisi waga makesiwena namwaya minana\"\n\n→ subject = \"legisi\" (that woman), object = \"waga\" (those canoes), verb = makesiwena\n\nSo object is \"waga\" → is that correct?\n\nBut \"waga\" = those → so likely the demonstrative is attached to the noun.\n\nIn fact, in ex.4, the object is \"waga\", and \"namwaya minana\" — if \"waga\" is object, why is \"namwaya\" present?\n\nPossibly \"waga\" = those canoes → holds nominal group.\n\nBut in ex.4, \"waga makesiwena namwaya minana\" — if \"waga\" is object, then subject is \"namwaya minana\"?\n\nNo, \"legisi\" is first → subject.\n\nSo structure: subject + demonstrative (object) + verb + noun?\n\nBut verb is \"makesiwena\" → must have object.\n\nLikely: \"makesiwena\" is verb + object → object = \"waga\" → so \"waga\" = those canoes\n\nThen \"namwaya minana\" — perhaps \"namwaya\" is subject? But \"legisi\" is first.\n\nPossibly \"legisi\" = that, \"waga\" = those canoes, \"makesiwena\" = saw, \"namwaya minana\" = the woman? No.\n\nAlternative: \"namwaya\" = woman, \"minana\" = those → so all is compound.\n\nWait, perhaps \"waga\" is an interrogative or demonstrative.\n\nIn ex.13: \"How many women will look after this man?\" → Navila vivila biyamata tomwaya mtona?\n\n\"Navila vivila\" = how many → vila, quantity for women → \"vivila\"\n\n\"biyamata\" = will look after (verb form?)\n\n\"tomwaya\" = this man → demonstrative → \"to-\" + \"ma-\" + \"wan\" for man → \"tomwaya\"?\n\n\"mtona\" = this man?\n\nSo \"tomwaya\" = this woman? No.\n\n\"mtona\" = this → \"tomwaya\" = this man?\n\nSo probably: \"tomwaya\" = this man.\n\nSo \"will look after this man\" → biyamata tomwaya\n\nSo structure: how many women will look after this man? → Navila vivila biyamata tomwaya mtona?\n\nWait, \"mtona\" is separate?\n\n\"tomwaya\" = this man?\n\nThen \"mtona\" = this — duplicate?\n\nNo, \"tomwaya\" is from \"to-\" (man) + \"ma-\" + \"wan\"? → \"tomwaya\"\n\n\"mtona\" = this man?\n\nSo perhaps \"tomwaya\" and \"mtona\" are different.\n\nIn ex.2: \"This white man arrived\" → Lekota dimdim mtona.\n\n\"mtona\" = this man.\n\nSo demonstrative for man: mtona → this man\n\nFor woman: mina-namwaya → those old women?\n\nIn ex.4: \"Legisi waga makesiwena namwaya minana\"\n\n→ legisi = that woman → subject\n→ waga = those → object?\n→ makesiwena = saw\n→ namwaya minana → woman and those?\n\nToo many words.\n\nPossibly waga = those canoes → so noun phrase is \"waga\" → makesiwena → saw those canoes.\n\nThen subject is \"legisi\" (that woman).\n\nThen \"namwaya\" is the subject noun? But \"legisi\" = that woman.\n\nSo \"namwaya\" unexplained.\n\nAlternative: \"legisi\" = that, \"waga\" = those canoes, \"makesiwena\" = saw, \"namwaya\" = woman → but redundant.\n\nPossibly the noun phrase for subject is \"namwaya\", and \"minana\" is demonstrative.\n\nSo \"Legisi\" = that, \"namwaya\" = woman, \"minana\" = those → so \"that woman (namwaya) those (minana)\" → no.\n\nBetter: the demonstrative is used only for object.\n\nSo in ex.4: \"Legisi waga makesiwena namwaya minana\" → likely means \"That woman saw those canoes\" → so \"waga\" = those canoes → \"makesiwena\" = saw → \"namwaya\" = the woman → \"legisi\" = that → so the subject is \"namwaya\", and \"legisi\" is a demonstrative for that?\n\nBut \"legisi\" is first.\n\nActually, from ex.4: \"that woman\" = legisi, \"saw\" = makesiwena, \"those canoes\" = waga?\n\nBut \"waga\" not canoes.\n\nCanoes class = ke- → canoes = ke?\n\nSo \"ke\" + noun?\n\nIn ex.4: no \"ke\".\n\nBut in ex.8: \"how many dogs\" → \"ka’ukwa\" — dogs → class = na? — so \"ka’ukwa\" = dogs?\n\n\"ka’ukwa\" → likely the quantity for dogs?\n\nNo — \"Navila ka’ukwa lekotasi?\" → \"how many dogs arrived?\" → so \"ka’ukwa\" = dogs.\n\nSo quantity word for dogs → ka’ukwa.\n\nSimilarly, \"nayu\" = two → Cl-yu.\n\nSo \"vila\" = how many.\n\nBack to 19: \"how many canoes did those old women see?\"\n\n- Quantity: vila kevila → how many canoes\n- Verb: past → le-makesi\n- Subject: \"those old women\" → plural → nunumwaya → demonstrative \"those\" → mina-\n→ mina-nunumwaya\n\nStructure: QVX → vila kevila le-makesi mina-nunumwaya\n\nBut in ex.4, when subject is a woman, it's \"legisi\" → a demonstrative, so maybe subject is marked with demonstrative?\n\nBut in ex.4, \"legisi\" = that woman, so \"legisi\" is the demonstrative.\n\nIn ex.2: \"This white man arrived\" → \"Lekota dimdim mtona\" → \"mtona\" = this man → demonstrative.\n\nIn ex.1: \"One man will catch these four fish\" → \"Bibani navasi yena minasina tetala tau.\"\n\n\"navasi\" = one? (quantity) → \"navasi\" = one → like \"one\"?\n\"yena\" = these\n\"minasina\" = fish\n\"tetala tau\" = four fish → plural?\n\n\"tetala\" = four — quantity?\n\n\"tetala\" = 4 → as in \"Cl-vasi\" = 4?\n\nSo Cl-tala = 1, Cl-yu = 2, Cl-vasi = 4.\n\nSo \"tetala\" = 4.\n\nBack to 19: quantity \"vila kevila\" → how many canoes\n\nSubject: old women → plural → nunumwaya → \"those\" → mina- → \"mina-nunumwaya\"\n\nVerb: past → le-makesi\n\nSo sentence: vila kevila le-makesi mina-nunumwaya\n\nBut in ex.4: \"Legisi waga makesiwena namwaya minana\" → if subject is \"legisi\", object is \"waga\", verb \"makesiwena\", then what is \"namwaya minana\"?\n\nPossibly \"namwaya\" = woman, \"minana\" = those → object is \"waga\" = those canoes?\n\nBut \"waga\" not canoes.\n\nUnless \"waga\" = canoes with \"ke\"?\n\nBut no \"ke\".\n\nIn ex.4 object is \"waga\", and \"waga\" is not canoes.\n\nUnless the class is attached: \"ke\" + \"waga\"?\n\nNo.\n\nBut in ex.8: \"how many dogs\" → \"ka’ukwa\" — so \"ka’ukwa\" = dogs → so class + quantity = \"ka’ukwa\"\n\nSimilarly, for canoes: ke- + vila → kevila\n\nSo for object: \"kevila\" = how many canoes → quantity phrase\n\nBut in ex.4, the object is \"waga\", which is \"those canoes\" → so \"waga\" = those canoes → so the noun must be \"waga\" with class?\n\nBut waga is in ex.4 as object → so likely \"waga\" = canoes → so class is used?\n\nBut class is only for noun.\n\nIn ex.4, \"waga\" is a demonstrative for canoes → but in ex.8, \"ka’ukwa\" = dogs.\n\nSo possibly each noun has a demonstrative form.\n\nFor women: mina-namwaya = those old women\n\nFor canoes: mina-ke? → \"mina-ke\" = those canoes?\n\nIn ex.4: \"waga\" is used → so likely not.\n\n\"makesiwena\" → saw → past → so verb is \"makesi\"\n\nSo in ex.4: \"legisi\" = that woman? → subject\n\n\"waga\" = those canoes → object\n\n\"makesiwena\" = saw\n\n\"namwaya\" = woman? → redundant.\n\nPossibly the subject is \"namwaya\", and \"legisi\" is demonstrative.\n\nBut \"legisi\" is not used as demonstrative for woman; \"mina-namwaya\" is.\n\nIn ex.4, \"namwaya minana\" → woman and those.\n\nSo likely: \"namwaya\" = woman, \"minana\" = those → so the subject is \"namwaya\" and \"minana\" = demonstrative.\n\nBut \"minana\" is for \"those\", not \"this\".\n\nIn ex.2: \"This white man arrived\" → \"mtona\" = this man.\n\nIn ex.4: \"waga\" = those canoes → so \"waga\" is object demonstrative.\n\nIn ex.1: \"these four fish\" → \"yena minasina tetala tau\"\n\n\"yena\" = these → demonstrative for fish → since fish = minasina → \"yena\" = these\n\nSo demonstratives: for fish → yena, for men → mtona, for things → ka’ukwa?\n\nSo for canoes → what?\n\nNo example.\n\nIn ex.4: object is \"waga\" → so \"waga\" = those canoes → so likely canoes have demonstrative \"waga\"?\n\nBut \"waga\" is used for canoes.\n\nIn ex.13: \"how many women will look after this man?\" → \"Navila vivila biyamata tomwaya mtona?\"\n\n\"tomwaya\" = this man → from \"to\" + \"ma\" + \"wan\" → man\n\n\"mtona\" = this man → so \"tomwaya\" and \"mtona\" both?\n\n\"mtona\" = this man → so \"tomwaya\" may be a different form.\n\nPossibly \"tomwaya\" = this old man or something.\n\nBut in ex.4, \"waga\" is used for canoes.\n\nSo likely: in object, demonstrative is used: for canoes → \"waga\" or \"waga\" as demonstrative.\n\nBut in ex.4, \"waga makesiwena namwaya minana\" → \"waga\" = object, \"namwaya\" = subject, \"minana\" = those?\n\nNo.\n\nBetter: \"waga\" = those canoes → so object is \"waga\"\n\n\"makesiwena\" = saw\n\n\"legisi\" = that woman → subject\n\n\"namwaya\" = woman → redundant.\n\nPossibly \"legisi\" = that, and \"namwaya\" = the woman, so subject is \"namwaya\", and \"legisi\" is adverb.\n\nBut not standard.\n\nAlternative: the sentence is \"that woman saw those canoes\" → subject = \"namwaya\", verb = \"makesiwena\", object = \"waga\" (those canoes)\n\nSo \"legisi\" is \"that\" → demonstrative for subject.\n\nSo in general, demonstratives can be attached to subject or object.\n\nFor sentence 19: \"how many canoes did those old women see?\"\n\n- Subject: those old women → mina-nunumwaya\n- Verb: past → le-makesi\n- Object: none? no, \"how many\" is quantity, so object is implicit.\n\nSo only quantifier and verb and subject.\n\nSo structure: vila kevila le-makesi mina-nunumwaya\n\nNow 20", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12002.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 1, + "output": "Step-by-step analysis of the Kilivila translation rules and patterns:\n\nFrom the given examples, identify key patterns:\n\n1. **Word order**: V(O)S, QVX, (Qt)N(D)(A) \n - Interrogatives start with a question marker (Q), followed by verb or quantity, then noun phrases.\n\n2. **Verb forms**:\n - le- = past tense\n - bi- = future tense\n - -si = plural subject marker (e.g., -gisi-si → -gisesi)\n\n3. **Nouns**:\n - man → tau / tauwau (plural)\n - child → gwadi / gugwadi\n - chief → guyau / gweguyau\n - old woman → namwaya / nunumwaya\n - canoe → ke- (kema? ke- is used for canoes)\n - thing → kwe-\n\n4. **Class prefixes**:\n - men: te- before quantity; to- in noun phrases\n - women/animals: na-\n - children: gudi-\n - canoes: ke-\n - things: kwe-\n\n5. **Demonstratives**:\n - (a-)ma-Cl(-si)(-we)-na → e.g. mto- (this), mna (that)\n - ma-to- → mto-\n - ma-na- → mina-\n\n6. **Quantities**:\n - vila = how many?\n - yu = 2\n - vas- = 4\n - tala = 1\n\nTarget translation for each:\n\n---\n\n**19. How many canoes did those old women see?**\n\n- Question: How many canoes?\n → quantity: vila → \"vila ke-\" (how many canoes)\n- Subject: those old women → \"nunumwaya\" (plural old woman)\n- Verb: past tense → \"lekota\" (see)\n- Structure: QVX: \"Navila\" (how many) + \"ke\" (canoe) → \"Navila ke...\"?\n- But for \"did see\", use past verb: lekota = saw\n- Subject: \"nunumwaya\" (those old women)\n- So: \"Navila kevila lekotasi\" → for \"how many canoes did those women see\"\n\nWait: in sentence 4: \"Legisi waga makesiwena namwaya minana\" = \"That woman saw those canoes\"\n\n\"makesiwena\" = saw (verb); \"namwaya\" = old woman; \"waga\" = those\n\nSo: [demonstrative] + [verb] + [object]\n\nInterrogative: \"How many canoes did X see?\"\n\n→ Navila kevila lekotasi\n\nBut subject = \"those old women\" → \"nunumwaya\"\n\nSo: \"Navila kevila nunumwaya lekotasi?\"\n\nBut in (18): \"Legisesi ketala waga vivila minasiwena\" = \"Those women saw one canoe\"\n\n\"ketala\" = one canoe → \"tala kewa\" → but here \"keta\" not present.\n\nIn (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\n→ \"Navila\" + quantity + verb\n\nSimilarly, (21) is: \"How many children will eat these pigs?\" → \"Kwevila gudigwadi bintala tala tena minasina?\"\n\nWait — look at (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n→ \"Kwevila\" + \"lekamkwamsi\" (those white men) + \"mtosiwena\" (eaten)\n\nSo pattern: Q + noun class + verb + object?\n\nNo — verb must come after.\n\nActually: Interrogative: Q + quantity + noun + verb + subject?\n\nWait.\n\nIn (5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\nStructure:\n- Amtona → which\n- tau → man\n- lekalimati → killed (le- + kalimati)\n- nayu → 2 (yu)\n- bunukwa → pigs\n\nSo: (Qt) + N + verb + Qt + noun?\n\nNo — lekalimati (verb) is before object.\n\nSo: (which man) + verb + quantity + noun\n\nBut in (5): Amtona tau lekalimati nayu bunukwa?\n\n→ Amtona tau (which man) + lekalimati (killed) + nayu bunukwa (two pigs)\n\nSo verb comes after the subject phrase?\n\nNot exactly — the verb is \"lekalimati\", independent.\n\nIn (4): \"Legisi waga makesiwena namwaya minana\" = \"The woman saw those canoes.\"\n\n→ Legisi = subject, waga = object, makesiwena = saw\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\" → women saw one canoe → \"ketala\" = one, \"waga\" = canoes, \"vivila\" = how many?\n\nNo — \"ketala\" = one, \"vivila\" = how many?\n\nIt's not matching.\n\nBack to (18): \"Legisesi ketala waga vivila minasiwena\"\n\n\"Legisesi\" = those women \n\"ketala\" = one \n\"waga\" = those canoes? \n\"vivila\" = how many? \n\"minasiwena\" = saw\n\nBut \"vivila\" appears earlier.\n\nActually: \"waga vivila\" = those canoes? No.\n\n\"vivila minasiwena\" = saw how many?\n\nNo — \"vivila\" is quantity.\n\nIn (8): \"Navila ka’ukwa lekotasi?\" = \"How many dogs arrived?\" \n\"ka’ukwa\" = dogs → \"ke\" class (dogs?) — dogs would be na-dog?\n\nWait — no dog class.\n\nFrom the list: no dog class. But in (23): \"Two wild dogs saw that old man.\"\n\nSo we must have a class for \"dog\".\n\nLooking at given data: only animals with classes are for women, children, canoes.\n\nBut animals may have na- prefix.\n\nSo probably:\n- dogs = na- (animal) → nado?\n\nBut in (12): \"The clever chief killed one wild pig\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam\"\n\n\"bunukwa\" = wild pig → pig class?\n\nNo pig class given.\n\nBut \"bunukwa\" is used as object.\n\nSo likely, nouns are formed with:\n- men: ta- or tau\n- women: na- (e.g. namwaya)\n- children: gudi-\n- canoes: ke-\n- things: kwe-\n\nSo for \"dog\": must be na-dog → nado?\n\nBut \"wild dog\" → \"nado\" (dog), \"wild\" → ? adjective?\n\nIn (10): \"that beautiful child\" → \"dakuna\" (beautiful)\n\nThus: adjectives come before noun? \"dakuna gwadi\"\n\nSo \"wild dog\" → \"nado\" → \"wagai nado\" → but only if adjectives are used.\n\nNow back to 19: How many canoes did those old women see?\n\n→ \"Navila kewa lekotasi\" → no.\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\"\n\n\"Legisesi\" = female plural (old woman) → \"nunumwaya\"\n\"keta\" = one canoe → \"ketala\" = one\n\"waga\" = those canoes\n\"vivila\" = how many? — but \"vivila\" is quantity\n\nWait — \"vivila\" appears in (18) after \"waga\" → \"waga vivila\" = those how many?\n\nNo.\n\nActually: In (4): \"Legisi waga makesiwena namwaya minana\" → woman saw those canoes → \"waga makesiwena\" = saw those canoes\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\"\n\nPossibility: root verb \"makewena\" → see\n\n\"vivila\" = how many? → but used as quantity for canoes?\n\n\"Minasiwena\" = saw\n\nSo perhaps: \"Legisesi ketala waga vivila minasiwena\" = those women saw one canoe? \nBut \"vivila\" would mean \"how many\", not \"one\".\n\n\"ketala\" = one\n\nSo \"ketala\" = quantity → one\n\nSo the structure is: Subject + quantity + object + verb?\n\nNo — verb is \"minasiwena\"\n\nSo: \"those women\" + \"saw\" + \"one canoe\"?\n\nBut that would be \"Legisesi ketala waga minasiwena\"\n\nBut it says \"vivila\" → which is \"how many\"?\n\nContradiction.\n\nAlternate: perhaps \"vivila\" is object or quantity.\n\nBut \"kewa\" not given.\n\nWait — in (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\n\"Navila\" = how many \n\"ka’ukwa\" = dogs → must be na- or ke-?\n\nDogs → animal → na- → \"na-ka\" or \"nado\"?\n\nNo specific dog class.\n\nBut in (23): \"Two wild dogs saw that old man.\"\n\nSo \"wild dogs\" = \"nayu\" (2) + \"waga\" (wild) + \"nado\"?\n\n\"nayu na-dog\"?\n\nBut nayu is quantity.\n\nPossibly: \"nayu nado\" = two dogs.\n\nSo \"nayu\" = 2, \"nado\" = dog.\n\nBack to 19.\n\n\"how many canoes did those old women see?\"\n\nFrom analogy:\n\n(8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" + quantity (implied) + noun + verb?\n\nBut \"ka’ukwa\" = dogs → album? or class?\n\nBut \"ka’ukwa\" may be \"teno\"? No.\n\nIn (4): \"Legisi waga makesiwena namwaya minana\" → old woman saw those canoes\n\nSo verb \"makesiwena\" = saw\n\nSo \"saw\" = makesiwena\n\nThus: \"see\" = makesiwena or lekotasi?\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\" — this seems to be a mistake.\n\nWait — it says: \"Legisesi ketala waga vivila minasiwena\"\n\n\"vivila\" is not in (18) as quantity.\n\nBut in (11): \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n→ \"Kwevila\" = how many things \n\"lekamkwamsi\" = those white men \n\"mtosiwena\" = ate\n\nSo pattern: Q + noun class + verb + object\n\nIn (9): \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n→ \"Amakena\" = which canoe \n\"waga\" = that \n\"legisesi\" = the chiefs (gweguyau = chief plural) \n→ \"which canoe did the chiefs see?\"\n\nSo: \"Amakena waga\" = which canoe, then verb \"legisesi\" (did see)\n\nNo — \"legisesi\" is the verb \"saw\"\n\nSo: \"Amakena waga legisesi gweguyau\" → which canoe did the chiefs see?\n\n\"legisesi\" = verb \"saw\"\n\nSo structure: (Q) + (object) + verb + subject\n\nBut in (5): \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n\n→ \"Amtona tau\" = which man → subject \n\"lekalimati\" = killed \n\"nayu bunukwa\" = two pigs → object\n\nSo still verb before object.\n\nSo verb is between subject and object? No — in (5): subject + verb + object\n\n\"Amtona tau\" = which man \n\"lekalimati nayu bunukwa\" = killed two pigs\n\nSo verb after subject, before object.\n\nIn (1): \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\"\n\n\"navasi\" = one → quantity? \"tetala\" = one → \"tetala\" = one \n\"minasina\" = fish \n\"tau\" = man\n\nSo \"tetala minasina tau\" → one fish man? \n\"navasi\" = one → quantity \n\"yena\" = \"these\" → demonstrative \n\"minasina\" = fish \n\"tetala tau\" = one man\n\nSo structure: quantity + noun + verb → \"tetala minasina tau\" = these four fish? No — \"tetala\" = one, not four.\n\nWait — 1: \"One man will catch these four fish.\"\n\n\"Bibani navasi yena minasina tetala tau.\"\n\n\"navasi\" = one? Or \"yena\" = these?\n\n\"tetala\" = one\n\nSo \"tetala\" = one fish → but \"one man\" → likely \"navasi\" = one\n\n\"navasi\" = one\n\n\"tetala\" = one (fish)\n\nSo \"navasi\" = quantity for man\n\n\"yena minasina\" = these fish\n\n\"tetala\" = one → so \"one man\" = \"tetala tau\"?\n\n\"tetala tau\" = one man\n\n\"yena minasina\" = these fish\n\n\"navasi\" = one → but appears before?\n\nOnly one \"navasi\" — may be for man.\n\nSo \"tetala tau\" = one man\n\n\"navasi\" = one (same)\n\nSo perhaps \"navasi\" is the quantity for man.\n\nSo poetic structure: QN + verb + object\n\nNow back to 19: How many canoes did those old women see?\n\n→ quantity: vila = how many \nnouns: canoes → ke- \nsubject: old women → nunumwaya \nverb: see → lekotasi or makesiwena?\n\nIn (4): \"Legisi waga makesiwena namwaya minana\" → woman saw those canoes → \"makesiwena\"\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\"\n\n\"vivila\" → appears after \"waga\" → \"waga vivila\"\n\nIf \"vivila\" = how many → \"how many canoes\"\n\nBut \"waga\" = those\n\nSo \"waga vivila\" = those how many? → like \"those canoes?\"\n\nThen \"minasiwena\" = saw\n\nBut subject is \"Legisesi\" = women\n\nSo: \"Legisesi waga vivila minasiwena\" = the women saw those canoes?\n\nBut \"vivila\" is quantity.\n\nOnly in interactive questions does \"vila\" function as \"how many\".\n\nIn (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\n\"Navila\" = how many \n\"ka’ukwa\" = dogs → so \"dovila\" not present.\n\nBut \"ka’ukwa\" = plural dogs?\n\n\"ka’ukwa\" = likely \"na-ka\" or \"ke\" for dog? Not clear.\n\nBut in (23): \"Two wild dogs saw that old man.\"\n\n→ \"nayu\" = two (quantity) \n\"nayu\" + \"gudi\" or \"na\" + dog?\n\nNo dog given.\n\nBut in (5): \"Which man killed two pigs?\" → \"nayu bunukwa\" → two pigs\n\nSo \"nayu\" = 2, \"bunukwa\" = pig\n\nSo class for pig? \"bunukwa\"\n\nThus, nouns have class prefixes.\n\nCanoes have \"ke\" → \"ke-\"\n\nSo canoes → \"ke\"\n\nSo \"how many canoes\" → \"vila ke\"\n\nThen verb: see → lekotasi or makesiwena?\n\nIn (4): \"makesiwena\" = saw\n\nIn (5): \"lekalimati\" = killed\n\nSo past → le- \nfuture → bi-\n\nSo \"saw\" = \"lekotasi\"\n\nSo \"Navila kevila lekotasi\" → how many canoes did see?\n\nBut subject missing.\n\nTo ask \"how many canoes did X see\" → must have subject.\n\nIn (8): \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"Navila\" + \"ka’ukwa\" (dogs) + \"lekotasi\" (arrived)\n\nBut \"arrived\" = lekotasi?\n\nIn (2): \"This white man arrived\" → \"Lekota dimdim mtona\" → \"lekota\" = arrived\n\nSo \"lekota\" = arrived\n\n\"makesiwena\" = saw\n\nSo for \"saw\", use \"makinawena\" or \"makewena\"?\n\n(4): \"waga makesiwena\" = saw\n\nSo \"makesiwena\" = saw\n\nSo for \"saw\" = makesiwena\n\nThus: \"Navila kevila makewena\"\n\nBut subject is missing.\n\nIn (18): \"Legisesi ketala waga vivila minasiwena\" — likely typo.\n\nAssume: \"how many canoes did those women see?\" = \"Navila kevila lekotasi\" or \"makesiwena\"?\n\nLikely in expression: Q + noun + verb + subject\n\nBut no.\n\nIn (9): \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\"\n\n\"Amakena waga\" = which canoe \n\"legisesi\" = the chiefs saw \n\"gweguyau\" = chiefs\n\nSo object + verb + subject\n\n\"Amakena waga\" = which canoe \n\"legisesi\" = verb \"saw\" \n\"gweguyau\" = subject\n\nWait — \"gweguyau\" = plural chief\n\nSo \"Amakena waga legisesi gweguyau\" → which canoe did the chiefs see?\n\nYes.\n\nSo pattern: (Q) + (object) + verb +", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11680.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 2, + "output": "Step 1: Analyze the verb patterns.\n\nIn Kilivila, verbs are marked as:\n- le- = past tense\n- bi- = future tense\n- -si = plural subject (e.g., gisesi for plural \"they\")\n\nAlso, interrogative forms use QVX: Q (question word), V (verb), X (object or complement)\n\nStep 2: Identify noun forms.\n\nFrom examples:\n- man → tau (singular), tauwau (plural)\n- child → gwadi (singular), gugwadi (plural)\n- chief → guyau (singular), gweguyau (plural)\n- old woman → namwaya (singular), nunumwaya (plural)\n- canoe → ke- (class: canoes)\n- fish → not explicit, but \"beautiful fish\" appears in example 10 → \"gudimanabweta\" → likely \"gudimanabweta\" = beautiful stone → likely \"gudimanabweta\" = beautiful fish → fish may be a thing (kwe-?) or an object.\n\nBut in 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → 'that beautiful child saw this stone' → 'gudimanabweta' = beautiful stone → so stones = kwe- → fish is not kwe-. But fish is mentioned as \"beautifull fish\" → possibly a noun class.\n\nNote: Example 1: \"these four fish\" → \"tetala tau\" → \"tetala\" = 4, \"tau\" = fish → so \"tetala tau\" = four fish → so fish = tau\n\nThus, fish = tau (same as man)\n\nSimilarly, pig → \"bunukwa\" in example 5: \"killed two pigs\" → \"nayu bunukwa\" → bunukwa = pig\n\nSo pig = bunukwa\n\nStep 3: Class markers (Cl):\n\n- men: te- (before Qt), to- (for object?)\n- women/animals: na-\n- children: gudi-\n- canoes: ke-\n- things: kwe-\n\nSo:\n- old woman → namwaya (class = women/animals → na- prefix)\n- canoe → ke- → ke- + noun → ke- + \"kala\"? → no, only known is \"ke\" + \"naw\" → not used.\n\nIn example 4: \"those canoes\" → \"namwaya minana\" → \"minana\" = those? or \"minana\" = plural of \"mana\" = those?\n\nLooking at demonstratives:\n- \"a-\"ma-Cl(-si)(-we)-na → e.g., \"ma-to\" → mto-, \"ma-na\" → mna-, \"ma-tau\" → mtau?\n\nFrom example 2: \"This white man arrived\" → \"Lekota dimdim mtona.\"\n→ \"le\" = past, \"kota\" = man? but \"mtona\" = this man?\n\n\"mtona\" = ma-to- → ma-to → mto- → so mtona = this man\n\nIn 4: \"those canoes\" → \"waga makesiwena namwaya minana\" → \"waga\" = saw? \"makesiwena\" = those? or makesi = see?\n\nWait: \"makesiwena\" → \"makesi\" = see → \"waga\" = object?\n\n\"Legisi waga makesiwena namwaya minana\" → \"those canoes\" = \"namwaya minana\" → so \"namwaya\" = old woman? no → \"namwaya\" = old woman → \"minana\" = those?\n\nSo \"namwaya minana\" = those old women → so \"minana\" = those → as demonstrative?\n\nThen \"minana\" = ma-na- (ma-na- + na? → ma-na → mna → but minana?)\n\nPossibly: ma-na → mina? But minana → perhaps plural?\n\nFrom example 10: \"that beautiful child saw this stone\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n→ \"gudimanabweta\" = beautiful stone → so \"makwena\" = this stone → so \"makwena\" = ma-kwe-na → \"kwe\" = thing → so \"ma-kwe-na\" = this thing?\n\nThus:\n- \"ma-kwe-na\" = this thing → \"kwe\" = thing\n- \"ma-to\" = this man → \"mtona\"\n- \"ma-tau\" = this man? → \"mtau\"? → but \"ma-tau\" not seen\n→ \"mtona\" = this man → so \"mtona\" = ma-to- + a? → ma-to → mtona\n\nSimilarly, in example 4: \"those canoes\" → \"namwaya minana\" → \"minana\" = those → ma-na → mna? → minana → perhaps ma-na + na? → ma-na → mina → minana → plural?\n\nOr maybe the demonstrative is end-formed.\n\nIn 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → \"ka’ukwa\" = dogs? → \"ka’ukwa\" = what is ka’ukwa?\n\n\"ka’ukwa\" → likely \"kwa\" = dogs? → from \"kamkwamsi\" → k we → kwe → kwe = thing → kwa = dog?\n\nPossibly:\n- \"ka’ukwa\" = two dogs? Or quantity?\n\nIn 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → \"Navila\" = how many → \"ka’ukwa\" = dogs → \"lekotasi\" = arrived?\n\nSo \"ka’ukwa\" = dogs → so class: animals → na-?\n\nBut \"kamkwamsi\" = women eat → so \"kamkwamsi\" → class = kwe? → kwe for things?\n\nBack to demonstratives:\n\nFrom example 2: \"This white man\" → \"Lekota dimdim mtona\" → \"mtona\" = this man → \"ma-to\" → so \"ma-to\" → mtona\n\nSimilarly, \"this white child\" → not given, but 10: \"this stone\" → \"makwena\" → \"ma-kwe-na\" → so \"ma-kwe\" + \"na\" = this thing\n\nSo:\n- man → ma-to → mtona\n- woman → ma-na → mna? → in 4: \"those canoes\" = \"minana\" → so \"minana\" = those? → perhaps \"ma-na\" → mina → minana → plural?\n\nPossibility: demonstrative = ma-Cl- (na) → so:\n- this man → mtona (ma-to)\n- this woman → mna (ma-na)\n- those canoes → minana = ma-na + na?\n\nYes. So demonstratives follow: ma-Cl + -na or -we?\n\nIn 4: \"those canoes\" → \"namwaya minana\" → so \"minana\" = those canoes → so \"minana\" is the demonstrative\n\nSimilarly, in 19: \"those old women\" → \"nunumwaya\" → plural → \"nunumwaya\" = those old women?\n\nSo \"nunumwaya\" = plural of \"namwaya\" → so \"nunumwaya\" = those old women\n\nSo \"those old women\" = \"nunumwaya\"\n\nSimilarly, \"these four canoes\" → quantity + class + noun?\n\nIn example 1: \"these four fish\" → \"tetala tau\" → \"tetala\" = 4 → \"tau\" = fish\n\nSo quantity → Cl-vila = how many? Cl-tala = one, Cl-yu = two, Cl-vasi = four\n\nSo Cl-vasi = 4\n\nSo in 19: \"how many canoes did those old women see?\" → structure:\n\nInterrogative → QVX: \"navila\" = how many → then class of canoes → \"ke\" → \"ke-vasi\" = four canoes?\n\nBut shift: \"how many canoes\" → \"navila ke\" → then subject → \"those old women\" → \"nunumwaya\" → then verb → \"saw\" → \"le\" + verb?\n\n\"see\" → in example 4: \"waga makesiwena\" → \"makesiwena\" → \"makesi\" = see → \"waga\" = object? → \"waga\" = those canoes?\n\nSo verb = makesi → past tense → \"le\" + makesi → \"lemakesi\"\n\nBut in 19: see → past → \"le\" + makesi\n\nSo full structure:\n\n\"navila ke vasi\" → how many canoes (4) → but \"vasi\" = 4 → but \"ke\" = canoe → so \"ke vasi\" = four canoes?\n\nBut the question is \"how many\" → so \"navila ke?\" → then \"did those old women see?\"\n\nBut \"see\" → \"makesi\" → but in example 4: \"waga makesiwena\" → with object \"waga\"\n\nSo past → \"le\" + \"makesi\"\n\nSo → \"navila ke vasi lekotasi nuna?\" → no\n\nNeed subject → subject is \"those old women\" → \"nunumwaya\"\n\nSo → \"navila ke vasi lemakotasi nunumwaya?\" → but \"le\" = past, \"makotasi\" = saw?\n\nIn 4: \"waga makesiwena\" → \"makesiwena\" → so \"makesi\" + \"wena\" → \"wena\" = object?\n\nWait: \"makesiwena\" → object is \"namwaya\"? No → \"waga\" = object → so object → \"waga\" = those canoes\n\nSo \"le\" + \"makesi\" + \"waga\" → \"the old women saw those canoes\"\n\nSo verb: (le) + makesi → then object → \"waga\"\n\nSo \"navila ke vasi lemakotasi nunumwaya waga?\" → no → else order?\n\nOrder: V(O)S → verb-object-subject?\n\nNo — in example 4: \"Legisi waga makesiwena namwaya minana\"\n\n\"Legisi\" = they saw → \"waga\" = those canoes → \"makesiwena\" = verb → \"namwaya minana\" = those old women?\n\n→ So object before verb? → \"waga\" before \"makesiwena\" → then \"namwaya minana\"\n\nSo structure: Subject after verb? No — \"Legisi waga makesiwena namwaya minana\"\n\n→ \"Legisi\" = verb (saw) → \"waga\" = object → \"makesiwena\" = form of saw? → actually \"makesi\" = see → so \"makesi\" is the verb, \"waga\" is object → so verb-object-subject?\n\nBut \"waga\" is object → after verb → then subject → after?\n\nYes — in example 4: verb-object-subject → \"legisi waga makesiwena namwaya minana\" → but \"legisi\" = saw, \"waga\" = object, \"makesiwena\" = ??\n\n\"makesiwena\" = may be a form of \"see\" with object marked?\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"Legisi\" = saw → \"dakuna\" = this → \"makwena\" = this stone → \"gwadi magudiwena\" = this child → so object → \"dakuna\" = this stone → so \"dakuna\" is object → \"gwadi\" = child → object?\n\nStructure: Legisi + [object] + [object]? → \"dakuna makwena\" → \"dakuna\" = this, \"makwena\" = stone?\n\nPossibly \"dakuna\" = demonstrative for stone → \"makwena\" = stone? → no → \"makwena\" = this stone → so \"makwena\" = this stone\n\nSo \"Legisi\" = saw → then \"dakuna\" = this? → \"makwena\" = stone → so subject → \"gwadi\" = child → object?\n\nSo \"Legisi makwena gwadi\" → saw stone, child? — too many objects.\n\nBetter: \"Legisi dakuna\" = saw this stone → \"dakuna\" = object → \"gwadi\" = subject? — but \"gwadi\" is a child — so \"gwadi\" might be subject?\n\nBut 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\nPerhaps: \"Legisi\" = saw → \"dakuna\" = this stone → \"makwena\" = this → so \"dakuna\" = object → then \"gwadi\" = this child → object?\n\nOr: \"makwena\" = stone, \"gwadi\" = child → two objects?\n\nBut only one verb.\n\nIn example 4: \"Legisi waga makesiwena namwaya minana\"\n\n\"Legisi\" = saw — \"waga\" = object → \"makesiwena\" → might be a form?\n\n\"makesiwena\" → \"makesi\" = see → \"wena\" = of? or diachronically, \"makesi\" is the verb.\n\nPerhaps \"makesi\" is the verb and \"waga\" is object → so \"waga makesi\" = saw those canoes → then \"namwaya minana\" = those old women → so \"namwaya minana\" = subject?\n\nSo structure: object + verb + subject → V(O)S — so verb in middle?\n\nBut in English, \"they saw those canoes\" → verb in middle.\n\nSo Kilivila: object + verb + subject?\n\nIn 4: \"waga makesiwena namwaya minana\" → object (waga), verb (makesiwena), subject (namwaya minana)\n\nYes — V(O)S pattern → object first, verb, subject.\n\nSimilarly, in 1: \"Bibani navasi yena minasina tetala tau\" → \"yena minasina\" = these four fish? → \"navasi\" = will catch → \"yena minasina\" = these four fish?\n\n\"yena\" = these → \"minasina\" = fish? → \"tetala tau\" = four fish → \"tetala\" = 4 → \"tau\" = fish\n\nBut \"minasina\" → not \"tau\"\n\n\"minasina\" = fish? → in 1: \"yena minasina tetala tau\" → so \"yena\" = these, \"minasina\" = fish, \"tetala tau\" = four fish → so \"minasina\" and \"tetala tau\" both mean fish → so \"minasina\" = fish → so fish = minasina?\n\nBut in 10: \"beautiful fish\" → \"gudimanabweta\" → so \"makwena gwadi\" → probably not.\n\nIn 5: \"which man killed two pigs\" → \"Amtona tau lekalimati nayu bunukwa?\" → \"Amtona tau\" = which man? → \"lekalimati\" = killed → \"nayu bunukwa\" = two pigs\n\n\"nayu\" = two → \"bunukwa\" = pig\n\nSo \"lekalimati\" = kill\n\nIn 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"Leyamatasi\" = looked after → \"teyu\" = two → \"tauwau\" = men → \"nunumwaya\" = old women → subject\n\n\"teyu\" = quantity — Cl-tala = 1, Cl-yu = 2, Cl-vasi = 4 → so \"teyu\" = 2\n\nSo quantity = Cl + quantity word → Cl-tala = one, Cl-yu = two, Cl-vasi = four\n\nThus, for numbers:\n- 1 → tala\n- 2 → yu\n- 4 → vasi\n\nSo back to 19: \"How many canoes did those old women see?\"\n\n→ Interrogative: \"navila\" = how many\n→ Noun class: canoes → \"ke\"\n→ Quantity: \"vasi\" = 4 → but only if 4\n→ So \"navila ke vasi\" = how many canoes (four)?\nBut the question is \"how many\", so \"navila ke?\" → then past tense → \"le\" + \"makesi\"\n→ Subject: \"those old women\" → \"nunumwaya\"\n\nStructure: navila ke vasi lemakotasi nunumwaya?\n\nBut \"le\" + \"makesi\" = saw → but \"makotasi\" = saw?\n\nIn example 4: \"makesiwena\" → not \"makotasi\"\n\n\"makesi\" = see → in 4: \"waga makesiwena\" → so \"makesi\" is verb → with object marker?\n\n\"makesiwena\" → \"wena\" = object? → or just form?\n\nPossibly \"makesi\" is the verb, and object is separate.\n\nBut in structure: object + verb + subject → so here, object = canoes → \"ke vasi\" → but canoes are the object?\n\nNo — the verb is \"see\", so object is what is seen.\n\nSo \"see\" → verb → object → canoes → \"ke vasi\" → but \"ke vasi\" = four canoes → so object = ke vasi\n\nSubject = nunumwaya\n\nSo → \"navila ke vasi lemakotasi nunumwaya\" → but \"navila\" is how many? → so how many canoes?\n\nBut \"navila ke vasi\" = how many canoes (four)?\n\nBut the question is asking for a number — it's \"how many\", not \"how many canoes were there\"?\n\nSo structure → Q + object + verb + subject?\n\nBut in example 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\" → \"Bikota\" = will arrive → \"gwadi\" = child → \"magudiwena\" = that?\n\n\"magudiwena\" = that → from \"ma-gudi-na\" = that child?\n\nSo \"magudiwena\" = that child → so \"gwadi\" = child → \"magudiwena\" = that → so object?\n\nNo — in this, only one", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11367.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "sample_index": 3, + "output": "Step-by-step derivation:\n\nWe are to translate the following into Kilivila, using the provided pattern and examples.\n\nPattern guide:\n- Word order: V(O)S or QVX; (Qt)N(D)(A)\n- Verbs:\n - le- = past\n - bi- = future\n- Noun plurals:\n - man → tau / tauwau\n - child → gwadi / gugwadi\n - chief → guyau / gweguyau\n - old woman → namwaya / nunumwaya\n - canoe → ke- (no plural given, assumed singular or same)\n - thing → kwe-\n- Class markers (Cl):\n - men: te- before Qt; to-\n - women/animals: na-\n - children: gudi-\n - canoes: ke-\n - things: kwe-\n- Demonstratives:\n - (a-)ma-Cl(-si)(-we)-na → e.g., mto- (ma-to-), mna (ma-na-)\n- Quantity:\n - Cl-vila = how many?\n - Cl-tala = 1\n - Cl-yu = 2\n - Cl-vasi = 4\n\nNow process each sentence:\n\n19. How many canoes did those old women see?\n\n- Interrogative: \"how many\" → \"vila\" (quantity)\n- Subject: \"those old women\" → \"nunumwaya\" (plural of old woman)\n- Verb: past tense → \"le\"\n- Object: \"canoes\" → \"ke-\"\n\nStructure: Qt-N-vil-a + subject + verb + object?\n\nBut structure follows QVX: Q + V + X (subject/object)\n\nSo: Q + verb + subject + object?\n\nActually, from example 18: \"Legisesi ketala waga vivila minasiwena\" — \"Those women saw one canoe.\"\n\nSo \"Q\" = interrogative, then verb, then subject, then object?\n\nWait: 18 says: \"Legisesi ketala waga vivila minasiwena\" = \"Those women saw one canoe.\" → \"ketala\" = one canoe?\n\n\"ke\" + \"tala\" = one canoe → ke-tala = one canoe.\n\nSimilarly, \"vila\" = how many?\n\nSo: How many canoes did those old women see?\n\n→ \"Navila ke-tala vivila namwaya tawau?\" → but need to check.\n\nActually, 18: \"Legisesi ketala waga vivila minasiwena\" → \"The women saw one canoe\" — here \"ketala\" is object.\n\nSo: verb + object (direct object) + subject?\n\nNot matching.\n\nLook at 13: \"Navila vivila biyamatasi tau mtona?\" → \"How many women will this old man look after?\"\n\nHere: \"Navila\" = how many, then \"vivila\" = will see, then \"biyamatasi\" = women? But \"biyamatasi\" → \"bi\" + \"yamatasi\" → \"bi\" = future, \"yamatasi\" = women?\n\n\"vivila\" = will see?\n\n\"Navila vivila biyamatasi tau mtona\" → \"How many women will this old man look after?\"\n\nSo structure: Qt (Navila) + verb (vivila) + subject (biyamatasi) + object (tau mtona)\n\nBut \"vivila\" = verb, \"biyamatasi\" = subject? So subject after verb?\n\nSo: Qt-verb-subject-object?\n\nYes — matches pattern QVX: Q + V + X\n\nSo: Qt + verb + subject + object\n\nTherefore: How many canoes did those old women see?\n\n→ \"Navila ke-tala lekotasi namwaya wau\" → no.\n\n\"ke-tala\" = one canoe? But we want \"how many canoes\"\n\nSo quantity: \"ke-vila\" → how many canoes?\n\nThen verb: \"lekotasi\" → saw? \"le\" + \"kotasi\" — but \"kotasi\" not in list.\n\nWait: \"see\" → in sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"The old woman saw those canoes\"\n\n\"makesiwena\" = saw? → \"make\" + \"si\" + \"wen\" (object?) → \"makesiwena\" = saw?\n\n\"legisi\" = that woman (demonstrative)\n\n\"makesiwena\" = saw?\n\nSo \"make\" → verb?\n\nNot in list.\n\nWait: in sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"The old woman saw those canoes\"\n\n\"makesiwena\" → \"make\" + \"si\" + \"wen\" → \"make\" as verb?\n\nBut no \"make\" dictionary.\n\nWait — sentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" → \"The clever chief killed one wild pig\"\n\n\"lekalimati\" → verb \"killed\"?\n\nSo verb: \"le-\" prefix for past, \"bi-\" for future.\n\n\"le\" + \"kalimati\" = killed?\n\n\"le\" + \"kotasi\" = saw?\n\nYes — likely.\n\nSo \"le\" + \"kotasi\" = saw?\n\nIn sentence 4: \"makesiwena\" — \"make\" as verb? But sentence 2: \"Lekota dimdim mtona\" → \"This white man arrived\" → \"lekota\" = arrived?\n\n\"le\" + \"kota\" = arrived?\n\nYes. So \"le\" + (verb stem)\n\nThus, \"le\" + \"kotasi\" = saw?\n\nBut in sentence 4: \"makesiwena\" — \"make\" is not \"kotasi\"?\n\nWait — let's look for \"see\" verb.\n\nSentence 4: \"Legisi waga makesiwena namwaya minana\" → \"the old woman saw those canoes\"\n\n\"makesiwena\" → likely \"make\" as verb?\n\nBut no \"make\" in list.\n\nWait — sentence 18: \"Legisesi ketala waga vivila minasiwena\" → \"those women saw one canoe\"\n\n\"vivila\" = saw?\n\n\"vivila\" → verb \"see\"? → yes, \"vivila\" = saw?\n\nSo \"vivila\" = verb \"see\" in past?\n\nThen \"le\" is past, so \"vivila\" = past tense verb \"see\"?\n\nSo verb: \"vivila\" = saw\n\nThus, how many canoes did those old women see?\n\n→ \"Navila ke-vila lekotasi namwaya wau?\"\n\nNo — \"vivila\" is the verb.\n\nSo: Qt + verb + subject + object?\n\nBut \"ke-vila\" = how many canoes?\n\nClass: canoes → \"ke-\"\n\nSo: ke-vila = how many canoes?\n\nThen: ke-vila + vivila + subject + object?\n\nSubject: \"those old women\" → \"namwaya wau\"? or \"nunumwaya\"?\n\n\"nunumwaya\" = plural old woman → so subject = \"nunumwaya\"\n\nObject: \"canoes\" → \"ke-tala\"? no — we have quantity only for \"how many\"\n\nBut \"vila\" is already used.\n\nWait — in example 18: \"Legisesi ketala waga vivila minasiwena\" → \"those women saw one canoe\"\n\n\"ketala\" = one canoe → ke + tala\n\nSo \"ke-tala\" = one canoe\n\nThus, \"vila\" = how many?\n\nSo for \"how many canoes\", use \"ke-vila\"\n\nThen verb: \"vivila\" = saw\n\nThen subject: \"nunumwaya\" (plural of old woman)\n\nThen object? Do we need object?\n\nYes — \"see\" takes object: \"see those canoes\"\n\nBut in which position?\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"the old woman saw those canoes\"\n\n\"makesiwena\" → saw?\n\n\"legisi\" = old woman? → subject\n\n\"waga\" = those canoes? → object\n\nSo object after verb?\n\nSo: subject + verb + object?\n\nBut in QVX: Q + V + X → Q + verb + X\n\nBut \"X\" includes subject/object?\n\nIn 18: \"Legisesi ketala waga vivila minasiwena\" → subject (legisesi) + object (ketala) + verb (vivila) + subject (minasiwena)?\n\nNo — \"minasiwena\" = \"one woman\"?\n\n\"minasiwena\" = \"one woman\"?\n\n\"minasina\" = \"some fish\" → not.\n\nWait: \"minasiwena\" → possibly \"one woman\"?\n\nBut \"minasiwena\" → mna + si + wen?\n\n\"mna\" = that? \"mina\" = that?\n\nFrom guidance: \"ma-to- > mto-\", \"ma-na- > mna\"\n\nSo \"ma-na\" = \"that\" for women?\n\nSo \"mina\" = that woman?\n\n\"minasiwena\" = that woman?\n\nSo \"Legisesi\" → that woman\n\n\"ketala\" → one canoe\n\n\"vivila\" → saw\n\n\"minasiwena\" → that woman?\n\nBut the sentence says \"those women saw one canoe\"\n\nSo subject: \"legisesi\" = those women?\n\n\"legisesi\" → \"that woman\" → but plural?\n\n\"legisesi\" = \"that woman\" — but \"those women\" needs plural.\n\nIn example 18: \"Legisesi ketala waga vivila minasiwena\"\n\n\"legisesi\" = those women?\n\n\"minasiwena\" = one woman?\n\nNo — likely \"legisesi\" = those women → subject\n\n\"ketala\" = one canoe — object\n\n\"vivila\" → saw? verb\n\nSo order: subject + object + verb?\n\n\"legisesi ketala vivila minasiwena\" → that woman saw one canoe?\n\nBut the translation says \"those women saw one canoe\"\n\nSo probably \"legisesi\" = those women → plural\n\n\"vivila\" = saw\n\n\"ketala\" = one canoe — object\n\nSo object after verb?\n\nSo: subject + verb + object?\n\n\"legisesi vivila ketala minasiwena\" — but that’s not what is written.\n\nActually: \"Legisesi ketala waga vivila minasiwena\"\n\n\"Legisesi\" (subject) + \"ketala waga\" (object) + \"vivila\" (verb) + \"minasiwena\" (subject?) — redundant?\n\n\"minasiwena\" = that woman?\n\nSo perhaps double subject?\n\nUnlikely.\n\nPerhaps \"vivila\" is the verb, and \"ke-tala\" is object.\n\nBut \"vivila\" appears after the object.\n\nPossibly word order: subject + object + verb\n\nBut in 13: \"Navila vivila biyamatasi tau mtona?\"\n\n\"Navila\" (how many) + \"vivila\" (verb) + \"biyamatasi\" (subject) + \"tau mtona\" (object)\n\nYes — so: Qt + verb + subject + object\n\nSo structure: Qt + verb + subject + object\n\nThus, for 19: How many canoes did those old women see?\n\n→ \"Navila ke-vila lekotasi nunumwaya wau?\"\n\nBut \"ke-vila\" = how many canoes?\n\n\"lekotasi\" = saw?\n\n\"nunumwaya\" = those old women?\n\n\"ke-vila\" may be redundant if followed by \"ke-\" class.\n\nBut \"ke-vila\" = how many canoes?\n\nThen verb: \"lekotasi\" → past saw\n\nSubject: \"nunumwaya\" → those old women\n\nObject? — do we have object?\n\nThe sentence is \"how many canoes did those old women see\" — no object specified.\n\nSo object is missing — does \"see\" take an object?\n\nYes — in sentence 4: \"saw those canoes\"\n\nBut here, the question is \"how many canoes did they see\", so object is \"canoes\" — implied.\n\nSo in structure: Qt + verb + subject + object?\n\nBut object is canoes → so must be included.\n\nBut in the sentence, object is \"canoes\", and only one object — the quantity is about the canoes.\n\nSo perhaps: \"Navila ke-vila lekotasi nunumwaya\"?\n\nBut then where is the object?\n\nIn sentence 18: \"Legisesi ketala waga vivila minasiwena\" — \"those women saw one canoe\" → object is \"ketala waga\"\n\n\"waga\" = those canoes?\n\nSo object = \"waga\" → demonstrative + noun?\n\n\"waga\" = those?\n\nIn guidance: (a-)ma-Cl(-si)(-we)-na → \"waga\" → \"ma-ke-?\" → canoes?\n\n\"ma-ke\" → possibly \"waga\" = those canoes?\n\nBut in sentence 4: \"waga makesiwena namwaya minana\" — \"waga\" = those canoes → object\n\nSo object = \"waga\"\n\nBut in question 19: no object mentioned — \"how many canoes did they see\" — \"canoes\" is object.\n\nSo \"canoes\" = ke- (class) + no demonstrative?\n\nSo object = \"ke-\"\n\nBut need to specify \"canoes\" — so \"ke-tala\" or \"ke-vila\"?\n\n\"ke-vila\" = how many canoes — quantity\n\nBut object is formed as \"ke-?\"\n\nFrom sentence 18: object is \"ketala\" = one canoe\n\nSo \"ke-tala\" = one canoe\n\nThus, for \"how many\", we need \"ke-vila\"\n\nBut in the sentence, \"how many canoes\" is the quantity — so \"ke-vila\"\n\nThen verb: \"lekotasi\" = saw\n\nSubject: \"nunumwaya\" = those old women\n\nObject: \"ke\"? — but no number.\n\nIn questions, if object is not specified, it is the entity being quantified.\n\nSo is \"canoes\" the object?\n\nYes — so object = \"ke-\"\n\nBut \"ke\" class → object for canoes.\n\nSo object = \"ke-\"\n\nBut is it \"ke\" or \"ke-vila\"?\n\nNo — \"vila\" is quantity.\n\nSo object = \"ke\" (canoes)\n\nThus: Navila ke-vila lekotasi nunumwaya ke?\n\nBut \"ke\" twice — bad.\n\nAlternatively, the object is not explicitly stated — just implied.\n\nBut in example 18: \"Legisesi ketala waga vivila minasiwena\" — the object is \"ketala waga\"\n\nSo structure: subject + object + verb + subject?\n\nNo — likely subject + object + verb\n\nBut earlier 13: \"Navila vivila biyamatasi tau mtona\" — Qt + verb + subject + object\n\nSo for question with no object, it might be incomplete.\n\nBut logically, \"how many canoes did they see\" implies the object is canoes.\n\nSo can we say: \"Navila ke-vila lekotasi nunumwaya?\"\n\nBut where is the object?\n\nNo — in all cases, the verb takes an object.\n\nSo likely object is \"ke-\"\n\nBut \"ke\" alone is not clear.\n\nWait — in sentence 4: \"waga\" = those canoes — so object is \"waga\"\n\nAnd in 18: \"ketala waga\" — \"one canoe\" — \"ketala\" = one, \"waga\" = canoes\n\nSo object = \"waga\"\n\nThus, in question 19: how many canoes did those old women see?\n\nObject is \"canoes\" — so \"waga\"\n\nQuantity: \"ke-vila\"? or \"ke-tala\"?\n\n\"ke-vila\" = how many canoes?\n\nYes.\n\n\"lekotasi\" = saw?\n\nSo sentence: \"Navila ke-vila lekotasi nunumwaya waga\"\n\nBut is \"waga\" correct? It means \"those canoes\"?\n\nYes.\n\nSo: how many canoes did those old women see?\n\n→ \"Navila ke-vila lekotasi nunumwaya waga\"\n\nBut is \"ke-vila\" correct?\n\nYes — based on pattern.\n\nSimilarly, 20. These four white men will look after this clever child.\n\n\"will\" → bi- future\n\nSubject: \"these four white men\"\n\nClass: men → \"to-\"\n\nQuantity: \"four\" → \"vasi\"\n\nSo \"to-vasi\" = these four men?\n\nBut \"ma-to\" → \"mto-\", \"ma-to\" = these?\n\n\"ma-to\" = these → so \"to-vasi\" = these four men?\n\nYes.\n\n\"look after\" → in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" → \"The old women looked after two men\"\n\n\"leyamatasi\" = looked after?\n\n\"teyu\" = two?\n\n\"teyu\" = two → \"te\" + \"yu\"\n\nClass: men → \"tauwau\"\n\nSo verb: \"leyamatasi\" → looked after\n\n\"bi\" + \"yamatasi\" = will look after?\n\nSo future: \"biyamatasi\"\n\nThus, for 20:\n\nSubject: these four white men → \"to-vasi mtona\" → \"to\" + \"vasi\" + \"mtona\" = these four white men?\n\n\"mtona\" = white man?\n\nYes.\n\nVerb: \"biyamatasi\" = will look after\n\nObject: \"this clever child\"\n\n\"this\" → \"ma\" + \"gudi\" → \"magudi\"?\n\n\"clever\" → \"kwetala\"?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"That clever woman will see something\"\n\n\"kwetala\" = clever\n\n\"minawena\" = something?\n\nSo \"kwetala\" = clever\n\nChild → \"gwadi\"\n\n\"this\" → \"ma\" + \"gwadi\" → \"maga\" or \"magudi\"?\n\n\"ma-gwadi\" = this child?\n\nPossibly.\n\nIn sentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\"\n\n\"gwadi\" = child\n\n\"magudiwena\" = this child?\n\n\"magudiwena\" = this + child?\n\n\"makwena\" = this stone?\n\n\"magudiwena\" = this", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12112.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nTeacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Teacher rule card for distillation only. This is not a fair no-leak evaluation hint. The official solution text below has this row's target final answer strings redacted; use the remaining rules and derivation style to solve the requested units.\n\nProblem 3.\n\n • Word order:\n\n – V(O)S (V = verb; O = object; S = subject)\n\n – QVX (Q = interrogative element)\n\n – (which | Qt)N(D)(A) (Qt = quantity, N = noun, D = demonstrative pronouns, A\n = adjective)\n\n • verb:\n\n – le- past\n – bi- future\n – -si subject = plural (-gisi-si > -gisesi)\n\n • noun:\n singular plural\n man tau tauwau\n child gwadi gugwadi\n chief guyau gweguyau\n old woman namwaya nunumwaya\n ∼ singular = plural\n\n • class (Cl):\n\n – men: te- (before Qt); to-\n – women/animals: na-\n – children: gudi-\n – canoes: ke-\n – things (for example stones): kwe-\n\n • demonstrative pronouns: (a-)ma-Cl(-si)(-we)-na, ma-to- > mto-, ma-na- > mina-\n\n • quantity: Cl-vila how many?, Cl-tala 1, Cl-yu 2, Cl-vasi 4\n\nEighteenth International Linguistics Olympiad (2021) 3\nIndividual Contest Solutions\n\n (a) 14. Navila vivila biyamata tomwaya mtona?\n How many women will this old man look after?\n 15. Bikamkwamsi kweyu vivila minasina.\n These women will eat two things.\n 16. Amagudina gwadi lekota?\n Which child arrived?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n How many men will see the wild children?;\n How many men will the wild children see?\n 18. Legisesi ketala waga vivila minasiwena.\n Those women saw one canoe.\n\n (b) 19. How many canoes did those old women see?\n [TARGET ANSWER REDACTED]\n 20. These four white men will look after this clever child.\n [TARGET ANSWER REDACTED]\n 21. How many children will eat these pigs?\n [TARGET ANSWER REDACTED]\n 22. Which woman caught those beautiful fish?\n [TARGET ANSWER REDACTED]\n 23. Two wild dogs saw that old man.\n [TARGET ANSWER REDACTED]", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 14149.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10331.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12135.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12449.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10320.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well,", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11179.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}", + "generated_tokens": 2521, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 5772.0, + "ioling_final_answer_chars": 175.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10682.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11965.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9356.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9235.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11503.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11825.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11554.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_anchor_iid", + "sample_index": 0, + "output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nBut sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\nSo \"te", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12079.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.", + "hint": "", + "planner_output": "", + "anchor_output": "" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "groot_1x4", + "sample_index": 0, + "output": "We are asked to find the theoretically possible translations of “word” and “to exhaust” into Rotuman, based only on the given vocabulary and linguistic patterns.\n\nFirst, consider \"to exhaust\". This involves depletion, consumption, or reduction. In the given list:\n\n- \"puhra.ki\" means \"to boil, to bubble up\" — a process involving intense internal change and the expulsion or reduction of contents. This is metaphorically similar to \"to exhaust\", as boiling down something reduces it to a smaller state, almost to nothing. In many languages, \"to boil down\" is a metaphor for reduction or exhaustion. This is a direct semantic parallel.\n- \"hül ha.fu\" means \"to blow (of a hurricane)\" — forceful expulsion, which may imply removal or depletion of something, but not necessarily a process of consuming or reducing to nothing.\n- \"fäeag\" means \"to use\" — direct consumption, but not necessarily to the point of exhaustion.\n- \"ma.tit mamasa\" means \"ice\", which is cold and solid, not related directly.\n- \"moafmofa\" means \"littered with rubbish\" — not clearly related to consumption or depletion.\n\nThe most plausible candidate for “to exhaust” is “puhra.ki”, because of the metaphorical extension of boiling down — reducing something entirely through process. This fits the semantic pattern of depletion.\n\nNow, for “word”. There is no direct word for “word” in the list. However, look for possible roots or verbs that might relate to linguistic content.\n\n- \"pala\" means \"to pierce\" — could imply a sharp symbol or mark, possibly related to written form?\n- \"nu‘suar tiro\" = \"window\" — could metaphorically relate to seeing words?\n- \"fäeag 'u‘u\" = \"to use sign language\" — involves communication, possibly using signs that could be considered \"words\".\n- \"to‘a\" = \"hero\" — irrelevant.\n- \"huli\" = \"to turn over\" — could be associated with turning pages?\n- \"huni\" = \"lower end\" — not relevant.\n- \"lala\" = \"deep\" — could relate to depth of meaning?\n\nBut the key is root reuse and semantic extension. We see \"fäeag\" (to use) is used in \"fäeag ‘u‘u\" — to use sign language. Sign language involves signs, which are linguistic units. So “word” may be derived from the root of \"to use\" or \"to signify\".\n\nAlso, \"pala\" (to pierce) might relate to writing — a word could be seen as a piercing mark, like a shape or symbol. But no direct link.\n\nAlternatively, “word” may be semantically linked to “sign” or “symbol”. We have \"fäeag ‘u‘u\" = \"to use sign language\" — so “sign” is part of the language. Could “sign” be derived from “pala” (to pierce), as signs pierce or mark the surface?\n\nBut “sign” is not directly given.\n\nAnother possibility: in Austronesian languages, lexical items often undergo relational or cognitive extension. \"Word\" might be expressed via a verb meaning \"to use\" or \"to signify\", especially since language is made of units used.\n\nThus, the only verb in the vocabulary that involves usage or representation is \"fäeag\" (to use). In “fäeag ‘u‘u”, it means to use sign language — so \"to use\" is the root of language use. Hence, “word” might be a noun derived from \"to use\".\n\nBut no noun form of \"to use\" exists.\n\nAlternatively, could “word” be expressed via \"pala\"? \"Pala\" means \"to pierce\", which may imply making a mark — a word as a mark.\n\nBut no support.\n\nAnother idea: “lala” = deep — \"deep\" could be associated with depth of meaning, but not directly.\n\nGiven that no word for “word” exists, but \"to use\" is central to language, the only plausible theoretical translation of “word” would be a noun derived from a root meaning \"to use\" or \"to signify\", and the only such verb is \"fäeag\".\n\nThus, “word” could be related to \"fäeag\", and metaphorically, a “word” is a unit used in language.\n\nTherefore, the theoretically possible translation of “word” is a form of \"fäeag\" — possibly \"fäeag\" itself as a noun or a form, though not directly given.\n\nHowever, in absence of any other root, and due to semantic extension, the only plausible candidate is formed from the root of “to use”.\n\nBut is there any other verb?\n\n\"pigi\" is not in the list.\n\nOnly \"fäeag\" is directly related to language use.\n\nSo, the most likely theoretical translation of “word” would be *fäeag*, or a form derived from it.\n\nBut in the list, \"fäeag ‘u‘u\" is given — “to use sign language”. So \"fäeag\" is used for “to use” — and signs are used in language. So \"word\" could be tied to \"sign\" or \"used item\". Hence, “word” might be *fäeag*.\n\nAlternatively, could it be *pala*, as \"to pierce\" could mean to make a symbol?\n\nNo direct support.\n\nGiven the lack of any other candidate, and the importance of “to use” as the verb related to language, the most plausible theoretical translation for “word” would be *fäeag*, assuming a nominalization or semantic extension.\n\nFor “to exhaust”, as discussed, puhra.ki is the best fit due to the metaphor of reduction.\n\nTherefore:\n\n- \"word\" → theoretically possible translation: *fäeag* (via semantic extension from “to use” in language)\n- \"to exhaust\" → theoretically possible translation: *puhra.ki* (via metaphorical extension of boiling down to reduction)\n\nFinal answer:\n\n\\boxed{d.1: fäeag; d.2: puhra.ki}", + "generated_tokens": 1300, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: fäeag; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 5112.0, + "ioling_final_answer_chars": 25.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.", + "planner_output": "\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\n\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\n\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\n\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n", + "anchor_output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "groot_1x4", + "sample_index": 1, + "output": "The given compound examples show that Rotuman forms derived verbs through combinations of roots and affixes, often involving locative or endpoint-based meanings. The root “fåeag” means “to use,” as in “fäeag ‘u‘u — to use sign language.” This suggests a pattern where a root is combined with a locative or endpoint noun to form a derived verb with a completive or intensive meaning.\n\nIn the data, “kia” means “base of the neck,” a physical endpoint. “to‘a” means “hero,” which may denote a point or integral part. “hün kia” is “base of the neck,” suggesting “kia” functions as a locative noun. When used in a compound like “faiimā kia,” it may denote “to reach the base” or “to use completely.”\n\nSimilarly, “a‘öf fau” means “year’s end,” where “fau” is “year” and “a‘öf” may function as a locative or end-of-time marker. This suggests that suffixes or precatives denoting endpoints (like end of time, end of year) are known. Therefore, “to exhaust” could be derived from “to use” + endpoint, i.e., “fåeag” + “kia” → “fäeag kia,” meaning “to use to the end” or “to exhaust.”\n\nSimilarly, for “word,” we observe that many compound words in Rotuman are built from roots and locatives. No direct root for “word” appears, but common Austronesian languages use locative or structural components to form nouns. “Pala” means “to pierce,” “nu‘suar tiro” is “window,” “pogi” is “night.” No clear word for “word” exists. However, in compound formation, a noun might be formed with a locative or endpoint suffix.\n\nIn Austronesian morphology, a word like “for word” or “to speak word” may be formed using a root like “pala” (to pierce) or “piri” (to curl), but none directly match. However, if “word” is treated as an abstract concept, it may be semantically derived from a locative or endpoint idea. Since “kia” is used for endpoint, and “fåeag kia” is plausible for “to exhaust,” a possible root for “word” could be derived from a verb meaning “to speak” or “to convey,” like “fåeag” (to use) or “pala” (to pierce). But no such word exists.\n\nThus, the only plausible paths for “word” and “to exhaust” are based on the use of endpoint locatives. For “to exhaust,” fäeag kia is a grammatically valid, logically derived compound from the lexical data, using known components. For “word,” no established root exists, but in Austronesian languages, abstract nouns are often formed via possessive or locative compounds. “Niusur” or “niu” (copra) appears, and “nu‘sura” (door) suggests a spatial association. “Pala” (to pierce) may suggest a meaning of “an object that pierces” — possibly as a metaphor for a “word.” However, no such match is direct.\n\nStill, the only theoretically possible translation for “to exhaust” using the given data is fäeag kia — a compound where “to use” is completed at the endpoint “kia” (base of the neck, as a physical end).\n\nFor “word,” there is no direct root or compound in the data, but in Austronesian languages, words like “kala” or “sila” may mean “word,” and in Rotuman, “pōrā” or “ta‘a” may imply such meaning. However, in the data, no such form exists. But “pala” (to pierce) or “piri” (to curl) could be abstracted. Still, no tangible link.\n\nGiven that the problem states we cannot translate these with certainty, we infer only the theoretically possible forms based on morphological patterns. The only plausible derived verb for “to exhaust” is “fäeag kia,” using “to use” + endpoint. For “word,” the absence of a root suggests a possible abstract noun derived from a locative or act, but no such form is given. However, in compound formations like “hül ha.fu” (to blow of a hurricane), a noun is used as a modifier. “fau” (year) is used in “a‘öf fau” (year’s end), showing that year + end of time compounding is valid.\n\nTherefore, a word for “word” might be formed via a compound with a locative element. Since “kia” means “base of the neck,” it could be used as a locative for abstract things. If “kia” means “end,” then “word” might be “kia” or “kia-” as a root. But this is speculative.\n\nThe only grounded possibility, based on pattern, is that “to exhaust” is formed as fäeag kia, and “word” might be formed as kia — as a locative abstract noun meaning “the end,” implying “word” as the terminal point of speech. Thus, kia is used as a residue.\n\nBut considering common Austronesian patterns — especially compound verbs with locatives — and the lack of direct terms, the theoretically possible forms are:\n\n- “to exhaust” → fäeag kia \n- “word” → kia (as a locative endpoint, metaphorically “the thing at the end”)\n\nThis is speculative, but logically follows from patterns in the data.\n\n\\boxed{d.1: kia; d.2: fäeag kia}", + "generated_tokens": 1254, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: kia; d.2: fäeag kia", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 4646.0, + "ioling_final_answer_chars": 24.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Consider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.", + "planner_output": "\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\n\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\n\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\n\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n", + "anchor_output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "groot_1x4", + "sample_index": 2, + "output": "The target is to find theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, based only on the given vocabulary and linguistic patterns.\n\nFirst, consider \"word\". There is no direct word for \"word\" in the list. However, several verbs relate to speech or sound: \"pala\" means \"to pierce\", which may imply a sharp sound; \"piri\" means \"to curl\", unrelated; \"fau\" means \"year\", not relevant. \"Ele\" means \"to be near\", and \"ele\" alone is also \"shallow\", a possible contradiction. But \"to be near\" could imply something accessible — a known thing, a familiar thing. Words like \"word\" or \"name\" often refer to something known or accessible. The stem ‘el‘ele (shallow) and ‘ele (to be near) suggest a semantic field of proximity and accessibility. In some languages, \"word\" is derived from \"to speak\" or \"to make a known sound\". No verb directly means \"to speak\" or \"to say\" is given. However, \"to be near\" may be a plausible root for \"word\" as \"something known or accessible\". Thus, a theoretical form could be based on *‘ele*, meaning \"near\", interpreted as \"accessible\" or \"known\", hence \"word\" as something known. Therefore, a plausible form is *‘ele*, or possibly *el‘ele*, but the latter means \"shallow\". This leads to *‘ele* as the best candidate, with the semantic interpretation of \"near\" implying \"that which is known\" — a natural candidate for \"word\" in a linguistic context.\n\nNow, for \"to exhaust\". No direct word matches. But \"to blow\" (hül ha.fu) suggests action involving force or emission. \"To boil\" (puhra.ki) involves forceful emission of steam. \"To cut\" (olo) suggests removal. \"To turn over\" (huli) implies change. \"To blow\" suggests depletion. \"To boil\" may involve excessive heat leading to depletion. \"To cut\" could imply removing something completely. \"To exhaust\" is a state of complete removal or overuse. The verb \"hül ha.fu\" (to blow) is likely a strong emission. \"To boil\" (puhra.ki) could be analogous — a process that consumes energy or removes content. So, verbs like *hül* (to blow) or *puhra.ki* (to boil) may be analogous. \"To exhaust\" could be derived from a root meaning \"to blow out\" or \"to remove completely\". In many languages, \"to exhaust\" is derived from \"to blow out\" or \"to deplete\". The form *hül* (blow) is strong; *hül ha.fu* is \"to blow of a hurricane\" — violent and complete. \"To exhaust\" may thus be theoretically based on *hül* or *hül*. Also, *certain verbs imply complete removal*, such as \"cut\" (olo), which may imply removal of material — possibly a form of exhaustion. However, no perfect match. The most plausible candidate is a form based on *hül*, meaning \"to blow\", as in \"to blow out\" — which is a common metaphor for exhaustion. Thus, *hül* or *hül ha.fu* might be extended.\n\nTherefore, the theoretically possible translation of \"word\" is *‘ele*, based on \"to be near\" (accessible/knowable). For \"to exhaust\", the form *hül* is plausible due to its association with forceful emission and complete removal. Though no direct match, this follows known patterns in the verb structure.\n\n\\boxed{d.1: ‘ele; d.2: hül}", + "generated_tokens": 798, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: ‘ele; d.2: hül", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 3083.0, + "ioling_final_answer_chars": 19.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Use absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.", + "planner_output": "\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\n\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\n\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\n\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n", + "anchor_output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "method": "groot_1x4", + "sample_index": 3, + "output": "The task is to find theoretically possible translations for ‘word’ and ‘to exhaust’ in Rotuman, based on the given examples.\n\nFirst, consider ‘word’. There is no standalone word for ‘word’ in the list. However, several compound forms exist: \n- ‘nu‘suar tiro’ = window \n- ‘nu‘sura’ = door \n- ‘maf tiro’ = spectacles \n- ‘pala’ = pierce \n- ‘riamrima’ = shiny \n\nNote that ‘tiro’ appears in both ‘maf tiro’ and ‘nu‘suar tiro’. It might act as a root meaning “small object” or “instrument” — as spectacles and window both involve an object. There is no known compound involving ‘word’ directly. But compound formation in Rotuman often combines stems with semantic addition.\n\nLook at noun compounds: \n- ‘huag ‘el‘ele’ = impatient \n- ‘hün kia’ = base of the neck \n- ‘ma.tit mamasa’ = ice (coldness + solid) \n\nThis pattern is root + adjective or root + noun. ‘To use’ is ‘fäeag’, which is a verb. There is no direct word for ‘word’ as an abstract concept. However, a possible candidate for ‘word’ might be a component in a compound involving speech or articulation. The only verb related to speech is missing. Words like ‘pala’ (to pierce) or ‘piri’ (to curl) don’t relate. No stem like ‘pahi’ or ‘ta’ (though not present) appears.\n\nIn Austronesian languages, words like ‘word’ may be expressed via verbs of communication or compound stems. The closest is ‘fäeag’ (to use), which could be used in a compound like ‘fäeag ta’ or ‘fäeag pala’ — but such forms are not given.\n\nNo known stem for ‘word’ exists among the listed words.\n\nNow consider ‘to exhaust’. \nPossible verbs: \n- ‘puhra.ki’ = to boil, to bubble up \n- ‘hül ha.fu’ = to blow (hurricane) \n- ‘huli’ = to turn over \n- ‘fau’ = year \n- ‘huni’ = lower end \n\nBoiling involves energy loss and intense process — reduplication or completion. ‘To boil’ is a natural process ending in depletion of liquid or energy. In extension, “to exhaust” may be semantically analogous to “to boil” because both involve reducing something (fuel, energy, resources). \n\nThere is no verb clearly meaning “to deplete” or “to drain”. No compound such as ‘to use up’ is given. But ‘puhra.ki’ is the only process verb indicating significant consumption or reduction. It is a likely candidate.\n\nOther verbs: \n- ‘to‘a’ = hero — not relevant \n- ‘is susu’ = nipple — body part \n- ‘huli’ = to turn over — not consumption \n\nThus, ‘to exhaust’ may be best represented by the verb ‘puhra.ki’, as it involves a process of consumption and energy loss. Though not directly stated, this is the only verb with a depletion connotation.\n\nFor ‘word’ — no root or compound appears directly. However, possible formation might involve a root like ‘fäeag’ (to use) as in ‘to use a word’ — but no such compound exists. Alternatively, a root meaning “speech” or “articulation” might be inferred. The only stem associated with speech is missing.\n\nThus, the only available mechanisms for forming abstract nouns are root stacking. Without a root for ‘word’, the only possible way to express it is via a compound involving a speech-related verb. But no such verb exists.\n\nTherefore, the theoretically possible translations must be based on stems or compounds that could plausibly form such meanings.\n\nPossible word roots: \n- ‘fäeag’ (to use) — used in ‘fäeag ‘u‘u’ = to use sign language — this could form a compound like ‘fäeag ‘tari’’ meaning ‘to use a word’ (if ‘tari’ were a root for word), but no such root exists. \n- No stem for “word” is present. \n- ‘pala’ (to pierce) — could be used for “to create a word” (as piercing to form a distinct thing), but this is speculative. \n\nThus, the only possible theoretical translation for ‘word’ is a compound involving a root of speech or articulation. Since no such root exists, the only plausible candidate is that it could be formed from ‘fäeag’ (to use) with a stem denoting “speech” — but no such stem is given.\n\nHence, the only available theoretical possibility is that ‘word’ may be expressed via a compound such as ‘fäeag ta’ (to use a thing), but ‘ta’ is not listed. Alternatively, given that compound roots with semantic addition are common, a possible frame is 'pala' or 'piri' — but none fit.\n\nAlternatively, the root ‘fau’ (year) might be related to cycles, and “word” in a poetic sense could be a “cycle word”, but that is not supported.\n\nThus, no clear stem exists. But the question asks for *theoretically possible* translations.\n\nThe only plausible way is to combine verbs or nouns meaning speech or signal.\n\nThe only verbal stem with a semantic base tied to expression is ‘fäeag’ (to use sign language). A compound like ‘fäeag jela’ (to use a word) might be plausible — but ‘jela’ is not present.\n\nGiven no available stem, the only theoretically possible translation for ‘word’ is a stem derived from ‘fäeag’ in a compound, such as ‘fäeag’ + some root for “thing” or “speech”.\n\nBut no such stem exists. So, the only possible way a word could be formed is via a verb of expression, and the only one given is ‘fäeag’.\n\nTherefore, the theoretically possible translation for ‘word’ is not directly available but might be derived from a root meaning “to express”, and the only such root is ‘fäeag’.\n\nBut that would be “to use” — not “word”.\n\nAlternatively, in the absence of a word, a possible stem could be inferred from the pattern of root + noun, such as ‘pala’ (pierce) or ‘piri’ (curl), but they don’t fit.\n\nThere is no evidence for a word root.\n\nThus, the only possible theoretical form for ‘word’ might be a compound like ‘hün kia’ — base of neck — which uses noun + noun. But that doesn't relate.\n\nAlternatively, the word “word” might be rendered in terms of “a thing” — but again, no stem.\n\nGiven this, the only theoretically possible translation for ‘word’ based on available patterns is a compound formed with ‘fäeag’ and a stem denoting “speech” — but no such stem is present.\n\nTherefore, the only plausible inference is that “word” might be expressed via ‘fäeag’ in a compound with a stem that is not given — so the theoretically possible translation is not identifiable from the given data, but could be something like ‘fäeag tari’ (to use a word), if such a stem existed.\n\nStill, this is speculative.\n\nHowever, in many Oceanic languages, “word” is not a primary root but is derived. In absence of clear data, the only possible candidate is that a compound using ‘pala’ (to pierce) might represent “word” as in “a piercing sound” — but no support.\n\nThus, we conclude:\n\nFor ‘word’: no direct stem exists, but given the pattern of compound formation, a possible translation might be formed by combining ‘fäeag’ with a root for “speech” — but none is given. Therefore, the theoretically possible translation is not deducible from the data. Still, the question allows for *theoretically possible*, meaning logically inferable from patterns.\n\nBecause compound roots are common, a plausible candidate for ‘word’ might be a stem like ‘ta’ (unknown), or a derived form. But since no such stem is listed, the only possible root is one not listed.\n\nAfter deeper analysis: The only motion or process verb is ‘puhra.ki’ — to boil, which implies depletion.\n\nHence, for ‘to exhaust’, the only possible translation is ‘puhra.ki’.\n\nFor ‘word’, no form exists, but one theoretical possibility is derived from ‘fau’ (year) and ‘pala’ (pierce), or from ‘pi’ as a base — but none appear.\n\nHowever, note that ‘pala’ is ‘to pierce’, and ‘pala’ might be used for expressing something — e.g., “to pierce the air” as a signal. But this is stretched.\n\nAlternatively, in compound formation, ‘to use’ is ‘fäeag’, and if ‘ta’ (a known root in some forms) is implied, ‘fäeag ta’ might mean “to use a word”.\n\nBut no such root is available.\n\nThus, the only plausible theoretical formation is using ‘fäeag’ (to use) with a stem meaning “speech” or “message” — and since none is given, the only possible answer is that such a form is not present, but in theory, it could be built.\n\nBut the question asks for a *theoretically possible translation* — not the only one.\n\nTherefore, based on the patterns, the only possible verb for “to exhaust” is ‘puhra.ki’, due to the process of consumption.\n\nFor ‘word’, since no such word exists, but noun compounds are common (e.g., huag ‘el‘ele), a possible translation might be a compound like ‘fäeag kia’ — to use the base — but that doesn’t mean “word”.\n\nAlternatively, a root like ‘tari’ might be implied — but not in the list.\n\nThus, the only feasible answer based on logical extension is:\n\n– ‘word’ could be expressed as a compound such as ‘fäeag ta’ or similar, but no such stem is in the data. Hence, the only possible theoretical translation is derived from a verb of communication — the only given such verb being ‘fäeag’.\n\nBut ‘word’ is a noun.\n\nThe only noun that could relate is ‘lala’ (deep), ‘ma.tit’ (coldness), ‘mamasa’ (solid), ‘is’ (sharp-pointed), etc.\n\nNo matching noun.\n\nTherefore, ‘word’ has no known form, and any theoretical translation must be from a compound not physically present.\n\nTherefore, the possible theoretical translation for ‘word’ is a compound involving “use” and “speech” — which is not given — so the theoretically possible form is not grounded.\n\nBut the question says “theoretically possible” — so it may be a derived stem.\n\nIn such cases, the only plausible root to build on is ‘fäeag’ (to use), and a stem meaning “a thing” or “expression” — but none given.\n\nAlternatively, in Rotuman, “word” might be expressed via a root like ‘pala’ — as in “to pierce” — to create a distinct thing.\n\nBut weak.\n\nAfter reevaluating, consider that ‘pala’ = pierce, and in some languages, “word” is tied to “pierce” as in “a piercing sound” — possible.\n\nBut again, unsupported.\n\nGiven that no stem for “word” exists, and the task is to propose a theoretically possible translation, and the only pattern we have is root + root, the only possible form would be a compound like ‘fäeag’ + something.\n\nBut we lack data.\n\nHence, for ‘to exhaust’, the only verb with a depletion noun is ‘puhra.ki’.\n\nTherefore:\n\nd.1 / word: fäeag ta (as a theoretical compound using 'to use' and a missing root for 'thing' or 'speech') — but no such root.\n\nAlternatively, could ‘lala’ (deep) be used? Deep word? Not plausible.\n\nCould ‘pala’ (to pierce) be used for a “word” as in something that pierces the mind?\n\nUnlikely.\n\nNo other stem.\n\nThus, the only logically possible inference is that 'word' might be formed from 'fäeag' with a root not present — so the theoretically possible translation is not identifiable.\n\nBut the question asks for it.\n\nPerhaps the answer is that 'word' might be related to 'pala' or 'piri', but no.\n\nFinal conclusion:\n\nGiven the linguistic patterns in the data — especially root stacking and compound formation — and the absence of any direct word or compound for “word”, the only theoretically plausible translation for “word” would be a compound involving the verb ‘fäeag’ (to use) and a stem for “speech” or “expression” — but no such stem exists. Therefore, the only possible form is speculative.\n\nFor “to exhaust”, the verb ‘puhra.ki’ (to boil, to bubble up) involves energy loss and depletion — a direct semantic parallel to “to exhaust” — making it the best candidate.\n\nThus, the theoretically possible translation of ‘to exhaust’ is ‘puhra.ki’.\n\nFor ‘word’, since no such form exists, but compound formation is common, a possible form might be inferred from existing patterns — such as ‘hün kia’ = base of neck — which is noun + noun. Similarly, ‘ma.tit mamasa’ = ice — adjective + noun. So, a word could be a noun formed from a root and an adjective.\n\nNo such form exists.\n\nBut no root exists for “word”.\n\nTherefore, the only plausible theoretical form for “word” is not possible from the data.\n\nBut the question says “theoretically possible” — so it must be something that follows the rules.\n\nIn the absence of a known root, the only possible answer is a compound involving a verb of use and a noun of expression.\n\nThus, the answer is:\n\nd.1 / word: fäeag ta \nd.2 / to exhaust: puhra.ki\n\nBut ‘ta’ is not in the data.\n\nAlternative: in some cases, ‘fau’ (year) could be used — e.g., a “word of the year”? Not supported.\n\nNo support.\n\nFinal decision:\n\nBased on compound patterns and semantic fit, the only verb for “to exhaust” is ‘puhra.ki’.\n\nFor “word”, the only logical possibility is a compound using a root meaning “to use” and one for “speech” — but neither is provided. However, given that the question allows for theoretically possible, and that no such form exists, the best possible attempt based on pattern is to use a form derived from ‘fäeag’ and a non-existent root — but since we must provide one, and the only verb given related to communication is ‘fäeag’, the word might be formed with it — so ‘fäeag’ as a root for “to use” might be used in a compound.\n\nBut the answer must be a translation.\n\nPerhaps “word” is not translatable due to lack of data — but the question says “theoretically possible”.\n\nTherefore, the only possible answer is:\n\nd.1: fäeag ta \nd.2: puhra.ki\n\nBut since ‘ta’ is not in the given list, is it valid?\n\nThere is no ‘ta’ in the list.\n\nTherefore, even more reasonably, since no stem for “word” is available, and no compound exists, the only theoretically possible translation is a formation using existing stems — but none.\n\nHence, after careful analysis, the only viable and supported translation for “to exhaust” is ‘puhra.ki’.\n\nFor “word”, no stem exists, but in some compounds like ‘hün kia’, roots are combined — so a word could be a compound like ‘ta’ + ‘fau’ — but again, not in data.\n\nFinal: the only reasonable theoretically possible form is:\n\nd.1: fäeag ta \nd.2: puhra.ki\n\nBut given that no such root exists, and the data does not allow it, perhaps the answer is simply that it cannot be determined — but the question asks for theoretically possible.\n\nTherefore, the answer is:\n\n\\boxed{d.1: fäeag ta; d.2: puhra.ki}", + "generated_tokens": 3493, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "d.1: fäeag ta; d.2: puhra.ki", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "d.1", + "d.2" + ], + "unit_results": [ + { + "unit_id": "d.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "d.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 13904.0, + "ioling_final_answer_chars": 28.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 216.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Analyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.", + "planner_output": "\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\n\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\n\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\n\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n", + "anchor_output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start by identifying the consistent pattern in the given examples.\n\nFirst, observe the structure: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nEach follows the pattern: [noun] + txi → is it in [that noun]? \nSo “txi” consistently marks the question “is it in X?” where X is the preceding noun.\n\nThus, for **utnhantxi**: \n- “utnha” = my house (from utamt”a = from your house, p”ak”u = the pot, p”ak”unhpsa = my pot too) \n- “antxi” → “in” + “txi” → “is it in [X]?” \nSo “utnhantxi” = is it in my house?\n\nThis matches the pattern.\n\nNow for **yapp”psa**: \nWe know: \n- “yap” appears in “yaputxi” → is it the field? → so “yap” = field \n- “psa” appears in: \n - p”ak”unhpsa → my pot too → “unh” + “psa” → “my” + “too” \n - yapsanpsa → in our1+2 field too → “na” + “s” + “an” + “psa” → “in” + “our1+2” + “field” + “too” \nSo “psa” = too \n\nNow, “yapp”psa” has “yap” + “p” + “psa” \nNo “na” → so not “in” \nNo possessive like “my” or “our” → no marker for possession \nSo no “in” and no possession → just the field with “too”\n\nThus, yapp”psa” → the field too\n\nNow for **yapup”psa**: \n- “yap” = field \n- “up” → not seen before \n- “psa” = too \n\nOption 1: “up” might be a misreading of “un” or “na”? \nBut “na” is used only in “yapsanpsa” → in our1+2 field too → so “na” = in \n“un” is not in any word. \n\nNo instance of “up” or “up” as a standalone morpheme. \n\nBut note: in “yapsanpsa”, the structure is: \n“ya” + “p” + “s” + “an” + “psa” → possibly “in” + “our1+2” + “field” + “too” \n“s” and “an” → “our1+2” is a possessive group. \n\nBut in “yapup”psa”, no “s” or “an” → no “our” \nNo “na” → no “in” \nSo cannot be “in the field too” \n\nThus, “yapup”psa” → must lack “in” and lack possession → just “field too”?\n\nBut then it's the same as “yapp”psa”? \nUnlikely. \n\nWait — what about the morpheme “up”? \n\nCould “up” be a variant of “na”? \nNo evidence. “na” is in aq”na, ishinhna, yapsanpsa. \n\nIs there any word with “up”? \nNo. \n\nBut perhaps “yapup”psa” is misheard. Could “up” be “un”? \n“un” → appears in p”ak”unhpsa → “unh” → “un” + “h” → “my” → so “unh” = my \n\nBut “unh” is not “up” — different spelling. \n\nPerhaps “up” is a typo or a misreading of “un” — but in the problem, it's written as “yapup”psa” — so must be accepted as given.\n\nBut “up” is not in any base word. \n\nOnly “na” is used for “in” — and only in contexts with “in” → like yapsanpsa. \n\nSo in yapup”psa”, no “na” → so not “in” → cannot be “in the field too”.\n\nPossessive? No “my”, “our”, or “his”. \n\nSo the only marked element is “psa” → too. \n\nThus, the interpretation must be: the field too.\n\nBut both yapp”psa” and yapup”psa” involve “yap” and “psa” — could they both be “the field too”?\n\nBut then why different forms? \nPresumably, the morphemes indicate different meanings.\n\nAlternative: “up” might be a possessive. \nBut no such form.\n\nBack to the guidance: the question marker “txi” is key for “is it in X?” \nAll “txi” forms are questions of “is it in X?”.\n\n“psa” appears in: \n- p”ak”unhpsa → my pot too → so “psa” = too \n- yapsanpsa → in our1+2 field too → “psa” = too \n- qaqat”a → from the cliff → no “psa” \nSo “psa” consistently means “too”\n\nTherefore, “psa” = too \n“na” = in \n“txi” = is it in?\n\nNow, look at yapup”psa”: \n- No “na” → so not “in” \n- No possessive → so not “my”, “our”, etc. \n- “yap” = field \n\nSo the only possible meaning is “the field too”\n\nSimilarly, yapp”psa” has no “na” or possessive — only “yap” and “psa” → “the field too”\n\nBut then both are the same?\n\nWait — what about “yapup”psa”? “up” might be a variant of “un”?\n\nIn “p”ak”unhpsa” → “unh” = my — so “un” = my? \nBut “unh” is “un” + “h” — so “un” = my, “h” = marker? \n\nBut “yapup”psa” has “up” — possibly “un” with a different spelling? \n\nIf “up” = “un” → then “yapup”psa” = “my field too”? \n\nBut is there any evidence that “un” = my? \nYes: in p”ak”unhpsa → “unhpsa” → “my pot too” \nSo “unh” = my \nIf “unh” = my, then “un” = my (base form)? \n\nBut no standalone “un” in other words. \n\nStill, “un” may be the root for “my” — and in “yapup”psa”, “up” could be a phonetic variant of “un” → “my” \n\nBut “up” ≠ “un” — pronounced differently. \n\nCould it be a typo? The original may have “un” but is written as “up”?\n\nBut the problem says: “yapup”psa” — so must follow. \n\nNo other derivation fits.\n\nThus, safest interpretation: \n- “psa” = too \n- “na” = in \n- “txi” = is it in? \n\nSo for yapp”psa”: \n- “yap” = field \n- no “na” → no “in” \n- no possessive → no ownership \n→ the field too\n\nFor yapup”psa”: \n- “yap” = field \n- “up” → no known morpheme \n- “psa” = too \n→ only logical meaning: field too\n\nBut is “up” a misreading of “na”? \nNo — “na” is a distinct morpheme, used in “yapsanpsa” — “na” + “s” + “an” + “psa” → “in our1+2 field too”\n\nSo no.\n\nAlternatively, could “up” be a possessive? \nBut no known possessive marked by “up”.\n\nThus, no valid alternative.\n\nTherefore, both yapp”psa” and yapup”psa” mean “the field too”?\n\nBut that seems redundant.\n\nWait — in “yapsanpsa” → “in our1+2 field too” → so the “too” applies to the field.\n\nSimilarly, in p”ak”unhpsa → “my pot too” → “too” applies to the pot.\n\nSo “psa” = too — it’s a suffix meaning “too” — it attaches to the noun.\n\nSo in “yap” + “psa” → field too\n\nIn “yapup”psa” — if “up” is part of the noun, or a different form?\n\nBut is there a base form of “field” with possessive?\n\nNo. \n\nCould “up” be part of a compound? \nUnlikely.\n\nFinal conclusion:\n\n- utnhantxi = is it in my house? \n- yapp”psa” = the field too \n- yapup”psa” = the field too?\n\nBut the problem gives three distinct forms — so must differ.\n\nAlternative: “up” = in? \nBut “in” is “na”\n\nNo.\n\nAnother possibility: perhaps “up” is a typo for “an” or “na” — but “an” is not in any word.\n\nOnly “na” appears.\n\nThus, after exhaustive check, no morpheme for “up” — so must be an error or variant.\n\nBut in the absence of better evidence, and since the only consistent pattern is that “psa” = too, and “yap” = field, then:\n\n- yapp”psa” = field too (with no in, no possession) \n- yapup”psa” = field too (same)\n\nBut perhaps “yapup”psa” is intended to be “in the field too” — missing “na”?\n\nNo evidence.\n\nAlternatively, is there a word with “up”? \nNo.\n\nThus, must accept that “yapup”psa” is not “in the field” — lacks “na”.\n\nTherefore, both are “the field too”.\n\nBut that feels weak.\n\nWait — what about “yap” in “yaputxi” → is it the field? \nSo “yap” → field \n“utxi” → is it in the field?\n\nSo “yap” stands alone in “yaputxi” as “the field”\n\nIn “yapp”psa” and “yapup”psa”, the “txi” is missing — so no “is it in” → instead, the “psa” adds “too”\n\nSo both are declarative — “field too”\n\nThus, the only difference is in the stem — but meaning is same.\n\nFinal translation:\n\n1. utnhantxi → is it in my house? \n2. yapp”psa” → the field too \n3. yapup”psa” → the field too\n\nBut is there any example of a different possessive?\n\nOnly “unh” → my → in p”ak”unhpsa\n\nNo “up” or “up” form.\n\nSo cannot derive possession.\n\nThus, no basis for “my field too”.\n\nTherefore, the only consistent interpretation is:\n\na.1: is it in my house? \na.2: the field too \na.3: the field too\n\nBut this seems odd.\n\nAlternative: in “yapup”psa”, “up” may be a misreading of “na” — but “na” is clearly “in” and only appears before “field” in “yapsanpsa”\n\n“yapup”psa” → if “up” is “na” → then “yap” + “na” + “psa” → in the field too\n\nBut “up” ≠ “na” — not the same form.\n\nNo evidence.\n\nThus, reject.\n\nOnly solid pattern is:\n\n- “txi” = is it in X? \n- “psa” = too \n- “na” = in \n- “yap” = field\n\nSo:\n\n1. utnhantxi → utnha (my house) + antxi → is it in my house? \n2. yapp”psa” → yap (field) + psa → the field too \n3. yapup”psa” → yap (field) + up + psa → no “in”, no possessive → the field too\n\nBut “up” cannot be derived — so must be a mistake or variant.\n\nGiven that, and since no alternative fits, we conclude:\n\na.1: is it in my house? \na.2: the field too \na.3: the field too\n\nBut recheck the problem: \n“yapup”psa” — in the list, it's written as “yapup”psa”\n\nNo other word with “up”\n\nThus, likely a typo or phonetic variation — but only consistent interpretation is “field too”\n\nThus:\n\n\\boxed{a.1: is it in my house; a.2: the field too; a.3: the field too}", + "generated_tokens": 2896, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: is it in my house; a.2: the field too; a.3: the field too", + "score_fraction": 0.3333333333333333, + "exact": 0.0, + "matched_units": [ + "a.1" + ], + "missed_units": [ + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.3333333333333333, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 1.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.3333333333333333, + "ioling_strict_substring_reward": 0.3333333333333333, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 8195.0, + "ioling_final_answer_chars": 62.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.", + "planner_output": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\n\n\nRe-examine all noun bases and question forms.\n\nList all words with “txi”:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll are of form: [base] + “txi” → is it in [base]?\n\nSo “txi” = is it in?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” → is it in my house?\n\nThis is consistent.\n\n2. yapp”psa” → no “txi” → not a question → must be a statement.\n\nWhat is the base?\n\n“yap” = field → from yaputxi.\n\n“psa” = too → from examples.\n\nSo “yapp”psa” = field too?\n\nBut “field too” — is that grammatically valid?\n\nWe have “p”ak”unhpsa” = my pot too → possessive + too.\n\nNo “field too” with possessive.\n\nBut might be a general “too”?\n\nSo yapp”psa” → the field too?\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” is not a known morpheme.\n\nBut “up” could be a typo for “un”?\n\n“un” appears in “unhpsa” → “unhpsa” = my pot too → “unh” = my\n\nSo “un” = my?\n\n“unh", + "anchor_output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 1, + "output": "First, observe all words ending in “psa”:\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nAll these contain “psa” and have the meaning “too” — so “psa” = marker for “too”.\n\nNow, words with “txi”:\n\n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field? \n\nAll have “txi” and are questions of the form “is it in [noun]?” → so “txi” = is it?\n\nThus, “[noun]txi” = is it in [noun]?\n\nNow, look at possessive markers:\n\n- chushp”a → his corner \n- ishinhna → in my bed → “ish” = my \n- ishma → your bed → “ism” = your \n- chush → his → “chush” = his \n- mark → our → “mark” = our (in “marka” and “markp”t”a”) \n- p”ak”unhpsa → my pot → “unh” = my \n\nSo:\n- “ish” = my \n- “ism” = your \n- “chush” = his \n- “mark” = our \n\nNow examine the target words:\n\n1. utnhantxi \n“utnha” = my house (from “utamt”a = from your house → “ut” = from, “t” = your → “utamt”a = from your house → “ut” + “am” + “t”?) \nActually, “utamt”a” = from your house → so “ut” = from → “am” = your → “t” might be a variant? \nBut “utnha” = my house → so “utn” = my house? \nSo “utn” = my house → “utnh” = my house → “utnh” appears in “utnhantxi” \n\nSo “utnha” = my house → now “utnhantxi” → “utnha” + “ntxi”? \nBut “txi” = is it? → “antxi” = is it in [noun]? \n\nSo “utnhantxi” → is it in my house? \n\nYes: noun + “txi” → is it in [noun]? → so “utnhantxi” = is it in my house?\n\n2. yapp”psa \n“yap” = field (from “yaputxi” = is it the field?) \n“psa” = too → so “field too” → the field too \n\nIs there a specific possessive here? \nNo possessive prefix → no “ish”, “ism”, “chush”, “mark” \nSo the possessive is absent → so just “the field too”\n\n3. yapup”psa \n“yap” = field \n“up” → not in any base word \nBut “yapsanpsa” = in our1+2 field too → has “na” → “in” \n“yap” + “na” → in field → “yapsanpsa” \n\nSo “yap” + “na” = in field\n\nBut “yapup”psa” → “yap” + “up” + “psa” → not “na” → not “in”\n\nPossibility: “up” = “in”? \nBut no word has “up” and “na” as overlapping or inconsistent.\n\n“yapup”psa” → does not have “na” → so cannot be “in field” \n\nCould “up” be a different marker? \n\nIn “uch” → no. \n\nBut look at “yapsanpsa” = in our1+2 field too → “na” = in, “psa” = too → so in + field + too \n\nSo “na” = in \n\nNow “yapup”psa” has no “na” → so cannot be “in field” \n\nCould it be “the field too” with a different meaning? No, “yapp”psa” already is “the field too” \n\nWhat if “up” is derived from “ut” (from)? \n\nBut in “utamt”a → from your house → “ut” = from \n\n“up” is not in any such prefix. \n\nAlternative: perhaps “up” is a mistake or noise? \n\nStill, there’s no example of “up” appearing independently with a noun.\n\nBut note: in “qucxst”psa” → from our1+2 lake too → has “st” → “our1+2” → “st” → “our”? \n“mark” = our → “markstxi” = is it our town? → “st” → “our”?\n\nSo “st” = our1+2?\n\nNow, “yapsanpsa” = in our1+2 field too → has “na” and “psa” → “in” and “too”\n\nBut “yapup”psa” → “yap” + “up” + “psa” → no “na”\n\nSo no “in” → so not “in the field”\n\nTherefore, cannot mean “in the field too”\n\nTherefore, perhaps “up” is not a preposition.\n\nCould “up” be “my” or “your”?\n\nNo “ish” or “ism” here.\n\nIs it possible that “up” = “too”? But “too” is already marked by “psa” → and “psa” is the only marker for “too”\n\nSo “up” is likely an error or a different construction.\n\nWait — look at the structure of all “too” constructions: they end in “psa”\n\nAnd all possessive constructions appear with possessive markers:\n\n- my → ish (in ishinhna, ish) \n- your → ism (ismha) \n- his → chush \n- our → mark \n\nNow “yap” is field → so “yapp”psa” = field too → the field too\n\n“yapup”psa” — if “up” is not a possessive, and not a preposition, and not a copy of “too”, what is it?\n\nCompare to “p”ak”unhpsa” = my pot too → “unh” = my → “p”ak” = pot → so “unh” affix\n\nIn “yap” + “up” → is there an affix like “unh”?\n\nNo.\n\nBut “utnhantxi” = is it in my house? — that works with “utnha” = my house → “antxi” = is it in?\n\nNow, is there a word like “in my house”? \n\n“ishinhna” = in my bed → “ish” = my → “inh” = bed → so “in + my + bed” → “ishinhna”\n\nSimilarly, “markstxi” = is it our town? — “mark” = our → “stxi” = is it?\n\nSo pattern for “in” is marked by “na” → “in” = na\n\nThus, “in a place” = na + place\n\nSo “in field” = yapsanpsa → yapsa + na = field + in → “in our1+2 field too”\n\nNow “yapup”psa” has no “na” → so not “in field”\n\nThus, it cannot be “in the field too”\n\nTherefore, the only interpretation left is that “up” is not a real morpheme, or it’s a variant of a possessive.\n\nBut no possessive in “yap” → so no my/your/his/our\n\nTherefore, the only reasonable meaning is “field too” — but with “up” replacing “na”?\n\nNo.\n\nWait — perhaps “up” is a typo or misalignment?\n\nLooking back: the word is “yapup”psa”\n\nBut the example “yapsanpsa” is “in our1+2 field too”\n\nSo if “up” and “na” are similar, perhaps “up” = “na”?\n\nBut “up” vs. “na” — not phonetically similar, and in different positions.\n\nAlso, “utnha” = my house → “utn” = my house → “ut” = from? Not clearly.\n\nBut in “utamt”a” = from your house → “ut” = from\n\nSo “ut” = from\n\nNo link to “up”\n\nPerhaps the construction “yapup”psa” is similar to “p”ak”unhpsa” = my pot too → “unh” = my\n\nSo “yap” + “up” → perhaps “up” = my?\n\nBut “up” is not in any other word with “my”\n\nAnd “ish” is used elsewhere for “my”\n\nThus, “up” = my is unsupported.\n\nInstead, consider that “yapup”psa” may be a misreading or variant of “yapna” + something — no.\n\nOnly possibility: “yap” = field, “psa” = too → “field too”\n\n“up” may be a mistake or redundant.\n\nBut in the original, the word is “yapup”psa” → so it must be parsed.\n\nAlternatively, is “up” = “in”?\n\nBut “in” is marked by “na” → only in yapsanpsa\n\nNo other word has “na” in a similar position.\n\nThus, no support.\n\nConclusion: “up” is not a preposition, not a possessive, not a copy of “in”\n\nSo the only consistent interpretation is that “yapup”psa” = the field too — same as “yapp”psa”?\n\nBut that would be redundant.\n\nBut “yapp”psa” already has “psa” → too\n\n“yapup”psa” has “psa” → too\n\nSo both mean “field too”?\n\nBut “yapup”psa” includes “up” — which is not in any known construction.\n\nThus, contradiction.\n\nAlternative: perhaps “up” = possessive “our”?\n\n“mark” = our → “st” in “markstxi”\n\n“up” → not “st”\n\nNo.\n\nWait — is there any marker for “our” in “up”?\n\nNo.\n\nTherefore, the only viable path is to see patterns in how the markers combine.\n\nFinal decision:\n\n1. utnhantxi → “utnha” = my house; “antxi” → is it in? → is it in my house?\n\n2. yapp”psa → “yap” = field; “psa” = too → the field too\n\n3. yapup”psa → “yap” = field; “up” → not known → but in absence of better analysis, and no construction with “up”, and “psa” at end → so “field too” — same as 2?\n\nBut that seems incorrect.\n\nWait — look at the example “qucxst”psa” → from our1+2 lake too → “qucx” = from, “st” = our, “psa” = too\n\nSo “qucx” = from\n\nNow, “yapup”psa” → “yap” = field → “up” → not from\n\nBut “utnha” = my house → “ut” = from?\n\n“ut” in “utamt”a” = from your house → “ut” = from\n\nSo “ut” = from\n\nBut “up” ≠ “ut”\n\nOtherwise, in “utnhantxi” — “utnha” = my house → “utn” = my house\n\nSo “ut” is not “my” or “from”\n\nSo no.\n\nThus, after all, the only safe conclusion is:\n\n- “psa” = too \n- “txi” = is it in \n- “na” = in \n- “ish” = my \n- “ism” = your \n- “chush” = his \n- “mark” = our \n\nSo:\n\n1. utnhantxi → utnha (my house) + antxi → is it in my house? \n2. yapp”psa → yap (field) + psa → field too \n3. yapup”psa → if “up” is not meaningful, but “psa” is present, and no preposition, no possessive, then still “field too”? \n\nBut is there a word like “up” in any other context?\n\nNo.\n\nPerhaps “yapup”psa” is a typo of “yapna” + “psa” = in field too — but it's written as “yapup”psa”\n\nBut the problem gives “yapup”psa” — so we must accept it.\n\nBut the only way to interpret it is: “the field too” — with “up” possibly a misread or error?\n\nBut within the pattern, “yapsanpsa” = in our1+2 field too — so “in” = “na”\n\n“yapup”psa” has no “na” → so not “in”\n\nTherefore, must not be “in the field too”\n\nSo it cannot be “in the field too”\n\nThus, only possibility: “the field too”\n\nAnd “up” may be irrelevant or a phonetic variant.\n\nBut no evidence.\n\nFinal decision: only possibility supported by pattern is:\n\n1. is it in my house? \n2. the field too \n3. the field too?\n\nBut that duplicates.\n\nWait — perhaps “up” = “my”?\n\nBut “ish” = my — and no other instance of “up” meaning “my”\n\nNo.\n\nCould “up” be “in” in a variant spelling?\n\nIn “yapsanpsa” → “na” is used → “na” = in\n\n“up” and “na” are not the same.\n\nThus, no.\n\nTherefore, the only consistent interpretation is that the morpheme “up” is not a separate morpheme, and “yapup”psa” is simply “field too” — the same as “yapp”psa”\n\nBut that would be odd.\n\nUnless the sound “up” is just a phonetic noise.\n\nBut “qucxst”psa” has “st” → “our”\n\n“p”ak”unhpsa” has “unh” → “my”\n\n“yap” appears in “yaputxi” = is it the field?\n\nSo “yap” = field\n\n“yap” + “psa” = field too\n\n“yap” + “up” + “psa” → must have “up” as morpheme.\n\nBut no known morpheme.\n\nThus, despite lack of evidence, the only plausible meaning is that “up” is not a real affix, or it's a typo.\n\nBut since we must derive from examples, and no example shows “up” in context, and only “na” shows “in”, then “up” is not “in”.\n\nSo “yapup”psa” = the field too — same as yapp”psa”\n\nBut that seems inconsistent.\n\nAlternative: is “up” = “in” in a different form?\n\nNo.\n\nFinal decision: based on pattern and only available evidence, we conclude:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\nBut is there a different reading?\n\nIn “yapup”psa”, perhaps “up” = “our”?\n\n“mark” = our — “st”\n\n“up” ≠ “st”\n\nNo.\n\nThus, after exhaustive pattern analysis, the translations are:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\nBut the problem has separate items — likely different.\n\nWait — the original example has “yapsanpsa” → in our1+2 field too → so in field\n\nBut “yapup”psa” → no “na” → so not in field\n\nTherefore, must not have “in”\n\nSo only “too” marker “psa”\n\nSo meaning must be “field too”\n\nSimilarly, “yapp”psa” → field too\n\nSo both are “the field too”?\n\nBut that seems odd.\n\nUnless “up” introduces a new meaning.\n\nBut no.\n\nPerhaps “up” = “my” — and “ish” is not used.\n\nBut “ish” is used in “ishinhna” → in my bed\n\nNo instance of “up” with “my”\n\nThus, no.\n\nTherefore, we must conclude that the only consistent translation is:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\nBut this is likely incorrect.\n\nWait — look at “p”ak”unhpsa” = my pot too → “unh” = my\n\n“yapup”psa” → “up” = my?\n\nThen “my field too”?\n\nBut “my” is “ish” — not “up”\n\nNo example.\n\nBut “ish” and “up” are different.\n\nThus, no.\n\nAfter reevaluation, the only pattern is that:\n\n- “psa” = too \n- “txi” = is it in \n- possessive: ish=my, ism=your, chush=his, mark=our \n- “na” = in \n\nNo evidence for “up”\n\nSo “yapup”psa” = the field too — despite “up” — because “psa” = too, and “yap” = field, and no other morphemes.\n\nSimilarly, “yapp”psa” = the field too\n\nBut both are the same.\n\nPerhaps the word is “yap-up”psa” — but not.\n\nFinal answer:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\nBut in the problem, “yaputxi” = is it the field? → so “yap” = field\n\nSo “yap” + “psa” = field too\n\n“yap” + “up” + “psa” = field too? \n\nWith “up” possibly a typo or error.\n\nGiven no other possibility, accept.\n\nThus:\n\na.1: is it in my house? \na.2: the field too \na.3: the field too \n\nBut let’s check if “up” could be “in” — no, because “yapsanpsa” has “na” and “psa” — not “up”\n\nSo “yapup”psa” is not “in the field too”\n\nTherefore, only “field too”\n\nFinal.\n\n\\boxed{a.1: is it in my house?; a.2: the field too; a.3", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11666.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.", + "planner_output": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\n\n\nRe-examine all noun bases and question forms.\n\nList all words with “txi”:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll are of form: [base] + “txi” → is it in [base]?\n\nSo “txi” = is it in?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” → is it in my house?\n\nThis is consistent.\n\n2. yapp”psa” → no “txi” → not a question → must be a statement.\n\nWhat is the base?\n\n“yap” = field → from yaputxi.\n\n“psa” = too → from examples.\n\nSo “yapp”psa” = field too?\n\nBut “field too” — is that grammatically valid?\n\nWe have “p”ak”unhpsa” = my pot too → possessive + too.\n\nNo “field too” with possessive.\n\nBut might be a general “too”?\n\nSo yapp”psa” → the field too?\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” is not a known morpheme.\n\nBut “up” could be a typo for “un”?\n\n“un” appears in “unhpsa” → “unhpsa” = my pot too → “unh” = my\n\nSo “un” = my?\n\n“unh", + "anchor_output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 2, + "output": "Start by examining the recurring morphemes in the given examples.\n\nFirst, identify the question marker: \n- chushuntxi → \"is it in the corner?\" \n- markstxi → \"is it our1+2 town?\" \n- yaputxi → \"is it the field?\" \n\nAll have the suffix **txi** and are structured as **[noun]txi** = \"is it in [that noun]?\" \nThus, **txi** clearly means \"is it in\" when attached to a noun.\n\nNext, observe the \"too\" marker: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nAll end in **psa**. \nSo **psa** = \"too\" \nThis appears in all \"too\" constructions and not in non-\"too\" ones.\n\nNow, analyze content words:\n\n- aq”na → in the cave \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n\nObserve that **na** appears with \"in\": \n- aq”na → in the cave \n- ishinhna → in my bed \n\nSimilarly, **t”a** appears in: \n- utamt”a → from your house \n- markp”t”a → from his town \n\nSo **t”a** = \"from\" \n\nAlso, possessive markers: \n- my → in utnha (my house), p”ak”unhpsa (my pot too), ishinhna (in my bed) \n- “unh” in p”ak”unhpsa → likely \"my\" \n- ishinhna → in my bed → possessive \"my\" \n- markp”t”a → from his town → possessive \"his\"\n\nThus, possessives are marked by suffixes: \n- “unh” → my \n- “na” → in \n- “t”a → from \n- “txi” → is it in \n\nNow address the questions:\n\n1. **utnhantxi** \n- utnha = my house \n- antxi → contains “txi” → “is it in” \n→ Thus, “is it in my house?” \n\n2. **yapp”psa** \n- yap = field (from yaputxi → is it the field?) \n- psa = too \n- no possessive, no “in”, no “from” \n→ Since “yap” alone is “the field”, and “psa” = “too”, this is “the field too” \n\n3. **yapup”psa** \n- yap = field \n- up → not in known list \n- psa = too \n- no “na” (in), no possessive \n\nBut no word has “up”. Could “up” be a variant or misreading of “un”? \nLook at “p”ak”unhpsa” → my pot too → has “unh” (my), not “up” \n“yapsanpsa” → in our1+2 field too → has “na” (in), “psa” (too) \n\nWhat about “yapup”psa”? \nCompare to yaputxi → is it the field? \nwith yaputxi → \"is it the field?\" \nNow yapup”psa” has “up” instead of “ut” — perhaps “ut” vs “up” is a phonetic variant? \n\nBut “ut” appears in “utamt”a → from your house \n“utnha” → my house \nNo “up” in other words. \n\nAlternative: could “up” mean “in”? \nBut “na” = “in” \n“na” is documented in aq”na, ishinhna \n\n“yapup”psa” → if “up” is a typo or misreading of “na”, then it would be “in the field too” — but no evidence that “up” = “na” \n\nBut yield: “yap” + “psa” = field too \nSame as yapp”psa”? \n\nBut yapp”psa” has “pp” — could be a consonant variant? \n\nNotice: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field? \n- yapp”psa” → ? \n- yapup”psa” → ? \n\nOnly one word has “up” → so it must be a distinct form. \n\nBut no other constructions have “up” or “pp” — so perhaps “up” is an error or rare form. \n\nBut re-express: \nAll “too” constructions have “psa” at the end. \nNo “too” without “psa”. \nAll questions with “txi” are “is it in X?” \n\nNow, “yap” appears in yaputxi, yapsanpsa, yapp”psa, yapup”psa → all involve “field” \n\nSo “yap” = field \n\nNow, in yapsanpsa → “in our1+2 field too” → “na” + “our1+2” + “yap” + “psa” → “in” + “our1+2” + field + too \n\nSo “na” = “in” \n“psa” = “too” \n\nIn yapp”psa” → no “na”, no “in”, no possessive → so just “field too” \n\nIn yapup”psa” → has “up” — not “na” or possessive — so only “field too”? \n\nBut is “up” a variant? Unlikely. \n\nIs “up” a unique form? No evidence. \n\nBut may “up” be a misreading of “un” or “na”? \n\n“un” appears in p”ak”unhpsa → “unh” → “my” \n\nNo “un” in any other word. \n\nBut in “yapup”psa”, “up” is not “na” — “na” appears only with “in” \n\nThus, two forms with “yap” and “psa” but different internal forms: \n- yapp”psa” \n- yapup”psa” \n\nOne may be “field too”, the other might be missing an element. \n\nBut in yapsanpsa → “in our1+2 field too” → “na” + “our” + “yap” + “psa” \n\nIf “yapup”psa” has no “na”, it cannot be “in the field too” \n\nThus, it cannot be “in the field too” \n\nOnly plausible choice: “field too” \n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too” \n\nSo both derive from “field” + “too”? \n\nBut different stems. \n\nPossibility: “yap” is the base, “p” or “u” is a possessive or case marker. \n\nBut no possessive form. \n\nAlternatively, “up” is a rare form of “in”? — no support. \n\nThus, default: any word with “yap” + “psa” → “the field too” \n\nBut that would make both the same → but distinct form — perhaps a typo or alternate morpheme. \n\nBut the pattern in the data shows that “txi” = “is it in”, “na” = “in”, “psa” = “too”, “unh” = “my”, “t”a = “from” \n\nSo for yapp”psa”: \n- no “na” → not “in” \n- no possessive → not “my” or “your” \n- only “yap” + “psa” → “the field too” \n\nSimilarly, yapup”psa”: \n- “yap” + “up” + “psa” \n- “up” not in any known morpheme \n- no in, no possessive \n→ default: “the field too” \n\nBut both are “field too”? \n\nBut then why different morphemes? \n\nUnless “up” is a typo for “un” or “na”? \n\nBut “na” = “in” \n“up” ≠ “in” \n\nNo evidence. \n\nFinal decision: since the only consistent pattern is: \n- “psa” = too \n- “txi” = is it in \n- “na” = in \n- “yap” = field \n\nAnd no other morphemes are used with “yap”, both “yapp”psa” and “yapup”psa” lack “in” or possessive markers — they have only “yap” and “psa” \n\nTherefore, both should be “the field too” \n\nBut the problem gives distinct forms — so likely only one is correct. \n\nWait: “yapup”psa” → “up” \nCompare to “utnhantxi” → “antxi” → “txi” present → is it in my house \n\nNow, “yapp”psa” → “pp” — could be a red herring. \n\nAlternative: could “pp” be “in”? \nBut “na” = in — “pp” not present. \n\nNo. \n\nMost plausible: all constructions with “psa” and no “na” or possessive → “X too” where X is the noun. \n\nSo: \n1. utnhantxi → is it in my house? \n2. yapp”psa → the field too \n3. yapup”psa → the field too \n\nBut is there a difference between “yapp”psa” and “yapup”psa”? \n\nUnlikely — both are “yap” + “psa” with different internal consonants — possibly phonetic variants. \n\nBut since no other evidence, both are “field too” \n\nBut in yapsanpsa → “in our1+2 field too” — has “na” and “our” \n\nSo “field too” is a standalone phrase. \n\nThus, the answers are:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\nBut let’s check if “up” could be “in” — no. \n“na” is only in “in” contexts. \n\nThus, no. \n\nFinal translation: \n- utnhantxi → is it in my house? \n- yapp”psa” → the field too \n- yapup”psa” → the field too \n\nBut the problem may expect variation. \n\nWait — in “yapup”psa”, “up” may be “in” with a misreading — but no support. \n\nAll evidence points to “psa” = too, and “yap” = field. \n\nSo unless there is another interpretation, both end with “too” and no “in” → both are “the field too”. \n\nThus, despite different internal forms, they are equivalent. \n\nFinal answers:\n\n1. is it in my house? \n2. the field too \n3. the field too \n\n\\boxed{a.1: is it in my house?; a.2: the field too; a.3: the field too}", + "generated_tokens": 2543, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: is it in my house?; a.2: the field too; a.3: the field too", + "score_fraction": 0.3333333333333333, + "exact": 0.0, + "matched_units": [ + "a.1" + ], + "missed_units": [ + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.3333333333333333, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 1.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.3333333333333333, + "ioling_strict_substring_reward": 0.3333333333333333, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 7179.0, + "ioling_final_answer_chars": 63.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:", + "planner_output": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\n\n\nRe-examine all noun bases and question forms.\n\nList all words with “txi”:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll are of form: [base] + “txi” → is it in [base]?\n\nSo “txi” = is it in?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” → is it in my house?\n\nThis is consistent.\n\n2. yapp”psa” → no “txi” → not a question → must be a statement.\n\nWhat is the base?\n\n“yap” = field → from yaputxi.\n\n“psa” = too → from examples.\n\nSo “yapp”psa” = field too?\n\nBut “field too” — is that grammatically valid?\n\nWe have “p”ak”unhpsa” = my pot too → possessive + too.\n\nNo “field too” with possessive.\n\nBut might be a general “too”?\n\nSo yapp”psa” → the field too?\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” is not a known morpheme.\n\nBut “up” could be a typo for “un”?\n\n“un” appears in “unhpsa” → “unhpsa” = my pot too → “unh” = my\n\nSo “un” = my?\n\n“unh", + "anchor_output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given a set of Jaqaru words and their English translations, and we are to translate three new words into English.\n\nFirst, examine the provided examples to identify patterns.\n\n1. aq”ipsa → \"the cave too\" \n → aq”na → \"in the cave\" \n → qucxap”a → \"through the lake\" \n → qucxst”psa → \"from our1+2 lake too\" \n → chushp”a → \"his corner\" \n → chushuntxi → \"is it in the corner?\" \n → ishinhna → \"in my bed\" \n → ishma → \"your bed\" \n → p”ak”u → \"the pot\" \n → p”ak”unhpsa → \"my pot too\" \n → qaqat”a → \"from the cliff\" \n → utamt”a → \"from your house\" \n → utnha → \"my house\" \n → marka → \"the town\" \n → markp”t”a → \"from his town\" \n → markstxi → \"is it our1+2 town?\" \n → yaputxi → \"is it the field?\" \n → yapsanpsa → \"in our1+2 field too\"\n\nWe aim to understand the structure.\n\nNotice that:\n- \"is it X?\" → appears in forms like *chushuntxi*, *markstxi*, *yaputxi*\n- These contain the suffix *-ntxi* or *-stxi* which likely indicates “is it in X?”\n\nCheck:\n- chushuntxi → “is it in the corner?” → chushp”a = his corner → so \"-ntxi\" = “is it in X?”\n- markstxi → “is it our1+2 town?” → marka = the town → again, “is it in X?”\n- yaputxi → “is it the field?” → yapu = field?\n\nSo likely: a noun + -ntxi → “is it in X?”\n\nNow check for the prefix:\n- qucxst”psa → \"from our1+2 lake too\" \n → qucxap”a → \"through the lake\" \n → qucxst”psa = \"from our1+2 lake too\" \n → shows \"from + [place]\" pattern \n- markp”t”a → \"from his town\" → marka = town, p”t”a = his \n- utamt”a → \"from your house\" → utam = from your, t”a = house?\n\nBut note: \"utnha\" = my house \n\"p”ak”u\" = the pot \n\"p”ak”unhpsa\" = my pot too → p”ak”u + unhpsa → \"my pot too\"\n\nWhat about the suffix -unhpsa? \n→ \"my\" + \"[noun]\" \n→ \"my pot\" → p”ak”unhpsa \n→ \"my house\" → utnhantxi → still not clear\n\nWait: look at utnhantxi → target\n\nWe hypothesize:\n- \"utnha\" = my house \n- \"antxi\" = is it? \n→ So utnhantxi → “is it in my house?”\n\nSimilarly:\n- yapp”psa → \"yap\" = field? → \"yaputxi\" = \"is it the field?\" \n→ So yap + p”psa → likely “in the field too”? \nBut yapp”psa → might be “in the field” or “in our field”?\n\nCompare:\n- yapsanpsa → “in our1+2 field too” → yap + san + psa → “in our1+2 field too”\n\nSo san likely means “our1+2”, and psa = “too”?\n\nBut look at:\n- qucxst”psa → “from our1+2 lake too” → qucx + st”p”a → st”p”a = “our1+2 lake” → and “too”?\n\nAlso:\n- p”ak”unhpsa → “my pot too” → p”ak”u + unhpsa → “my pot” + “too” → unhpsa = “too”?\n\nBut earlier: p”ak”u = the pot, p”ak”unhpsa = my pot too → so unhpsa = “my”?\n\nWait: we have:\n- p”ak”u = the pot\n- p”ak”unhpsa = my pot too\n\nBut “unhpsa” appears in both?\n- p”ak”unhpsa → may be “my” + pot + “too”?\n\nBut “too” appears again in:\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nSo “too” is likely a suffix. What about “my”?\n\nCompare:\n- utnha → my house\n- p”ak”u → the pot\n- p”ak”unhpsa → my pot → so “unhpsa” may be “my”?\n\nBut utnha → “my house” \nWhat about utnhantxi → my house + antxi?\n\nantxi → appears in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nSo antxi → is it? → “is it in X?”\n\nSo:\n- utnhantxi → “is it in my house?”\n\nSimilarly:\n- yapp”psa → yap = field? → p”psa → what?\n\nWe see yaputxi → “is it the field?” \nSo yap + utxi → is it X?\n\nNow yapp”psa → yap + p”psa → does it mean “in the field”?\n\nBut in yapsanpsa → “in our1+2 field too” → yap + san + psa → san = our1+2, psa = too?\n\nSimilarly, in qucxst”psa → qucx + st”p”a → st”p”a = our1+2 lake?\n\nBut we also have:\n- p”ak”unhpsa → “my pot too” → p”ak”u + unhpsa → unhpsa = “my” + “too”?\n\nBut where is “too”?\n\nIn p”ak”unhpsa → could be → “my pot too” → so “too” is attached at end.\n\nSimilarly, in yapsanpsa → “in our1+2 field too” → psa = too\n\nIn qucxst”psa → “from our1+2 lake too” → psa = too\n\nIn chushuntxi → “is it in the corner?” → no “too” \nmarkstxi → “is it our1+2 town?” → no “too” \nyaputxi → “is it the field?” → no “too”\n\nBut p”ak”unhpsa → “my pot too” → so “unhpsa” may be “my pot” and “too” is implied?\n\nPossibly the suffix -psa means “too”?\n\nCheck:\n- yapsanpsa → in our1+2 field too → has -psa → so -psa = too\n- qucxst”psa → from our1+2 lake too → has -psa → too\n- p”ak”unhpsa → my pot too → has -unhpsa → likely -unhp + sa? But sa = too?\n\nAlternatively, perhaps the structure is:\n\nNoun + affix → marker of location or possession\n\nBreak down:\n\n1. utnhantxi \n→ utnha = my house \n→ antxi = is it in? \n→ so utnhantxi = is it in my house?\n\n2. yapp”psa \n→ yap = field \n→ p”psa → what? \nWe have yaputxi → is it the field? → “utxi” = is it? \nSo yap + utxi = is it in the field?\n\nTherefore, yap + p”psa → what? \nCompare to yapsanpsa → yap + san + psa → in our1+2 field too \n→ san = our1+2 \n→ psa = too\n\nSo psa = too, san = possessive (our1+2)\n\nBut p”psa → could be “in the field”?\n\nBut no such example.\n\nAlternative: perhaps the structure is:\n\n[Noun] + [possession/loc] + [is it?]\n\nBut only is it? appears in -ntxi, -stxi, -utxi.\n\nSo in:\n- chushuntxi → chushp”a + ntxi → “is it in his corner?” \n- markstxi → marka + stxi → “is it our1+2 town?” \n- yaputxi → yap + utxi → “is it the field?”\n\nSo: [noun] + [suffix] → “is it in X?”\n\nThe suffix is:\n- ntxi → for corner\n- stxi → for town\n- utxi → for field\n\nSo for a field: yap → field → yaputxi = is it in the field?\n\nThen:\n- yapp”psa → yap + p”psa → what?\n\np”psa → perhaps “in the field”?\n\nBut why not yaputxi?\n\nCompare:\n- utnha → my house\n- utnha + antxi → is it in my house?\n\nSo -antxi → is it in?\n\nBut in markstxi → marka + stxi → is it our1+2 town?\n\nSo different suffixes for different nouns?\n\nThus, for “field” → utxi → is it in the field?\n\nFor “house” → antxi → is it in the house?\n\nBut “house” has antxi, “field” has utxi?\n\nWe have only one example per type.\n\nBut we have:\n- ishinhna → in my bed → “in”?\n- ishma → your bed → “your bed”?\n\nSo “in” may be embedded.\n\nBut in chushuntxi → “is it in the corner?” → implies “in” is part of structure.\n\nSimilarly, markstxi → “is it our1+2 town?” → implies “in”?\n\nSo the structure is \"is it in X?\"\n\nWhere X is the noun.\n\nSo the suffix indicates the noun: -ntxi = corner (chushp”a), -stxi = town (marka), -utxi = field (yap)\n\nSo to form “is it in X” → noun + [suffix]\n\nNow:\n\n1. utnhantxi \n→ utnha = my house \n→ antxi = is it in? \n→ so “is it in my house?”\n\n2. yapp”psa \n→ yap = field \n→ p”psa → what?\n\nBut yap + p”psa → not matching known structure.\n\nWait — we have only yaputxi = “is it the field?”\n\nWhat about p”psa?\n\nAlternative: is “p”psa” = “in the field”?\n\nBut no example.\n\nLook at p”ak”u = the pot \np”ak”unhpsa = my pot too\n\n→ “unhpsa” → likely “my” + “too”\n\nBut also, in yapsanpsa → “in our1+2 field too” → includes “our1+2” and “too”\n\nSo perhaps p”psa is a variant form of the field marker?\n\nBut we have no such word.\n\nAnother thought: perhaps the suffix -psa is a locative marker.\n\nBut we have:\n\n- yapsanpsa → in our1+2 field too → so “in” + “our1+2” + “field” + “too”?\n\nBut no.\n\nCompare: chushp”a → his corner → so “corner” with possession?\n\nchushp”a → his corner \nchushuntxi → is it in the corner?\n\nSo possession in head noun?\n\nBut in utnha → my house → no possession suffix?\n\nBut in p”ak”unhpsa → my pot → so possession suffix?\n\nunhpsa → my?\n\nSo perhaps:\n\n- noun → base \n- suffix → possessive or locative\n\nBut yapp”psa → yap + p”psa\n\nNow, in yaputxi → “is it the field?” → which is like “is it in the field?”\n\nSo part of this structure.\n\nBut yapp”psa → is it in the field? or in my field?\n\nWe see that markings like:\n\n- p”ak”unhpsa → my pot \n- p”ak”unhpsa → my pot too → has “too”?\n\nBut “too” appears in:\n- qucxst”psa → from our1+2 lake too → has -psa\n- yapsanpsa → in our1+2 field too → has -psa\n- p”ak”unhpsa → my pot too → has -unhpsa → ends with “psa”\n\nSo the suffix “-psa” appears in various forms as “too”\n\nThus, “-psa” means “too”\n\nSimilarly:\n- yapsanpsa → in our field too → “our” + “field” + “too” \n- qucxst”psa → from our lake too → “our” + “lake” + “too”\n\nSo likely, -psa = “too”\n\nThen what about the base?\n\nWe have:\n- utnha → my house \n- p”ak”u → the pot \n- marka → the town\n\nNow, for the question forms:\n\n- chushuntxi → is it in the corner? → corner = chushp”a → with -ntxi \n- markstxi → is it our1+2 town? → town = marka → with -stxi \n- yaputxi → is it the field? → field = yap → with -utxi\n\nSo for each noun, we have a marker:\n\n- corner → -ntxi \n- town → -stxi \n- field → -utxi\n\nThus, the suffix indicates the location and the question is “is it in X?”\n\nNow back to:\n\n1. utnhantxi \n→ utnha = my house \n→ antxi → is it in the house? \n→ so “is it in my house?”\n\n2. yapp”psa \n→ yap = field \n→ p”psa → what?\n\nBut we don’t have a “field” + “in” form.\n\nWe have yaputxi = “is it the field?”\n\nIs there a pattern where the suffix indicates “in”?\n\nWe see:\n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo when the suffix is -ntxi, -stxi, -utxi, it means “is it in X?”\n\nSo “yap” + “utxi” = is it in the field?\n\nThen what is “yap” + “p”psa?\n\nPossibility: “p”psa” is not a standard form — but perhaps it's a misspelling?\n\nWait — typo? Original says: yapp”psa\n\nCould it be yap + p”psa?\n\nBut in other forms — is there a word like “is it in the field”?\n\nWe have yaputxi → yes.\n\nBut what if “p”psa” is a different suffix?\n\nAlternative: look at p”ak”unhpsa → “my pot too”\n\nWe have:\n- “unh” → my?\n- “psa” → too?\n\nSo “unh” + “psa” → my + too?\n\nSimilarly, in yapsanpsa → “in our1+2 field too” → “san” = our1+2, “psa” = too\n\nSo “psa” consistently means “too”\n\nTherefore, “p”psa” → likely “in the field too”?\n\nBut that would require “in” + “field” + “too”\n\nWe have yaputxi = “is it the field?” — which is “in the field?”\n\nSo perhaps yap + utxi = “is it in the field?”\n\nThen yapp”psa → maybe a mistake?\n\nBut let’s consider the three items:\n\n1. utnhantxi → “is it in my house?”\n\n2. yapp”psa → ?\n\n3. yapup”psa → ?\n\nNote that:\n\n- yaputxi → “is it the field?” → field \n- yapsanpsa → “in our1+2 field too” → in field too \n- yapup”psa → yap + up”psa → what?\n\nWait — in p”ak”unhpsa → “my pot too” → so “unhpsa” = my + too?\n\nBut we have no such structure in field.\n\nAlternatively, perhaps the suffix -antxi, -stxi, -utxi are used with nouns to form “is it in X?”\n\nBut in yapp”psa → yap is field → p”psa = “too”?\n\nThen yapp”psa = “in the field too”?\n\nBut that would be “in our1+2 field too” → we have that as yapsanpsa\n\nUnless the possessive marker san is missing?\n\nWe have qucxst”psa → from our1+2 lake too → includes “our1+2”\n\nmarkstxi → is it our1+2 town? → includes our1+2\n\nSo 1+2 = our (group)\n\nThus, the structure for:\n\n- specific place with possession + question or location\n\nBut for the given words:\n\n1. utnhantxi → utnha = my house → antxi = is it in? → “is it in my house?”\n\n2. yapp”psa → yap = field → p”psa → so “in the field too”? But “too” is marked by psa.\n\nBut we also have a word yaputxi = is it the field?\n\nSo p”psa” is not “too” when in field?\n\nBut in other cases, “psa” = too.\n\nHowever, in yapp”psa, there is no “in” marker — only the word.\n\nAnother clue: in p”ak”unhpsa → my pot too → unhpsa = my + too\n\nSimilarly, utnha → my house\n\nSo might “unhpsa” be “my + too”?\n\nBut “p”psa” → could be “in + field”?\n\nBut we have yaputxi = “is it the field?” → so “in the field” is implied.\n\nSo", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11180.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 186.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nutnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?", + "planner_output": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\n\n\nRe-examine all noun bases and question forms.\n\nList all words with “txi”:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll are of form: [base] + “txi” → is it in [base]?\n\nSo “txi” = is it in?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” → is it in my house?\n\nThis is consistent.\n\n2. yapp”psa” → no “txi” → not a question → must be a statement.\n\nWhat is the base?\n\n“yap” = field → from yaputxi.\n\n“psa” = too → from examples.\n\nSo “yapp”psa” = field too?\n\nBut “field too” — is that grammatically valid?\n\nWe have “p”ak”unhpsa” = my pot too → possessive + too.\n\nNo “field too” with possessive.\n\nBut might be a general “too”?\n\nSo yapp”psa” → the field too?\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” is not a known morpheme.\n\nBut “up” could be a typo for “un”?\n\n“un” appears in “unhpsa” → “unhpsa” = my pot too → “unh” = my\n\nSo “un” = my?\n\n“unh", + "anchor_output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start by analyzing the verb structure. The key verb is *baNgul*, which appears in sentences like:\n\n- (9) *bala garan baNgul biñéiriñéu banéan* → \"The lizard is following the smoke.\"\n- (13) *bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan* → \"The mother-in-law is looking at the smoke.\" Here, *baNgun* is used for \"looking at\", while *baNgul* is used for \"following\".\n\nThus, *baNgul* specifically means \"to follow\" — a directional or spatial action from one entity to another.\n\nNow examine sentence 17: \n**17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.**\n\nBreak it down:\n- *balan* = the strong one / the one with a property; in context, \"balan\" is often used with a noun to describe a person with a quality.\n- *ñalNga* = \"quiet\" → \"the quiet one\"\n- *baNgul* = \"is following\"\n- *NumaNgu* = \"the one that is always being followed\" → passive state\n- *guniymuNagu* = \"the one that is searching\" → active state\n- *bambunman* = \"the one who is healthy\"\n\nSo, *NumaNgu guniymuNagu bambunman* = \"the one who is always being followed and is searching for the healthy one\"\n\nThus, the full structure is: \n\"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nThis matches the pattern seen in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is following the strong father.\" \nHere, *Numa* is the subject (passive: being followed), and *guli* = \"is following\", so the subject is performing the action.\n\nIn sentence 17, *NumaNgu* is the object of \"following\" — so it is being followed (passive), not the one doing the following.\n\nTherefore, it is not the subject, but the object — confirming the grammatical role.\n\nNow sentence 18: \n**18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.**\n\n- *bala* = the one (subject)\n- *diban* = \"fat\"\n- *bilmbalmuNa* = \"the one who is always pushing stones\" (based on 12: “fat doctor is pushing the big stone” → \"diban\" = fat; \"bilmbal\" = pushing)\n- *baNgun* = \"is looking at\"\n- *biñéiriñéu* = \"the smoke\"\n- *guniñu* = \"the little feather\" (or \"the feather\", contextually)\n\nSo: \"The fat one is looking at the smoke\" — but the object is the smoke, and \"biñéiriñéu\" is the smoke.\n\nBut notice: in (9), *bala garan baNgul biñéiriñéu banéan* → lizard is following smoke. \nHere, *baNgun* = \"looking at\", which is different from *baNgul* = \"following\".\n\nSo *baNgun* = \"to look at\", a directional verb, but different in semantics from *baNgul* = \"to follow\".\n\nThus, sentence 18: \"The fat one is looking at the smoke.\"\n\nBut the object is \"biñéiriñéu\", which is \"smoke\" — confirmed by earlier use.\n\nSo translation: \"The fat one is looking at the smoke.\"\n\nNow sentence 19: \n**19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.**\n\n- *bayi* = the one that is (passive? or agent?)\n- *bargan* = likely \"the one and only\", or \"the one with the property\" → similar to \"silent\" or \"the one who is never speaking\"? From context, *bargan* may be a noun meaning \"the one who is always searching\" or similar.\n- *baNgul* = is following\n- *yaóaNgu* = \"the one that is always being blamed\" → from (1), \"boozed is making the man that is always being blamed tired\"\n- *gubimbuluNunéanaymuNagu* = \"the one that is always being followed\" → similar to *NumaNgu*\n- *banéan* = the smoke\n\nSo: the subject is \"the one who is searching\" (bargan), and it is following someone with two properties:\n- always being blamed\n- always being followed\n\nThus: \"The one who is searching is following the one who is always being blamed and always being followed.\"\n\nCheck consistency: in (1), \"bayi yaóa...\" → \"boozed is making the man that is always being blamed tired\" → shows \"yaóa\" = \"always being blamed\"\n\nIn (16): \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father\" → shows \"Numa\" = being followed, and \"yaóaNgu\" = being blamed.\n\nSo, *yaóaNgu* = \"the one that is always being blamed\"\n\nThus in (19): \n\"bargan\" → likely \"the one who is searching\" \n→ \"is following\" → \"baNgul\" \n→ \"yaóaNgu gubimbuluNunéanaymuNagu banéan\" → \"the one who is always being blamed and always being followed\"\n\nSo: \"The one who is searching is following the one who is always being blamed and always being followed.\"\n\nFinal translations:\n\n17. The quiet one is following the one who is always being followed and is searching for the healthy one. \n18. The fat one is looking at the smoke. \n19. The one who is searching is following the one who is always being blamed and always being followed.\n\n\\boxed{b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the smoke; b.3: The one who is searching is following the one who is always being blamed and always being followed}", + "generated_tokens": 1450, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the smoke; b.3: The one who is searching is following the one who is always being blamed and always being followed", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 4829.0, + "ioling_final_answer_chars": 252.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.", + "planner_output": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "anchor_output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "The quiet one is following the one who is always being followed and is searching for the healthy one. \nThe fat one is looking at the one who is being followed and is searching for the one who is being looked at. \nThe death adder is following the one who is always being offended and is looking for the one who is being searched for.\n\n\\boxed{b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the one who is being followed and is searching for the one who is being looked at; b.3: The death adder is following the one who is always being offended and is looking for the one who is being searched for}", + "generated_tokens": 156, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the one who is being followed and is searching for the one who is being looked at; b.3: The death adder is following the one who is always being offended and is looking for the one who is being searched for", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 688.0, + "ioling_final_answer_chars": 344.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.", + "planner_output": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "anchor_output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "The quiet one is following the one who is always being followed and is searching for the healthy one. \nThe fat one is looking at the quiet one who is searching for the bent spear. \nThe death adder is following the man who is always being followed and is searching for the healthy one.\n\n\\boxed{b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the quiet one who is searching for the bent spear; b.3: The death adder is following the man who is always being followed and is searching for the healthy one}", + "generated_tokens": 134, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: The quiet one is following the one who is always being followed and is searching for the healthy one; b.2: The fat one is looking at the quiet one who is searching for the bent spear; b.3: The death adder is following the man who is always being followed and is searching for the healthy one", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 592.0, + "ioling_final_answer_chars": 296.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "planner_output": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "anchor_output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given 17 sentences in Dyirbal and their English translations. We are to translate three new sentences (17, 18, 19) into English.\n\nWe will analyze the structure of the given examples, identifying patterns in word order, affixes, and semantic roles.\n\nStep 1: Identify common structure.\n\nNotice that many sentences follow a pattern:\n\n[Agent] + [verb] + [object] + [modifier phrase]\n\nOr:\n\n[Agent] + [verb] + [modifier phrase] + [object]\n\nE.g., \n1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman. \n→ \"Booze is making the man that is always being blamed tired.\" \n→ Subject: boozy agent (bayi) → verb: is making → object: man → modifier: \"always being blamed\"\n\n2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu. \n→ \"The strong man is blaming the mother that is always following death adders.\" \n→ Subject: strong man → verb: blaming → object: mother → modifier: \"always following death adders\"\n\nSo: \n[agent] + [verb] + [object] + [modifier phrase describing object]\n\nThe modifier is applied to the object. The modifying element often includes:\n- an adjective or state (like \"always being blamed\", \"always following\")\n- a noun phrase (like \"death adders\", \"sugar\", \"smoke\")\n\nSome verbs:\n- \"yaóa\" → \"is making\" (in 1)\n- \"yabu\" → \"is blaming\" (in 2)\n- \"waymin\" → \"is making\" (in 3)\n- \"gurugu\" → \"is making\" (in 5, 8)\n- \"garan\" → \"is following\" (in 9, 13)\n- \"duNan\" → \"is searching\" (in 10)\n- \"diban\" → \"is fat\" (as state, in 12, 13)\n\nWe see:\n- \"guran\" or \"garan\" means \"to follow\"\n- \"diban\" means \"fat\"\n- \"mali\" or \"malayigara\" → \"smoke\"\n- \"bambun\" → \"sugar\"\n- \"gurugugu\" → \"booze\"\n- \"biNgunman\" → \"tired\"\n- \"biñéiriñéu\" → \"lizard\" (in 9, 15)\n- \"Numa\" → \"strong\"\n- \"guli\" → \"death adders\"\n- \"bunda\" → \"grassy thing\"?\n- \"bubu\" → \"quick\", \"quiet\"?\n\nWe identify recurring patterns:\n\n1. The verb often comes after the agent. \n2. The object (which can be a noun or a modified noun) appears after the verb. \n3. The modifier (adjective or noun phrase) is attached to the object via a possessive or relative structure. \n4. The noun \"Numa\" → \"strong\" (as in 2 and 16) \n5. \"baNgul\" → \"is carrying\" or \"is following\"? \n - In 2: \"is blaming\" → \"yabu\" → so not necessarily \"carrying\" \n - In 11: \"mother that is always being ignored\" → \"NaéilmuNagu\" = \"being ignored\" \n - In 12: \"fat doctor\" → \"diban éagiñ\" → \"fat\" + \"doctor\" \n - In 13: \"mother-in-law that is always pushing stones\" → \"dibanbilmbalNaymuNagu\" → \"fat\" + \"mother-in-law\" + modifier\n\nWe observe the structure of modifiers:\n- \"NunéaymuNa\" → \"is always being blamed\"\n- \"bimabanéalNaymuNa\" → \"is always following\"\n- \"éugagunman\" → \"is tired\"\n- \"gubimbulu\" → \"tired doctor\" or \"offended father\" (in 6 and 8)\n\nSo, it seems that the pattern for describing an object is:\n[adjective phrase] + [noun] \nAnd that this adjective phrase is attached via a suffix or affix.\n\nWe also see:\n- \"baNgul\" → often follows an agent and precedes a noun or object → \"is following\" or \"is carrying\"\n- In 9: bala garan baNgul biñéiriñéu banéan → \"lizard is following the smoke\"\n- In 13: bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan → \"mother-in-law is looking at smoke\" → note: \"waymindu\" is \"always pushing\", \"dibanbilmbal\" = fat mother-in-law\n\nNow, look at the new sentences.\n\nSentence 17: balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n\nBreak it down:\n- balan → agent → \"the strong\" or \"the one who is strong\" → in sentence 2, \"balan\" = strong man → \"Numa\" means \"strong\"\n- ñalNga → this is likely an adjective. In example 15: “biñéiriñ” = quiet boy → so “ñalNga” likely means “quiet” or “quiet one”\n- baNgul → verb, \"is following\"\n- NumaNgu → \"the strong one\"\n- guniymuNagu → likely a modified noun; “guni” appears earlier in 16: “guli” → death adders; “guli bar” → “following death adders”\n- bambunman → \"sugar\" → “bambun” = sugar, “-man” may mean “is making” or “is causing”\n\nWait. But “baNgul” is “following”, and “bambunman” → if it means “is making sugar”, that doesn’t fit.\n\nCould “bambunman” be “sugar that is making”?\n\nBut in example 1: “bayi yaóa NunéaymuNa baNgu gurugugu biNgunman” → “booze is making the man that is always being blamed tired”\n\nSo “yaóa” = making, then \"biNgunman\" = tired → the object becomes tired.\n\nSimilarly, “bambunman” could be “sugar is making” → so “bambun” = sugar → “man” = tired → “bambunman” = sugar is making the man tired?\n\nBut in sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nIf \"baNgul\" means \"is following\", then:\n\"The quiet one is following the strong one that is always being followed by sugar makers?\" → strange.\n\nAlternative: Structure might be:\n[agent] + [verb] + [object] + [modifier]\n\nThe verb is \"baNgul\" = \"follows\"\n\nSo: \"The quiet [agent] is following [object] + [modifier]\"\n\nThe object is \"NumaNgu\" → \"the strong one\"\n\nThe modifier is \"guniymuNagu\" → possibly \"that is always being followed by\" or \"that is always being pursued by\"?\n\nBut compare to sentence 2: “biman bimabanéalNaymuNa” → \"strong man is following the mother that is always following death adders\"\n\nSo \"bimabanéalNaymuNa\" → \"that is always following death adders\"\n\nThus, \"guniymuNagu\" → likely \"that is always being followed by [something]\"\n\nBut in example 16: “guli baNgul yaóaNgu banéalmuNagu munduman” → “the man that is always being followed is offending the strong father”\n\nSo \"banéalmuNagu\" = “is being followed”\n\n\"guniymuNagu\" → “is being followed by”?\n\nBut usually the pattern is: [noun] + [verb] + [that is always being + [adjective]]\n\nBut in the new one: “NumaNgu guniymuNagu bambunman”\n\nPossibly: \"NumaNgu\" = the strong one \n\"guniymuNagu\" = that is always being followed by \n\"bambunman\" = sugar that is making?\n\nBut sugar making what?\n\nWait — in sentence 3: \"balan waymin bambun baNgu éugaNgu éamiman\" → \"sugar is making the healthy mother-in-law fat\"\n\nSo \"waymin\" = \"is making\" \n\"bambun\" = sugar \n\"baNgu\" = the object \n\"éugaNgu\" = healthy \n\"éamiman\" = fat\n\nSo \"making\" is a verb, and the object is “the healthy mother-in-law”, and it’s being made fat.\n\nSo “bambunman” → may be “sugar is making” → and “man” = person → so “sugar is making the man fat”?\n\nBut “bambunman” appears only with “baNgul”.\n\nIn sentence 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → “big grasshopper is searching for the bent spear”\n\n\"baNgay\" = searching \n\"waóu\" = big \n\"baNgun\" = for \n\"bundiñéu\" = bent \n\"éagiñéu\" = spear\n\nSo object is spear with adjective.\n\nBack to 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\"\n\n\"baban\" is not clearly functioning as mere sugar. \"bambunman\" may be the object of the verb \"is making\", not \"is following\".\n\nWait — but the verb is \"baNgul\" = following.\n\nSo perhaps the sentence is:\n\n\"The quiet one is following the strong one that is always being followed by sugar makers?\"\n\nUnlikely.\n\nAlternative: Could “bambunman” be a compound involving \"making\"?\n\nIn sentence 4: \"bala yila wura baNgul bargandu biNgundu guniñu\" → \"the tired wallaby is searching for the little feather\"\n\nSo verb “baNgul” = “searching for” — so “baNgul” may mean “searching for”\n\nIn example 14: “baNgay” = searching → “baNgay” is different from “baNgul”\n\nSo “baNgul” appears with “follow” or “carry”\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → “lizard is following the smoke”\n\nIn 13: “bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan” → “mother-in-law is looking at (the) smoke”\n\nSo “baNgul” = “following”\n\nSo sentence 17: “the quiet one is following the strong one that is always being followed by sugar?”\n\nBut that’s odd.\n\nAnother possibility: “guniymuNagu” is a relative clause modifying “NumaNgu”\n\nAnd “bambunman” is a resulting state.\n\nCompare to sentence 8: “bayi gurimbulu biNgun baNgu gurugugu éagunman” → “booze is making the tired doctor fall asleep”\n\nSo “gurimbulu” = “tired” → “biNgun” = the tired → “gurugugu” = booze → “éagunman” = fall asleep\n\nSo \"making someone tired\" → verb + object + result\n\nBut no such \"making\" in 17.\n\nWait — perhaps the verb is not \"following\" but \"making\".\n\nCould “baNgul” be a variant of “yaóa” or “waymin”?\n\nIn 2: “yabu” = blame \nIn 6: “gurugu” = booze \nIn 12: “diban” = fat\n\nNo.\n\nAnother idea: “bambunman” could be a noun phrase meaning \"sugar is making\" — so it modifies the object.\n\nBut “NumaNgu” is being followed by sugar that is making?\n\nStill feels off.\n\nLook at sentence 15: “bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan” → “the quiet boy is looking at the tired lizard”\n\n“biñéiriñ” = quiet boy \n“biNgun” = tired \n“baNgul” = looking at \n“ñalNgaNgu” = tired lizard? \n“mugurugu” = quiet? \n“buóan” = feather?\n\nWait — “ñalNgaNgu” = the tired one \nSo \"the quiet boy is looking at the tired lizard\"\n\nThus, structure: agent + verb + [object] + [modifier]\n\nIn 15: \nagent: bayi biñéiriñ → quiet boy \nverb: biNgun baNgul → “is looking at” \nobject: ñalNgaNgu → the tired lizard \nmodifier: nil\n\nSo “baNgul” = “looking at” → not just “following”\n\nSimilarly, in 3: “bambun baNgu” → sugar is making → so “baNgu” = the object\n\nSo in example 9: “bala garan baNgul biñéiriñéu banéan” → \"lizard is following the smoke\"\n\n\"garan\" = follow \n\"baNgul\" = following? \nBut \"biñéiriñéu\" = lizard? — no\n\nWait — \"bala\" = lizard \n\"garan\" = follow \n\"baNgul\" = ? — but no object following\n\nActually: \"bala garan baNgul biñéiriñéu banéan\"\n\nPossibly: lizard is following the smoke (biñéiriñéu) — then banéan = smoke?\n\n“banéan” = smoke → earlier in 9: “banéan” = smoke\n\nIn 13: “dibanbilmbalNaymuNagu buóan” → “mother-in-law that always pushes stones is looking at smoke”\n\nSo “baNgun” = looking at\n\nSo “baNgul” may not be “following” in all cases.\n\nBut in 2: \"baban yabu\" → \"strong man is blaming\"\n\n\"yabu\" = blame → verb\n\nIn 9: \"garan\" = follow → verb\n\nSo verb can be different.\n\nSo “baNgul” may be a dative or prepositional phrase.\n\nIn 14: “baNgay” = search \n“baNgul” = follow\n\nThey are different verbs.\n\nSo now, back to 17: “balan ñalNga baNgul NumaNgu guniymuNagu bambunman”\n\nLet’s identify morphemes:\n\n- balan → agent → \"the strong\"\n- ñalNga → likely an adjective → \"quiet\"\n- baNgul → verb → “follows”\n- NumaNgu → \"the strong one\" → could be the object\n- guniymuNagu → \"that is always being followed by\"\n- bambunman → \"sugar is making\"?\n\nBut again, if “baNgul” = “follows”, and “bambunman” is a relative, then:\n\n“The quiet one is following the strong one that is always being followed by sugar that is making [someone]?”\n\nBut what?\n\nAlternatively, perhaps “bambunman” is the object of the following.\n\nIs “bambunman” a noun? In sentence 3: “bambun” = sugar\n\n“bambunman” = sugar is making?\n\nIn sentence 1: “gurugugu biNgunman” → “booze is making the man tired”\n\nSo “biNgunman” = \"the man is tired\"\n\nSimilarly, “bambunman” = “the man is being made by sugar” → sugar is making the man tired?\n\nBut in this sentence, the verb is \"baNgul\", not \"yaóa\"\n\nSo unless “baNgul” means “is making”, which seems not the case.\n\nBut in sentence 4: “yila wura baNgul bargandu” → “is searching for the little feather”\n\nSo “baNgul” = “searching for”\n\nSimilarly, in 9: “bala garan baNgul biñéiriñéu banéan” → “lizard follows the smoke”\n\nSo “baNgul” = “follows”\n\nSo “bambunman” must be the object being followed.\n\nBut “bambunman” is not a noun, it's a compound.\n\nPerhaps “bambunman” = “sugar” — but only “man” is the ending.\n\nNo other \"man\" compound.\n\nAnother possibility: “guniymuNagu” is a relative clause modifying the object “NumaNgu”\n\nAnd “bambunman” is the thing being followed.\n\nSo: “the quiet one is following the strong one that is always being followed by sugar”\n\nBut that is redundant.\n\nCompare to sentence 2: “biman bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu” → “the strong man is blaming the mother that is always following death adders”\n\nSo: agent + verb → verb = \"blaming\" → object = \"mother\" → \"that is always following death adders\" → \"bimabanéalNaymuNa\" → \"that is always following\" + \"death adders\"\n\nSo structure: [agent] [verb] [object] [that is always doing X with Y]\n\nSimilarly, in 17: \nagent: balan ñalNga → \"the quiet one\" \nverb: baNgul → \"following\" \nobject: NumaNgu → \"the strong one\" \nmodifier: guniymuNagu → \"that is always being followed by\" + \"bambunman\" → sugar?\n\n“bambunman” → “sugar is making”?\n\nBut “sugar” does not “make” in this context.\n\nCould “bambunman” be a noun meaning \"maker of something\"?\n\nIn 3: sugar is making the mother-in-law fat — so sugar is the agent.\n\nSo in 17: “the strong one is being followed by sugar that is making [something]”\n\nBut there's no object.\n\nUnless “bambunman” is an adjective.\n\nBut no.\n\nAnother idea: “bambunman", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 3.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12453.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 472.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "anchor_output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start with the given verb forms and their English translations.\n\nFirst, identify key patterns:\n\n- Person markers:\n - First person singular: \"ne-\"\n - Second person plural: \"ke-\"\n - Third person: \"kaw-\"\n\n- Verb roots and semantic domains:\n\n1. \"kewǣpeqtaq\" = we1+2 begin → root: \"wǣp\" + \"eq\" (begin) → suggests \"wǣp\" = begin\n2. \"wǣpohnæw\" = he begins walking → again \"wǣp\" + \"ohnæw\" → so \"wǣp\" is \"begin\"\n3. \"kepītahtæq\" = we1+2 come eating it → \"ke\" + \"pītahtæq\" → \"pītaht\" = come eating\n4. \"pītenam\" = he passes it here → \"pī\" + \"ten\" → so root \"pī\" = pass\n5. \"kekēskahtæq\" = we1+2 bite it through → \"ke\" + \"kēs\" + \"kaht\" → \"kēs\" = bite\n6. \"pāhkeh\" (pāhkeqtaw) = he opens up → \"pāhke\" + \"qtaw\" → \"pāhke\" = open\n7. \"nekāweqtam\" = I lie down → \"ne\" + \"kāweqt\" → \"kāweqt\" = lie down\n8. \"nekāwāhpem\" = I fall over laughing → \"ne\" + \"kāwāh\" + \"pem\" → \"kāwāh\" = fall over\n9. \"nekǣtahan\" = I pry it out by tool → \"ne\" + \"kǣta\" + \"han\" → \"kǣta\" = pry out\n10. \"kawāham\" = he fells it by tool → \"kaw\" + \"āha\" → \"āha\" = fell\n11. \"pahkǣsam\" = he cuts it off → \"pahk\" + \"ǣs\" → \"pahk\" = cut\n12. \"tawǣsam\" = he cuts a hole in it → \"taw\" + \"ǣs\" → \"taw\" = cut a hole\n13. \"pāhkaham\" = he opens it by tool → \"pāhka\" + \"ham\" → \"pāhka\" = open by tool\n14. \"ketǣnam\" = he takes it out by hand → \"ket\" + \"ā\" + \"nam\" → \"ket\" = take out\n15. \"keq\" in \"kekēskahtæq\" and others suggests a suffix pattern.\n\nNow, analyze each translation in b:\n\n1. \"I begin to eat it\"\n\n- We need: first person singular (\"ne-\"), \"begin\", and \"to eat it\"\n- \"begin\" root is \"wǣp\" (from wǣpohnæw, kewǣpeqtaq)\n- \"eat\" does not appear directly, but \"come eating\" appears in \"kepītahtæq\" = we1+2 come eating it\n- \"pītaht\" = come eating → may be related to \"begin to eat\"\n- But \"begin\" and \"come\" are separate: \"wǣp\" is for begin, \"pī\" is for come\n- Is there a verb root for \"eat\"?\n- \"kepītahtæq\" = we come eating → \"eating\" is the activity → \"tæq\" may be the verbal ending or aspect marker\n- \"eating\" is a progressive or ongoing action\n- Synonym for \"begin\" might be used with \"eating\"\n- But no form with \"ne\" + \"wǣp\" + something with \"eating\"\n- However, \"pītaht\" is the root for eating? Possibly — if \"come eating\" implies starting to eat\n- But in \"kepītahtæq\", \"come\" is used, not \"begin\"\n- Yet \"begin\" and \"come\" are parallel in meaning in context\n- But is there a way to use \"wǣp\" + \"eating\"?\n\nWait — in \"kepītahtæq\", we have \"we come eating it\" — so \"pītaht\" = come eating\nBut \"we begin to eat\" would be parallel — perhaps the verb \"to begin\" can be combined with a complement like \"eating\"\n- But no verb form for \"I begin to eat\"\n- However, \"ne\" + root for \"begin\" → ne wǣp?\n- No form in data with \"ne wǣp\"\n- But \"ne\" appears with \"kāweqtam\", \"nekāwāhpem\", \"nekǣtahan\" → so \"ne\" is used with verbs of lying, falling, prying\n- \"begin to eat\" may not be a direct compound\n- But \"come\" and \"begin\" are different\n- However, in some languages, \"begin\" and \"come\" are fused\n- But in the data, \"begin\" = wǣp, \"come\" = pī?\n- \"pītenam\" = he passes it here → pī = pass\n- No word for \"eat\"\n- So maybe \"eating\" is derived from \"pītaht\"\n- But that verb is for \"come eating\"\n- So perhaps \"begin to eat\" = \"begin + to eat\" = not found\n- However, the form \"kepītahtæq\" is \"we come eating\", so likely \"pītaht\" = to begin to eat?\n- But that contradicts wǣp being \"begin\"\n\nAlternative: could \"begin to eat\" be \"ne wǣpītahtæq\"?\n\n- \"wǣpītahtæq\" → would mean \"I begin to eat it\"\n- In \"kepītahtæq\" = we come eating — the \"ke\" is for we, \"pītaht\" is the verb\n- So \"pītaht\" is part of a verb that means \"come eating\"\n- But \"wǣp\" is separate: begins walking, begins\n- So \"wǣp\" and \"pī\" are distinct\n- So \"wǣp + pītaht\" = begin + come eating? Unlikely\n\nBut maybe the root for \"begin\" is used syntactically with \"eating\" in a different way.\n\nAnother idea: is there a verb for \"eat\" that can be combined?\n\nWe have no standalone \"eat\" verb.\n\nBut \"kepītahtæq\" includes \"eating\" — so \"pītaht\" may be the verb meaning \"eat\" or \"consume\"\n\nSo in form \"ne pītahtæq\" = I eat it?\n\nBut no such form exists.\n\nWe have \"ne\" + verb roots: \n- nekāweqtam = I lie down\n- nekāwāhpem = I fall over laughing\n- nekǣtahan = I pry it out\n\nAll are verbs with specific actions.\n\nSo for \"I begin to eat it\", there is no direct form.\n\nBut let’s look for another.\n\nWait: in \"kepītahtæq\" = we1+2 come eating it → \"come\" and \"eating\" are fused.\n\nIs \"begin\" used similarly?\n\nIn \"wǣpohnæw\" = he begins walking → \"wǣp\" + \"ohnæw\" → \"begin\" + \"walking\"\n\nSo \"begin\" is marked by \"wǣp\", and it combines with a noun or action.\n\nSo \"begin to eat\" would be \"wǣp + eating\"\n\nSo \"ne wǣp + eating\" → need a form for \"eating\"\n\nFrom \"kepītahtæq\", \"eating\" is expressed by \"pītaht\"\n\nBut in that form, \"pītaht\" is combined with \"come\"\n\nSo perhaps \"pītaht\" = eat or eat through\n\nSo for \"I begin to eat it\", it may be \"ne wǣpītaht\"\n\nBut that is not in the data.\n\nBut pattern: \"we begin\" = kewǣpeqtaq → \"ke\" + \"wǣp\" + \"eqtaq\"?\n\n\"eqtaq\" may be the ending.\n\n\"we begin\" = kewǣpeqtaq → root \"wǣp\", suffix \"eqtaq\"?\n\n\"we begin walking\" = wǣpohnæw → wǣp + ohnæw\n\nSo roots are not always combined.\n\nBut perhaps \"begin to eat\" requires \"wǣp\" + \"eating\"\n\nSo \"ne wǣpītaht\" — but no word for eating\n\nBut is \"pītaht\" used for \"eating\"?\n\nOnly in \"kepītahtæq\"\n\n\"kepītahtæq\" = we come eating → so only used with \"we\"\n\nSo no form with \"ne\" + \"pītaht\"\n\nThus, no clear form.\n\nBut perhaps the verb \"pītaht\" is used in first person as well — but not in data.\n\nWait — another possibility: is \"begin to eat\" the same as \"come to eat\"?\n\nIn some languages, \"begin\" and \"come\" are used interchangeably.\n\nBut \"come\" is used in \"kepītahtæq\" = we come eating it.\n\nSo \"come eating\" = start to eat?\n\nYes — so \"come\" can mean \"begin\".\n\nSo then \"come\" is used as a synonym for \"begin\".\n\nSo \"I begin to eat\" = \"I come to eat\" = \"ne pītaht\"?\n\nBut \"pītaht\" is not standalone.\n\n\"kepītahtæq\" is \"we come eating\", with \"it\" implied.\n\nSo \"ne pītahtæq\" might mean \"I come eating it\"\n\nBut no such form exists.\n\nBut in \"ne\", we have verbs like \"ne kāweqtam\" — first person with verb roots.\n\nSo perhaps \"ne pītahtæq\" would be valid.\n\nBut is \"pītaht\" the verb?\n\nCompare: \"pītenam\" = he passes it here → \"pī\" + \"ten\" → not \"pītaht\"\n\n\"pītaht\" appears in \"kepītahtæq\" — only with \"ke\"\n\nSo no evidence of standalone form.\n\nBut perhaps \"pītaht\" is the root.\n\nFollowing semantic alignment: \"begin\" is in \"wǣp\", \"come\" in \"pī\"\n\nIn \"kepītahtæq\", both \"come\" and \"eating\" are embedded.\n\nSo for \"I begin to eat\", if \"begin\" is equivalent to \"come\", then it may be \"ne pītaht\"\n\nBut \"pītaht\" is not \"begin\", it's \"come\"\n\nSo no.\n\nBut the only verb root for \"begin\" is \"wǣp\"\n\nSo \"I begin to eat\" must involve \"wǣp\"\n\nSo \"ne wǣp\" + \"eating\"\n\nNow, what form is \"eating\" in?\n\nFrom \"kepītahtæq\" → \"eating\" is \"taht\"\n\nIn \"kepītahtæq\", \"taht\" is part of the verb — \"tahtæq\"\n\n\"æ\" is a vowel, so \"tahtæq\" = eating\n\nSo \"taht\" may be the root for \"eating\"\n\nBut not with \"ne\"\n\nSo, in first person: \"ne wǣp taht\" or \"ne wǣpītaht\"?\n\nBut not in data.\n\nBut pattern from similar verbs:\n\n- \"we begin\" = kewǣpeqtaq → \"ke\" + \"wǣp\" + \"eqtaq\"? \"eq\" might be a suffix\n- \"he begins walking\" = wǣpohnæw → \"wǣp\" + \"ohnæw\"\n\nSo \"wǣp\" combines with action.\n\nSo \"begin to eat\" = \"wǣp\" + \"eating\"\n\nSo \"ne wǣpītaht\" — combining \"ne\" + \"wǣp\" + \"ītaht\"\n\nBut \"ītaht\" may come from \"pītaht\"\n\nBut \"pītaht\" appears only with \"ke\"\n\nSo likely, the verb \"begin to eat\" is not directly available.\n\nBut in the absence of a better form, and given that \"come eating\" is in the data, and \"begin\" may be used in place of \"come\", then perhaps \"ne pītahtæq\" is intended.\n\nBut \"pītaht\" is not \"begin\", it's \"come\"\n\nSo conclusion: no direct form.\n\nBut perhaps \"pītaht\" is the verb root used for \"begin eating\" — so it is used for both.\n\nOr is there a different pattern?\n\nLook at the second request:\n\n2. \"we1+2 lay it flat by hand\"\n\nWe need: \"we1+2\" = \"ke-\" or \"kew\"\n\n\"lay\" — what verb means \"lay flat\"?\n\nWe have:\n- \"kepītahtæq\" = come eating\n- \"pāhkeqtaw\" = he opens up\n- \"ketǣnam\" = he takes it out by hand\n- \"nekǣtahan\" = I pry it out by tool\n- \"pahkǣsam\" = he cuts it off\n- \"tawǣsam\" = he cuts a hole in it\n\nNo verb for \"lay flat\"\n\nBut \"lay flat\" might be \"place it flat\"\n\nIs there a verb for \"place\"?\n\nClosest is \"kepītaht\" = come eating — not place.\n\n\"pāhkeqtaw\" = open up\n\n\"ketǣnam\" = take it out by hand — opposite of lay\n\n\"ne\" actions are for lying/down\n\nNo verb for \"lay flat\"\n\nBut \"kewǣpeqtaq\" = we begin — not relevant\n\nWait — \"pāhkaham\" = he opens it by tool — open\n\nNo static placement.\n\nBut perhaps \"lay\" is used as \"place\", and no form exists.\n\nBut maybe from \"walk out\" or \"pass\"?\n\nNo.\n\nThird request:\n\n3. \"he digs a hole\"\n\nWe have:\n- \"kewǣpānæhkæq\" = we1+2 begin to dig → so \"kewǣpānæhkæq\"\n- Root is \"wǣpān\" = begin to dig?\n\n\"we begin to dig\" = kewǣpānæhkæq → so \"wǣpān\" = begin to dig\n\nSo \"he digs a hole\" = third person, so \"kaw\" + \"wǣpān\" → but \"kaw\" + what?\n\nFrom \"kewǣpānæhkæq\" = we begin to dig → \"kew\" + \"wǣpānæhkæq\"\n\n\"we\" = kew, so \"kaw\" = he → \"kaw wǣpān\" + something?\n\nThe form may be \"kaw wǣpānæhkæq\"? But that would be \"he begin to dig\" — illogical.\n\nBut \"begin to dig\" is the verb, not \"dig a hole\"\n\nSo is \"dig a hole\" the same as \"begin to dig\"? No.\n\nWe have \"tawǣsam\" = he cuts a hole in it → \"cuts a hole\"\n\nSo \"cut a hole\" = tawǣsam\n\n\"dig a hole\" — is that the same as \"cut a hole\"?\n\nIn meaning, perhaps not — \"dig\" is from soil, \"cut\" from material.\n\nSo no direct verb for \"dig a hole\"\n\nBut \"begin to dig\" is available in \"kewǣpānæhkæq\"\n\nSo maybe \"he digs a hole\" = \"kaw wǣpānæhkæq\"? But then it's \"he begins to dig\" — not \"he digs\"\n\nSo not the same.\n\nBut is there a verb in data for \"dig\"?\n\nOnly \"begin to dig\" — so no standalone \"dig\"\n\nSo \"he digs a hole\" must be formed from the root \"wǣpān\", with \"kaw\"\n\nSo \"kaw wǣpān\" + suffix?\n\n\"we begin to dig\" = kewǣpānæhkæq\n\nSo the full verb is \"kewǣpānæhkæq\"\n\nSo the stem is \"wǣpānæhkæq\"\n\nSo for \"he\" = \"kaw\" + \"wǣpānæhkæq\" = \"kaw wǣpānæhkæq\"\n\nBut this means \"he begins to dig\" — not \"he digs a hole\"\n\nBut perhaps in context, \"dig a hole\" = \"begin to dig\" — not accurate.\n\nBut is there another verb?\n\nWe have no \"dig\" verb.\n\n\"cut a hole\" = tawǣsam\n\n\"cut\" is different.\n\nSo unless \"dig\" is a type of \"cut\", it may not be.\n\nBut in Menominee, \"dig\" might be covered under \"begin to dig\"?\n\nUnlikely.\n\nSo perhaps the intended form is \"kaw wǣpānæhkæq\" — as \"he begins to dig\"\n\nBut the translation says \"he digs a hole\", not \"he begins to dig\"\n\nSo not matching.\n\nFourth request:\n\n4. \"he walks out\"\n\nWe have:\n- \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣto\" + \"hnæq\" → so root \"kǣto\" = walk out\n\nSo \"we walk out\" = kekǣtohnæq\n\nThird person → \"kaw\" + kǣto → \"kaw kǣtohnæq\"\n\nSo \"he walks out\" = kaw kǣtohnæq\n\nThis is consistent.\n\nNow go back to second: \"we1+2 lay it flat by hand\"\n\nWhat verb means \"lay flat by hand\"?\n\nWe have:\n- \"ketǣnam\" = he takes it out by hand — take out\n- \"kepītahtæq\" = we come eating\n- \"pāhkeqtaw\" = he opens up\n- \"ne\" = first person\n\nNo verb for \"lay flat\"\n\nBut \"lay flat\" may be a variant of \"place\"\n\nClosest: \"pāhkeqtaw\" = open up — not place.\n\n\"walk out\" = kaw kǣtohnæq\n\n\"begin\" = wǣp\n\nPerhaps \"lay it flat\" is not a standard verb.\n\nBut maybe there is a verb that means \"place it flat\" —", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11146.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.", + "planner_output": "\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\n\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\n\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\n\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n", + "anchor_output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "We are given a list of Menominee verb forms with English translations. We are to translate four sentences into Menominee, based on the patterns in the provided examples.\n\nLet’s go step by step.\n\n1. \"I begin to eat it\" \nWe are looking for a verb meaning \"begin to eat\". \nWe see: \n- \"kewǣpeqtaq\" = we1+2 begin \n- \"kekǣtohnæq\" = we1+2 bite it through \n- \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it \n- \"wǣpohnæw\" = he begins walking \n- \"kewǣpānæhkæq\" = we1+2 begin to dig \n\nThe verb \"begin\" appears with \"kewǣ-\" and \"wǣp-\" as roots. \n\"begin to eat\" should logically involve \"begin\" + \"eat\". \nBut no verb combines \"begin\" with \"eat\". However, we have \"kekǣtohnæq\" = \"we1+2 bite it through\", and \"ketāwahtæq\" = \"we1+2 bite, gnaw a hole in it\". \n\"eat\" is closely related to \"bite\" in meaning. \n\"bite it\" is used in surface forms. Perhaps \"eat\" can be modeled as \"gnaw\", which is close. \nSo, \"I begin to eat it\" → likely derived from \"begin\" + \"bite\" = \"begin to gnaw\". \nBut we need a form with \"I\" (first person singular) and \"begin\". \nWe have \"kewǣpeqtaq\" = we1+2 begin — no first person. \n\"begin to dig\" is \"kewǣpānæhkæq\" — we1+2. \nIs there a first-person \"begin\"? We don’t have it. \nBut \"begin\" is also in \"wǣpohnæw\" for \"he begins walking\". \nCould \"begin to eat\" be expressed as a variant of \"begin\" + \"bite\"? \nBut no first-person \"begin to bite\". \nWait — is \"bite\" used in the form with \"he\" or \"we\"? \n\"kēskenam\" = he breaks it through by hand \n\"ketǣnam\" = he takes it out by hand \n\"kekǣtohnæq\" = we1+2 bite it through \n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it \n\nSo \"bite\" is used in \"we1+2\" forms. \nNo \"I bite\". \nBut we may need to generalize: perhaps \"begin to eat\" = \"begin to bite\" → a compound. \nBut no such form. \n\nAlternatively, is there a verb for \"eat\"? Not directly. \nBut “eat” is a common action. Let’s consider if \"bite\" in the given data can be interpreted more broadly. \n\"bite\" is used in \"gnaw\", which is strong. \nSo \"begin to gnaw\" might be \"begin to eat\". \nBut again, no form with \"begin\" and \"gnaw\" in first person. \n\nHowever, look: is there a verb that means \"begin\" with a different root? \n\"we1+2 begin\" is \"kewǣpeqtaq\" \n\"he begins walking\" is \"wǣpohnæw\" \nSo \"begin\" as a verb is used with different roots depending on the meaning. \n\nNow: \"I begin to eat it\" \nIf \"eat\" ≈ \"gnaw\" (from \"ketāwahtæq\"), and \"begin\" is expressed via \"kewǣ-\" or \"wǣp-\", then perhaps \"I begin to gnaw\" must be formed. \nBut no first person in such forms. \n\nWait — look at \"nekāweqtam\" = I lie down \n\"nekāwāhpem\" = I fall over laughing \n\"nekǣtahan\" = I pry it out by tool \n\"pītenam\" = he passes it here \n\"ketǣnam\" = he takes it out by hand \n\"kekēskahtæq\" = we1+2 bite it through \n\nFirst person singular is used in: \n- nekāweqtam (I lie down) \n- nekāwāhpem (I laugh) \n- nekǣtahan (I pry it out by tool) \n\nSo first person exists with specific roots. \n\nSimilarly, \"we1+2\" is \"we and you\". \n\nNow, the verb for \"begin\" appears with \"kewǣ-\" for \"we1+2\" and \"wǣp-\" for \"he begins walking\". \n\nSo \"I begin to eat it\" → could be modeled from \"wǣpō-\" or \"kewǣ-\" with a root for \"eat\". \n\nBut no direct verb. \n\nHowever, \"begin to eat\" is not in the list, but the closest related action is \"begin to bite\". \n\nPerhaps the verb \"begin to eat\" is not directly given, but we can assume that the verb for \"bite\" (from \"kepītahtæq\") is related. \n\nWait — \"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths \nThis is \"come eating\", not \"begin to eat\". \n\nBut \"come eating\" is a form of consuming. \n\nSo perhaps \"begin to eat\" is not straightforward. \n\nBut look: all action verbs use the root + suffix. \n\nTry to find a verb with \"lay\" or \"put\". \n\n2. \"we1+2 lay it flat by hand\" \nWe are to translate this. \nLook for verbs with \"lay\", \"put\", \"place\", or \"set down\". \n\nWe see: \n- \"kēskenam\" = he breaks it through by hand \n- \"ketǣnam\" = he takes it out by hand \n- \"nekǣtahan\" = I pry it out by tool (tool) \n- \"pahkǣsam\" = he cuts it off \n- \"tawǣsam\" = he cuts a hole in it \n- \"pāhkeqtaw\" = he opens up \n\nNo verb with \"lay\", \"put\", \"set\", or \"place\". \n\nBut look at \"pāhkeqtaw\" = he opens up — could this be related? \n\"open up\" is not \"lay flat\". \n\nWhat about \"pahkǣsam\" = he cuts it off — not \"lay flat\". \n\n\"lay it flat\" might mean to place it down on a surface. \n\nIs there a root meaning \"place\"? \n\nThe only verb that has \"by hand\" is: \n- \"kēskenam\" = breaks by hand \n- \"ketǣnam\" = takes out by hand \n- \"nekǣtahan\" = prys out by tool \n\nSo \"by hand\" is used with break, take out, pry. \n\n\"lay\" is not directly covered. \n\nBut consider: \"lay flat\" might be equivalent to \"place down\", which is similar to \"set down\". \n\nIs there a verb like \"set\"? Not in list. \n\nWait — perhaps \"pāh\" is used for opening, cutting. But \"pāhkeqtaw\" = opens up. \n\nNo verb for \"place\". \n\nBut perhaps we can infer that \"lay\" is not covered, but in Menominee, \"by hand\" is used in multiple contexts. \n\nBut no verb combines \"lay\" + \"by hand\". \n\nAlternative: perhaps \"lay it flat\" is meant to be translated using a verb such as \"place\" or \"set\", and the only verb close might be from \"pāh\" meaning \"to open\", or from \"kew\" meaning \"begin\", or from \"kepī\". \n\nBut none. \n\nWait — look at \"pītenam\" = he passes it here \n\"pahkǣsam\" = he cuts it off \n\"tawǣsam\" = cuts a hole \n\"pāhkeqtaw\" = opens up \n\nNo \"place\". \n\nSo for \"we1+2 lay it flat by hand\", we may need to infer a form based on a root meaning \"to place\" or \"to put\". \n\nBut none exist. \n\nNow: \"he digs a hole\" \nWe see \"kewǣpānæhkæq\" = we1+2 begin to dig \n\"pahkǣsam\" = he cuts it off \n\"tawǣsam\" = he cuts a hole in it \n\n\"he cuts a hole in it\" = tawǣsam \n\"he digs a hole\" = more likely \"digs\", which may be equivalent to \"cut\" or \"make a hole\". \n\n\"begins to dig\" = kewǣpānæhkæq — \"we1+2\" begin to dig \n\n\"he digs a hole\" → look for a verb with \"dig\" or \"make a hole\". \n\n\"tawǣsam\" = he cuts a hole in it → this is likely the verb for \"cut a hole\", which may be a subset of \"dig a hole\". \n\n\"dig\" and \"cut\" may be similar. \n\nIn the list, \"tawǣsam\" = he cuts a hole in it → so \"he cuts a hole\" = tawǣsam \n\nBut \"he digs a hole\" = may be equivalent. \n\nSo \"he digs a hole\" = tawǣsam? \n\nBut tawǣsam has \"he\", and \"cuts a hole in it\". \n\n\"dig\" may be synonymous with \"cut a hole\". \n\nSo likely, tawǣsam is used here. \n\nBut tawǣsam is \"he cuts a hole in it\" — which is very close to \"he digs a hole\". \n\nSo \"he digs a hole\" → tawǣsam \n\nNow, \"he walks out\" \nWe see: \n- \"kekǣtohnæq\" = we1+2 walk out \n- \"wackōhnæw\" = he walks roundabout, by a detour \n- \"ketǣnam\" = he takes it out by hand \n- \"pāhkaham\" = he opens it by tool \n\n\"we1+2 walk out\" = kekǣtohnæq \n\"he walks out\" → should be a form with \"he\" and \"walk out\". \n\nBut \"kekǣtohnæq\" is for \"we1+2\". \n\nIs there a form for \"he walks out\"? \n\n\"kepītahtæq\" = we1+2 come eating it — not walking \n\n\"wackōhnæw\" = he walks roundabout — a detour, not \"out\" \n\n\"keke\" roots? \n\n\"kekǣtohnæq\" = we1+2 walk out \n\"ke\" may be root for \"walk\" — kewǣpeqtaq = begin, kewǣpānæhkæq = begin to dig, kekǣtohnæq = walk out \n\nSo \"walk out\" is in \"kekǣtohnæq\" — we1+2. \n\nBut the target is \"he walks out\". \n\nIs there a verb for \"he walks out\"? \n\nWe don’t have it. \n\nBut all verbs in the list have either \"we1+2\" or \"he\" with specific forms. \n\nSo for \"he walks out\", we might need to infer from \"kekǣtohnæq\" with \"he\" instead of \"we1+2\". \n\nBut the form for \"he\" is never given for \"walk out\". \n\n\"wackōhnæw\" = he walks roundabout — different from \"walk out\". \n\n\"keke\" forms? No. \n\nBut perhaps \"he walks out\" is \"kekǣtohnæq\" with a different subject. \n\nBut in Menominee, verbs may have subject agreement. \n\nSo perhaps \"he walks out\" = kekǣtohnæq with subject \"he\", but we don’t have a standalone form. \n\nBut in the list, \"walking\" is only in \"wǣpohnæw\" = he begins walking, and \"kekǣtohnæq\" = walk out. \n\nSo \"walk out\" is expressed as kekǣtohnæq — which is for \"we1+2\". \n\nThus, for \"he walks out\", we may use a form like kekǣtohnæq, but with subject \"he\". \n\nBut is there a root for \"walk\"? Yes, \"ke\" in \"kekǣtohnæq\" — \"ke\" + \"kǣto\" = walk. \n\nAnd \"wǣpohnæw\" = he begins walking — \"wǣp\" root. \n\nSo \"walk\" as a verb has two forms: \n- wǣpohnæw = he begins walking \n- kekǣtohnæq = we1+2 walk out \n\n\"walk out\" seems to be \"kekǣtohnæq\" — which is used for \"we1+2\". \n\nBut since the verb is \"he walks out\", and no form is given, we must assume that \"walk out\" is expressed in the form \"kekǣtohnæq\" with the subject \"he\", or we infer that \"he walks out\" is analogous to \"we1+2 walk out\", but with subject \"he\". \n\nBut no such form is in the list. \n\nAlternatively, is \"walk out\" given in \"wackōhnæw\"? No, that's a detour. \n\nSo the closest is \"kekǣtohnæq\" — walk out — with \"we1+2\". \n\nBut for \"he\", we don't have a form. \n\nPerhaps the verb root \"ke\" + \"kǣtohnæq\" is used. \n\nBut all forms are given with subject specified. \n\nNow, go back to the first sentence: \"I begin to eat it\" \n\nWe have no verb for \"eat\", but \"bite\" is present. \n\n\"begin to eat\" = begin to bite? \n\nWe have \"kepītahtæq\" = we1+2 come eating it — brings it in mouth — related to eating. \n\n\"ketāwahtæq\" = we1+2 bite, gnaw a hole in it — so \"bite\" is used. \n\n\"begin to eat\" → not directly, but \"begin to gnaw\" could be a stretch. \n\nBut no first person form. \n\nBut first person verbs are present: \n- nekāweqtam = I lie down \n- nekāwāhpem = I fall over laughing \n- nekǣtahan = I pry it out by tool \n\nSo perhaps \"I begin to eat it\" → use \"kewǣ\" root with \"eat\" root. \n\nBut no such root. \n\nAnother possibility: the verb for \"begin\" with \"eat\" is missing, but \"eat\" is not in the list. \n\nBut in Menominee, \"eat\" may be built from \"bite\" or \"gnaw\". \n\nSo \"I begin to eat it\" = I begin to bite it → using the root \"ke\" or \"kew\". \n\nBut \"begin\" is in \"kewǣpeqtaq\" for we1+2. \n\nSo for first person, we may use the root \"kewǣ\" as in \"we1+2 begin\". \n\nBut first person? \n\n\"we1+2\" = \"we and you\" — so \"I\" is not included. \n\nFirst person singular is not used with \"begin\" in the list. \n\nYet, \"I lie down\" = nekāweqtam — so first person exists with different roots. \n\nSo for \"begin\", there may be no first person form. \n\nBut the request is to translate \"I begin to eat it\" — so it must be possible. \n\nPerhaps \"begin to eat\" is not the primary meaning, but the action of \"gnaw\" is used. \n\nBut still. \n\nPerhaps the verb root for \"eat\" is not listed, but the closest is \"bite\", so \"I begin to bite it\". \n\nNow, is there a form for \"I begin to bite\"? \n\nWe have \"we1+2 bite it through\" = kekǣtohnæq \n\"we1+2 bite, gnaw\" = ketāwahtæq \n\nSo \"bite\" is used in we1+2. \n\nNo first person. \n\nBut perhaps the verb for \"begin\" with \"bite\" is \"kewǣ\" + \"bite\" → \"kewǣp[...]\". \n\nBut no example. \n\nPerhaps the pattern is that verbs with \"begin\" use \"kewǣ-\" and the action is added. \n\nFor example: \n- kewǣpeqtaq = begin \n- kewǣpānæhkæq = begin to dig \n\nSo \"begin to eat\" = kewǣp[eat]? \n\nBut what is the root for \"eat\"? \n\nNo such root. \n\nBut if we assume that \"eat\" ≈ \"gnaw\", then maybe \"kewǣp...\" with gnaw root. \n\nBut no such form. \n\nWait — look at \"kepītahtæq\" = we1+2 come eating it — \"come eating\" — not begin. \n\n\"come eating\" may mean \"start to eat\" — so \"come eating\" = start to eat. \n\nSo perhaps \"begin to eat\" is \"come eating\". \n\nSo \"I come eating it\" → but \"come eating\" is \"we1+2 come eating it\". \n\nWe need \"I come eating it\"? \n\nNo first person. \n\nBut \"we1+2\" = \"we and you\", not \"I\". \n\nSo no. \n\nThus, for \"I begin to eat it\", we may have to use a form like \"I begin to gnaw it\" — which is not given. \n\nBut perhaps the only pattern is that \"begin\" is combined with a root. \n\nFor \"he digs a hole\" = tawǣsam (he cuts a hole in it) — so likely tawǣsam. \n\nFor \"he walks out\" = we have kekǣtohnæq = we1+2 walk out — so for \"he\", if no form, it may be interpreted as kekǣtohnæq with subject, or perhaps it's not given. \n\nBut wait — another verb: \"wackōhnæw\" = he walks roundabout — not out. \n\n\"keke\" root? \n\nPerhaps the verb for \"walk out\" is not directly listed, but the only verb for \"walk\" is in kekǣtohnæq. \n\nSo for \"he walks out\", we must use kekǣtohnæq with \"he\" as subject. \n\nBut in the list, \"we1+2 walk out\" is given. \n\nPerhaps \"he walks out", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12200.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Target: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.", + "planner_output": "\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\n\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\n\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\n\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n", + "anchor_output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "Step 1: Analyze the given verb forms and their translations to identify common roots and patterns.\n\nList of given forms:\n\n- kewǣpeqtaq → we1+2 begin \n- kawāham → he fells it by tool \n- nepītohnæm → I walk here (to this place) \n- kēskenam → he breaks it through by hand \n- pahkǣsam → he cuts it off \n- kekǣtohnæq → we1+2 walk out \n- pītenam → he passes it here \n- kewǣpānæhkæq → we1+2 begin to dig \n- tawǣsam → he cuts a hole in it \n- nekǣtahan → I pry it out by tool \n- pāhkaham → he opens it by tool \n- kekēskahtæq → we1+2 bite it through \n- wackōhnæw → he walks roundabout, by a detour \n- newāckesan → I cut around it \n- ketǣnam → he takes it out by hand \n- ketāwahtæq → we1+2 bite, gnaw a hole in it \n- wǣpohnæw → he begins walking \n- nekāweqtam → I lie down \n- pāhkeqtaw → he opens up \n- kepītahtæq → we1+2 come eating it; we1+2 bring it in our mouths \n- nekāwāhpem → I fall over laughing \n\nStep 2: Identify verbs related to \"eat\", \"lay flat\", \"dig a hole\", and \"walk out\".\n\nFirst, \"I begin to eat it\".\n\nLook for a verb meaning \"begin to eat\".\n\nWe have:\n- kepītahtæq → we1+2 come eating it; we1+2 bring it in our mouths \n→ This involves \"eating\" or \"bringing into mouth\", which is close.\n\nBut is there a direct verb for \"begin to eat\"?\n\nThe only verb with \"eating\" is kepītahtæq, which involves bringing food into mouth — \"come eating\" or \"bring in mouth\".\n\nPossibly, \"begin to eat\" could be derived from this. But \"begin\" is already in \"kewǣpeqtaq\" and \"wǣpohnæw\".\n\n\"Begin\" appears in:\n- kewǣpeqtaq → we1+2 begin \n- wǣpohnæw → he begins walking \n\nSo \"begin\" is a root or auxiliary.\n\nWe need \"I begin to eat it\". The verb \"eat\" is implied in \"kepītahtæq\" – \"bring in mouth\".\n\nSo perhaps \"I begin to eat it\" = \"I begin bringing it into mouth\".\n\nThus, possibly \"kewǣpeqtaq\" + \"kepītahtæq\"? But not a compound.\n\nBut note: \"kepītahtæq\" is in the \"we1+2\" form, not \"I\".\n\nWe need \"I\" form.\n\nNo standalone \"I begin to eat\" verb.\n\nPossible derivation: \"begin\" + \"eat\".\n\nBut in the language, \"begin\" verbs may combine with action verbs.\n\n\"kepītahtæq\" → \"we1+2 come eating it\" → implies \"eating\" is the main verb.\n\n\"Begin to eat\" → could be a form of \"begin\" + \"eat\".\n\nIs there a \"begin to eat\" form?\n\nWe have \"kewǣpeqtaq\" → \"we1+2 begin\" — but no subject.\n\nBut we have \"wǣpohnæw\" → \"he begins walking\" — so \"begin\" is a verb.\n\nSo \"begin\" is a prefix or root.\n\n\"kepītahtæq\" is about eating.\n\nBut is there a form like \"begin + eat\"?\n\nNo direct form. Thus, likely a combination: \"I begin to eat\" = \"I begin bringing it in mouth\" → possibly \"kewǣpeqtaq\" + \"kepītahtæq\", but must find form.\n\nWait — all verbs are simple. Perhaps the verb is derived from \"kepītahtæq\" with \"begin\".\n\nBut no such form.\n\nAnother possibility: the verb \"come eating\" is \"kepītahtæq\". \"I come eating\" = I begin eating.\n\nSo perhaps \"I begin to eat it\" = \"I come eating it\".\n\nBut \"come eating\" is not \"begin\".\n\n\"Begin\" is distinct.\n\nBut note: \"kewǣpeqtaq\" = we begin → may act as a root.\n\nBut no \"I begin to eat\".\n\nLook again: \"kepītahtæq\" = we1+2 come eating it.\n\n\"Come eating\" might imply the start of eating — so \"begin eating\".\n\nSo \"I begin to eat it\" might be the \"I\" form of \"come eating\" → nekā? + \"kepītahtæq\"?\n\nBut no \"I\" form of that.\n\nAlternatively, no verb for \"begin to eat\" exists directly.\n\nBut among the given verbs, only \"kepītahtæq\" has \"eating\" — and \"we1+2\".\n\nSo likely, the translation of \"I begin to eat it\" is \"**nekā** + **kepītahtæq**\" → but no such form.\n\nWait — \"ne\" is used for \"I\" in several verbs:\n\n- nepītohnæm → I walk here \n- nekǣtahan → I pry it out \n- nekāweqtam → I lie down \n- nekāwāhpem → I fall over laughing\n\nSo subject marker \"ne\" is used for \"I\".\n\nSimilarly, \"we1+2\" is marked with \"ke\" or \"kew\".\n\nSo \"I begin to eat it\" → likely uses \"ne\" + \"begin\" + \"eat\".\n\nWhere is \"begin + eat\"?\n\n\"kepītahtæq\" has \"eating\" — so perhaps \"ne + kepītahtæq\"?\n\n\"ne\" + \"kepītahtæq\" → \"I come eating it\"?\n\nIs \"come eating\" equivalent to \"begin to eat\"?\n\nIn context, yes — \"come eating\" implies starting to eat.\n\nThus, \"I begin to eat it\" = \"I come eating it\" → **nekāpītahtæq**? But no such form.\n\nWait — the form is \"kepītahtæq\", not \"pītahtæq\".\n\nSo breaking it down: the verb root is \"pītahtæq\".\n\nSo \"ne\" + \"kepītahtæq\" → \"I come eating it\".\n\nYes — likely.\n\nBut is this a valid form?\n\nWe have \"ne\" in other verbs like \"nekāweqtam\", \"nekāwāhpem\", so \"ne\" is used for \"I\".\n\nAnd \"kepītahtæq\" is the verb for \"we1+2 come eating it\".\n\nSo likely, the \"I\" form is \"ne + kepītahtæq\" → **nekāpītahtæq**?\n\nBut in the form, it's \"kepītahtæq\", not \"pītahtæq\".\n\nIn \"kepītahtæq\", the \"ke\" is part of \"we1+2\".\n\nSo \"ke\" is the subject prefix for \"we1+2\".\n\nFor \"I\", it should be \"ne\".\n\nSo the verb for \"I come eating it\" is **ne + pītahtæq**?\n\nBut the form is \"kepītahtæq\" → so \"ke\" + \"pītahtæq\" = \"we1+2 come eating\".\n\nThus, removing \"ke\" and replacing with \"ne\", we get **ne + pītahtæq**.\n\nBut is \"pītahtæq\" a valid form?\n\nWe don’t have \"ne\" + \"pītahtæq\", but we have \"ne\" in other forms.\n\nHowever, \"ne\" + \"pītahtæq\" would be \"I come eating\".\n\n\"Come eating\" = beginning eating.\n\nSo likely, \"I begin to eat it\" = \"I come eating it\" → **ne pītahtæq** → but with the root.\n\nBut in the data, \"kepītahtæq\" → \"we1+2 come eating it\" → so the verb is \"pītahtæq\".\n\nSo \"I begin to eat it\" = **ne pītahtæq** → likely **ne pītahtæq**.\n\nBut is it written as \"ne pītahtæq\"?\n\nPerhaps not — the verb forms have the subject prefix attached.\n\nSo \"ne + pītahtæq\" → **ne pītahtæq**? But the original form is \"kepītahtæq\".\n\nOnly change is subject from \"ke\" to \"ne\".\n\nSo \"ne pītahtæq\" — yes, but is \"pītahtæq\" the root?\n\nWait — in \"kepītahtæq\", \"ke\" is the subject, \"pītahtæq\" is the verb.\n\nSo without \"ke\", with \"ne\" → **ne pītahtæq**.\n\nBut the root may not be independent.\n\nYet, in the absence of a standalone \"I begin to eat\", and given that \"come eating\" starts an eating action, this is the only plausible match.\n\nSo: **ne pītahtæq**\n\nBut the form given is \"kepītahtæq\" — so root is \"pītahtæq\".\n\nTherefore, \"I come eating it\" → **ne pītahtæq**\n\nSo answer to first item: **ne pītahtæq**\n\nStep 3: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay flat by hand\".\n\nWe have:\n\n- nepītohnæm → I walk here \n- kēskenam → he breaks it through by hand \n- ketǣnam → he takes it out by hand \n- kepītahtæq → we1+2 come eating it (bring in mouth) \n- pahkǣsam → he cuts it off \n- kekǣtohnæq → we1+2 walk out \n- kewǣpānæhkæq → we1+2 begin to dig \n\nIs there a verb for \"lay flat\"?\n\n\"lay flat\" → \"place it flat\".\n\nBy hand → \"by hand\".\n\nWe have verbs with \"by hand\" or \"by hand\".\n\n- kēskenam → breaks it through by hand \n- ketǣnam → takes it out by hand \n- pāhkaham → opens it by tool \n- nekǣtahan → prys it out by tool \n\nSo \"by hand\" appears in \"kēskenam\", \"ketǣnam\".\n\nBut not \"lay flat\".\n\n\"lay flat\" may imply a directional placement.\n\nIs there a verb for \"place\"?\n\nWe have no direct verb.\n\nBut \"we1+2 walk out\" → \"kekǣtohnæq\"\n\n\"we1+2 walk here\" → not given.\n\n\"lay flat\" could be a passive or derived form.\n\nPossible that \"lay flat\" is derived from a verb like \"place\".\n\nBut no such verb.\n\nWait — \"kewǣpānæhkæq\" = we1+2 begin to dig → implies digging.\n\n\"pahkǣsam\" = cuts it off → not flat.\n\n\"pītenam\" = passes it here → movement.\n\n\"pāhkeqtaw\" = he opens up → opening.\n\nNo verb for \"lay flat\".\n\nBut perhaps \"we1+2 lay it flat by hand\" is a translation of \"we1+2 place it flat by hand\".\n\nIs there a verb root for \"place\"?\n\nWe have \"walk\" → \"nepītohnæm\", \"kekǣtohnæq\".\n\nNo \"place\".\n\nBut perhaps \"lay\" is a form of \"place\".\n\nAlternatively, is there a verb for \"set down\"?\n\nNot in the list.\n\nHowever, in Menominee, verbs may be used with context.\n\nBut from the list, only \"walk\" and \"break\", \"take\", \"cut\" are present.\n\nWait — the form for \"he walks\" is \"wackōhnæw\" → he walks roundabout.\n\n\"nepītohnæm\" → I walk here → so \"walk\" is represented.\n\nNo \"lay\".\n\nBut \"lay flat by hand\" may be equivalent to \"place it down by hand\".\n\nStill no verb.\n\nPerhaps \"kepītahtæq\" is too close to eating.\n\nAlternative: perhaps \"we1+2 lay it flat by hand\" = \"we1+2 begin to place it flat\" → but still no verb.\n\nWait — look at \"kepītahtæq\" = \"we1+2 come eating it\".\n\nNo.\n\nBut perhaps \"lay flat\" is not directly expressed.\n\nCould it be \"he takes it and lays it flat\" — but no.\n\nNo match.\n\nWait — is there a verb for \"place\"?\n\nNone in the list.\n\nBut consider: \"pāhkeqtaw\" = he opens up → may be a spatial opening.\n\nNo.\n\nAlternatively, \"we1+2 lay it flat by hand\" might be a translation of a preserved verb.\n\nBut only \"walk\" and \"cut\" and \"open\" are active.\n\nConclusion: there may be no direct verb.\n\nBut in the context, \"lay flat by hand\" might be derived from \"take and place\", or from a root.\n\nBut no example.\n\nIs there a verb like \"set\"?\n\nNo.\n\nWait — \"ne\" + \"pītahtæq\" is for eating.\n\nBut perhaps \"we1+2\" has a verb for \"put down\".\n\nNo.\n\nAlternative: \"we1+2 lay it flat\" = \"we1+2 place it flat\".\n\nBut no such verb.\n\nThus, possibly, there is a missing form — however, in the data, we have no \"lay flat\".\n\nBut let's look at structure.\n\nNote: \"he breaks it through by hand\" → \"kēskenam\"\n\n\"he takes it out by hand\" → \"ketǣnam\"\n\n\"he opens it by tool\" → \"pāhkaham\"\n\nSo verbs with \"by hand\" or \"by tool\" are marked.\n\n\"lay flat by hand\" → likely a verb with \"by hand\".\n\nBut no such verb.\n\nTherefore, the closest verb might be \"kepītahtæq\" — but that's for eating.\n\nNo.\n\nPerhaps \"we1+2 walk here\" = \"nepītohnæm\" → I walk here.\n\nWe don't have \"we1+2 walk here\".\n\n\"kekǣtohnæq\" = we1+2 walk out.\n\n\"nepītohnæm\" = I walk here.\n\nSo \"here\" is included.\n\nBut \"lay flat\" is not \"walk\".\n\nThus, no direct match.\n\nTherefore, likely \"we1+2 lay it flat by hand\" = \"we1+2 place it down by hand\".\n\nBut no verb.\n\nWait — perhaps \"kewǣpānæhkæq\" = we1+2 begin to dig.\n\n\"Begin to dig\" is given.\n\nBut \"lay flat\" is different.\n\nConclusion: missing verb — but perhaps not.\n\nAlternative idea: \"lay flat\" may be a form of \"set down\", and perhaps it is implied in \"set\" or \"put\".\n\nBut not in list.\n\nTherefore, may be a misalignment.\n\nBut look at \"pahkǣsam\" = he cuts it off.\n\n\"newāckesan\" = I cut around it.\n\n\"tawǣsam\" = he cuts a hole.\n\n\"cut\" is used.\n\n\"lay\" is not.\n\nSo perhaps no form.\n\nBut we have to pick one.\n\nPerhaps \"lay it flat\" is derived from \"place\", and no such form.\n\nBut perhaps \"we1+2 lay it flat by hand\" = \"we1+2 begin to place\" — not in list.\n\nAlternatively, is there a verb that means \"set\" or \"place\"?\n\nNo.\n\nTherefore, likely, the intended verb is missing, but in the context, \"we1+2 lay it flat by hand\" may be a translation of a verb like \"kēskenam\" or \"ketǣnam\", but these are for \"break\" or \"take\".\n\nNo.\n\nSo probably, no direct form.\n\nBut let’s move to third item.\n\nStep 4: \"he digs a hole\"\n\nWe have:\n\n- tawǣsam → he cuts a hole in it \n- kewǣpānæhkæq → we1+2 begin to dig \n\nSo \"dig\" is the meaning of \"begin to dig\" → so \"dig\" is a verb.\n\n\"he digs a hole\" → is equivalent to \"he cuts a hole in it\"?\n\nIn context, \"cut a hole\" vs \"dig a hole\" — is there a distinction?\n\n\"cut\" may mean a narrow opening; \"dig\" may mean excavation.\n\nBut in Menominee, the verb \"tawǣsam\" is given for \"he cuts a hole in it\".\n\n\"begin to dig\" is \"kewǣpānæhkæq\" → we1+2 begin to dig.\n\nSo \"he digs\" would be the singular.\n\nBut no standalone \"he digs\".\n\nSo likely, \"he digs\" = \"he cuts a hole\" → because \"cut a hole\" is a common expression.\n\nFurther, since \"dig\" is not directly represented, and \"cut a hole\" is, it's likely that in this context, \"he digs a hole\" is translated as \"tawǣsam\".\n\nTherefore, answer: **tawǣsam**\n\nStep 5: \"he walks out\"\n\nWe have:\n\n- kekǣtohnæq → we1+2 walk out \n- wackōhnæw → he walks roundabout \n- nepītohnæm → I walk here \n\nSo \"we1+2 walk out\" is \"kekǣtohnæq\".\n\n\"he walks out\" → needs singular \"he\".\n\nIs there a singular \"he walks out\"?\n\nWe have \"kekǣtohnæq\" for \"we1+2 walk out\".\n\nNo standalone \"he walks out\".\n\nBut \"we1+2\" includes \"we and you\".\n\nSo for \"he\", what can we use?\n\nWe have \"wackōhnæw\" → he walks roundabout — not \"out\".\n\nNo verb for \"he walks out\".\n\nBut \"walk out\" is \"walk out from a place\".\n\n\"he walks out\" → perhaps derived from \"walk\" with \"out\".\n\nWe have no \"he walks out\".\n\nBut we have \"we1+2 walk out\" → kekǣtohnæq.\n\nSo for \"he\", perhaps the form is missing", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12139.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Target: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.", + "planner_output": "\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\n\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\n\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\n\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n", + "anchor_output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given a list of Menominee verb forms and their English translations. We are to translate four English phrases into Menominee, using only the patterns evident from the examples.\n\n---\n\n1. \"I begin to eat it\"\n\nWe are looking for a verb meaning \"begin to eat it\".\n\nIn the list:\n- \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is a verb root.\n- \"kekǣtohnæq\" = we1+2 walk out\n- \"kewǣpānæhkæq\" = we1+2 begin to dig → so \"begin to dig\" is kewǣpānæhkæq\n\nNotice: \"begin\" appears in \"kewǣpeqtaq\" (we1+2 begin) and \"kewǣpānæhkæq\" (we1+2 begin to dig). Both start with \"kewǣp\".\n\nIf \"begin\" is the root, then the verb \"begin to eat\" would likely involve the same root with a suffix meaning \"to eat\".\n\nWe don’t have a direct verb for \"eat\", but we do have:\n- \"kepītahtæq\" = we1+2 come eating it; we1+2 bring it in our mouths → suggests “eating” is involved.\n\nAlso: \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\", which is a form of eating.\n\nGiven that \"begin\" is marked with \"ke\" in \"kekǣtohnæq\" and \"kewǣpeqtaq\", and \"we1+2\" is \"ke-\".\n\nFor \"I\", the subject is first person singular. In the examples:\n- \"nepītohnæm\" = I walk here → \"ne\" + \"pītohnæm\"\n- \"nekāweqtam\" = I lie down → \"ne\" + \"kāweqtam\"\n- \"nekǣtahan\" = I pry it out by tool → \"ne\" + \"kǣtahan\"\n\nSo the first person singular marker is \"ne-\", attaching to the verb root.\n\nTherefore, \"I begin\" would be \"ne\" + the form of \"begin\".\n\nFrom \"kewǣpeqtaq\" = we1+2 begin → root = \"kewǣp\" + \"eqtaq\"? Or the entire stem is built around \"kewǣp\".\n\nBut in \"kewǣpānæhkæq\" = begin to dig → it’s \"kewǣpānæhkæq\", so \"kewǣp\" is the base.\n\nSo likely, \"begin to eat\" would be \"ne\" + \"kewǣp\" + \"something\".\n\nBut we lack a direct form for \"eat\".\n\nHowever, look at \"kekēskahtæq\" = we1+2 bite it through → \"bite\" is separate.\n\nBut \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → again, \"bite/gnaw\".\n\n\"Come eating it\" in \"kepītahtæq\" — this suggests \"to eat\" may be embedded.\n\nBut perhaps the verb \"begin to eat\" is analogical to \"begin to dig\", which is \"kewǣpānæhkæq\".\n\nSo \"begin to eat\" might be \"ne\" + \"kewǣp\" + \"something\" for \"eat\".\n\nWe lack a direct eating verb.\n\nBut notice: \"ne\" is the subject marker for \"I\".\n\nSo perhaps \"I begin to eat\" = \"ne\" + \"kewǣpeqtaq\" → but that’s \"we1+2 begin\", not \"I\".\n\nWe need a first-person form.\n\nSo pattern: \"we1+2\" = \"ke-\", \"I\" = \"ne-\"\n\nIn \"kewǣpeqtaq\" = we1+2 begin → root = \"kewǣp\"\n\nSo \"I begin\" = \"ne\" + \"kewǣp\" → nekewǣp?\n\nBut no such form is given. However, \"ne\" is used in I-walk, I-pry, I-lie down — so it likely attaches directly.\n\nBut \"kewǣpeqtaq\" has a suffix \"eqtaq\" — meaning \"begin\"?\n\nAlternatively, is \"begin\" in the form \"kewǣp\", and \"eat\" is a separate verb?\n\nWait — \"kepītahtæq\" = we1+2 come eating it — this is a compound verb meaning \"come eating it\".\n\nBut “come eating” may not be “begin to eat”.\n\nIs there a verb meaning \"to eat\"?\n\nPossibly not directly, but perhaps \"begin to eat\" must be constructed.\n\nAlternatively, observe: \"he bites\" is \"ketāwahtæq\" — \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it.\n\nSo perhaps \"bite\" is a verb, and \"since biting is part of eating\", perhaps \"begin to eat\" is analogous to \"begin to bite\"?\n\nBut that seems stretched.\n\nWait — in \"kekēskahtæq\" = we1+2 bite it through — similar meaning.\n\nBut no verb for \"begin to eat\" is present.\n\nBut look: \"kewǣpeqtaq\" = we1+2 begin.\n\nSo perhaps \"I begin to eat it\" = \"ne\" + \"kewǣpeqtaq\"? But \"kewǣpeqtaq\" is for \"we1+2\".\n\nBut the pattern from earlier examples shows:\n- \"nepītohnæm\" = I walk here → \"ne\" + \"pītohnæm\"\n- \"nekāweqtam\" = I lie down → \"ne\" + \"kāweqtam\"\n- \"nekǣtahan\" = I pry it out by tool → \"ne\" + \"kǣtahan\"\n\nSo the structure is \"ne\" + verb root.\n\nTherefore, \"I begin\" would be \"ne\" + \"kewǣp\" — but what is the full form?\n\nThe full form for \"we1+2 begin\" is \"kewǣpeqtaq\".\n\nWhat’s the verb root? Possibly \"kewǣp\" is the root, and \"eqtaq\" is the suffix for \"begin\"?\n\nBut \"kewǣpānæhkæq\" = begin to dig → \"kewǣpānæhkæq\" — here the suffix is different.\n\nThis suggests that the verb root with \"begin\" is variable.\n\nBut \"kewǣpeqtaq\" and \"kewǣpānæhkæq\" both start with \"kewǣp\", so perhaps \"kewǣp\" is the base.\n\nSo for \"I begin\", the form would be \"ne\" + \"kewǣp\" → but with what suffix?\n\nWe have no example of \"I begin\" or \"I begin to eat\".\n\nBut perhaps \"to eat\" is not a separate verb — perhaps \"begin to eat\" is \"begin to consume\" and is not directly present.\n\nBut reconsider: \"kepītahtæq\" = we1+2 come eating it — may mean \"we come to eat it\", or \"we come to consume it\".\n\n\"come eating\" implies eating as an action.\n\nBut we still lack a direct verb for \"begin to eat\".\n\nAlternative: perhaps \"begin to eat\" is derived from \"begin\" with \"eat\" as a noun or transitive verb.\n\nBut no such form.\n\nBut observe: in Menominee, verbs are often segmented with subject markers and root verbs.\n\nGiven the absence of a direct \"eat\" verb, and that \"bite\" and \"gnaw\" are given as \"ketāwahtæq\", which includes \"bite\" or \"gnaw\", perhaps \"begin to eat\" is not directly translatable unless inferred via another verb.\n\nBut perhaps the verb \"begin\" is used with a different object.\n\nWait — perhaps \"begin to eat\" can be formed by combining the root of \"begin\" with a root for \"eat\".\n\nBut without a verb for \"eat\", we must rely on pattern.\n\nAlternatively, is there a verb with \"eat\"?\n\nNo.\n\nBut look: \"kepītahtæq\" = we1+2 come eating it — this may be a verbal noun, not \"begin to eat\".\n\nAnother possibility: \"begin to eat\" = \"ne\" + \"kewǣp\" + \"something\".\n\nBut all forms with \"begin\" start with \"kewǣp\".\n\nSo \"ne\" + \"kewǣp\" + ??\n\nBut \"kewǣpeqtaq\" has \"eqtaq\", \"kewǣpānæhkæq\" has \"ānæhkæq\".\n\nNo clear suffix.\n\nBut actually, \"kewǣp\" is the root, and the suffix indicates the action.\n\nSo perhaps \"I begin to eat\" is formed by \"ne\" + \"kewǣp\" + \"eat\" — but no such form.\n\nPerhaps it is implied that \"begin to eat\" = \"ne\" + \"kewǣpeqtaq\" — meaning I begin (it).\n\nBut \"it\" is the object.\n\nIn \"kewǣpeqtaq\" = we1+2 begin — no object.\n\nSimilarly, \"kewǣpānæhkæq\" = begin to dig — object is \"it\".\n\nSo \"begin to eat it\" may simply be \"ne\" + \"kewǣpeqtaq\" with object implied.\n\nBut \"kewǣpeqtaq\" is \"we1+2 begin\" — no object.\n\nLikewise, \"kewǣpānæhkæq\" = begin to dig — object is \"it\".\n\nSo perhaps \"begin to eat it\" is a form that should use the same root.\n\nGiven that \"begin\" is only used with \"we1+2\", and no first-person form exists, but the pattern for first person is \"ne-\", then likely \"I begin to eat it\" = \"nekewǣpeqtaq\"\n\nThis is analogous to:\n- \"nepītohnæm\" = I walk here\n- \"nekāweqtam\" = I lie down\n\nSo first-person verb = \"ne\" + verb root.\n\nSo \"begin\" root = \"kewǣp\", thus \"ne\" + \"kewǣp\" = nekewǣp → but with what suffix?\n\n\"eqtaq\" may be necessary.\n\n\"we1+2 begin\" = \"kewǣpeqtaq\", so perhaps the full verb with \"begin\" includes \"eqtaq\".\n\nTherefore, \"I begin\" = \"ne\" + \"kewǣpeqtaq\" = nekewǣpeqtaq.\n\nBut is that consistent?\n\n\"we1+2 begin\" = kewǣpeqtaq → that is the full form.\n\nIf \"I begin\" = ne + kewǣpeqtaq, that would be nekewǣpeqtaq — consistent with \"ne\" marking first person.\n\nSimilarly, \"he walks\" is \"kaw\" + stem.\n\nSo this is plausible.\n\nTherefore, \"I begin to eat it\" → nekewǣpeqtaq.\n\nBut does it specify \"to eat\"? The verb \"begin\" may be used in the context of beginning an action, including eating.\n\nSince \"begin\" is the only verb given for starting an action, and eating is an action, it's reasonable.\n\nSo tentatively: **nekewǣpeqtaq**\n\n---\n\n2. \"we1+2 lay it flat by hand\"\n\n\"we1+2 lay\" — do we have a verb for \"lay\"?\n\nLook at verbs with \"by hand\":\n\n- \"kēskenam\" = he breaks it through by hand → \"by hand\"\n- \"nekāwāhpem\" = I fall over laughing → not relevant\n- \"pāhkeqtaw\" = he opens up → not relevant\n- \"pītenam\" = he passes it here → not relevant\n\nWe have \"nepītohnæm\" = I walk here → not relevant.\n\nBut \"kēskenam\" has \"by hand\" → marker may be \"kēs\" + \"kenam\"\n\nBut no exact verb for \"lay flat\".\n\nHowever, look at \"pāhkaham\" = he opens it by tool → \"by tool\"\n\n\"nekǣtahan\" = I pry it out by tool → \"by tool\"\n\nSo \"by hand\" appears as a locative or manner marker.\n\nIn \"kēskenam\" = he breaks it through by hand → \"by hand\"\n\nThe form \"kēskenam\" may have \"kēs\" as root, and \"kenam\" as \"break through\", with \"by hand\" as an aspect.\n\nBut \"lay it flat\" — perhaps \"lay\" is similar to \"place down\", \"put down\".\n\nDo we have a verb meaning \"to put down\"?\n\nNot directly.\n\n\"we1+2 walk out\" is already established.\n\nBut \"we1+2 lay it flat by hand\" — flat, by hand.\n\nIs \"by hand\" a suffix?\n\nIn \"kēskenam\", \"by hand\" is part of the verb.\n\nBut again, no \"lay\" verb.\n\nAlternatively, \"lay flat\" may be modeled on \"walk here\" — \"nepītohnæm\", which has \"here\".\n\n\"walk here\" = \"I walk here\"\n\nBut \"lay it flat\" is a different action.\n\nPerhaps \"lay flat\" is not directly there.\n\nBut we have \"kewǣpānæhkæq\" = begin to dig — that’s not related.\n\nWait — \"pahkǣsam\" = he cuts it off → not relevant.\n\nAnother possibility: \"by hand\" is marked in the verb root.\n\nFor example, in \"kēskenam\" = he breaks it through by hand — \"kēskenam\"\n\nIn \"pāhkaham\" = he opens it by tool — \"pāhkaham\"\n\nSo likely, the verb has a body part or tool marker in the root.\n\n\"by hand\" may be part of the verb stem.\n\nBut we lack a verb for \"lay flat\".\n\nBut perhaps \"lay\" is not a standard verb — or it is analogous to \"put down\".\n\nIn Menominee, verbs may be compounding.\n\nAlternatively, possibly \"flat\" is denoted by suffix.\n\nBut we have no such form.\n\nBut notice: \"we1+2 walk out\" is given — which is \"kekǣtohnæq\"\n\nSimilarly, \"we1+2 begin to dig\" = kewǣpānæhkæq\n\n\"we1+2 come eating it\" = kepītahtæq\n\nSo \"we1+2 lay it flat\" — perhaps we need a verb root.\n\nBut none is present.\n\nPerhaps \"lay\" is implied in \"cut\" or \"break\"?\n\nNo.\n\nWait — perhaps \"lay it flat\" = \"put it down\", and in the language, that is expressed by a root like \"pāh\" or \"kā\".\n\nWe have \"pāhkeqtaw\" = he opens up — not relevant.\n\n\"pāhkaham\" = he opens it by tool — \"pāh\" is common in opening.\n\nBut no \"lay flat\".\n\nAnother idea: in Algonquian languages, \"lay\" may be derived from \"place\".\n\nBut no such verb.\n\nPerhaps the closest is \"place\" or \"put\", but not directly.\n\nBut look: \"pāhkeqtaw\" = he opens up — may involve opening something.\n\n\"kepītahtæq\" = come eating — not.\n\nPerhaps \"lay it flat\" is not a literal translation, but we must construct from pattern.\n\nBut no verb for \"lay flat\".\n\nWait — in the list, is there any verb that means \"put down\"?\n\nOnly \"walk here\" might be similar, but not.\n\nAlternatively, is \"lay it flat\" equivalent to \"set it down\"?\n\nNo clear match.\n\nBut perhaps the verb for \"lay\" is not present, so we must infer.\n\nBut we have \"we1+2 walk out\" → which is \"kekǣtohnæq\"\n\n\"we1+2 begin to eat\" → likely derived.\n\nBut we are missing a verb.\n\nPerhaps the verb \"lay\" is formed from \"pāh\" or other roots.\n\nBut no.\n\nActually, rechecking the list: no verb for \"lay flat\".\n\nBut in Menominee, actions are often marked with roots and tools.\n\n\"by hand\" is used in \"kēskenam\" — \"break it through by hand\"\n\nSo \"by hand\" is a manner marker.\n\nSo \"we1+2 lay it flat by hand\" may be a verb with \"by hand\" in the stem.\n\nBut is there a verb for \"lay\"?\n\nNot found.\n\nBut wait — is \"lay it flat\" a compound action?\n\nNo standard form.\n\nPerhaps \"lay\" is not present, so we must go with the closest.\n\nBut the only possible option is to use a verb with \"by hand\".\n\nBut no verb for \"lay\".\n\nAlternatively, is there a verb meaning \"place\"?\n\nWe have \"pāhkeqtaw\" = he opens up — not.\n\nNo.\n\nBut perhaps the only relevant pattern is the subject marking.\n\nFor \"we1+2\", the subject marker is \"ke-\".\n\nSo \"we1+2 lay it flat by hand\" = \"ke\" + verb stem.\n\nWhat is the verb stem?\n\nWe have no example.\n\nBut perhaps \"lay flat\" is not a standard verb, so we must look elsewhere.\n\nAlternatively, \"lay it flat\" may be equivalent to \"set it down\", and \"set\" is a verb.\n\nBut not in list.\n\nAnother possibility: \"kewǣpānæhkæq\" = begin to dig — digging may involve placing.\n\nNo.\n\nAll else fails — perhaps the verb is missing, but we must construct.\n\nBut we have a verb with \"by hand\": \"kēskenam\" — \"break\" with \"by hand\".\n\nSo perhaps \"lay\" is formed similarly.\n\nBut we lack a root.\n\nPerhaps \"lay\" is derived from a root like \"pāh\", but no such form.\n\nWait — \"pāhkeqtaw\" = he opens up → opens.\n\n\"pāhkaham\" = he opens it by tool → opens.\n\nSo \"pāh\" is root for \"open\".\n\nNot for \"lay\".\n\nTherefore, we cannot derive a form.\n\nBut perhaps the verb \"lay flat\" is simply \"ke\" + \"lay\" root.\n\nBut no such root given.\n\nTherefore, likely, the only possible form is to use a comparable verb.\n\nBut there is no such.\n\nPerhaps \"lay it flat\" is not a literal translation — or perhaps it's built from \"put down\".\n\nBut no.\n\nWait — is there a verb like \"set\" or \"place\"?\n\nNo.\n\nTherefore, I suspect that the verb for \"lay\" is missing, but in the context, it may be assumed to have a form like \"kewǣp", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12614.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 170.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Target: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.", + "planner_output": "\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\n\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\n\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\n\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n", + "anchor_output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 0, + "output": "The days of the Nooni week are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. \nThis is established by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon comes before Bvutfu. \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is two days after the current day (spoken on Bvusɔw). \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka. \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden. \n\nThus, the order is: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. \n\nTime reference expressions: \n- \"fɔ̀ shě X\" = \"the day after tomorrow is X\" (cf. sentence 5) \n- \"ntfǔː nú X\" = \"the day after tomorrow is X\" → consistent with \"fɔ̀ shě\" \n- \"ntfǔː nú\" = \"tomorrow is X\" → in sentence 8: \"Tomorrow is Bvuŋkaden\" \n- \"cǐ nú\" = \"yesterday was\" \n- \"bèsèn nǔ\" = \"today, we\" \n- \"wvù tɔ̀ nɔ̂ː\" = \"he found\" \n- \"me nú\" = \"I will\" or \"I am\" \n- \"kwɔ᷆ːn\" = \"the woman\" \n- \"nǔ\" = \"you (sg)\" \n- \"bóy\" = \"the woman\" \n- \"fí\" = \"help\" \n- \"cɔ́ŋ\" = \"steal\" \n- \"wáy\" = \"the market\" \n- \"é\" = \"the\" \n- \"mé\" = \"me\" \n- \"yɛ᷅n\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n- \"bɔ́\" = \"they\" \n- \"bɔ́ nɔ̂ː\" = \"they saw\" \n\nNow parse each sentence spoken on Bvuŋkaden:\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː \n→ \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" \nBut \"fɔ̀ shě X\" → \"the day after tomorrow is X\" \nSo: On Bvusɔw, you (will be such that) the day after tomorrow is Bvutfu. \nBut this is illogical — Bvusɔw is two days before Bvutfu. \nAlternative: perhaps \"bvúsɔ̀w\" is the day, and \"nǔ fɔ̀ shě\" is a temporal event. \nBut \"fɔ̀ shě ntfǔː\" is a time marker — \"the day after tomorrow is Bvutfu\". \nSo the structure is: On Bvusɔw, you have the day after tomorrow be Bvutfu. \nThis is inconsistent with temporal logic. \nYet, the pattern must be preserved. \nIn sentence 5: \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" \nDespite oddity, this is the only grammatical parse using the known pattern. \n→ \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" \n\n17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n \n\"me nú\" = \"I will\" \n\"ŋgéː\" = \"steal\" \n\"nyɛ́n\" = \"the market\" \n\"kèŋkfǔ\" = \"the yam\" \n\"lé\" = \"the\" \n\"ɛ̀bɛ̀n\" = \"woman\" \nSo: \"I will steal the market the woman\" → grammatically broken. \nWait: \"nyɛ́n\" may be \"saw\" — in sentence 15, \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"they saw me at the market\" \nSo \"yɛ᷅n\" = \"saw\" \n\"nyɛ́n\" likely = \"saw\" — but that would be \"me nú ŋgéː saw\" \nNo. But \"ŋgéː nyɛ́n\" might be \"steal and saw\"? \nNo. \nBut in sentence 2: \"you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" \nSo \"yúː cɔ́ŋ\" = \"will steal\" \n\"ŋgéː\" = \"steal\" \n\"nyɛ́n\" = \"the market\" \n\"kèŋkfǔ\" = \"the yam\" \n\"lé\" = \"the\" \n\"ɛ̀bɛ̀n\" = \"woman\" \nPossibly: \"I will steal the market from the woman\" \nBut grammar is off. \nAlternatively, \"ŋgéː nyɛ́n\" = \"steal the market\" \n\"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam the woman\"? \nNo. \nWait: in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"the woman saw the market at Bvutfu\" \nSo \"yɛ᷅n wáy\" = \"saw the market\" \nThus, \"nyɛ́n\" = \"saw the market\"? \nBut \"nyɛ́n\" = \"to see\" — must be. \nSo \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"I will steal, and saw the yam the woman\"? \nNo. \nPossibly: \"I will steal the yam that the woman saw\" — but \"nyɛ́n\" is not \"that the woman saw\" \nAnother idea: \"nyɛ́n\" = \"the market\", \"kèŋkfǔ\" = \"the yam\", so \"steal the market the yam\"? \nNo. \nPerhaps typo or misreading: \"ŋgéː nyɛ́n\" = \"steal the market\", and \"kèŋkfǔ\" = \"the yam\", \"lé\" = \"the\", \"ɛ̀bɛ̀n\" = \"woman\" → \"the yam of the woman\"? \nThen: \"I will steal the market, the yam of the woman\" — odd. \nAlternative: \"I will steal the yam, which the woman saw\"? \nBut \"nyɛ́n\" = saw. \nPossibly: \"I will steal the yam that the woman saw\" \nThis is plausible. \n\"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" → \"I will steal the yam that the woman saw\" \nYes — \"nyɛ́n\" = \"that the woman saw\" → matches \"yɛ᷅n\" pattern. \nIn sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"they saw me at the market\" \nSo \"yɛ᷅n\" = saw \n\"nyɛ́n\" = \"saw\" — must be. \nSo in this context, \"nyɛ́n\" = \"saw\" \nThen \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" = \"I will steal the yam that the woman saw\" \nYes — this fits. \n\n18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn \n\"wvù\" = \"he\" \n\"tɔ̀\" = \"found\" \n\"nɔ̂ː\" = \"the\" \n\"yɛ᷅n\" = \"saw\" \n\"bèsèn\" = \"today\" \n\"ě\" = \"the\" \n\"bvúmbòn\" = \"the market\" \n\"bèsèn ě\" = \"today the\" \nSo: \"he found the market today the woman\" — malformed. \n\"bèsèn ě\" = \"today the\" → \"today the market\"? \nWait: in sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → \"he found the book at Bvuŋka\" \nSo \"tɔ̀ nɔ̂ː\" = \"found the\" \n\"yɛ᷅n\" = \"saw\" \nSo: \"he saw the market today the woman\"? \nBut \"bèsèn ě\" = \"today the\" → \"today the market\"? \nBut \"bvúmbòn\" is \"market\" \nSo: \"he saw the market today\" — but \"ě\" is \"the\", so \"the market\" \nThus: \"he saw the market today\" \nBut the structure is: wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn \nSo: he found the market today the woman? \n\"yɛ᷅n\" = saw \nSo \"he saw the market today\" — and \"the woman\" is missing. \nBut \"ě\" = \"the\", so \"the market\" — \"bvúmbòn\" is the market \nThus: \"he saw the market today\" \nBut why \"ě\"? \nIn sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"the woman saw the market at Bvutfu\" \nSo \"yɛ᷅n wáy\" = \"saw the market\" \nSo \"yɛ᷅n\" = \"saw\" \nSo here: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" = \"he found the market today\" \nBut \"tɔ̀\" = \"found\", not \"saw\" \nIn sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\" → \"he found the book\" \nSo \"tɔ̀ nɔ̂ː\" = \"found the\" \nThus: \"he found the market today\" \nBut \"bèsèn ě\" = \"today the\", so \"today the market\" → clearly \"today the market\" \nSo: \"he found the market today\" \nBut \"ě\" appears only once — it's part of \"bèsèn ě\" \n\"bèsèn\" = \"today\", \"ě\" = \"the\" (determiner) \nSo \"today the market\" \nThus: \"he found the market today\" \nYes. \n\n19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n \n\"bèsèn nǔ\" = \"today, you\" \n\"bóy\" = \"the woman\" \n\"tɔ́\" = \"will help\" \n\"fɔ̀wǎy\" = \"the market\" \n\"bvúzhı᷇ːde᷆n\" = \"Bvuzhiden\" — the day after Bvuzhi? \nNote: days are: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden \nSo after Bvuzhi is Bvuŋka → Bvuŋkaden \nSo Bvuzhiden = day after Bvuzhi? \nBut in sentence 8: \"Tomorrow is Bvuŋkaden\" — spoken on Bvuŋka \nSo future day after Bvuzhi is Bvuŋka \nThus Bvuzhiden is Bvuŋka? No — the next day after Bvuzhi is Bvuŋka \nBut the day after Bvuŋka is Bvuŋkaden \nSo Bvuzhiden = day after Bvuzhi = Bvuŋka \nBut in the sentence: \"bvúzhı᷇ːde᷆n\" — likely Bvuzhiden \nSo: \"today, you will help the woman at the market\" \nBut \"tɔ́ fɔ̀wǎy\" = \"will go to the market\" or \"will help at the market\"? \nIn sentence 3: \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"On Bvuzhi, the woman will help me\" \nSo \"fí\" = \"help\" \nSo \"tɔ́ fɔ̀wǎy\" = \"will go to the market\" — not \"help\" \nBut if \"tɔ́\" = \"will\", and \"fɔ̀wǎy\" = \"to the market\", then \"you will go to the market\" \nBut \"bóy\" = \"the woman\", so \"you will help the woman at the market\"? \nBut \"help\" is not \"go to\" — \"fí\" = help \nSo the verb for \"help\" is \"fí\" \n\"tɔ́\" is not \"help\" — in sentence 12: \"me nú nfí dìɛ̀msɛ̌n\" → \"I am about to help the man\" \nSo \"nfí\" = \"help\" \nThus \"tɔ́\" = \"will\" or \"will go\"? \nIn sentence 4: \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà\" → \"he found the book\" → so \"tɔ̀\" = \"found\" \nIn sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"today, we will steal the car\" → \"cɔ́ŋ\" = steal, \"géː\" = steal \nSo \"tɔ̀\" and \"tɔ́\" are both present — \"tɔ́\" is likely \"will\" \nThus, \"tɔ́ fɔ̀wǎy\" = \"will go to the market\" \nSo: \"today, you will go to the market\" \nBut the woman is the subject — \"bóy\" = \"the woman\" \nSo \"you will go to the market with the woman\"? \nOr \"you will go to the market to help the woman\"? \nBut no verb for \"help\" here. \nSentence 3: \"help me\" → \"fí me\" \nSo \"tɔ́ fɔ̀wǎy\" = \"will go to the market\" \nThus: \"today, you will go to the market\" \nAnd \"bóy\" is likely the object or separator — but \"bóy\" is not with \"go\" — so syntactically, \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy\" = \"today you (will) go to the market\" \nBut \"bóy\" is \"the woman\" — where does it fit? \nAlternative: \"bèsèn nǔ\" = \"today you\", \"bóy\" = \"the woman\", \"tɔ́ fɔ̀wǎy\" = \"will go to the market\" → so \"today you will go to the market with the woman\"? \nBut no evidence. \nMore likely: \"bóy\" is the subject — but \"nǔ\" is \"you\" \nNo. \nPerhaps it's \"the woman will go to the market\" — but subject is \"nǔ\" \nOnly conclusion: \"today, you will go to the market\" \nAnd \"bóy\" is a misplacement — but in sentence 3: \"kwɔ᷆ːn nǔ bóy fí me\" → \"the woman will help me\" — so \"nǔ bóy\" = \"you the woman\"? \nNo — \"nǔ\" is subject, \"bóy\" is object — but \"fí me\" \nSo in 19: \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy\" — \"today you the woman will go to the market\" — meaningless \nPerhaps \"bóy\" is a typo for \"bóy\" as property — no. \nBest interpretation: \"today, you will go to the market\" \nBut Bvuzhiden is a day — so \"at Bvuzhiden\" \nWait — the full phrase: \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n\" \n\"bvúzhı᷇ːde᷆n\" = Bvuzhiden — a day \nSo: \"today, you will go to the market at Bvuzhiden\" — but Bvuzhiden is a day, not a place \nIn sentence 4: \"On Bvuŋka, he found the book\" — \"on X\" \nSo \"on Bvuzhiden\" might be the time \nSo: \"today, you will go to the market on Bvuzhiden\" \nBut \"today\" is present, \"on Bvuzhiden\" is future — conflicting. \nBut the sentence is spoken on Bvuŋkaden — so \"today\" = Bvuŋkaden \nSo \"on Bvuzhiden\" = a past or future day \nSo: \"on Bvuzhiden, you will go to the market\" \nAnd \"today\" might be a mistake — no. \n\"bèsèn\" is \"today\" — used as time reference \nSo likely: \"on Bvuzhiden, you will go to the market\" \nBut why \"today\" then? \nAnother possibility", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9667.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"", + "planner_output": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "anchor_output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 1, + "output": "Analyze the sentences to identify the pattern of time references in Nooni.\n\nFirst, observe the days mentioned:\n\n- Bvutfu: appears in sentences 1, 2, 5, 13, 15, and as a future day.\n- Bvusɔw: sentences 2, 4, 6, 7.\n- Bvuzhi: sentence 3.\n- Bvuŋka: sentences 4, 5, 8, 9, 10, 11, 12, 13, 14, 15.\n- Bvuŋkaden: appears in 8, 11, and the target sentences (16–19), spoken on Bvuŋkaden.\n\nNote the temporal markers:\n\n- \"Tomorrow\" → Bvuŋkaden (sentence 8: \"Tomorrow is Bvuŋkaden\")\n- \"The day after tomorrow\" → sentence 5: \"The day after tomorrow is Bvutfu\"\n- \"The day before yesterday\" → sentence 11: \"The day before yesterday was Bvuŋka\"\n- \"Today\" → sentence 6: \"Today, he killed the woman\"\n- \"Yesterday\" → sentence 1: \"Yesterday was Bvutfu\"\n- \"On Bvusɔw\" → sentence 2: \"On Bvusɔw, you will steal the yam\"\n\nNow, the key is to map relative days to fixed days based on reference points.\n\nFrom sentence 8: \"Tomorrow is Bvuŋkaden\" — so if the sentence is on Bvusɔw, tomorrow is Bvuŋkaden.\n\nBut sentence 11 says: \"The day before yesterday was Bvuŋka\". Since that is spoken on Bvuŋka, the day before yesterday was Bvuŋka → so today is Bvuŋka → yesterday was Bvusɔw, two days ago was Bvutfu? Let's validate.\n\nSequence of days:\n\n- Bvusɔw (day X)\n- Bvutfu (day X+1)\n- Bvuzhi (day X+2)\n- Bvuŋka (day X+3)\n- Bvuŋkaden (day X+4)\n\nCheck sentence 1: spoken on Bvutfu → \"Yesterday was Bvutfu\"? That can’t be. Wait.\n\nSentence 1: “spoken on Bvutfu” → “Yesterday was Bvutfu” — which would mean yesterday was Bvutfu, so today is Bvutfu → yesterday was Bvutfu → impossible.\n\nLikely error in interpretation.\n\nRe-read: “spoken on Bvutfu” — implies the sentence is being spoken on Bvutfu. So the speaker is on Bvutfu.\n\nSo day of speech is Bvutfu.\n\nSentence 1: “Yesterday was Bvutfu” → yesterday was Bvutfu → then today is Bvutfu+1 → so later day.\n\nBut only one Bvutfu in the week.\n\nSo “Yesterday was Bvutfu” → so today is Bvutfu+1.\n\nBut in sentence 5: “The day after tomorrow is Bvutfu” → so day after tomorrow is Bvutfu → so today is Bvutfu – 2.\n\nContradiction unless days are cyclic.\n\nThus, days are not linear. Instead, they form a cycle.\n\nFrom sentence 5 (spoken on Bvusɔw): \"The day after tomorrow is Bvutfu\".\n\nSo on Bvusɔw, day after tomorrow is Bvutfu → so Bvutfu is two days after Bvusɔw.\n\nFrom sentence 11 (spoken on Bvuŋka): \"The day before yesterday was Bvuŋka\" → so day before yesterday was Bvuŋka → today is Bvuŋka+2.\n\nSo in the week, the days follow a sequence.\n\nEarlier: sentence 8 (spoken on Bvukema): \"Tomorrow is Bvuŋkaden\"\n\nSo from Bvukema, tomorrow is Bvuŋkaden.\n\nFrom sentence 4 (spoken on Bvusɔw): \"On Bvuŋka, he found the book\" — so Bvuŋka is a relative day.\n\nBut we need to establish temporal order.\n\nTry to reconstruct relative days.\n\nAssume the week has fixed order.\n\nFrom sentence 5: (on Bvusɔw) — \"The day after tomorrow is Bvutfu\" \n→ Bvutfu is two days after Bvusɔw\n\nFrom sentence 11: (on Bvuŋka) — \"The day before yesterday was Bvuŋka\" \n→ so Bvuŋka is two days before today → so today is Bvuŋka+2\n\nSo today is Bvuŋka+2 → so Bvuŋka occurs two days before the day of speech.\n\nSo if the speech is on Bvuŋka, then two days earlier was Bvuŋka → contradiction.\n\nNo: the sentence is spoken on Bvuŋka → \"the day before yesterday was Bvuŋka\" → means two days before today was Bvuŋka → so today is Bvuŋka+2.\n\nThus, today is not Bvuŋka, but Bvuŋka+2.\n\nSo Bvuŋka occurs two days before.\n\nNow, we need to place other days.\n\nFrom sentence 8: spoken on Bvukema → \"Tomorrow is Bvuŋkaden\"\n\nSo Bvuŋkaden is tomorrow after Bvukema.\n\nSo in order: \nBvukema → tomorrow → Bvuŋkaden.\n\nNow, sentence 3: \"On Bvuzhi, the woman will help me\" — spoken on Bvuzhi? Not stated.\n\nAll sentences state which day they are spoken on.\n\nSentence 3: spoken on Bvuzhi — so it is on Bvuzhi.\n\nSimilarly, all others.\n\nWe know:\n\n- Bvusɔw → day X\n- Bvutfu → X+2 (from sentence 5)\n- So if Bvusɔw is X, Bvutfu is X+2 → so Bvutfu is two days after Bvusɔw\n\nFrom sentence 11: spoken on Bvuŋka — \"the day before yesterday was Bvuŋka\" → so two days before today was Bvuŋka → today is Bvuŋka+2 → so Bvuŋka is two days before the day of speech.\n\nSo if the speech is on Bvuŋka, then Bvuŋka was two days before → impossible.\n\nWait: \"The day before yesterday was Bvuŋka\" → so the day before yesterday was Bvuŋka → so today is Bvuŋka+2 → so Bvuŋka occurred two days prior.\n\nTherefore, in the week, Bvuŋka is two days before the day on which the sentence is spoken.\n\nSo when spoken on Bvuŋka, the day before yesterday was Bvuŋka → that would mean Bvuŋka was two days before today → so today is Bvuŋka+2.\n\nYes.\n\nSimilarly, sentence 1 (spoken on Bvutfu): \"Yesterday was Bvutfu\" → so yesterday was Bvutfu → so today is Bvutfu+1.\n\nBut earlier, from sentence 5: Bvutfu is two days after Bvusɔw → so Bvusɔw → Bvutfu (in two days).\n\nSo if the day of speech is Bvutfu, then yesterday was Bvutfu → so today is Bvutfu+1.\n\nSo Bvutfu occurs, and yesterday was Bvutfu → that means Bvutfu is not today, but yesterday — so today is Bvutfu+1.\n\nSo Bvutfu is one day before the day of speech.\n\nTherefore: on day D, if spoken, and yesterday was D, then D is yesterday → so day of speech is D+1.\n\nBack to time markers:\n\nLet’s list the days and their relative positions.\n\nAssume days are in a cycle: D1, D2, D3, D4, D5.\n\nUse the known:\n\n- On Bvusɔw: day after tomorrow is Bvutfu → so Bvutfu = Bvusɔw + 2\n- On Bvuŋka: day before yesterday was Bvuŋka → so Bvuŋka = today – 2 → so Bvuŋka is two days before the day of speech\n- On Bvutfu: yesterday was Bvutfu → so Bvutfu = speech day – 1 → so Bvutfu is one day before the day of speech\n- On Bvukema: tomorrow is Bvuŋkaden → Bvuŋkaden = Bvukema + 1\n\nNow, try to build a sequence.\n\nLet the day of speech on Bvusɔw be day 0.\n\nThen: \n- Day 0: Bvusɔw \n- Bvutfu = day +2 → day 2 \n- So Bvutfu at day 2\n\nNow, sentence 1: spoken on Bvutfu → day 2 \n\"Yesterday was Bvutfu\" → yesterday was Bvutfu → so Bvutfu was at day 1 → contradiction → day 2 is today, yesterday is day 1 → so Bvutfu must be at day 1.\n\nContradiction.\n\nThus, “Yesterday was Bvutfu” cannot mean Bvutfu occurred yesterday.\n\nRe-interpret: the speaker says “Yesterday was Bvutfu” — meaning at the time of speaking on Bvutfu, yesterday was Bvutfu → but that would mean the day of speech is Bvutfu, and yesterday is Bvutfu → impossible.\n\nUnless it is a typo or misgloss.\n\nCheck: sentence 1: “fɔgò cǐ nú bvúmbòn” → “Yesterday was Bvumbon”\n\nAnd the sentence is spoken on Bvutfu.\n\nSo: on Bvutfu, “Yesterday was Bvumbon” → so Bvumbon was yesterday → so Bvutfu is one day after Bvumbon.\n\nSo: Bvumbon = Bvutfu – 1\n\nSimilarly, from sentence 5: \"The day after tomorrow is Bvutfu\" — spoken on Bvusɔw → so from Bvusɔw, two days later is Bvutfu → so Bvutfu = Bvusɔw + 2\n\nNow, from sentence 8: spoken on Bvukema → \"Tomorrow is Bvuŋkaden\" → so Bvuŋkaden = Bvukema + 1\n\nFrom sentence 11: spoken on Bvuŋka → \"The day before yesterday was Bvuŋka\" → so Bvuŋka = speech day – 2\n\nSo Bvuŋka is two days before the day of speech.\n\nSo if spoken on Bvuŋka, Bvuŋka was two days before → so the day of speech is Bvuŋka + 2.\n\nNow, try to establish order.\n\nLet day 0: Bvusɔw\n\nThen:\n\n- Bvutfu = day 0 + 2 → day 2\n- Sentence 1: spoken on Bvutfu → day 2 → “Yesterday was Bvumbon” → so Bvumbon = day 1\n- So day 1 = Bvumbon\n\nSo far:\n- day 0: Bvusɔw\n- day 1: Bvumbon\n- day 2: Bvutfu\n\nFrom sentence 8: spoken on Bvukema → \"Tomorrow is Bvuŋkaden\"\n\nWe need to place Bvukema.\n\nFrom sentence 14: spoken on Bvuŋka → \"Today, we will steal the car\" → so day of speech is Bvuŋka\n\nSentence 13: \"On Bvutfu, the woman saw the market\" → so Bvutfu = day 2\n\nSentence 12: spoken on Bvuŋka → \"I am about to help the man\" → so daily reference\n\nSentence 10: spoken on Bvuŋka → \"The man is about to see him\"\n\nSentence 15: spoken on Bvuŋka → \"They saw me at the market just now\"\n\nSo all days below are captured.\n\nBack to Bvukema.\n\nNo sentence ties Bvukema to others directly.\n\nBut sentence 8: on Bvukema → tomorrow is Bvuŋkaden.\n\nSo Bvuŋkaden = Bvukema + 1\n\nNow, what about Bvuzhi?\n\nSentence 3: spoken on Bvuzhi → \"On Bvuzhi, the woman will help me\"\n\nNo temporal marker.\n\nSentence 2: \"On Bvusɔw, you will steal the yam\" — so on Bvusɔw.\n\nNow, from sentence 11: spoken on Bvuŋka — \"The day before yesterday was Bvuŋka\" → so Bvuŋka = today – 2 → so today is Bvuŋka + 2.\n\nSo if the speech is on Bvuŋka, Bvuŋka was two days before → so Bvuŋka is not the speech day — contradiction.\n\nNo: \"the day before yesterday was Bvuŋka\" — so on the day of speech (Bvuŋka), two days ago was Bvuŋka → only possible if two days ago was Bvuŋka → so Bvuŋka = speech day – 2.\n\nThus, the day of speech is Bvuŋka + 2.\n\nSo if the speech is on a day D, then D = Bvuŋka + 2.\n\nThus, Bvuŋka is two days before D.\n\nSo when the sentence is spoken on some day, Bvuŋka was on D–2.\n\nTherefore, for a sentence spoken on day D, the event \"the day before yesterday was Bvuŋka\" implies Bvuŋka = D–2.\n\nSimilarly, \"tomorrow is Bvuŋkaden\" → Bvuŋkaden = D+1, where D is day of speech.\n\nSo we can now build the relative calendar.\n\nLet’s assign days:\n\nSet day 0: Bvusɔw\n\nThen:\n- Bvutfu = day 0 + 2 = day 2 (from sentence 5)\n- On Bvutfu (day 2), \"yesterday was Bvumbon\" → so Bvumbon = day 1\n\nSo:\n- day 0: Bvusɔw\n- day 1: Bvumbon\n- day 2: Bvutfu\n\nNow, which day is Bvuzhi?\n\nSentence 3: spoken on Bvuzhi → \"On Bvuzhi, the woman will help me\"\n\nWe have no direct time link.\n\nSentence 4: spoken on Bvusɔw → \"On Bvuŋka, he found the book\" → so on Bvusɔw, Bvuŋka occurred.\n\nSo Bvuŋka = day 0 – 1? But days are cyclic.\n\nIf on day 0, Bvuŋka occurred → then Bvuŋka = day 0 or day 0 – 1?\n\nBut \"On Bvuŋka, he found the book\" — means the event happened on Bvuŋka.\n\nSo on day 0 (Bvusɔw), the reference is to Bvuŋka → so Bvuŋka is on some day.\n\nThus, the day of the event is Bvuŋka.\n\nSo if the sentence is spoken on day 0 (Bvusɔw), and it says \"On Bvuŋka, he found the book\", then the event is on Bvuŋka.\n\nSo Bvuŋka is a specific day in the week.\n\nSimilarly, from sentence 11: spoken on Bvuŋka → \"The day before yesterday was Bvuŋka\" → so Bvuŋka = speech day – 2\n\nSo if speech day is Bvuŋka, Bvuŋka = Bvuŋka – 2 → impossible.\n\nThus, the sentence is not spoken on Bvuŋka? But it is stated as “spoken on Bvuŋka”.\n\nContradiction.\n\nUnless “spoken on Bvuŋka” means the event is on Bvuŋka, but the sentence is reported as spoken on that day.\n\nBut the label is “spoken on Bvuŋka” — so the utterance is on Bvuŋka.\n\nBut then “the day before yesterday was Bvuŋka” — would mean Bvuŋka was two days before — so impossible.\n\nTherefore, the only interpretation is that “the day before yesterday was Bvuŋka” is taken relative to the speech day.\n\nSo if the speech is on day D, then D–2 = Bvuŋka → so Bvuŋka = D–2.\n\nSo if spoken on Bvuŋka, then Bvuŋka = Bvuŋka – 2 → only if two days have passed — contradiction.\n\nUnless the day of speech is not Bvuŋka, but the sentence is about Bvuŋka.\n\nBut the first part says: “spoken on Bvuŋka”\n\nSo the utterance is on Bvuŋka.\n\nThus, on Bvuŋka, the day before yesterday was Bvuŋka → impossible.\n\nTherefore, the only resolution is that “the day before yesterday was Bvuŋka” is a misgloss or error.\n\nBut in sentence 11: “kefwé cí nú bvûŋka᷆ː” → “The day before yesterday was Bvuŋka”\n\nAnd it is spoken on Bvuŋka.\n\nSo it must be that \"the day before yesterday was Bvuŋka\" refers to the day before yesterday relative to the speech day.\n\nSo on Bvuŋka, two days ago was Bvuŋka → impossible.\n\nThus, the only logical conclusion is that \"the day before yesterday was Bvuŋka\" is a mistake — or it means something else.\n\nAnother possibility: \"Bvuŋka\" is a day name, and the sentence is saying that two days before the current day, it was Bvuŋka — so current day is Bvuŋka + 2.\n\nSo if the sentence is spoken on day D, then D = Bvuŋka + 2.\n\nSo Bvuŋka = D – 2.\n\nBut the sentence is spoken on Bvuŋka — so D = Bvuŋka.\n\nTherefore, Bvuŋka = Bvuŋka – 2 → impossible.\n\nThus, contradiction.\n\nTherefore, the day of speech is not Bvuŋka.\n\nBut the problem states: “spoken on Bvuŋka”\n\nUnless “spoken on Bvuŋka” means the event is on Bvuŋka.\n\nBut the sentence says “spoken on Bvuŋka” — so the utterance is on", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12007.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Re-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"", + "planner_output": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "anchor_output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 2, + "output": "The days of the Nooni week are ordered as: Bvumbon → Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. \nThis is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → current day is Bvutfu. \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is two days after current day → current day is Bvusɔw. \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka. \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden. \nThus, Bvuŋkaden is the day after Bvuŋka.\n\nTemporal markers: \n- \"fɔ̀ shě X\" → \"the day after tomorrow is X\" \n- \"ntfǔː\" → \"tomorrow\" \n- \"ntfǔː de᷆n\" → \"tomorrow\" (in future tense) \n- \"cǐ\" → \"yesterday\" \n- \"bèsèn\" → \"will\" (future) \n- \"wvù tɔ̀\" → \"he found\" \n- \"yɛ᷅n\" → \"saw\" \n- \"kèŋkfǔ\" → \"the yam\" \n- \"me nú\" → \"on that day, I\" \n- \"ŋgéː\" → \"will help\" \n- \"kwɔ᷆ːn\" → \"the woman\" \n\nNow analyze each sentence:\n\n16. \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"bvúsɔ̀w\" = day Bvusɔw \n- \"nǔ\" = you (sg) \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n→ On Bvusɔw, you will have the day after tomorrow be Bvutfu. \nBut Bvutfu is after two days from Bvusɔw? \nOrder: Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden → ? \nFrom earlier: Bvutfu is after Bvusɔw → Bvusɔw → Bvutfu? Not matching. \nWait: sentence 5: \"The day after tomorrow is Bvutfu\" → so from Bvusɔw, day after tomorrow is Bvutfu? \nBvusɔw → tomorrow → Bvuzhi → the day after tomorrow → Bvuzhi? \nNot Bvutfu. \nBut in sentence 1, \"yesterday was Bvumbon\", current day is Bvutfu. \nSo order: Bvumbon → Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden \nSo from Bvutfu: next is Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden \nSo from Bvusɔw, day after tomorrow is Bvuzhi, not Bvutfu. \nBut sentence 5 says: \"The day after tomorrow is Bvutfu\" → so from current day, two days forward is Bvutfu. \nIf current day is Bvusɔw, then: \n- today: Bvusɔw \n- tomorrow: Bvuzhi \n- day after tomorrow: Bvuzhi? No — two days forward = Bvuzhi? \nOnly if \"day after tomorrow\" = Bvutfu → Bvutfu must be two days after current day. \nSo order must be: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden \nFrom Bvutfu: Bvusɔw is the next day. \nSo \"day after tomorrow\" from Bvusɔw? \n- Bvusɔw → tomorrow → Bvuzhi → day after tomorrow → Bvuzhi? No — two days after Bvusɔw is Bvuzhi. \nSo only if Bvutfu is three days after Bvusɔw → not possible. \nRe-examine sentence 1: \"Yesterday was Bvumbon\" — so current day is Bvutfu. \nSo Bvumbon is yesterday → then Bvutfu is today. \nSentence 5: \"The day after tomorrow is Bvutfu\" — from current day (which is Bvusɔw), day after tomorrow is Bvutfu. \nSo from Bvusɔw: \n- today: Bvusɔw \n- tomorrow: Bvuzhi \n- day after tomorrow: Bvuzhi → not Bvutfu. \nContradiction. \nTherefore, the day order must be: Bvumbon → Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden \nFrom Bvusɔw, day after tomorrow is Bvuzhi, not Bvutfu. \nUnless \"the day after tomorrow\" refers to a time, not a day name. \nBut in sentence 5: \"The day after tomorrow is Bvutfu\" — clearly past reference. \nIf Bvutfu is two days after current day, current day must be Bvusɔw, and Bvutfu is two days after → so must be Bvuzhi. \nTherefore, Bvutfu = Bvuzhi? \nBut they are different day names. \nThus, contradiction in the system. \nAlternative: the days are cyclic or non-linear? \nNo — only one order. \nAnother fix: in sentence 5: \"The day after tomorrow is Bvutfu\" — if current day is Bvusɔw, day after tomorrow is Bvuzhi → so Bvutfu = Bvuzhi? But they are distinct. \nThus, misgloss. \nBut sentence 1: \"Yesterday was Bvumbon\" — so current day is Bvutfu. \nSentence 5: \"The day after tomorrow is Bvutfu\" — \"the day after tomorrow\" from current day (Bvutfu) → so day after tomorrow is Bvutfu? Impossible. \nTherefore, current day is not Bvutfu. \nIf current day is Bvusɔw, then yesterday was Bvuzhi, not Bvumbon. \nBut sentence 1 says \"on Bvutfu, yesterday was Bvumbon\" → so when speaking on Bvutfu, yesterday was Bvumbon. \nSo present day is Bvutfu → yesterday was Bvumbon → order: Bvumbon → Bvutfu. \nSentence 5: \"The day after tomorrow is Bvutfu\" — from current day, day after tomorrow is Bvutfu. \nSo from today (Bvutfu), day after tomorrow is Bvutfu → impossible. \nTherefore, current day is not Bvutfu. \nBut sentence 1 is spoken on Bvutfu. \nSentence 4 is spoken on Bvusɔw. \nSentence 8 is spoken on Bvuŋka. \nSentence 11 is \"The day before yesterday was Bvuŋka\" — from current day, day before yesterday was Bvuŋka. \nSo current day is after Bvuŋka → so current day is Bvuŋkaden. \nYes — from Bvuŋka, the day before yesterday is Bvuŋka? No — day before yesterday (two days prior) was Bvuŋka → so current day is Bvuŋkaden. \nSimilarly, \"Tomorrow is Bvuŋkaden\" (sentence 8) — from current day (Bvuŋka), tomorrow is Bvuŋkaden. \nSo Bvuŋkaden is after Bvuŋka. \nNow, sentence 11: \"The day before yesterday was Bvuŋka\" — so current day is Bvuŋkaden → day before yesterday was Bvuŋka. \nMatches. \nSentence 5: \"The day after tomorrow is Bvutfu\" — current day is Bvusɔw → so day after tomorrow is Bvutfu. \nSo from Bvusɔw, two days after is Bvutfu. \nSo order: Bvusɔw → tomorrow → ? → day after tomorrow → Bvutfu \nSo Bvutfu is two days after Bvusɔw → Bvusɔw → Bvuzhi → Bvutfu \nSo order: Bvusɔw → Bvuzhi → Bvutfu \nThen sent 1: \"Yesterday was Bvumbon\" — current day is Bvutfu → yesterday was Bvumbon → so Bvumbon → Bvutfu \nThus: Bvumbon → Bvutfu → Bvuzhi → Bvuŋka → Bvuŋkaden \nBut from Bvusɔw: day after tomorrow is Bvutfu → so Bvusɔw → Bvuzhi → Bvutfu → yes. \nSo complete order: Bvumbon → Bvutfu → Bvuzhi → Bvuŋka → Bvuŋkaden \n\nNow temporal markers: \n- \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \n- \"ntfǔː\" = \"tomorrow\" \n- \"cǐ\" = \"yesterday\" \n- \"bèsèn\" = will \n- \"yɛ᷅n\" = saw \n- \"kèŋkfǔ\" = yam \n- \"bvúmbòn\" = Bvumbon \n\nNow:\n\n16. \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" \nBut \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \nSo: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" \nBut \"have\" is not used. In English, we say \"the day after tomorrow is Bvutfu\" — so better: \"On Bvusɔw, you (do) have the day after tomorrow be Bvutfu\" — not natural. \nPerhaps \"nǔ\" is not \"you\" — or it's a time reference. \nBut in sentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"On Bvusɔw, you will steal the yam\" \nSo \"nǔ\" with time = agent on that day. \nSo here, \"on Bvusɔw, you will have the day after tomorrow be Bvutfu\" — though awkward. \nBut grammar suggests: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" \nAccept as is. \n\n17. \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = on that day, I \n- \"ŋgéː\" = will help \n- \"nyɛ́n\" = the woman \n- \"kèŋkfǔ lé ɛ̀bɛ̀n\" = the yam saw the woman \nBut \"saw\" is not common for yam. \nIn sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo \"yɛ᷅n wáy\" = saw the market \nSo \"kèŋkfǔ lé ɛ̀bɛ̀n\" = saw the woman \nBut \"kèŋkfǔ\" is yam — so \"the yam saw the woman\" — odd. \nBut in sentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" = \"Today, we will steal the car\" \nSo \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is not a verb. \nThus, \"kèŋkfǔ\" is \"the yam\", \"lé\" is \"saw\", \"ɛ̀bɛ̀n\" is \"the woman\" → \"the yam saw the woman\" \nBut in context, the woman is the subject of \"help\". \nSo \"I will help the woman who saw the yam\" — but \"saw the yam\" is not attributed to her. \nPerhaps \"kèŋkfǔ\" is a typo or should be \"nyɛ́n\" repeated. \nBut only one \"lé\". \nBest: \"I will help the woman who saw the yam\" — with \"ɛ̀bɛ̀n\" as object of \"saw\". \nSo: \"On that day, I will help the woman who saw the yam\" \n\n18. \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = he \n- \"tɔ̀ nɔ̂ː\" = found \n- \"yɛ᷅n\" = saw \n- \"bèsèn\" = will \n- \"ě\" = the \n- \"bvúmbòn\" = Bvumbon \nSo: \"He will have seen the Bvumbon\" — but \"saw\" is present. \n\"bèsèn\" = will → so \"will have seen\"? \nBut \"yɛ᷅n\" = saw → present. \n\"bèsèn\" modifies the verb. \nIn sentence 7: \"you heard the thief a long time ago\" — past. \nHere, \"bèsèn\" = future → \"he will see\" or \"he will have seen\"? \nBut \"yɛ᷅n\" is \"saw\", so past. \nContradiction. \nPossibility: \"bèsèn\" is not future. \nSentence 14: \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" = \"we will steal the car\" — so \"bèsèn\" = future. \nSentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" — past. \nSo \"bèsèn\" only in future. \nSo here, \"bèsèn\" is future tense. \n\"yɛ᷅n\" is saw — but future saw? \nOnly if \"yɛ᷅n\" is \"will see\". \nBut in sentence 13, \"yɛ᷅n wáy\" = saw the market — past. \nSo \"yɛ᷅n\" is past. \nIn this sentence, \"bèsèn\" must be attached to \"yɛ᷅n\" — so \"he will have seen\" or \"he will see\". \nIn Nooni, future of \"saw\" may be \"will see\" or \"will have seen\". \nBut \"bèsèn\" is likely future marker. \nSo \"he will see Bvumbon\" — but \"Bvumbon\" is a day. \n\"yɛ᷅n bèsèn ě bvúmbòn\" = saw the future Bvumbon? \nNo — \"bèsèn\" is future, \"yɛ᷅n\" is saw. \nSo \"he will have seen the Bvumbon\" → but Bvumbon is a day name. \nPerhaps \"saw the day Bvumbon\" — but it's not a place. \nMore likely: \"he will have seen the woman (on Bvumbon)\" — but \"bvúmbòn\" is not \"the woman\". \n\"ɛ̀bɛ̀n\" is woman, \"bvúmbòn\" is day. \nSo \"bèsèn ě bvúmbòn\" = the future day Bvumbon? \nNot clear. \nBut in sentence 1: \"Yesterday was Bvumbon\" — so Bvumbon is a day. \nSo \"he will have seen the day Bvumbon\" — not idiomatic. \nFinal: \"He will have seen Bvumbon\" — as a day. \nBut better: \"He will see the day Bvumbon\" — with \"bèsèn\" future, \"yɛ᷅n\" present. \nBut \"yɛ᷅n\" is not future. \nConclusion: the structure is \"he will have seen the day Bvumbon\" — so past perfect. \nBut \"bèsèn\" is future, not past perfect. \nMissing link. \nIn sentence 7: \"you heard the thief a long time ago\" — past. \nSo \"bèsèn\" only in future. \nThus, \"he will see the day Bvumbon\" — but \"saw\" is not \"will see\". \nTherefore, likely \"bèsèn\" is forming future of \"see\", so \"he will see the day Bvumbon\" — but \"yɛ᷅n\" is \"saw\", not \"see\". \nSo perhaps \"yɛ᷅n\" is \"will see\" in future tense. \nIn context, the only consistent structure is: \"He will see the day Bvumbon\" \nBut \"saw\" is used in past. \nPerhaps it's a verb with temporal modifier. \nFinal: \"He will have seen Bvumbon\" — accept. \n\n19. \"bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n\" \n- \"bèsèn\" = will \n- \"nǔ\" = you \n- \"bóy\" = the woman \n- \"tɔ́\" = will \n- \"fɔ̀wǎy\" = the market \n- \"bvúzhı᷇ːde᷆n\" = the day after Bvuzhi \nSo: \"You will help the woman will go to the market on the day after Bvuzhi\" — redundant. \n\"bèsèn\" and \"tɔ́\" both future. \n\"tɔ́\" may be a second future. \nBut \"bóy", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10424.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "planner_output": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "anchor_output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given Nooni sentences spoken on different days of the Nooni week, and we are to translate four sentences (16–19) spoken on **Bvuŋkaden** into English. We must infer the grammatical and semantic patterns from the provided examples.\n\nStep 1: Identify the days and their relationships.\n\nFrom the problem:\n\n- Bvutfu: mentioned in 1, 2, 3, 5, 13\n- Bvusɔw: 2, 4, 5, 6, 7\n- Bvukema: 8, 9, 10, 11\n- Bvuŋka: 4, 12, 13, 14, 15\n- Bvuŋkaden: 8, 16–19 (target)\n\nWe see that the days appear to be ordered in a week. Key day markers appear with directional references:\n\n- “Tomorrow is Bvuŋkaden” (8): → tomorrow = Bvuŋkaden\n- “The day before yesterday was Bvuŋka” (11): → two days before current day = Bvuŋka\n- “The day after tomorrow is Bvutfu” (5): → two days after current day = Bvutfu\n\nLet’s suppose the days follow a sequence:\n\nLet current day be X.\n\nFrom (11): the day before yesterday was Bvuŋka → Bvuŋka = X - 2 \nFrom (5): the day after tomorrow is Bvutfu → Bvutfu = X + 2 \nFrom (8): tomorrow is Bvuŋkaden → Bvuŋkaden = X + 1\n\nSo the sequence is:\n\n- X-2: Bvuŋka \n- X-1: ??? \n- X: ??? \n- X+1: Bvuŋkaden \n- X+2: Bvutfu \n\nBut we also have Bvusɔw mentioned in (2), (4), (6), (7). Bvusɔw appears in the past and future as a reference.\n\nWe are told that these are spoken on different days; so we can assign days based on adjacency.\n\nFrom sentence (8): “Tomorrow is Bvuŋkaden” → Bvuŋkaden is tomorrow \nFrom (8): “The day before yesterday was Bvuŋka” → Bvuŋka = two days prior \nFrom (5): “The day after tomorrow is Bvutfu” → Bvutfu = two days after\n\nSo day order (in sequence): \n- Day -2: Bvuŋka \n- Day -1: ? \n- Day 0: ? \n- Day +1: Bvuŋkaden \n- Day +2: Bvutfu \n\nWe also have Bvusɔw mentioned in (2): “On Bvusɔw, you will steal the yam” \n(4): “On Bvuŋka, he found the book” \n(6): “Today, he killed the woman” → so Bvusɔw is a day that occurs on a day before or after.\n\nLet’s now check which day corresponds to which.\n\nFrom (4): “On Bvuŋka, he found the book” → Bvuŋka is a day. \nFrom (6): “Today, he killed the woman” → today is Bvusɔw? \nSentence (6) is spoken on Bvusɔw → so current day when (6) is spoken is Bvusɔw.\n\nThus:\n\n- (6): spoken on Bvusɔw → so event is “today” → “Today, he killed the woman.” \n- (4): spoken on Bvusɔw → “On Bvuŋka, he found the book” → so Bvuŋka is two days before today.\n\nSo day order:\n\n- Today: Bvusɔw \n- Two days ago: Bvuŋka \n- Two days after: Bvutfu (from sentence 5: “The day after tomorrow is Bvutfu”) \n- Tomorrow: Bvuŋkaden (from sentence 8)\n\nSo:\n\n- Bvusɔw = current day \n- Bvuŋka = -2 \n- Bvutfu = +2 \n- Bvuŋkaden = +1\n\nSo the week order is:\n- Bvuŋka (-2)\n- ? (-1)\n- Bvusɔw (0)\n- Bvuŋkaden (+1)\n- Bvutfu (+2)\n\nNow we can assign all days.\n\nFrom (13): “On Bvutfu, the woman saw the market” → Bvutfu is two days after Bvusɔw → consistent.\n\nAll references are consistent now.\n\nNow we translate the sentences spoken on **Bvuŋkaden**, which is **one day after Bvusɔw**.\n\n---\n\n16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě ntfǔː” = the day after tomorrow is [Bvutfu]? Wait.\n\nCompare to sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu.”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow is [X]”\n\nTherefore, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) will have the day after tomorrow be [something]? No.\n\nWait — “fɔ̀ shě ntfǔː” is a noun phrase: “the day after tomorrow is [day]”\n\nSo the phrase “fɔ̀ shě ntfǔː” means “the day after tomorrow is [something]” — so it's a day-reference.\n\nBut here: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nThis is structured as “On Bvusɔw, you have the day after tomorrow is X” — that doesn't make sense.\n\nWait — perhaps it's a typo or misordering.\n\nWait — in sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu.”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nSo it’s a day noun phrase.\n\nBut here: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” → “On Bvusɔw, you (sg) [something]”\n\nWhat could “fɔ̀ shě ntfǔː” be? It is “the day after tomorrow”, so “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nBut it doesn’t have a target day. So could it mean “You(sg) will be on the day after tomorrow”?\n\nWait — compare to sentence 2: “On Bvusɔw, you(sg) will steal the yam.”\n\nSo structure: “On [day], subject will [action]”\n\nBut here: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nThe verb “fɔ̀ shě” is the subject? Or object?\n\nIn sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you(sg) will steal the yam.”\n\nSo “wɔ̀” = on, “nǔ” = you, “yúː cɔ́ŋ” = will steal, “kèŋkfǔ” = the yam, “bvúsɔ̀w” = on Bvusɔw.\n\nSo structure: “on [day], subject [verb] object”\n\nHere: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\n“nǔ” = you, “fɔ̀ shě” = verb? “fɔ̀ shě” appears in “fɔ̀ shě ntfǔː” → likely a verb.\n\nBut “fɔ̀ shě” in previous example is “the day after tomorrow” — with “ntfǔː” = day name.\n\nWait — in sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow is [day]”\n\nSo “fɔ̀ shě ntfǔː” is a complete clause — “the day after tomorrow is [day]”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” does not make sense.\n\nAlternative: is “fɔ̀ shě” a verb?\n\nIn sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → “On Bvutfu, the woman saw the market.”\n\n“yɛ᷅n wáy” = saw the market → “yɛ᷅n” is verb (to see), “wáy” = the market.\n\nSo verbs are: “yɛ᷅n” (see), “cɔ́ŋ” (steal), “bɛ̂ː” (killed), “wvù” (found), “me nú” (I will choose), “mbɛ̂ː” (chose), “dìɛ̀msɛ̌n” (is about to see)\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nIs “fɔ̀ shě” a verb?\n\nLook at (5): “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě” is part of a time phrase, not a verb.\n\nSo “fɔ̀ shě” is not a verb; it's a time expression: “the day after tomorrow”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow” — meaning “the day after tomorrow”\n\nBut sentence says: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nThat would be: “On Bvusɔw, you (sg) the day after tomorrow” — grammatically odd.\n\nPerhaps it's a misordering.\n\nCompare to sentence 3: “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “On Bvuzhi, the woman will help me.”\n\nSo structure: “On [day], subject will [verb] [object]”\n\nSentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nIf “fɔ̀ shě” is verb, but in other cases it's used as time phrase.\n\nPerhaps it's “you will be on the day after tomorrow”?\n\nBut “on the day after tomorrow” = fɔ̀ shě ntfǔː?\n\nYes — “fɔ̀ shě ntfǔː” = “on the day after tomorrow”?\n\nNo — in sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow” (as a noun phrase)\n\nSo it cannot stand alone.\n\nBut in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” — perhaps the “fɔ̀ shě ntfǔː” is the object?\n\nSo “you (sg) will [fɔ̀ shě ntfǔː]”?\n\nBut “fɔ̀ shě ntfǔː” is not a thing — it’s a day.\n\nWait — in sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě ntfǔː” = “the day after tomorrow”, and “is” is implied in the verb structure.\n\nBut in sentence 16, no verb is given.\n\nCompare to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” — “I will see the thief at the car” — uses “nú” (will), “ŋgéː” (see), “nyɛ́n” (the), “kèŋkfǔ” (thief), “lé” (at), “ɛ̀bɛ̀n” (car)\n\nSo verb is “ŋgéː” = see.\n\nSimilarly, sentence 18: “wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn” → “he heard the woman on the day before yesterday” → “wvù” = he found, “tɔ̀” = the, “nɔ̂ː” = woman, “yɛ᷅n” = on, “bèsèn” = day before yesterday, “ě” = the, “bvúmbòn” = market?\n\n“bèsèn” = day before yesterday — a time reference.\n\nSentence 19: “bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n” → “On the day before yesterday, the woman will go to the market” → “bèsèn” = day before yesterday, “nǔ bóy” = the woman, “tɔ́” = will, “fɔ̀wǎy” = go to, “bvúzhı᷇ːde᷆n” = market.\n\nSo “bèsèn” is a time reference — “day before yesterday”\n\nSimilarly, “fɔ̀ shě” appears with “ntfǔː” (day name) to mean “the day after tomorrow”\n\nThus, “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n\nBut in sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nNo verb? No structure like “you will [do X]”\n\nUnless “fɔ̀ shě” is a verb.\n\nBut in other uses, it's not.\n\nWait — is there a verb “fɔ̀ shě”?\n\nLook at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “today, we will steal the car”\n\nNo “fɔ̀ shě”\n\nBack to sentence 16: perhaps “fɔ̀ shě” is misread.\n\nAlternative: could “fɔ̀ shě” be a verb meaning “will be”?\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” = “the day after tomorrow is Bvutfu”\n\nSo “fɔ̀ shě” is linked to “is”, not a verb.\n\nSo likely not.\n\nPerhaps it's a typo, and it's meant to be “fɔ̀ shě ntfǔː” as a phrase meaning “on the day after tomorrow”\n\nSo “on Bvusɔw, you (sg) [on the day after tomorrow]” — nonsense.\n\nAlternative: perhaps “fɔ̀ shě” is “to go” or “to come”?\n\nNo — “fɔ̀wǎy” = go to, “wɔ̀” = on, “kèŋkfǔ” = steal.\n\nNo verb called “fɔ̀ shě”\n\nPerhaps the structure is: “On Bvusɔw, you (sg) will be on the day after tomorrow” — that is odd.\n\nWait — sentence 4: “wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː” → “On Bvuŋka, he found the book”\n\nSo “on day, subject [verb] object”\n\nSo likely any sentence with “on day” is followed by subject-verb-object.\n\nIn 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nSo “on Bvusɔw, you (sg) fɔ̀ shě ntfǔː”\n\nIf “fɔ̀ shě” is a verb and “ntfǔː” is object, but ntfǔː is a day name — doesn't make sense.\n\nUnless “ntfǔː” is not object.\n\nPerhaps “fɔ̀ shě” is a verb meaning “to be” and “ntfǔː” is the day?\n\nSo “you will be on the day after tomorrow”?\n\nBut in Nooni, “fɔ̀ shě” is not “to be”.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu” — “fɔ̀ shě” is not a verb of being.\n\nIn fact, the verb “is” is not used explicitly — it's embedded in “fɔ̀ shě ntfǔː nú” = “the day after tomorrow is [day]”\n\nSo “fɔ̀ shě” is a noun phrase.\n\nTherefore, in 16, “fɔ̀ shě ntfǔː” is a noun phrase — the day after tomorrow.\n\nSo “on Bvusɔw, you (sg) the day after tomorrow” — still ungrammatical.\n\nPerhaps it's “on Bvusɔw, the day after tomorrow”?\n\nBut “nǔ” is subject.\n\nAnother possibility: typo in original? Or misreading.\n\nWait — look at sentence 8: “ntfǔː nú bvûŋka᷆ːde᷆n” → “tomorrow is Bvuŋkaden” — so “ntfǔː” = tomorrow, “is” → “nú” = verb?\n\nNo — “ntfǔː nú” = “tomorrow is”\n\nSimilarly, sentence 11: “kefwé cí nú bvûŋka” → “the day before yesterday was Bvuŋka” → “kefwé cí” = the day before yesterday, “nú” = was.\n\nSo “X nú day” = “X is day” or “X was day”\n\nSo “fɔ̀ shě ntfǔː nú” → “the day after tomorrow is day”\n\nSo “fɔ̀ shě ntfǔː” is a noun phrase, “nú” is verb.\n\nNow, in sentence 16: “", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 4.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10344.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 340.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "anchor_output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "Step-by-step analysis of the Inuktitut sentences to derive the pattern:\n\nFirst, identify verb roots and person/number marking from the given examples.\n\nSentence 1: *Qingmivit takujaatit* → \"Your dog saw you\" \n- \"takujaatit\" → saw (past tense, 1st person?) \n- Verb ends in \"-vit\" and \"-atit\" → likely \"-vit\" is suffix for \"saw\", and \"it\" marks 1st person subject? \n- \"Qingmivit\" = your dog → possessive marker \"v\" + noun \n→ So \"saw\" is marked by suffix in verb. \n\nSentence 2: *Inuuhuktuup iluaqhaiji qukiqtanga* → \"The boy shot the doctor\" \n- \"qukiqtanga\" → \"qukiq\" + \"tanga\" → shoot \n- \"tanga\" appears in sentence 12: *qukiqsijuq* → similar pattern \n- \"qukiqsijuq\" → also in sentence 12: \"the hunter shot a polar bear\" \n- Note: \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → sijuq = object marker \n→ So \"qukiq\" is root for \"shot\", and the suffix \"-suq\" or \"-sijuq\" is object marker. \n→ Subject is marked separately: \"Angunahukti\" = hunter (3rd person). \n\nSentence 5: *Qingmiq iputujait* → \"You speared the dog\" \n- \"iputujait\" → speared \n- Subject: \"Qingmiq\" → likely \"you\" \n→ Could \"Qingmiq\" be \"you\"? But \"Qingmi\" means \"dog\" — the possessive \"v\" is in \"Qingmivit\" \n→ So \"q\" may be a first-person marker? But \"Qingmi\" is not a direct form for \"you\" \n→ Perhaps \"you\" is not a noun but marked in verb: so \"iputujait\" = speared (by you) \n→ So verb suffix \"-ait\" → first person? \n→ Compare with sentence 11: *Ukiakhaqtutit* → \"you fell\" \n- Verb ends in \"-utit\" → clearly first person \n→ So \"you\" → marked by verb suffix: -utit \n\nThus, first-person subject is marked in the verb with a suffix. \n- \"utit\" = you (in past tense) \n- So \"you shot\" should be verb root + \"utit\" \n\nBut in sentence 2, \"qukiqtanga\" → has no -utit → subject is \"the boy\" (3rd person) \n- The verb suffix is not first-person here \n- So \"qukiqtanga\" likely = root + object marker (tanga) = \"shot\" \n- Similarly, \"qukiqsijuq\" = root + object marker → \"shot\" \n\nSo for \"you shot\", first person subject implied by verb suffix? \n→ But in sentence 5: *Qingmiq iputujait* → \"you speared the dog\" \n- \"iputujait\" ends in \"-ait\" → not \"utit\" \n- Unless \"ait\" = first person? \n- In sentence 11: *Ukiakhaqtutit* → \"you fell\" → ends in \"-utit\" \n- So \"utit\" = first person \n→ \"iputujait\" is \"you speared\" → so if \"ait\" is first person, then it differs from \"utit\" \n→ but “ait” and “utit” are different \n→ So only one first-person suffix? \n\nNow, sentence 3: *Aanniqtutit* → \"You hurt yourself\" \n- \"aanniqtutit\" → hurt + you \n- Ends in \"-utit\" → so verb has first person suffix \n→ So when subject is \"you\", verb has \"-utit\" \n→ Thus, \"you hurt\" = \"aanniqtutit\" → root \"aanniqt\" + \"utit\" \n\nSimilarly, sentence 10: *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" \n- \"aanniqtanga\" → hurt + object = your teacher \n- No first-person in subject → verb without -utit \n→ So only when \"you\" is subject, verb has -utit \n\nThus, consistent: \n- When subject is \"you\", verb has suffix \"-utit\" \n- For other subjects, no person suffix in verb \n- Object is marked with possessive or object marker \n\nNow, translation of (b): \n\n19. The shaman hurt you. \n- \"The shaman\" = subject, 3rd person \n- \"hurt\" → verb root from sentence 3: \"aanniqt\" \n- Object: \"you\" → marked with \"-utit\" \n→ So verb: \"aanniqt\" + \"utit\" = \"aanniqtutit\" \n→ But sentence 3 is \"aanniqtutit\" = \"you hurt yourself\" \n→ That was \"you hurt you\" — object is \"yourself\" (self-possessive) \n→ So \"aanniqtutit\" = \"you hurt yourself\" \n→ So root is \"aanniqt\", and for object = \"you\", use \"utit\" \n→ But in present case: \"the shaman hurt you\" → subject: shaman, object: you \n→ So verb root \"aanniqt\" + object marker? \n→ Object \"you\" — how marked? \n→ In sentence 3, \"aanniqtutit\" = \"you hurt yourself\" → object is \"yourself\" → possessed by subject \n→ But here, object is \"you\", not possessed \n→ In Inuktitut, obj markers: in sentence 2: \"iluaqhaiji\" → doctor → marked as object \n→ Not possessed → so likely object is marked via case or separate suffix \n→ But in the list, no object marker like \"sijiit\" or \"sijuq\" \n→ In sentence 1: \"Qingmivit\" = your dog → possessive \n→ In sentence 2: \"iluaqhaiji\" = doctor → not possessive \n→ So object is just noun \n→ So \"the shaman hurt you\" = \"angatkuq\" (shaman) + \"aanniqtutit\"? \n→ But that would be \"shaman hurt you\" → verb must take person/number \n→ Subject is 3rd person → no verb suffix \n→ So verb: \"aanniqt\" + object? \n→ But object not marked — \"you\" is not possessed \n→ In sentence 3: \"you hurt yourself\" — object is \"yourself\" → so possessor is subject \n→ So when object is \"you\", it may be marked with possessive or by context \n→ But in sentence 19: \"the shaman hurt you\" → object is \"you\", so it may be \"aanniqt\" + \"you\" \n→ But only \"aanniqtutit\" has \"you\" with -utit \n→ So perhaps verb always takes \"-utit\" when object is \"you\"? \n→ But that doesn't make sense — only when subject is \"you\" → in sentence 3 \n→ Therefore, in sentence 3: \"you hurt yourself\" — both subject and object are \"you\" \n→ In sentence 19: subject is shaman, object is you → object not subject \n→ So object should not get -utit \n\nSo where is the object marker?\n\nSentence 4: *Iluaqhaijiup aarqijaatit* → \"The doctor cured you\" \n- \"aarqijaatit\" → cured \n- \"aariq\" + \"jaatit\" → cured \n- Object: \"you\" → does it have a marker? \n- In sentence 4: \"iluaqhaijiup aarqijaatit\" → \"up\" may be possessive → \"iluaqhaijiup\" = doctor + \"up\" → \"your doctor\" \n→ But sentence 4: \"the doctor cured you\" → so \"iluaqhaiji\" = doctor \n→ \"aarqijaatit\" = cured + you → verb ends in -jaatit → but is that first person? \n→ In sentence 3: \"aanniqtutit\" → you hurt yourself → verb has -utit \n→ In sentence 4: \"aarqijaatit\" → no -utit \n→ So object is \"you\" — how marked? \n→ Only if object is possessed → but \"you\" is not possessed \n→ So likely \"you\" is inherent in structure \n→ Thus, if \"you\" is object, no suffix needed \n→ But in sentence 3, \"you hurt yourself\" → object is \"yourself\" → possessed \n→ In sentence 4, \"doctor cured you\" → object is \"you\" → not possessed \n→ So object marked differently \n\nBut the verb verb form: \n- Sentence 3: aanniqtutit → \"you hurt yourself\" \n- Sentence 4: aarqijaatit → \"the doctor cured you\" \n→ No -utit → so verb does not mark \"you\" as object \n→ So \"you\" as object is unmarked \n→ Therefore, for \"the shaman hurt you\" → \n→ subject: \"angatkuq\" \n→ verb: \"aanniqt\" + object mark? \n→ But no object marker \n→ So likely just \"angatkuq aanniqt\" + object? \n→ But missing suffix \n→ In sentence 3: \"aanniqtutit\" = you hurt yourself → subject and object both you \n→ So possibly, verb root with -utit only when object is \"you\" and subject is not? \n→ But not consistent \n\nAlternative: in all cases, \"you\" is marked by -utit in verb when object is \"you\" \n→ In sentence 4: \"aarqijaatit\" — ends with -jaatit \n→ Look at suffix: \"jaatit\" → similar to \"utit\" → could this be a form? \n→ Not clearly linked \n\nBut sentence 8: *Iluaqhaijivit inuuhuktuit aarqijanga* → \"Your doctor cured your boy\" \n- \"iluaqhaijivit\" = your doctor \n- \"inuuhuktuit\" = your boy (cured) \n- \"aarqijanga\" = cured \n→ \"aarqijanga\" = verb root \"aarqij\" + \"anga\" → cured \n→ Object: \"your boy\" — possessed \n→ So object with possessive \n→ Thus, object markers are often possessive \n→ In sentence 4: \"iluaqhaijiup aarqijaatit\" → \"up\" = possessive \n→ So \"iluaqhaijiup\" = your doctor → \"up\" = possessive \n→ \"aarqijaatit\" = cured you \n→ So object \"you\" is not marked with possessive — only if possessed \n→ So in general, object is marked by possessive or case \n→ But \"you\" as object is not possessed → so no marker \n→ So \"the shaman hurt you\" = \"angatkuq aanniqt\" + object? \n→ But no connection \n→ Perhaps the verb is not marked for person when subject is third person \n→ So root + object \n→ But what about the object \"you\"? \n→ In sentence 3: \"you hurt yourself\" → self-marked \n→ In sentence 4: \"the doctor cured you\" → \"you\" not self-marked \n→ So possibly, \"you\" is just a pronoun \n→ Therefore, for \"the shaman hurt you\" → \"angatkuq aanniqt\" + you \n→ But how written? \n→ Sentence 3: \"aanniqtutit\" — you hurt yourself \n→ So verb is \"aanniqt\" + \"utit\" \n→ So \"hurt you\" → must use \"aanniqtutit\" \n→ But that would be \"you hurt you\" \n→ Contradiction \n→ So only when subject is \"you\", verb has suffix \n\nThus, for third person subject + object \"you\" → object not marked with suffix \n→ So verb is just \"aanniqt\" + object noun \n→ But in sentence 4: \"aarqijaatit\" → verb ends with \"jaatit\" \n→ And \"you\" is object \n→ So \"jaatit\" may be object marker \n→ In \"aanniqtutit\", \"utit\" = first person \n→ But \"jaatit\" in \"aarqijaatit\" → different \n\nSearch patterns: \nSentence 3: \"aanniqtutit\" → \"you hurt yourself\" → subject and object you \nSentence 4: \"aarqijaatit\" → \"the doctor cured you\" → subject (doctor), object (you) \n→ Both have -jaatit or -utit? \n\"utit\" in 3, \"jaatit\" in 4 \n→ Not the same \n→ So perhaps different forms \n→ But in both, object is \"you\" \n→ So likely, \"you\" as object → verb has a suffix that marks it \n→ But different in different verbs \n→ So no consistent suffix \n\nBest guess: the verb for \"hurt\" is \"aanniqt\", and when object is \"you\", it is marked with \"-it\", and for third person subject, the verb takes the form with \"-it\" \n→ But in sentence 4: \"aarqijaatit\" → ends with \"jaatit\" \n→ \"jaat\" in \"aarqijaatit\" → possible root \n→ So perhaps \"aanniqt\" is similar \n→ So for \"hurt\" → verb root \"aanniqt\", and object \"you\" → suffix \"-it\" \n→ So \"aanniqtit\" — but in sentence 3, \"aanniqtutit\" \n→ \"utit\" vs \"it\" — not clear \n\nFinal: based on sentence 3: \"you hurt yourself\" = aanniqtutit \n→ So when subject is \"you\", verb has -utit \n→ When object is \"you\", and subject is not, then it may be a different form \n→ In sentence 4: \"the doctor cured you\" = \"aarqijaatit\" → no -utit \n→ But \"jaatit\" ends in \"it\" \n→ So likely, general object marker is \"-it\" \n→ So \"hurt you\" = aanniqt + it = aanniqtit \n→ But in sentence 3, it is \"aanniqtutit\" \n→ So when subject is you, it's -utit; when object is you, it's -it? \n→ But both have \"it\" \n→ \"utit\" is a specific form \n\nFrom sentence 11: \"Ukiakhaqtutit\" = you fell → verb has -utit \n→ So -utit = first person subject \n→ So for object \"you\", it is not marked with -utit \n\nTherefore, in \"the shaman hurt you\" → \n- Subject: \"angatkuq\" (shaman) \n- Verb: root \"aanniqt\" + object marker \n- Object: \"you\" → how marked? \n→ In sentence 4: \"iluaqhaijiup aarqijaatit\" → \"up\" = possessive for doctor, object is \"you\" → not possessive \n→ So object is just \"you\" \n→ So verb is \"aanniqt\" + object suffix \n→ In sentence 4: verb is \"aarqijaatit\" → likely \"aarqij\" + \"jaatit\" \n→ \"jaatit\" may be the object marker \n→ Similarly, \"aanniqt\" + \"it\" = \"aanniqtit\"? \n→ In sentence 3: \"aanniqtutit\" – has \"utit\" because subject is you \n→ So the suffix may be different \n\nBut in sentence 3: \"aanniqtutit\" = you hurt yourself \n→ So only one form has -utit \n→ In sentence 4: \"aarqijaatit\" = doctor cured you – verb ends with -jaatit \n→ So -jaatit is used when object is \"you\" \n→ So likely, the object marker is -it (or -jaatit) \n→ But we need a general rule \n\nPerhaps the verb root is used with a suffix indicating the object. \nFor \"you\" as object, use -it \nSo \"aanniqtit\" = hurt you \nBut in sentence 3, \"aanniqtutit\" is used for \"you hurt yourself\" — same object \n→ So why different? \n→ Only because subject is \"you\" \n→ So if object is \"you\", and subject is not, use -it \n→ In sentence 4: \"aarqijaatit\" — looks like \"aanniqt\" with -jaatit \n→ \"jaatit\" is likely the object form \n→ So for \"hurt you\", use \"aanniqtit\" or \"aanniqtjaatit\"? \n→ But too long \n\nGiven that in sentence 3: \"you hurt yourself\" = aanniqtutit — subject and object \n→ So for \"the shaman hurt you\" → object is \"you\", subject is third person \n→ Verb has no person marker \n→ But has object marker \n→ In sentence 4: \"aarqijaatit\" = doctor cured you \n→ Root: \"aarqij\" \n→ Suffix: \"jaatit\" \n→ So likely, for \"hurt you\", use \"aanniqtit\" \n→ But in that sentence, it's \"aanniqtutit\" — so -utit is for subject \n\nTherefore, for past tense \"hurt you\" with third person subject, use \"aanniqt\" + \"it\" = \"aanniqtit\" \n→ But not in data \n→ So not supported \n\nAlternative: only \"you\" as subject triggers -utit \n→ When object is you, verb has -it \n→ In sentence 4: \"aarqijaatit\" — ends in -jaatit \n→ \"jaat\" may be a form of -it \n→ So assume \"aanniqt\" + \"it\" = \"aanniqtit\" \n→ So for 19: \"angatkuq aanniqtit\" \n\nBut \"aanniqtit\"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12482.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point.", + "planner_output": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "anchor_output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well," + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "First, identify the verb roots and markings from given examples.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"takujaatit\" = saw (with \"it\" = you, first person) \n- \"Qingmivit\" = your dog → possessive \"v\" + \"Qingmi\" → \"Qingmi\" = dog\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"qukiqtanga\" = shot \n- Subject: \"Inuuhuktuup\" = the boy (3rd person, marked with -tuup) \n- Object: \"iluaqhaiji\" = the doctor (noun) \n- Verb: \"qukiqtanga\" → root \"qukiq\" + \"tanga\" → object marker \"tanga\" likely for \"the doctor\"\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n- \"aanniqtutit\" → hurt + \"you\" \n- Verb: \"aanniqt\" + \"utit\" → \"utit\" = first person \n- So \"you hurt\" = verb with first person suffix \"-utit\"\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"aarqijaatit\" → cured + \"you\" \n- \"aarqij\" + \"aatit\" → \"aatit\" = first person \n- So \"cured you\" = verb with first person suffix \"-aatit\"? But \"aaniqtutit\" has \"utit\", not \"aati\". \n However, \"aarqijaatit\" likely has \"aati\" or \"aatit\" → first person. \n In example 3: \"aanniqtutit\" → \"you hurt yourself\" → \"utit\" = first person → so first person is marked by \"-utit\" in verbs.\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"iputujait\" = speared → root \"iputuj\" + \"ait\" → first person: \"ait\" likely = first person agent \n- \"Qingmiq\" = you? But \"Qingmi\" = dog → so \"q\" might be first person marker? \n But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. \n Thus, \"Qingmiq\" likely = the dog with \"q\" → not \"you\". \n Therefore, \"you\" must be marked in the verb: \"iputujait\" → \"ait\" = first person. \n So verb root for \"spear\" is \"iputuj\", with first person suffix \"-ait\".\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"aarqisijuq\" → cured → root \"aarqi\" + \"sijuq\" → object marker \"sijuq\" \n- Object: \"iluaqhaijimik\" = a doctor (with \"mik\" = object marker, or possessive?) \n- \"mik\" likely indicates object — used in 4 and 6 \n- So \"cured a doctor\" = verb with object marker\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n- \"qaijuq\" → came — likely root \"qaij\" + \"uq\" → no person marking → 3rd person\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"aarqijanga\" → cured + object \"your boy\" \n- \"aarqijaat\" or \"aarqijanga\" → verb with object marker \"anga\" \n- Subject: \"iluaqhaijivit\" = your doctor → possessive \"v\" + \"iluaqhaiji\" \n- Verb: \"aarqijanga\" → root \"aarqij\" + \"anga\" → object marker \"anga\" \n- So \"cured\" verb has object suffix\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"iputujanga\" → speared → root \"iputuj\" + \"anga\" → object marker \n- \"Angunahuktiup\" = the hunter → 3rd person \n- So \"spear\" verb takes object marker, not person\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"aanniqtanga\" → hurt → root \"aanniqt\" + \"anga\" → object marker \n- Subject: \"Qingmiup\" = the dog → \"up\" is possessive? Or marker for \"the\"? \n- \"up\" may indicate \"the\" or possessive; in \"Qingmivit\" = your dog → \"v\" = possessive \n- \"up\" used in \"Qingmiup\" → might be neutral article or \"the\" \n- So \"hurt your teacher\" = verb with object marker\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n- \"utit\" = first person → verb clearly marks first person: \"you fell\"\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"qukiqsijuq\" → shot → root \"qukiq\" + \"sijuq\" → object marker \n- No first person in subject → verb not marked for person\n\nThus, patterns:\n\n- Verbs carry person marking when subject is first person (like \"you fell\" → \"utit\")\n- When subject is not first person, verb has object marker (e.g., \"qukiqsijuq\" for \"shot a polar bear\")\n- Possessive markers are separate (e.g., \"v\" = your, \"up\" = the, \"mik\" = a)\n\nNow solve each of the required translations:\n\n19. \"The shaman hurt you.\" \n- \"The shaman\" → no possessive → \"Angatkuq\" → from example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" \n→ subject = \"Angatkuq\" = shaman \n- \"hurt\" → from example 3: \"aanniqtutit\" → \"you hurt yourself\" → \"aanniqt\" + \"utit\" = hurt + first person \n- \"you\" = first person → marked by \"-utit\" \n- So \"hurt you\" = \"aanniqtutit\" → but object? \n- \"aanniqtanga\" → hurt a person → with object marker \"anga\" \n- \"aanniqtutit\" = you hurt yourself → no object \n- So verb root is \"aanniqt\" \n- \"you\" = first person → marked by \"-utit\" \n- So \"the shaman hurt you\" = \"Angatkuq aanniqtutit\" → but \"utit\" = first person, not object \n- But \"aanniqtanga\" = hurt with object \n- In example 4: \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → \"aarqijaatit\" = cured + \"you\" → so \"aati\" or \"aatit\" = first person \n- In example 3: \"aanniqtutit\" = you hurt yourself → so \"utit\" = first person \n- So 'hurt you' requires \"aanniqt\" + object marker? \n- But in example 3, \"you hurt yourself\" has no object → self \n- In example 4, \"cured you\" has \"you\" as object → \"aarqijaatit\" → \"aati\" not \"utit\"? \n→ \"aati\" vs \"utit\" — different \n- In \"aanniqtutit\" → self → no object marker \n- In \"aanniqtanga\" → object → e.g., \"aanniqtanga\" → hurt someone else \n- But in sentence 4: \"aarqijaatit\" → \"cured you\" → \"aatit\" → first person \n- So \"you\" is marked by suffix only when subject is first person \n- But in \"the shaman hurt you\" → subject is third person, object is first person \n- So verb must take object marker \n- Root is \"aanniqt\" \n- Object: \"you\" → first person \n- So if object marker is \"-aati\", then: \"Angatkuq aanniqt aati\" → but no support \n- Example 4: \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → object \"you\" → verb \"aarqijaatit\" → \"aatit\" → first person \n- So \"aatit\" = first person object → so in \"hurt you\", object = first person → verb needs \"aati\" \n- Verb root \"aanniqt\" → \"aanniqt\" + \"aati\" = hurt you \n- So \"Angatkuq aanniqt aati\" → but no such form in data \n- In example 4: \"aarqijaatit\" → root \"aarqij\" + \"aati\" → object \n- So \"aati\" = object marker for first person \n- Similarly, \"aanniqt aati\" = hurt you \n- So translation: \"Angatkuq aanniqt aati\"\n\n20. \"The teacher saw the boy.\" \n- From example 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n- \"takujaatit\" = saw + you → you = first person → marked by \"-it\"? \n- \"takujaatit\" → root \"takuj\" + \"aatit\" → \"aati\" = first person \n- So \"saw you\" = \"takuj aati\" \n- But subject: \"your dog\" → possessive \n- In this case, subject = \"the teacher\" → no possessive \n- Object = \"the boy\" → \"inuuhuktuup\" in example 2 → \"the boy\" \n- So \"the teacher saw the boy\" → subject = \"teacher\" → no possessive \n- Object = \"the boy\" \n- So verb root \"takuj\" + object marker \n- Object form: in \"takujaatit\", object is \"you\" → first person → should be object marker \n- In example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"boy shot doctor\" → object marker \"tanga\" \n- In verse 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → object marker \"aati\" \n- So object markers vary: for \"doctor\" in example 2 → \"tanga\" \n- For \"you\" in example 4 → \"aati\" \n- So object marker depends on gender or person? \n- But in example 1: \"takujaatit\" → \"saw you\" → so for person, \"-aati\" \n- In example 2: \"qukiqtanga\" → object \"doctor\" → \"tanga\" \n- So object marker is abstract: attached to object \n- So for \"the boy\" → object marker needed \n- In example 2: \"iluaqhaiji\" → doctor → \"qukiqtanga\" → so root \"qukiq\" + \"tanga\" \n- So \"saw\" = \"takuj\" + object marker \n- Object \"the boy\" → likely \"inuuhuktuup\" → but how to mark? \n- Since no person in object, use object marker: possibly \"tanga\" or \"anga\" \n- In example 9: \"iputujanga\" → \"spear the wolf\" → object marker \"anga\" \n- In example 4: \"aarqijaatit\" → \"cured you\" → object marker \"aati\" \n- So different markers: for inanimate → \"anga\", for person → \"aati\"? \n- \"The boy\" is a person → so likely \"aati\" \n- So \"saw the boy\" = \"takuj aati\" \n- But \"takuj aati\" = saw you? \n- Must be attached to object \n- So \"teacher\" + \"saw\" + \"boy\" → \"teacher takuj aati\" \n- But in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so object \"you\" → suffix \"aati\" \n- So for \"the boy\", use \"aati\" \n- So \"the teacher saw the boy\" = \"Inuuhuktuup takuj aati\"? But \"Inuuhuktuup\" = the boy \n- So need a noun for teacher \n- No example with \"teacher\" → but \"iluaqhaiji\" = doctor, \"inuuhuktuup\" = boy \n- So teacher is not present in data \n- Possible form: \"aanniqt\" for teacher? Not known \n- But in sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"dog hurt teacher\" → \"aanniqtanga\" = hurt teacher \n- So \"teacher\" = \"aanniqt\" or \"iluaqhaiji\"? \n- \"iluaqhaiji\" = doctor → so teacher is likely \"aanniqt\" or \"ilinniaqt\" \n- Possibly \"ilinniaqt\" or similar \n- But no direct form \n- Since no \"teacher\" in examples, use for \"boy\" the object marker \n- So verb root \"takuj\" + object marker → likely \"aati\" for person \n- So \"teacher takuj aati\" → but must have full noun \n- In example 4: \"iluaqhaijiup aarqijaatit\" → \"doctor cured you\" → \"up\" used \n- In example 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"boy shot doctor\" → \"up\" not used \n- So \"up\" = possessive or article \n- \"teacher\" may be \"ilinniaqt\" or \"aanniqt\" \n- Likely \"ilinniaqt\" = teacher \n- So \"ilinniaqt takuj aati\" → teacher saw the boy \n\n21. \"Your wolf fell.\" \n- \"Your\" = possessive \"v\" \n- \"wolf\" = ? \n- From example 7: \"Nanuq qaijuq\" → \"polar bear came\" → \"qaijuq\" = came \n- No \"wolf\" \n- But \"your wolf\" → \"v\" + \"wolf\" \n- \"fell\" = from example 11: \"Ukiakhaqtutit\" → \"you fell\" → verb with first person \n- \"fell\" = \"uk\" + \"iakhaqt\" → root \"u\" or \"uk\"? \n- \"Ukiakhaqtutit\" → \"uk\" + \"iakhaqt\" + \"utit\" \n- So \"fell\" = \"uk\" + \"iakhaqt\" + \"utit\"? \n- But object: \"your wolf\" → not first person \n- So verb must have object marker? \n- In other verbs, object marked if present \n- But \"you fell\" has no object → self \n- So for \"your wolf fell\" → subject = \"your wolf\", verb = \"fell\" \n- Verb root \"u\" or \"uk\" → likely \"uk\" \n- But in example 7: \"Nanuq qaijuq\" → \"came\" → no person \n- So \"fell\" → likely \"uk\" + \"iakhaqt\" + object marker? \n- \"your wolf\" is the subject → so not object \n- So no object marker \n- So \"your wolf fell\" = \"v\" + \"wolf\" + \"uk iakhaqt utit\"? \n- But no \"wolf\" form \n- From example 8: \"iluaqhaijivit\" = your doctor \n- So \"wolf\" may be \"kataq\" or \"qaleq\" not given \n- But no wolf in data \n- Possible that \"wolf\" = \"pakt\" or \"kataq\" → missing \n- But strictly from data, only person and animal forms are known \n- In all cases, subject marked with possessive if needed \n- So \"your wolf\" = \"v\" + \"wolf\" \n- \"fell\" = verb with first person? No, subject is not first person \n- So no -utit \n- In \"you fell\" → first person → \"utit\" \n- So for \"your wolf fell\", no person → verb must be base form? \n- In sentence 7: \"Nanuq qaijuq\" → \"came\" without person marker \n- So for \"fell\", use \"uk\" + \"iakhaqt\"? \n- But in \"Ukiakhaqtutit\" → \"you fell\" → \"utit\" = first person \n- So without person, just \"uk iakhaqt\" \n- So \"your wolf fell\" = \"v\" + \"wolf\" + \"uk iakhaqt\" \n- But no \"wolf\" form \n- Implicit: \"wolf\" derived from example? \n- Not in data \n- But in 12: \"qukiqsijuq\" for \"shot\" \n- So for \"fell\", root is \"uk iakhaqt\" \n- So \"your wolf fell\" = \"v\" + \"wolf\" + \"uk iakhaqt\" \n- But what is \"wolf\"? In data, no wolf \n- Example 9: \"Angunahukti nanurmik qukiqsijuq\" → \"hunter shot polar bear\" → \"polar bear\" = \"nanurmik\" \n- So animal names are nouns \n- So \"wolf\" is a noun \n- So \"your wolf\" = \"v\" + \"wolf\" \n- So full phrase: \"v wolf uk iakha", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11512.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "planner_output": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "anchor_output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well," + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "We are given a set of Inuktitut sentences with English translations, and we are to translate five new sentences into Inuktitut.\n\nStep-by-step analysis:\n\nFirst, identify patterns in the given examples:\n\nExample 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \nStructure: Subject (your dog) + verb (saw) + object (you). \n\"Qingmi\" = dog; \"v\" = marked for third person, past tense; \"takujaatit\" = saw you. \n\"v\" appears after subject, and the verb has an \"it\" suffix meaning \"you\" as object. \nSo: [subject] + [verb root] + [object] → (S + V + O)\n\nExample 2: \n\"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \nSubject: \"Inuuhuktuup\" = the boy (possibly \"inuuhuk\" + \"tuup\" = boy) \nVerb: \"qukiqtanga\" = shot (qukiq + tanga = past tense, active) \nObject: \"iluaqhaiji\" = doctor \nSo: [subject] + [verb] + [object]\n\nExample 3: \n\"Aanniqtutit\" → \"You hurt yourself.\" \n\"Anni\" + \"qtut\" → hurt; \"it\" → yourself (reflexive). \nSo: [subject] + [verb root] + [reflexive marker it]\n\nExample 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \nSubject: \"iluaqhaiji\" → doctor \nVerb: \"aarqijaatit\" → cured you → \"aarqi\" = cure; \"j\" + \"aati\" = you; \"t\" = past tense. \nAgain, [subject] + [verb] + [object]\n\nExample 5: \n\"Qingmiq iputujait\" → \"You speared the dog.\" \n\"Qingmiq\" → you (subject) + \"iputuj\" = speared? But \"iputujait\" → speared (dog) \n\"iputuj\" + \"ait\" → past tense, object particle \nSo: [subject] + [verb] + [object] (with \"ait\" marking object)\n\nExample 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \nShaman: \"Angatkuq\" \nVerb: \"aarqisijuq\" = cured → \"aarqi\" + \"s\" + \"ijuq\" = past tense, object = doctor? \nObject: \"iluaqhaijimik\" = a doctor (mik = a, article). \nSo: [subject] + [verb] + [object with definite article]\n\nExample 7: \n\"Nanuq qaijuq\" → \"The polar bear came.\" \nNanuq = polar bear; qaijuq = came (past tense) \nNo object — intransitive verb.\n\nExample 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \nSubject: \"iluaqhaijivit\" = your doctor (iluaqhaiji + vit = your) \nVerb: \"aarqijanga\" = cured (aarqi + janga) \nObject: \"inuuhuktuit\" = your boy (inuuhuk + tuuit = your boy) \nSo: [your subject] + [verb] + [your object] → all with possessive markers\n\nExample 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \nSubject: \"Angunahuktiup\" = the hunter \nVerb: \"iputujanga\" = speared (iputuj + aanga) \nObject: \"amaruq\" = the wolf \nSo again: [subject] + [verb] + [object]\n\nExample 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \nSubject: \"Qingmiup\" = the dog \nVerb: \"ilinniaqtitsijiit\" = hurt → \"ilinniaqti\" + \"sijiit\" = hurt (with reflexive or object suffix?) \nObject: \"aanniqtanga\" = your teacher (aanniqt + a = your, \"a\" = possessive) \nSo verb has \"sijiit\" → likely object or intransitive. \nBut \"aanniqtanga\" = your teacher → object \nThus structure: [subject] + [verb] + [object]\n\nExample 11: \n\"Ukiakhaqtutit\" → \"You fell.\" → intransitive \n\"Ukiakhaq\" + \"tutit\" → fell → with \"tut\" = past tense, intransitive\n\nExample 12: \n\"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \nSubject: \"Angunahukti\" = the hunter \nVerb: \"qukiqsijuq\" = shot → \"qukiq\" + \"sijuq\" \nObject: \"nanurmik\" = a polar bear \nSo: [subject] + [verb] + [object]\n\nPattern summary:\n\n- Most verbs are intransitive or transitive.\n- Transitive verb: [subject] + [verb root] + [object]\n- Object is marked with a suffix: -it, -a, -mik, -jiit, -anga — but often a determiner prefix or possessive\n- Possession appears in prefixes: \"v\" for your (in 1), \"vit\" for your (in 8), \"up\" for you (in 5), \"mik\" for a (in 12), \"a\" for your (in 10 — \"aanniqtanga\")\n- Reflexive: \"it\" at end (e.g. \"aanniqtutit\") — \"you hurt yourself\"\n- Intransitive: no object → just subject + verb (e.g. \"Nanuq qaijuq\")\n\nMorphological patterns:\n\n- Subject: noun phrase with possessive or article\n- Verb: root + tense/aspect suffix\n- Object: object noun, sometimes with article or possessive\n\nNow, translate the requested sentences:\n\n19. The shaman hurt you. \n→ \"Shaman\" = \"Angatkuq\" (from ex.6) \n\" hurt\" = \"aanniqt\" (from ex.3: \"aanniqtutit\" = you hurt yourself) \n\"you\" = \"it\" (from ex.1, \"takujaatit\" → saw you) \nTense: past → suffix \"-it\" or \"-tut\"? \nEx.3: hurt yourself → \"aanniqtutit\" → \"ut\" = past \nEx.5: \"iputujait\" → speared → \"ait\" = past \nSo \"tut\" or \"it\"? \nIn ex.3: \"aanniqtutit\" — injured (aanniqt) + \"utit\" → past \n\"ut\" vs \"it\" — seems \"ut\" is past tense for transitive verb? \nBut ex.6: \"aarqisijuq\" → cured (past), not \"it\" \nBetter: verb base + past suffix. \n\"Angatkuq\" + \"aanniqt\" + \"it\" = the shaman hurt you \nCheck: ex.3: \"aanniqtutit\" → underwent injury — “ut” may be marker of past tense \nBut ex.4: \"aarqijaatit\" → cured you → has \"aati\" \nIn ex.3, \"aanniqtutit\" — “tut” → past \nIn ex.5: \"iputujait\" — \"ait\" → past \nSo multiple past suffixes? \nBut note: \"aanniqtutit\" — \"tut\" is past tense \n\"aanniqtit\" → would be present? Not likely. \nOverall, in transitive verbs, past tense is marked with a suffix like \"it\", \"t\", \"tut\", or \"jiit\" \nBut in ex.3: \"aanniqtutit\" → hurt yourself → \"utit\" \nIn ex.10: \"ilinniaqtitsijiit\" → hurt → \"sijiit\" → past \nSo the past tense mark is different per verb root.\n\nBut — in ex.19: \"The shaman hurt you\" — parallels \"You hurt yourself\" → object = \"you\" → \"it\" \nSo: \"Angatkuq\" + \"aanniqt\" + \"it\" → \"Angatkuq aanniqt it\"? \nBut in ex.3: \"You hurt yourself\" = \"aanniqtutit\" — subject = you, verb = hurt, object = yourself \nSo: \"aanniqtutit\" → \"aanniqt\" + \"utit\"? \nBut \"it\" is ending — not \"utit\" \nPossibility: \"aanniqt\" + \"ut\" = hurt → past? \nBut ex.3: \"aanniqtutit\" — elongated? \n\"ut\" + \"it\" → \"utit\"? \nPerhaps \"it\" is the suffix meaning \"you\", not past tense.\n\nWait — in ex.3: \"Aanniqtutit\" → you hurt yourself → past tense and reflexive \nSo past tense is -ut or -utit? \nIn ex.1: \"Qingmivit takujaatit\" → your dog saw you → verb is \"takujaatit\" — saw you \n\"takuj\" + \"aati\"? → \"aati\" = you → object \n\"takuj\" + \"aati\" → saw you → regular \nBut verb root + object suffix? \nEx.4: \"aarqijaatit\" → cured you → verb root \"aarqi\" + \"j\" + \"aati\" → cured you \n\"j\" → perhaps complement? \nBut in ex.3: \"aanniqtutit\" — \"aanniqt\" + \"utit\" → hurt yourself?\n\nBut in ex.10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher \n\"ilinniaqtitsijiit\" — hurt → verb with \"sijiit\" → past? \nAlso, \"aanniqtanga\" = your teacher\n\nSo the verb root is followed by a suffix denoting object and/or past.\n\nWe see:\n\n- For \"hurt\": root = aanniqt \n- \"aanniqtutit\" → you hurt yourself → reflexive \n- \"ilinniaqtitsijiit\" → hurt someone → past and object \n- So possibly, past tense is marked by suffixes like -sijiit, -utit, -aati, -it\n\nBut we must find the pattern for \"the shaman hurt you\"\n\nFrom ex.6: \"Angatkuq iluaqhaijimik aarqisijuq\" → the shaman cured a doctor \n\"aarqisijuq\" → cured → \"aarqi\" + \"sijuq\" \nSo past tense marked by \"sijuq\" \nSimilarly, in ex.12: \"qukiqsijuq\" → shot a polar bear → \"qukiq\" + \"sijuq\" \nIn ex.9: \"iputujanga\" → speared → \"iputuj\" + \"anga\" — not \"sijuq\"\n\nInconsistency in suffix? \nBut in ex.8: \"aarqijanga\" → cured → \"aarqi\" + \"janga\" \nSo \"janga\" and \"sijuq\" both past tense?\n\nCheck ex.5: \"Qingmiq iputujait\" — you speared the dog → \"iputuj\" + \"ait\" → past \nEx.2: \"qukiqtanga\" — shot → \"qukiq\" + \"tanga\" → past \nSo different verbs have different past suffixes.\n\nThis suggests that the past tense does not have one universal suffix. The object is marked differently per verb.\n\nWe need the object marker:\n\nIn ex.1: \"Qingmivit takujaatit\" → your dog saw you → \"aati\" = you \nIn ex.4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → \"aati\" = you \nIn ex.5: \"Qingmiq iputujait\" → you speared the dog → \"ait\" = dog \nSo \"aati\" = you, \"ait\" = object (dog), \"it\" = you (in reflexive)\n\nIn ex.10: \"aanniqtanga\" → your teacher — \"aanniqt\" + \"a\" → for object \"your teacher\"\n\nSo, in general:\n\n- Object: marked with suffix like -a, -it, -mik, -jiit, -anga — depending on verb\n- Reflexive: -it with subject being self\n\nNow back to 19: \"The shaman hurt you\"\n\n\"The shaman\" = \"Angatkuq\" \n\"hurt\" = from \"aanniqt\" \n\"you\" = \"it\" (as in ex.1 \"takujaatit\" — saw you; \"aati\" = you, but \"it\" also appears in \"aanniqtutit\" — hurt yourself)\n\nBut ex.3: \"aanniqtutit\" — \"aanniqt\" + \"utit\" → hurt you (yourself) \nSo \"ut\" is part of past tense? But in ex.10: \"ilinniaqtitsijiit\" — \"sijiit\" (past) \nSo verb-specific past suffix.\n\nBut what is the object marker for \"you\"?\n\nIn ex.1: \"takuj aati\" → saw you \nIn ex.4: \"aarqi aati\" → cured you \nSo \"aati\" = you (object)\n\nIn ex.3: reflexive → \"you hurt yourself\" → \"aanniqtutit\" → \"utit\" = past and reflexive \nSo \"it\" is not used as object.\n\nThus, for object \"you\", use \"aati\"\n\nSo for 19: \"Angatkuq aanniqt aati\" → the shaman hurt you?\n\nBut in ex.6: \"Angatkuq iluaqhaijimik aarqisijuq\" — the shaman cured a doctor → object = \"iluaqhaijimik\" (a doctor) → \"mik\" = article \nSo \"mik\" is used for \"a\"\n\nSimilarly, in ex.10: \"aanniqtanga\" → your teacher → \"a\" = possessive\n\nSo we need to determine: is \"aati\" used for \"you\" as object?\n\nYes: in ex.1, ex.4 → object \"you\" → \"aati\"\n\nSo: the shaman hurt you → \"Angatkuq aanniqt aati\"\n\nIs past tense marked? In \"aanniqt aati\" — no suffix. But in ex.3: \"aanniqtutit\" → includes \"utit\"\n\nSo if \"ut\" is past, then \"aanniqtut\" + \"it\"? But \"aanniqtutit\" — \"utit\"\n\nPossibility: verbal root + past tense suff + object marker\n\nIn ex.3: aanniqtutit → hurt yourself → reflexive → object = self → past\n\nIn ex.1: takuj aati → past with \"aati\" → \"takuj\" + \"aati\" → saw you — no past suffix?\n\nBut \"takuj\" — is it past? \"takujaatit\" → full form → \"aati\" at end\n\nWait — full form: \"takujaatit\" = saw you \n\"takuj\" + \"aati\" + \"it\"? → no\n\nActually: \"takuj\" + \"aati\" + \"it\"? → that would be too long.\n\nBreak down ex.1: \"Qingmivit takujaatit\" \nSubject: Qingmivit → your dog (Qingmi + vit) \nVerb: takujaatit → \"takuj\" + \"aati\" + \"it\"? \n\"takuj\" = saw → verb root, \"aati\" = you, \"it\" = past tense? \nBut in ex.4: \"aarqijaatit\" → \"aarqi\" + \"ja\" + \"aati\"? → no\n\n\"aarqijaatit\" → \"aarqi\" + \"ja\" + \"aati\"? \nActually, \"aarqijaatit\" — likely \"aarqi\" + \"j\" + \"aati\" → cured you \n\"j\" may be past tense.\n\nSo past tense may be incorporated into verb root or object.\n\nBest approach: look for equivalent constructions.\n\nEx.3: \"You hurt yourself\" → \"aanniqtutit\" — only verb form, no separate object marker \nEx.10: \"The dog hurt your teacher\" → \"ilinniaqtitsijiit aanniqtanga\" → verb has \"sijiit\", object has \"aanniqtanga\" \nSo verb root + past suffix + object\n\nSince \"hurt\" is the verb, and verb root is \"aanniqt\", and in ex.3 it has \"utit\", so use \"aanniqtutit\" for \"hurt you (reflexive)\" but we need \"hurt you (object)\"\n\nSo \"aanniqt\" + \"ut\" → hurt you? \nIn ex.10: \"ilinniaqtitsijiit\" → hurt → \"sijiit\" → past, object present → so \"sijiit\" = past tense with object\n\nThus, \"aanniqt sijiit\" → hurt (past)\n\nBut no standalone \"aanniqt\" + object suffix.\n\nWe see in ex.3: \"aanniqtutit\" → hurt yourself — reflexive \nIn ex.10: \"ilinniaqtitsijiit\" → hurt (object) — past tense with object \nSo the past tense is built into the verb form.\n\nTherefore, the verb \"hurt\" is marked with a past suffix like -sijiit or -ut\n\nIn ex.3: \"aanniqtutit\" → past \nIn ex.10: \"ilinniaqtitsijiit\" → past with object", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11232.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "anchor_output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well," + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given examples in Inuktitut with English translations, and we are to translate five new sentences into Inuktitut.\n\nStep 1: Identify patterns from the examples.\n\nLook at verb forms and their objects/subjects.\n\nExample 1: \n\"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog + saw (past tense, verb) \n- \"takujaatit\" = saw you (voice: transitive, object \"you\") \n→ Structure: [Subject] + [verb] + [object] \n→ Subject: \"your dog\" → \"Qingmivit\" (Qingmi + your + \"v\" for verb, i? Or a suffix for possession?) \nBut note: \"Qingmivit\" is likely \"your dog\" + past tense verb stem.\n\nWait — look at Example 3: \n\"Aanniqtutit\" → \"You hurt yourself\" \n→ \"Aanniqtutit\" → subject is \"you\", verb is \"hurt\", object is \"yourself\" \n→ \"aanni\" = hurt; \"qutit\" = past tense, reflexive? Possibly. \n\nExample 4: \n\"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" \n→ \"iluaqhaiji\" + \"up\" → \"the doctor\" \n→ \"aarqijaatit\" → cured you \n→ \"aarqisijuq\" in example 6 → \"cured a doctor\" \n→ So \"aarqisijuq\" = cured + object (doctor) \n→ \"aarqijaatit\" = cured you → verb root \"aarqij\" + suffix for \"you\", past tense\n\nExample 5: \n\"Qingmiq iputujait\" → \"You speared the dog\" \n→ \"Qingmiq\" = you + speared (verb) \n→ \"iputujait\" = speared the dog \n→ So \"iputujait\" = verb stem + object \"the dog\"\n\nExample 6: \n\"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = the shaman \n→ \"iluaqhaijimik\" = a doctor (determiner + noun) \n→ \"aarqisijuq\" = cured (verb) \nSo verb form: [noun] + [object] + [verb (past)] → verb is \"aarqisijuq\", which likely has suffix for \"cured\" and for object\n\nExample 7: \n\"Nanuq qaijuq\" → \"The polar bear came\" \n→ \"Nanuq\" = the polar bear \n→ \"qaijuq\" = came? (past tense)\n\nExample 8: \n\"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy\" \n→ \"iluaqhaijivit\" = your doctor \n→ \"inuuhuktuit\" = your boy \n→ \"aarqijanga\" = cured (verb?) \n→ \"aarqijaatit\" = cured you → \"aarqij\" + \"a\" + \"ng\" → looks like object + verb form \n→ likely verb is \"aarqij\" (to cure), with object suffix and past tense\n\nExample 9: \n\"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"Angunahuktiup\" = the hunter \n→ \"amaruq\" = the wolf \n→ \"iputujanga\" = speared \n→ \"iputuj\" is root for \"to spear\"\n\nExample 10: \n\"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" = the dog \n→ \"ilinniaqtitsijiit\" = hurt your teacher \n→ \"aanniqtanga\" = hurt (verb) + object \"teacher\" \n→ So verb \"aanniqt\" = hurt, with object suffix\n\nNow extract patterns:\n\nVerb roots and their object suffixes:\n\n- \"aarqij\" → cure → \"aarqijaatit\" = cured you \n- \"iputuj\" → spear → \"iputujait\" = speared the dog → \"iputujanga\" = speared (but \"anga\"? \"ait\"? \"anga\" vs \"ait\") \nWait: in example 5: \"iputujait\" \nIn example 9: \"iputujanga\" \nSo object form may depend on object's case/numeral?\n\nBut in example 5: \"You speared the dog\" → \"Qingmiq iputujait\" → \"iputujait\" \nIn example 9: \"The hunter speared the wolf\" → \"Angunahuktiup amaruq iputujanga\" → \"iputujanga\" \nSo both have same root, different suffix → \"ait\" vs \"anga\"\n\nBut in example 9, object is \"amaruq\" → \"the wolf\" — definite \nIn example 5, object is \"the dog\" — definite \nSo both are definite objects.\n\nPossibility: the verb is marked for object with suffix based on object's noun type? Or it's just a past tense suffix.\n\nMore importantly, look at possessive markers.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n\"Qingmivit\" = your dog → \"Qingmi\" (dog) + \"v\" (your) + \"it\" (past)? \nBut in example 8: \"iluaqhaijivit\" → \"your doctor\" → \"iluaqhaiji\" (doctor) + \"vit\" → \"your doctor\"\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself\" → \"aanniqt\" = hurt, \"utit\" = yourself? \n\"utit\" = reflexive suffix?\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" → object \"you\" → \"aarqijaatit\" → \"aarqij\" (cure) + \"a\" (you) + \"t\" + \"it\"? \n\nBut compare to example 1: \"takujaatit\" → saw you — \"takuj\" (saw) + \"a\" (you) + \"t\" + \"it\"?\n\nYes — both \"takujaatit\" and \"aarqijaatit\" have \"a\" + \"t\" + \"it\"? \n\"takujaatit\" → t, a, j, a, a, t, i, t → \"takuj\" + \"a\" + \"atit\"? Or \"takujaatit\" → \"takuj\" + \"a\" + \"atit\"?\n\nWait: possibly a pattern:\n\n- Objects are marked with suffix like \"a\" (you), \"up\" (the), \"mik\" (a), \"vit\" (your)\n\nSo:\n\n- \"takujaatit\" → saw you → object \"you\" marked with \"a\" + \"t\" + \"it\"? \nBut \"takuj\" is root, then \"a\" (you), then \"t\" (aspect?) + \"it\" (past)? \nCompare: example 5: \"iputujait\" → the dog → object \"dog\" → \"iputuj\" + \"ait\" → \"ait\" not \"a\" + \"t\" + \"it\"?\n\nIn example 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" \nIn example 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" \n\"ait\" vs \"anga\"\n\n\"ait\" and \"anga\" — could be different object markers?\n\nBut in example 1: \"takujaatit\" — \"a\" (you), \"t\" (tense), \"it\" (past)? \n\"aarqijaatit\" → cured you → same \"a\" + \"t\" + \"it\"\n\nBut \"iluaqhaijimik\" → \"a doctor\" → \"mik\" (a) \n\"amaruq\" → \"the wolf\" → \"up\"? \"amaruq\" → \"the wolf\"? No — \"Angunahuktiup\" = the hunter → \"up\"\n\n\"amaruq\" → is it \"the wolf\"? Yes — adjective or noun?\n\nPossibility: object markers:\n\n- \"a\" → you \n- \"mik\" → a (indeterminate) \n- \"up\" → the (definite) \n- \"vit\" → your (possessive)\n\nBut in example 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n→ \"iluaqhaijivit\" = your doctor \n→ \"inuuhuktuit\" = your boy \n→ \"aarqijanga\" = cured → verb form without \"a\" or \"t\"?\n\n\"aarqijanga\" → verb with past? Compared to \"aarqijaatit\" = cured you.\n\nSo \"aarqijaatit\" → cured you \n\"aarqijanga\" → cured (someone)? Or cured with object?\n\nWait — in example 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" \n→ \"aarqisijuq\" → cured a doctor → so object \"a doctor\" → \"mik\" (a) → \"iluaqhaijimik\"\n\nSimilarly, example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" \n→ \"ilinniaqtitsijiit\" = hurt your teacher → \"sijiit\" → your teacher?\n\nSo \"sijiit\" → object marked with \"siji\" + \"it\" → \"your teacher\"?\n\nPossibility: object markers built from possessive + noun + suffix?\n\nNow, go to the translations:\n\n19. The shaman hurt you.\n\n\"The shaman\" → in example 6: \"Angatkuq\" = the shaman \n→ \"Angatkuq\" — verb root? Or noun?\n\n\"Angatkuq\" → \"the shaman\" \nSimilarly, \"Nanuq\" → \"the polar bear\"\n\nSo \"Angatkuq\" = the shaman\n\nHurt → in example 3: \"Aanniqtutit\" → \"you hurt yourself\" → \"aanniqt\" = hurt, \"utit\" = yourself \n\nBut \"aanniqt\" is root → verb root for hurt\n\nSo \"aanniqt\" + object \n\nObject: \"you\" → represented by \"a\" + suffix?\n\nIn example 3: \"aanniqtutit\" — \"aanniqt\" + \"utit\" → \"utit\" = yourself? \nBut no \"a\" — is \"utit\" reflexive?\n\nCompare with example 1: \"takujaatit\" → saw you → \"a\" present?\n\nIn example 4: \"aarqijaatit\" → cured you → \"a\" present\n\nIn example 1: \"takujaatit\" → \"a\" + \"t\" + \"it\"? \"takuj\" + \"a\" + \"atit\"? But is it \"a\" + \"t\" + \"it\"?\n\n\"takujaatit\" — after \"a\", it's \"jaa\" — no. \nBreak down:\n\n- takujaatit → takuj + aatit? \n\nWait — better to use known constructions.\n\nFrom example 3: \"Aanniqtutit\" → you hurt yourself → object is \"yourself\", so reflexive — \"utit\"\n\nSo hurt someone else → \"aanniqt\" + object marker\n\nIn example 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" \n→ \"aanniqtanga\" = hurt → verb form \n→ \"ilinniaqtitsijiit\" = your teacher? \n→ verb is \"aanniqtanga\"\n\nCompare to \"aanniqtutit\" — \"utit\" vs \"aanniqtanga\"\n\nSo when object is \"you\", it's \"utit\"? \nBut in example 10, object is \"your teacher\" → \"sijiit\"? \n\n\"ilinniaqtitsijiit\" — appears to be \"ilinniaqtitsijiit\" = your teacher \n\n\"ilinniaqtitsijiit\" → \"ilinniaqt\" + \"sijiit\"? \n\nSimilarly, in example 8: \"inuuhuktuit\" → your boy → \"inuuhuk\" + \"tuit\"? \n\nSo:\n\n- possessive marker + noun → object\n\nSo verb takes object suffix:\n\n- when object is \"you\" → \"utit\" → reflexive \n- when object is \"a person\" → possessive + noun → e.g., \"sijiit\" (your teacher), \"tuit\" (your boy)\n\nBut in example 1: \"your dog saw you\" → \"Qingmivit takujaatit\" → \"takuj\" + \"a\" + \"atit\"? \"a\" for you?\n\n\"takujaatit\" → likely \"takuj\" + \"a\" + \"atit\"\n\nSimilarly, \"aarqijaatit\" → \"aarqij\" + \"a\" + \"atit\"\n\n\"iputujait\" → \"iputuj\" + \"ait\"? \n\"iputujanga\" → \"iputuj\" + \"anga\"\n\nSo verb suffix depends on object:\n\n- \"you\" → \"a\" + \"t\" (or \"at\") + \"it\"? \n- \"a person\" → \"mik\" + noun → \"iluaqhaijimik\" \n- \"my teacher\" → \"sijiit\" → object marker for \"your teacher\"\n\nBut for verbs: \n- hurt → \"aanniqt\" \n- cure → \"aarqij\" \n- see → \"takuj\" \n- spear → \"iputuj\"\n\nTense: all past — all verbs have -it or -anga or -ait → all past tense.\n\nSo for 19: \"The shaman hurt you\"\n\nSubject: \"the shaman\" → \"Angatkuq\" (from example 6) \nVerb: hurt → \"aanniqt\" \nObject: \"you\" → \"a\" + \"t\" + \"it\"? → \"a\" + \"t\" + \"it\" → \"atit\"? → \"aanniqtatit\"?\n\nBut example 3: \"Aanniqtutit\" → you hurt yourself — \"utit\" for yourself\n\nSo for \"you\", not reflexive, use \"a\" + \"t\" + \"it\" → \"atit\"?\n\n\"takujaatit\" → saw you → has \"a\" and \"atit\"? \"takuj\" + \"a\" + \"atit\"? — possible\n\nBut \"takujaatit\" — letters: t a k u j a a t i t → \"a\" then \"aatit\"? Or \"a\" + \"t\" + \"it\"?\n\nLikely: object marker for \"you\" is \"-a\" + \"-t\" + \"-it\" → \"-atit\"\n\nBut \"utit\" is reflexive (yourself).\n\nSo for \"you\" → use \"a\" + \"t\" + \"it\" = \"atit\"\n\nSo verb: \"aanniqt\" + suffix → \"aanniqtatit\"\n\nBut in example 3: \"aanniqtutit\" → not \"aanniqtatit\"\n\n\"utit\" vs \"atit\" — different.\n\n\"aanniqt\" + \"utit\" = you hurt yourself \n\"aanniqt\" + \"atit\" = you hurt you? — redundant?\n\nBut \"you\" is not reflexive — in example 10: \"the dog hurt your teacher\" → verb is \"aanniqtanga\", not \"aanniqtatit\"\n\nIn example 10: \"aanniqtanga\" — \"aanniqt\" + \"anga\" — so \"anga\" not \"atit\"\n\nSimilarly, in example 1: \"takujaatit\" — \"a\" + \"atit\"? → \"a\" + \"atit\"\n\nBut \"aarqijaatit\" — \"a\" + \"atit\"\n\nSo only when object is \"you\" is there \"atit\" or \"utit\"?\n\nExample 8: verb is \"aarqijanga\" — cured → \"aarqij\" + \"anga\"\n\nIn example 10: \"aanniqtanga\" — hurt → \"aanniqt\" + \"anga\"\n\nSo for object that is a person, the object marker may be \"anga\" or \"atit\"?\n\nBut in example 1: \"takujaatit\" — object \"you\" → \"atit\" \nIn example 4: \"aarqijaatit\" → object \"you\" → \"atit\"\n\nIn example 10: \"aanniqtanga\" → object \"your teacher\" → \"anga\"? \n\nBut \"ilinniaqtitsijiit\" — object marker \"sijiit\" — so not just \"anga\"\n\nPossibility: object markers:\n\n- \"a\" → you \n- \"mik\" → a \n- \"up\" → the \n- possessive + noun → \"your\" + noun\n\nAnd verb + object marker\n\nSo verb root + object suffix\n\nFrom examples:\n\n- \"takuj\" + \"a\" + \"atit\" = saw you \n- \"iputuj\" + \"ait\" = speared dog \n- \"iputuj\" + \"anga\" = speared wolf \n- \"aarqij\" + \"a\" + \"atit\" = cured you \n- \"aarqij\" + \"anga\" = cured doctor (in example 6: \"aarqisijuq\"? — \"isijuq\" for \"a doctor\"?)\n\nExample 6: \"aarqisijuq\" → cured a doctor → \"a\" + \"sij\" + \"uq\"? \n\n\"iluaqhaijimik\" → a doctor → \"mik\" \n\"aarqisijuq\" → \"aarqij\" + \"sijuq\"? \"sijuq\" — \"siju\" + \"q\" → \"sijuq\"?\n\nNo clear suffix.\n\nBut in example ", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10789.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "anchor_output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well," + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "groot_1x4", + "sample_index": 0, + "output": "The task is to translate several sentences into Nooni, spoken on Bvumbon. The key is to identify the temporal and grammatical patterns from the given examples.\n\nStep 1: Identify temporal markers. \nIn sentence 1: \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → \"fɔgò\" = \"yesterday\" \nSentence 5: \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"fɔ̀ shě\" = \"the day after tomorrow\" \nSentence 8: \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"ntfǔː\" = \"tomorrow\" \nSentence 11: \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\" → \"kefwé cí\" = \"the day before yesterday\" \n\nThus, temporal expressions use prefixes: \n- \"fɔ̀ shě\" = day after tomorrow \n- \"ntfǔː\" = tomorrow \n- \"kefwé cí\" = day before yesterday \n- \"fɔgò\" = yesterday \n\nNo universal temporal marker like \"today\" appears as a standalone word or prefix. \nHowever, sentence 9: \"Today, I chose the book\" → \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" → has no temporal prefix. \nSentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" marks \"just now\", not \"today\". \n\nSo \"today\" is not marked by a prefix. In the absence of a named day, \"today\" is implied by context — the day being spoken on (Bvumbon). Therefore, when a sentence says \"today\", it may be omitted or expressed by the speaker's current day.\n\nStep 2: Identify subject markers. \nSentence 1: \"On Bvumbon, I came to the market\" → \"me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn\" → \"me\" = I \nSentence 2: \"On Bvusɔw, you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" = you(sg) \nSentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"wvù\" = he \nSentence 14: \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"bèsèn\" = we \n\nSo \"me\" = I, \"wɔ̀\" = you(sg), \"wvù\" = he, \"bèsèn\" = we \nNote: \"wɔ̀\" is not used for \"today\" as a temporal marker, but as subject for \"you(sg)\".\n\nStep 3: Identify future and present tense markers. \nSentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = will \nSentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"me nú\" = I will \nSentence 14: \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"géː cɔ́ŋ\" = will steal \n\nSo \"will\" is expressed by the prefix \"kwɔ᷆ːn\" (for intransitive or transitive verbs), or by context. \n\"nú\" in \"me nú mbóy\" signals future (\"I will choose\"). \n\"nú\" appears in \"me nú mbóy\" and \"me nú mbɛ̂ː\" — both future. \nThus, \"nú\" = future tense.\n\nStep 4: Identify past tense. \nSentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"tɔ̀\" = heard (past), \"nɔ̂ː\" = long time ago \nSentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = just now (past), \"nɔ̂ː\" = just now \n\nSo past tense is marked by tense prefixes like \"tɔ̀\", \"bɔ́\", or by context. \n\"bɔ́\" = just now, \"tɔ̀\" = heard, \"fɔ̀\" = after, etc.\n\nStep 5: Translate the target sentences.\n\n20. On Bvusɔw, I helped the man. \n- \"I\" = \"me\" \n- \"helped\" = past tense; in sentence 3, \"bóy fí me\" = \"helped me\" → \"fí\" = help, \"bóy\" = the woman → so \"helped\" is \"bóy fí\" or \"fí\" verb with object? \n- In sentence 3: \"kwɔ᷆ːn nǔ bóy fí me\" → \"nǔ\" = the woman, \"fí\" = help, \"me\" = me → so \"fí\" is transitive, takes object. \n- In sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = saw \n- So \"saw\" = \"cǐ\", \"helped\" = \"fí\"? But \"fí\" is not used as a verb. \n\nWait: in sentence 3: \"the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\" → subject: \"nǔ bóy\", verb: \"fí\", object: \"me\" \nBut in sentence 2: \"you will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"yúː cɔ́ŋ\" = steal \nSo for \"help\", use \"fí\" as verb. \n\nBut in sentence 12: \"I am about to help the man\" → \"me nú nfí dìɛ̀msɛ̌n\" → \"nfí\" = am about to help \nThus, \"help\" = \"fí\", \"nfí\" = about to help (future immediate). \nSo \"helped\" = past \"fí\"? But in 3, it is \"kwɔ᷆ːn\", future. \n\nNo past form of \"fí\" is shown. \nBut sentence 15: \"They saw me\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = just now, past. \n\"helped\" is not directly attested. \n\nBut in sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = saw \nSo \"saw\" = \"cǐ\", \"helped\" = not directly. \n\nBut is there a past form of help? In the absence of an example, assume past tense is contextually implied. \n\nIn 20: \"I helped the man\" → \"me fí dìɛ̀msɛ̌n\" → no tense marker? But \"fí\" is only in future. \n\nWait: sentence 12: \"I am about to help\" → \"me nú nfí dìɛ̀msɛ̌n\" → \"nú\" = future \nThe past form may not exist — or may be built with a past prefix. \n\nNo example of past \"help\" exists. \nBut in sentence 7: \"you heard\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"tɔ̀\" = past, \"heard\" = \"yo᷅w cɔ̌ŋ\"? \"yo᷅w\" is \"the woman\" — not fit. \n\n\"yo᷅w cɔ̌ŋ\" = \"the thief\" → so \"heard the thief\" = \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"tɔ̀\" = heard \n\nSo \"heard\" = \"tɔ̀\", with object. \n\nSo verb \"help\" likely has a past form. In sentence 3: \"will help\" → \"kwɔ᷆ːn\", so \"will\" = \"kwɔ᷆ːn\" \nThen \"helped\" = \"fí\" with past tense? But \"fí\" appears only with future. \n\nAlternative: \"helped\" may be expressed via \"fí\" without tense prefix, but the context shows past. \n\nSince no example of past \"help\" exists, and the only future form exists with \"kwɔ᷆ːn\", perhaps the future \"will help\" is \"kwɔ᷆ːn fí\", and past is not marked. \n\nIn sentence 13: \"the woman saw\" = \"cǐ\", past. \nSo \"saw\" = \"cǐ\" → may be past. \n\nThus, for \"helped\", use \"fí\" with tense? Or in context, \"fí\" is used. \n\nBut in sentence 12: \"I am about to help\" → \"me nú nfí\" → \"nfí\" = help (future immediate) \nSo base verb is \"fí\" \n\nTherefore, \"I helped\" → must be future tense with \"nú\"? But \"nú\" = future, not past. \n\nNo past tense marker for help. \n\nThus, the only available form is \"fí\" — and since it's past, use without tense prefix. \nBut \"fí\" only appears with future in the data. \n\nCritical point: in sentence 3, \"kwɔ᷆ːn nǔ bóy fí me\" → \"fí\" is in the future clause. \nIn sentence 12: \"me nú nfí\" → future. \nSo \"fí\" is always with affix like \"kwɔ᷆ːn\" or \"nú\". \n\nThere is no example of \"fí\" without a future prefix. \n\nThus, \"helped\" must be with a past form. But no example. \n\nPossibility: the verb \"help\" is marked with \"fí\" and no tense, but in context, it's past. \n\nGiven that \"helped\" is past, and all tense markers are prefixes, perhaps \"fí\" is used without “nú” or “kwɔ᷆ːn”, but this is unsupported. \n\nAlternatively, the verb \"help\" is omitted or replaced. \n\nBut in sentence 15: \"They saw me\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = just now, so past. \n\nSo for “helped”, use \"fí\" with \"bɔ́\" = just now? But “bɔ́” is for \"just now\", not general past. \n\nNo general past marker. \n\nThis is a flaw. \n\nReconsider: in sentence 5, \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"nú\" = will \nSo \"I will choose\" = \"me nú mbóy ncáw\" → \"mbóy ncáw\" = choose \n\nIn sentence 3: \"the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me\" → \"kwɔ᷆ːn\" = will, \"fí\" = help \n\nTherefore, \"will\" = \"kwɔ᷆ːn\" (for \"will help\") \n\"will choose\" = \"nú\" (with \"me nú\") \n\nSo future tense is marked by \"nú\" or \"kwɔ᷆ːn\" depending on subject. \n\n\"nú\" is used with first person: \"me nú\" \n\"kwɔ᷆ːn\" is used with others: \"kwɔ᷆ːn nǔ\" = \"the woman will help\" \n\nThus, for \"I helped\", it is not future. \n\nBut there is no past tense verb for \"help\". \n\nIn the absence of data, assume that the verb \"help\" is not marked in past, or is used with a past tense prefix not present. \n\nBut in all examples, past tense is marked only with \"tɔ̀\" or \"bɔ́\". \n\nNo example of past \"help\". \n\nThus, for \"I helped the man\", use \"me fí dìɛ̀msɛ̌n\" — past form assumed from base. \n\nBut this is unsupported. \n\nBetter: in sentence 12: \"I am about to help\" → \"me nú nfí\" → \"nfí\" = about to help \n\"help\" = \"fí\" \nSo \"helped\" = not available. \n\nConclusion: the only possible form is \"me fí dìɛ̀msɛ̌n\" — taking \"fí\" as the verb \"help\" in past without tense marker. \n\nUse it with context. \n\n20. On Bvusɔw, I helped the man → \"me fí dìɛ̀msɛ̌n nú bvusɔw\" → \"fí\" = help, \"dìɛ̀msɛ̌n\" = man, \"nú bvusɔw\" = on Bvusɔw \n\nBut \"nú\" is future — not suitable. \n\n\"nú\" is for future — so cannot use for past. \n\nSo \"on Bvusɔw, I helped\" = \"me fí dìɛ̀msɛ̌n cǐ nú bvusɔw\" — \"cǐ\" = saw? No, \"cǐ\" = saw. \n\nNo \"helped\" verb. \n\nWait: in sentence 13: \"the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = saw \nSo \"helped\" must be with another verb. \n\nThere is no other example. \n\nFinal decision: despite lack of example, use \"fí\" for \"helped\", and accept that past tense is expressed without an explicit marker in the data. \n\nSo: \n20. me fí dìɛ̀msɛ̌n cǐ nú bvusɔw → but \"cǐ\" = saw, not \"helped\" \n\nNo. \n\nAnother possibility: \"helped\" = \"fí\" with object. \n\nIn sentence 3: \"nǔ bóy fí me\" = \"the woman help me\" → \"fí\" takes object. \n\nSo \"I helped the man\" = \"me fí dìɛ̀msɛ̌n\" — subject \"me\", verb \"fí\", object \"dìɛ̀msɛ̌n\" \n\nBut in past tense? No marker. \n\nSo use without tense. \n\nThus, 20: me fí dìɛ̀msɛ̌n cǐ nú bvusɔw \n\nBut \"cǐ\" = saw — cannot be used. \n\nNo. \n\nThe only verb for \"help\" is not found. \n\nGiven the data, we may assume that \"helped\" is expressed with \"fí\", and the day is added with \"cǐ nú\" or \"nú\". \n\nBut \"cǐ\" = saw. \n\nSo for \"helped\", use a placeholder. \n\nThis suggests a flaw in assumptions. \n\nRevisit: in sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = saw \n\nSo \"saw\" = \"cǐ\" \n\nIs \"help\" used? Only in \"fí\" with \"will\" or \"about to\". \n\nTherefore, \"helped\" not in data. \n\nThis cannot be. \n\nAlternative: \"helped\" = \"fí\" in past tense, and in sentence 12, \"me nú nfí\" = future, so past tense is not marked. \n\nBut in sentence 15: \"they saw me\" → \"bɔ́\" = just now — so past is marked. \n\nSo past tense is marked by context, not verb. \n\nThus, for 20: \"On Bvusɔw, I helped the man\" → \"me fí dìɛ̀msɛ̌n nú bvusɔw\" \n\nUse \"fí\" as verb, assume past. \n\nSimilarly: \n21. The thief stole the yam just now. \n- \"the thief\" = \"yo᷅kwɔ᷆ːn\" (from sentence 6: \"he killed the woman\" = \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"yo᷅kwɔ᷆ːn\" = woman? No — \"yo᷅kwɔ᷆ːn\" = woman? In sentence 6: \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"wvù\" = he, \"yo᷅kwɔ᷆ːn\" = the woman → so \"yo᷅kwɔ᷆ː", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10178.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "planner_output": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "anchor_output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "groot_1x4", + "sample_index": 1, + "output": "We are given a series of Nooni sentences spoken on different days of the Nooni “week” and their English translations. Our task is to translate five new sentences into Nooni, all spoken on **Bvumbon**, based on patterns observed in the existing examples.\n\n---\n\n### Step 1: Identify the structure of time expressions\n\nWe observe time references like:\n\n- \"Yesterday was Bvumbon\" → sentence 1 \n- \"On Bvusɔw, you(sg) will steal the yam\" → sentence 2 \n- \"The day after tomorrow is Bvutfu\" → sentence 5 \n- \"Tomorrow is Bvuŋkaden\" → sentence 8 \n- \"The day before yesterday was Bvuŋka\" → sentence 11 \n\nWe can extract the time markers and their relationships:\n\n| English | Nooni | Interpretation |\n|--------|-------|----------------|\n| Yesterday was X | fɔgò cǐ nú X | present tense, past |\n| Today is X | X de (or similar) | present |\n| The day after tomorrow is X | fɔ̀ shě ntfǔː nú X | future, +2 days |\n| Tomorrow is X | ntfǔː nú X de | future, +1 day |\n| The day before yesterday was X | kefwé cí nú X | past, -2 days |\n\nSo, time expressions use a base day (e.g. Bvumbon) and a temporal modifier.\n\n---\n\n### Step 2: Identify temporal adverbials\n\nFrom sentence 1:\n- \"Yesterday was Bvumbon\" → fɔgò cǐ nú bvúmbòn → “Yesterday was Bvumbon”\n\nFrom sentence 5:\n- \"The day after tomorrow is Bvutfu\" → fɔ̀ shě ntfǔː nú bvútfu᷅ → “The day after tomorrow is Bvutfu”\n\nFrom sentence 8:\n- \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → “Tomorrow is Bvuŋkaden”\n\nFrom sentence 11:\n- \"The day before yesterday was Bvuŋka\" → kefwé cí nú bvûŋka → “The day before yesterday was Bvuŋka”\n\nSo we see:\n\n- \"yesterday\" = fɔgò cǐ \n- \"tomorrow\" = ntfǔː \n- \"the day after tomorrow\" = fɔ̀ shě ntfǔː (literally \"the day after tomorrow\") \n- \"the day before yesterday\" = kefwé cí\n\nAlso note: \"On X\" is used to refer to events on that day.\n\nSo, “On Bvusɔw” → **wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w** (you will steal yam on Bvusɔw)\n\nThus, the structure for events on a day: \n**[on + day] + [subject] + [verb]**\n\n---\n\n### Step 3: Identify verb forms and auxiliary constructions\n\nLook at events involving **future** or **present**.\n\nSentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → “you will steal the yam on Bvusɔw”\n\nNote: \"will\" is expressed with “yúː cɔ́ŋ” (to steal)\n\nSentence 3: \"On Bvuzhi, the woman will help me\" → kwɔ᷆ːn nǔ bóy fí me bvúzhí → “the woman will help me on Bvuzhi”\n\n\"help\" = “fí” (to help)\n\nSentence 5: \"On Bvutfu, I will choose the car\" → me nú mbóy ncáw mutù bvútfu᷅ → “I will choose the car on Bvutfu”\n\nSo, present or future tense uses:\n- \"nú\" as a marker of relevance to a time point (on that day)\n- \"will\" is expressed via the verb stem in its basic form (e.g. cɔ́ŋ for steal, fí for help, ncáw for choose)\n\nNo separate auxiliary like \"will\" — verbs are used in their standard form with “nú” to denote the day.\n\nAlso, \"just now\" appears:\n\nSentence 15: \"They saw me at the market just now\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy → “they saw me at the market just now”\n\n\"just now\" = bɔ́ nɔ̂ː yɛ᷅n → “they saw just now”\n\nSo “just now” is **bɔ́ nɔ̂ː yɛ᷅n**\n\nCompare with sentence 7: \"You(sg) heard the thief a long time ago\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → “you heard the thief a long time ago”\n\nSo time expressions:\n\n- long time ago → tɔ̀ nɔ̂ː yo᷅w \n- just now → bɔ́ nɔ̂ː yɛ᷅n\n\nThus, time-of-occurrence modals are:\n\n- just now: bɔ́ nɔ̂ː yɛ᷅n \n- a long time ago: tɔ̀ nɔ̂ː yo᷅w \n\nNote: \"heard\" = cɔ̌ŋ (same as \"steal\"?) — might be a verb root.\n\n---\n\n### Step 4: Identify agent, object, and verb patterns\n\nGeneral structure:\n\nSubject + verb + object (if any) + time marker\n\nE.g., \n- \"On Bvusɔw, I helped the man\" → me nú fí dìɛ̀msɛ̌n → me nú + fí + dìɛ̀msɛ̌n → [I] [help] [the man]\n\nNote: In (12): \"I am about to help the man\" → me nú nfí dìɛ̀msɛ̌n → “am about to help”\n\n\"about to\" → **nfí** (future intention)\n\nIn (10): “The man is about to see him” → dìɛ̀msɛ̌n nú yɛ́n wvù lě → “the man is about to see him”\n\nSo “about to” = **nfí**\n\n\"see\" = yɛ́n \n\"help\" = fí\n\nSo verb roots:\n\n- steal = cɔ́ŋ \n- help = fí \n- choose = ncáw \n- hear = cɔ̌ŋ (same as steal?) — possibly root is shared? \n- see = yɛ́n \n- kill = bɛ̂ː? (saw in 6: “he killed the woman” → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n)\n\nYes: “he killed the woman” → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n → “he killed the woman”\n\nSo “kill” = bɛ̂ː (noun: ɛ̀bɛ̀n = woman)\n\nSo “will kill” = bɛ̂ː nǔ + object\n\nTherefore, for future events: subject + verb + object\n\nFor events in the recent past: verb + time adverbial like “just now”\n\n---\n\n### Step 5: Translate the required sentences — all spoken on Bvumbon\n\nWe now translate:\n\n#### 20. On Bvusɔw, I helped the man.\n\n- On Bvusɔw → wɔ̀ nǔ (subject) → but here subject is “I”\n- “I helped” → me nú fí dìɛ̀msɛ̌n\n- \"On Bvusɔw\" → so place the day at the front\n\nBut look at sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\n\nStructure: [on day] + [subject] + [verb] + [object]\n\nIn sentence 3: \"On Bvuzhi, the woman will help me\" → kwɔ᷆ːn nǔ bóy fí me bvúzhí\n\nSo pattern: [agent] [will] [help] [me] [on day]\n\nBut this has \"on day\" at the end.\n\nWait: in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → “you will steal the yam on Bvusɔw”\n\nSyntax: verb → then time?\n\nActually, all examples have time at the end: [verb + object] + [on day]\n\nCheck:\n\n- (2): wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → “you will steal the yam on Bvusɔw” → time at end\n- (3): kwɔ᷆ːn nǔ bóy fí me bvúzhí → “on Bvuzhi, the woman will help me” → again, time at end\n- (5): me nú mbóy ncáw mutù bvútfu᷅ → “on Bvutfu, I will choose the car” → time at end\n\nTherefore, the pattern is:\n\n**[subject] [verb] [object] [on day]**\n\nWith future/past tense expressed in verb form (e.g. cɔ́ŋ = steal, fí = help)\n\nSo for 20:\n\n- \"I\" = me \n- \"helped\" = fí \n- \"the man\" = dìɛ̀msɛ̌n \n- \"on Bvusɔw\" = bvúsɔ̀w\n\n→ me fí dìɛ̀msɛ̌n bvúsɔ̀w\n\nBut in earlier example, object comes before time?\n\nSentence 2: wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → object = yam, which comes just before time.\n\nAh — object is part of the verb phrase.\n\nSo better: subject + verb + object + (on day)\n\nThus: me fí dìɛ̀msɛ̌n bvúsɔ̀w\n\nYes — this matches sentence 3: kwɔ᷆ːn nǔ bóy fí me bvúzhí → the woman helps me on Bvuzhi → “bóy fí me” → “help me” → object after verb\n\nSo grammar: subject + verb + object (direct) + on X\n\nSo 20: me fí dìɛ̀msɛ̌n bvúsɔ̀w\n\n---\n\n#### 21. The thief stole the yam just now.\n\n- \"The thief\" = yo᷅kwɔ᷆ːn \n- \"stole\" = cɔ́ŋ \n- \"the yam\" = kèŋkfǔ \n- \"just now\" = bɔ́ nɔ̂ː yɛ᷅n\n\nIn sentence 7: \"You(sg) heard the thief a long time ago\" → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\n\"heard the thief\" → yo᷅w cɔ̌ŋ → “the thief” + “heard”\n\nSo in that case, object (thief) comes before verb.\n\nBut in other cases:\n\nSentence 5: me nú mbóy ncáw mutù bvútfu᷅ → “I will choose the car” — object after verb\n\nSentence 6: wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n → “he killed the woman” → object after verb\n\nSo pattern: subject + verb + object\n\nSo \"the thief stole the yam\" = yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ\n\nNow, “just now” = bɔ́ nɔ̂ː yɛ᷅n → added at end? But is it attached to the verb?\n\nIn sentence 15: “They saw me at the market just now” → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n\nSo “saw me” is the verb phrase, and “just now” is at start.\n\nSimilarly, in sentence 7: “you heard the thief a long time ago” → wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\n\nSo “long time ago” → time adverbial at front\n\nSimilarly, “just now” → bɔ́ nɔ̂ː yɛ᷅n → appears at front\n\nThus, time adverbial like “just now” appears at the beginning, not end.\n\nSo full sentence: bɔ́ nɔ̂ː yɛ᷅n yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ\n\nYes — “just now, the thief stole the yam”\n\nThis matches the pattern.\n\nSo 21: bɔ́ nɔ̂ː yɛ᷅n yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ\n\n---\n\n#### 22. On Bvuŋkaden, I will hear the car.\n\n- “on Bvuŋkaden” = nú bvûŋka᷆ːde᷆n → but from sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n\n\nStructure: “on X” → spoken on day, so use “nú + day”?\n\nIn sentence 2: wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w → “on Bvusɔw” → appears as “bvúsɔ̀w” at end\n\nSimilarly, sentence 3: kwɔ᷆ːn nǔ bóy fí me bvúzhí → “on Bvuzhi” at end\n\nSentence 5: me nú mbóy ncáw mutù bvútfu᷅ → \"on Bvutfu\" → day at end\n\nSo time phrase is at end: [subject verb object] + [on day]\n\nSo for “on Bvuŋkaden” → use “bvûŋka᷆ːde᷆n”\n\n\"hear\" = cɔ̌ŋ (from sentence 7: heard the thief)\n\n\"I\" = me \n\"hear the car\" = me cɔ̌ŋ mutù \n\"on Bvuŋkaden\" = bvûŋka᷆ːde᷆n\n\nSo: me cɔ̌ŋ mutù bvûŋka᷆ːde᷆n\n\nNote: in sentence 7: “you heard the thief” = wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ → subject + time + verb + object\n\nBut in that case, time at front.\n\nIn our examples, only when the time is “long time ago” or “just now”, it appears at front.\n\nBut for “on a day” — it is always at end.\n\nSo 22: me cɔ̌ŋ mutù bvûŋka᷆ːde᷆n\n\n---\n\n#### 23. Today, the woman will kill the man.\n\n- \"today\" → how is it expressed?\n\nIn sentence 9: \"Today, I chose the book\" → me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n → “today, I chose the book”\n\nSo “today” appears with the verb.\n\n\"Today\" is not explicitly marked as a separate temporal word — instead, when the day is present, it is just part of the clause.\n\nBut in other contexts, \"on X\" is used when referring to a distant day.\n\nIn sentence 4: \"On Bvuŋka, he found the book\" → wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː → object after verb, day at end\n\nSentence 9: \"Today, I chose the book\" → me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n → \"today\" = \"mbɛ̂ː\"?\n\nActually, “mbɛ̂ː” = “chose”?\n\nSentence 9: \"Today, I chose the book\" → me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\n\nSo \"chose\" = mbɛ̂ː\n\nSimilarly, “will kill” = bɛ̂ː\n\nIn sentence 6: “he killed the woman” → wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\n\nSo “kill” = bɛ̂ː\n\nSo “will kill” = bɛ̂ː\n\nTherefore, “the woman will kill the man” → kwɔ᷆ːn bɛ̂ː me lé\n\nNow, “today” — since the sentence is spoken on Bvumbon, and time is “today”, we use the same form as sentence 9.\n\nIn sentence 9: “Today, I chose the book” → me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n → verb (chose) at front, object after, day implied.\n\nBut in other days, “on X” is used.\n\nWhen the day is present, “today” is implied.\n\nIn sentence 4: \"On Bvuŋka, he found the book\" — not today\n\nSentence 9: \"Today, I chose the book\" — today\n\nSo on Bvumbon, the present day has “today” expressed by context.\n\nBut in the verb structure, “today” is not a separate adverb — instead, the verb form in present tense implies current time.\n\nSo for 23: “Today, the woman will kill the man” → kwɔ᷆ːn bɛ̂ː me lé\n\nNo need for “on today” — just present tense.\n\nAnd “will” is expressed through the verb — bɛ̂ː = kill, and since it's future, use that form.\n\nIn", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10372.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "anchor_output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "groot_1x4", + "sample_index": 2, + "output": "First, identify the pattern in the given examples by analyzing verb forms, time expressions, and reference structures.\n\nWe observe that time expressions are consistently structured around a day name (e.g., Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvuŋkaden) with prepositions or temporal markers indicating reference points.\n\nExamples:\n- (1) \"Yesterday was Bvumbon\" → \"fɔgò cǐ nú bvúmbòn\" → past, \"yesterday\" = fɔgò, \"was\" = cǐ, \"nú\" = on, \"bvúmbòn\" = day.\n- (2) \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" → future, \"will\" = cɔ́ŋ, \"on\" = bvúsɔw.\n- (3) \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → future, \"will\" = fí (in context), \"help\" = bóy, \"me\" = me.\n- (4) \"On Bvuŋka, he found the book\" → \"wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː\" → past, \"found\" = tɔ̀, \"book\" = ŋwà.\n- (5) \"The day after tomorrow is Bvutfu\" → \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → temporal shift: \"day after tomorrow\" = fɔ̀ shě, \"is\" = ntfǔː nú.\n- (6) \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → present, \"killed\" = bɛ̂ː, \"woman\" = ɛ̀bɛ̀n.\n- (8) \"Tomorrow is Bvuŋkaden\" → \"ntfǔː nú bvûŋka᷆ːde᷆n\" → \"tomorrow\" = ntfǔː, \"is\" = nú.\n- (11) \"The day before yesterday was Bvuŋka\" → \"kefwé cí nú bvûŋka\" → \"day before yesterday\" = kefwé, \"was\" = cí.\n\nSo temporal markers:\n- yesterday → fɔgò\n- today → wvù (used in 6, 12, 14)\n- tomorrow → ntfǔː\n- day after tomorrow → fɔ̀ shě\n- day before yesterday → kefwé\n- just now → wɔ̀ (in 15), also used in 21 → \"just now\" = wɔ̀ or wɔ̀ tɔ̀ (in 7: “you heard the thief a long time ago” → “a long time ago” = tɔ̀)\n\nNow trace verbs:\n- \"help\" → bóy (as in 3: \"bóy fí me\")\n- \"steal\" → cɔ́ŋ (in 2: \"you will steal the yam\" = cɔ́ŋ kèŋkfǔ)\n- \"see\" → wvù (in 10: \"the man is about to see him\" = wvù lě)\n- \"find\" → tɔ̀ (in 4: \"he found the book\" = tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà)\n- \"kill\" → bɛ̂ː (in 6: \"he killed the woman\" = bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n)\n- \"help\" → bóy (in 3: \"the woman will help me\" = nǔ bóy fí me)\n\nNote: \"about to\" appears in 10 and 12:\n- \"The man is about to see him\" → wvù lě\n- \"I am about to help the man\" → me nú nfí dìɛ̀msɛ̌n → \"about to\" = nú (in some uses), or \"am about to\" = me nú nfí\n\nSo \"about to\" seems to be expressed by *nú* when attached to the verb, or embedded as *nú* before verb.\n\nIn (12): me nú nfí dìɛ̀msɛ̌n → \"on Bvuŋka, I am about to help the man\"\n\nSo \"about to\" = nú, and affixes follow depending on verb.\n\nNow let’s analyze tense:\n- Present: \"Today, he killed\" → past tense: bɛ̂ː → past\n- \"Today, we will steal\" → future: cɔ́ŋ → future marker\n- \"I will hear\" → future verb\n- \"will\" = cɔ́ŋ (e.g., 2: \"you will steal\", 3: \"will help\")\n\nBut look at (14): \"Today, we will steal the car\" → \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" → \"we\" = bèsèn, \"will\" = cɔ́ŋ, \"steal\" = géː? Wait — in (2): you will steal → cɔ́ŋ kèŋkfǔ (kèŋkfǔ = yam), so stole = cɔ́ŋ\n\nBut in (14), \"we will steal\" = \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\" — “ge” appears as “géː” → maybe \"ge\" is \"steal\"?\n\nWait: in (2): “you will steal the yam” → “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → \"steal\" = cɔ́ŋ?\n\n\"steal\" is cɔ́ŋ in 2 and 14 — 14 says “we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → why \"géː\" before \"cɔ́ŋ\"?\n\nPossibility: “ge” is a thematic marker or object marker? But in 2: “you will steal the yam” → “cɔ́ŋ kèŋkfǔ”\n\n\"the yam\" = kèŋkfǔ → \"kèŋkfǔ\" is object of stealing.\n\nIn 14: “we will steal the car” → “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” → “géː” = \"we\"? No — \"we\" = bèsèn.\n\nMaybe “géː” is a missing affix or confusion in transcription.\n\nWait, in (14): “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” — this may be a typo or misalignment.\n\nAlternatively, “ge” could be “see” — but in 15: “they saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw” = bɔ́.\n\nSo “saw” = bɔ́.\n\nBut in (15): “they saw me” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = saw, “nɔ̂ː” = at, “yɛ᷅n” = me, “lé” = market.\n\nSo “see” = bɔ́.\n\nThus stealing = cɔ́ŋ.\n\nNow, “hear” — only in (22): “I will hear the car”\n\nWe are to translate:\n22. On Bvuŋkaden, I will hear the car.\n\nWe have:\n- \"I will hear\" → future of \"hear\"\n- \"the car\" → mutù ɛ̀bɛ̀n (from 14: \"steal the car\" → mutù ɛ̀bɛ̀n)\n\nSo \"hear\" must be a verb. We don't have it directly.\n\nBut in (7): \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → “heard” = tɔ̀, “thief” = yo᷅w.\n\nSo \"heard\" = tɔ̀ — past tense.\n\nBut what about future \"hear\"?\n\nIn (14): \"Today, we will steal\" = \"bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n\"\n\nBut no “hear” example.\n\nHowever, in (21): \"The thief stole the yam just now\" → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅”\n\n\"just now\" = cǐ? No — \"just now\" appears in (15): \"they saw me just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\"\n\nAnd \"fɔ̀wǎy\" = market → in (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\n“saw” = kwɔ᷆ːn? No — “kwɔ᷆ːn” is subject, “cǐ” = was, “nɔ̂ː” = on?\n\nWait: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” — “kwɔ᷆ːn” = the woman, “cǐ” = was, “nɔ̂ː” = on, “yɛ᷅n” = the market?\n\nBut “saw the market” — “saw” should be in middle.\n\nIn (15): “They saw me at the market just now” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = saw, “nɔ̂ː” = at, “yɛ᷅n” = me, “lé” = market.\n\nSo “saw” = bɔ́, used in present tense.\n\nBut in (13): “On Bvutfu, the woman saw the market” → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅”\n\n“cǐ” = was — this is past tense?\n\n“cǐ” is used in “yesterday was Bvumbon” → “fɔgò cǐ nú bvúmbòn” → “cǐ” = was.\n\nThus “cǐ” = \"was\" or past tense of \"be\".\n\nSo in (13): the woman saw the market → “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅”\n\nBut “cǐ” = \"was\", so “the woman was on the market”?\n\nThat doesn’t match the meaning.\n\nAlso, “wáy” = market? In (15): “saw me at the market” → “lé fɔ̀wǎy” — “lé” = market?\n\nIn (13): “yɛ᷅n wáy” — “wáy” = market?\n\nAnd “cǐ” = “was”, so “the woman was at the market”?\n\nBut it says “saw the market”.\n\nPossibility: “saw the market” is equivalent to “was at the market”.\n\nSo “see” → bɔ́, and “at the market” = nɔ̂ː fɔ̀wǎy → in (15): “nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “at” = nɔ̂ː, “me” = yɛ᷅n, “market” = lé fɔ̀wǎy.\n\nWait: “lé” = man? “fɔ̀wǎy” = market?\n\nIn (10): “The man is about to see him” → “dìɛ̀msɛ̌n nú yɛ́n wvù lě” → “man” = dìɛ̀msɛ̌n, “see” = wvù, “him” = yɛ́n, “lě” = “him”?\n\nInconsistent.\n\nLet’s reassign:\n- (10): “The man is about to see him” → dìɛ̀msɛ̌n nú yɛ́n wvù lě\n- (15): “They saw me at the market just now” → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\n\nSo:\n- “man” = dìɛ̀msɛ̌n\n- “see” = wvù (in 10) or bɔ́ (in 15)? Contradiction.\n\nPossibility: \"wvù\" = \"see\" in (10), and \"bɔ́\" = \"saw\" in (15).\n\nIn (10): “is about to see him” → “wvù lě” → “wvù” = see, “lě” = him?\n\nIn (15): “saw me at the market” → “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “bɔ́” = saw, “nɔ̂ː” = at, “me” = yɛ᷅n, “market” = fɔ̀wǎy?\n\nBut “lě” and “fɔ̀wǎy” — both possibly mean “place”?\n\nIn (10): \"see him\" → “wvù lě” → “lě” = him?\n\nIn (15): \"at the market\" → “nɔ̂ː fɔ̀wǎy” — “fɔ̀wǎy” = market.\n\nBut “yɛ᷅n” = me, “me” = yɛ᷅n → so “at the market” = nɔ̂ː fɔ̀wǎy, with object.\n\nSo “saw” = bɔ́, “see” = wvù.\n\nThus different verbs: see = wvù, saw = bɔ́?\n\nBut both are “see”.\n\nPossibility: wvù = \"to see\", bɔ́ = \"to see\" (same root)?\n\nCheck frequency.\n\nIn (10): \"is about to see him\" → \"dìɛ̀msɛ̌n nú yɛ́n wvù lě\" → present, \"about to\" = nú.\n\nIn (15): \"saw me\" → bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy → past.\n\nSo possibly \"wvù\" is \"to see\", and \"bɔ́\" is \"saw\" (past form?).\n\nBut in (13): \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\"\n\n“kwɔ᷆ːn” = woman, “cǐ” = was, “nɔ̂ː” = on, “yɛ᷅n” = market?\n\n“wáy” = market?\n\n“wáy é” = “the market”?\n\nPossibility: “wáy” = market, “é” = the?\n\nSo “on the market” → “nɔ̂ː wáy é” — but no article.\n\nIn (15): “at the market” → “nɔ̂ː fɔ̀wǎy” — “fɔ̀wǎy” = market?\n\nPossibility: “fɔ̀wǎy” = market, “wáy” = market?\n\nTranscription error?\n\nCompare:\n\n(13): “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” → likely: “the woman was at the market on Bvutfu”\n\nSo “was at the market” = cǐ nɔ̂ː yɛ᷅n wáy é\n\nBut “yɛ᷅n” is the market, “wáy” = market?\n\nInconsistency.\n\nPossibility: “wáy” = market, “yɛ᷅n” = object of “at”?\n\nNo.\n\nIn (15): “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” → “saw me at the market” → “at” = nɔ̂ː, “the market” = fé fɔ̀wǎy? Or “fɔ̀wǎy” = market.\n\n\"lé\" and \"fɔ̀wǎy\" — both pronounced similarly?\n\nPossibility: \"lé\" = market, \"fɔ̀wǎy\" = market.\n\nLikely a typo — “lé” and “wáy” are different vowels.\n\nBut in (13): “yɛ᷅n wáy” — “yɛ᷅n” might be “the market”?\n\nNo — “yɛ᷅n” is likely “the market”.\n\nThus, “the market” = yɛ᷅n wáy → “yɛ᷅n” = the, “wáy” = market?\n\nThen in (15): “at the market” → “nɔ̂ː yɛ᷅n fɔ̀wǎy” — with “fɔ̀wǎy” = market.\n\nSo “market” is a noun: wáy or fɔ̀wǎy?\n\nPossibility: “wáy” = market in (13), “fɔ̀wǎy” = market in (15) — likely same.\n\nThus, “market” = w", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8571.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "anchor_output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given a set of Nooni sentences spoken on different days of the Nooni “week” and their English translations. The task is to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe must identify a consistent pattern in the grammatical structure, especially concerning:\n\n- Reference to days (e.g., \"On X, Y happened\")\n- Tense/aspect markers (past, present, future, just now)\n- Subject-verb-object order\n- Modifiers like “just now”, “will”, “today”, “the day after tomorrow”, etc.\n- Prepositions and core vocabulary (e.g., \"steal\", \"help\", \"see\", \"hear\", \"kill\")\n\n---\n\n### Step 1: Observe day references and their constructions\n\nFrom the examples:\n\n- Sentence 1: *fɔgò cǐ nú bvúmbòn.* → \"Yesterday was Bvumbon.\" \n → Structure: [time adverb] + [past tense marker?] + \"was\" + [day]\n- Sentence 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w.* → \"On Bvusɔw, you(sg) will steal the yam.\"\n → Structure: \"On [day], [subject] [will] [verb] [object]\"\n- Sentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí.* → \"On Bvuzhi, the woman will help me.\"\n → Same pattern: \"On [day], [subject] [will] [verb] [object]\"\n\nSo: **\"On [day], [subject] [will] [verb] [object]\"** is a standard future tense for events on a specific day.\n\nSimilarly:\n\n- Sentence 4: *wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː.* → \"On Bvuŋka, he found the book.\"\n → \"On [day], [subject] [past tense] [verb] [object]\"\n\n- Sentence 5: *fɔ̀ shě ntfǔː nú bvútfu᷅.* → \"The day after tomorrow is Bvutfu.\"\n → Day reference via temporal expression.\n\n- Sentence 8: *ntfǔː nú bvûŋka᷆ːde᷆n.* → \"Tomorrow is Bvuŋkaden.\"\n → \"Tomorrow is [day]\"\n\n- Sentence 11: *kefwé cí nú bvûŋka.* → \"The day before yesterday was Bvuŋka.\"\n\nSo temporal expressions:\n- “Tomorrow” → *ntfǔː nú* → \"Tomorrow is [day]\"\n- “The day after tomorrow” → *fɔ̀ shě ntfǔː nú* → “The day after tomorrow is Bvutfu”\n- “Yesterday” → *fɔgò cǐ nú* → “Yesterday was Bvumbon”\n- “The day before yesterday” → *kefwé cí nú* → “The day before yesterday was Bvuŋka”\n\nNote: These are all head-final, and the time adverbial is placed before the verb.\n\n---\n\n### Step 2: Identify tense markers\n\n- Future: uses **cɔ́ŋ** or **cɔ́ŋ** in contexts like \"you will steal\" → *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ* \n ⇒ So “will” = **cɔ́ŋ**\n\n- Past: no explicit future marker; used in simple past like \"he found\" → *wvù tɔ̀ nɔ̂ː* \n ⇒ \"found\" = *tɔ̀ nɔ̂ː* (intransitive verb, commonly used for finding)\n\n- Present (current, just now): appears in *wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ* → “You heard the thief a long time ago” → past.\n\nBut sentence 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → \"They saw me at the market just now\" \n→ \"just now\" = *fɔ̀wǎy* (note: *fɔ̀wǎy* appears in 1 and 5)\n\nIn 1: *fɔgò cǐ nú bvúmbòn* → “Yesterday was” → not \"just now\"\n\nIn 5: *fɔ̀ shě ntfǔː nú bvútfu᷅* → \"The day after tomorrow is\"\n\nIn 15: *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “They saw me at the market just now” \nSo **\"just now\" = fɔ̀wǎy**?\n\nBut is it a tense marker or a time adverb?\n\nCheck use of *fɔ̀wǎy*: \n- Sentence 1: *fɔgò cǐ nú* → “Yesterday” → not *fɔ̀wǎy* \n- Sentence 5: *fɔ̀ shě ntfǔː* → “The day after tomorrow” \n- Sentence 15: *fɔ̀wǎy* → used with “saw” → “just now”\n\nSo **fɔ̀wǎy = just now**.\n\nThis appears in:\n- (15): “they saw me just now”\n- (7): “you heard the thief a long time ago” → uses “a long time ago” → different expression\n\nSo, “just now” = **fɔ̀wǎy**\n\nFuture = **cɔ́ŋ**\n\nPresent = marked by events happening at current time or in the near present.\n\nNow look at:\n- Sentence 6: *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n.* → “Today, he killed the woman.”\n → “Today” = *wvù* (with *bɛ̂ː*?) → actually *wvù* may be \"today\" or \"this day\"\n\nBut in sentence 9: *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n.* → “Today, I chose the book” → uses *mbɛ̂ː* (also appears in 6)\n\nThus: **today** = interpreted from context, often marked by the verb structure, or the word *wvù* or *mbɛ̂ː*\n\nBut sentence 6: *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n.* → “Today, he killed the woman” → uses *wvù* and *bɛ̂ː*\n\nSentence 9: *me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n.* → “Today, I chose the book” → uses *mbɛ̂ː*\n\nSo *mbɛ̂ː* is used with present tense, but also with possession or state?\n\nPossibly: *wvù* = “today” (like “on this day”) \nAnd *bɛ̂ː* = present tense marker?\n\nWait, in sentence 12: *me nú nfí dìɛ̀msɛ̌n.* → “I am about to help the man” → “about to” = *me nú nfí*\n\nSo “about to” = *nú* + *nfí*?\n\nSimilarly, sentence 10: *dìɛ̀msɛ̌n nú yɛ́n wvù lě.* → “The man is about to see him” → uses *nú yɛ́n wvù lě* → “is about to see”\n\nSo: **\"is about to\" = nú + [verb]**\n\nThus, “about to” = **nú + [verb]** (intransitive or transitive)\n\nSo now we have:\n\n- Future: **cɔ́ŋ** \n → used in: “will steal”, “will help”\n\n- Just now: **fɔ̀wǎy** \n → used as time adverb with verb: “saw just now”\n\n- Today: no explicit marker, but subject followed by verb structure \n → e.g., “Today, I chose” → uses *me mbɛ̂ː nca᷅w ŋwà* or *wvù bɛ̂ː...*\n\nBut note: in (9): *me mbɛ̂ː nca᷅w ŋwà* → “Today, I chose the book” → *mbɛ̂ː* marks present\n\nIn (6): *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n* → “Today, he killed the woman”\n\nSo both use **bɛ̂ː** as present tense.\n\nIn (14): *bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n.* → “Today, we will steal the car” \n→ \"will\" = *cɔ́ŋ* → future, not present → so not consistent\n\nSo **bɛ̂ː** = present tense marker (used with past or present events)\n\nWhen “will” is used, *cɔ́ŋ* appears, not *bɛ̂ː*\n\nSo:\n\n- Present tense = *bɛ̂ː* \n- Future tense = *cɔ́ŋ* \n- Just now = *fɔ̀wǎy* \n- Specific time reference: “On [day]” = structure: *On [day]* + [subject] + [verb] + [object]\n\nNow, verbs:\n\n- steal = *cɔ́ŋ kèŋkfǔ* → (from 2) \n- help = *fí* → (from 3: *kwɔ᷆ːn nǔ bóy fí me*) → \"will help me\" → *bóy fí me* \nSo “help” = *fí* (with object)\n\n- see = *yɛ᷅n* → from (15): *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “saw me at the market” → “see” = *yɛ᷅n* \n→ So “see” = *yɛ᷅n* \n→ “saw” = *bɔ́ nɔ̂ː yɛ᷅n* → past tense\n\n- hear = *yo᷅w* → from (7): *wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ* → “you heard the thief” → so “hear” = *yo᷅w*\n\n- kill = *ɛ̀bɛ̀n* → (6) “he killed the woman” → *yo᷅kwɔ᷆ːn ɛ̀bɛ̀n*\n\nSo core verb roots:\n\n- steal: *cɔ́ŋ kèŋkfǔ* \n- help: *fí* \n- see: *yɛ᷅n* \n- hear: *yo᷅w* \n- kill: *ɛ̀bɛ̀n*\n\nNow, object:\n\n- “the yam” = *kèŋkfǔ* \n- “the woman” = *nǔ bóy* (from 3: *kwɔ᷆ːn nǔ bóy fí me*) → “the woman” = *nǔ bóy* \n- “the man” = *dìɛ̀msɛ̌n* → (12: *me nú nfí dìɛ̀msɛ̌n*) → “the man” = *dìɛ̀msɛ̌n* \n- “the car” = *mutù* → in (5): *me nú mbóy ncáw mutù bvútfu᷅* → “I will choose the car” → *mutù*\n\nSo nominal heads:\n\n- yam = *kèŋkfǔ* \n- woman = *nǔ bóy* \n- man = *dìɛ̀msɛ̌n* \n- car = *mutù*\n\nNow, structure:\n\nFor [day] references:\n\n- On X → *nú* + [day] → but go back to examples:\n\nIn 2: *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w.* → \"On Bvusɔw, you will steal the yam\" → no *nú* before day\n\nIn 1: *fɔgò cǐ nú bvúmbòn* → “Yesterday was Bvumbon” → uses *nú* after day\n\nIn 4: *wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː.* → “On Bvuŋka, he found the book” → uses “On [day]”\n\nSo the pattern is:\n- When talking about events on a particular day (not in present or past), use: *On [day], [subject] [future/past tense] [verb] [object]*\n\nAnd the word “On” seems to be implied in the structure.\n\nIn sentence 8: *ntfǔː nú bvûŋka᷆ːde᷆n.* → “Tomorrow is Bvuŋkaden” → “Tomorrow is” → structure is [temporal expression] + \"is\" → different from event on a day.\n\nSo when saying “On [day], X happened”, the structure is: \n[subject] [tense marker] [verb] [object] → with day mentioned in the sentence.\n\nBut in sentence 3: *kwɔ᷆ːn nǔ bóy fí me bvúzhí.* → “On Bvuzhi, the woman will help me” → so **\"On [day]\" is not a separate word**, but rather **the day is the noun phrase that precedes the verb structure**.\n\nSo: verb structure is: \n[subject] [tense] [verb] [object] \nwith the day in the **location** or **time** position.\n\nIn all cases where “on [day]” appears, the day comes **before** the verb.\n\nSo for translation, we need to ensure the day is positioned immediately before the verb.\n\n---\n\nNow translate the required sentences, all on **Bvumbon**.\n\n### 20. On Bvusɔw, I helped the man.\n\n→ Subject: *me* \n→ Verb: “helped” = past tense → *fí* (no *cɔ́ŋ* for past) → past form is likely *fí* \nFrom (3): *kwɔ᷆ːn nǔ bóy fí me* → “will help me” → present/future → past may be just *fí*, no tense marker?\n\nBut in (15): *bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy* → “saw” = *bɔ́ nɔ̂ː* → past form \nSimilarly, “killed” = *wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n* → past tense: *bɛ̂ː* + verb\n\nSo: present tense uses *bɛ̂ː*, past tense uses *bɔ́ nɔ̂ː* for “see”, but “help” may not have a past marker?\n\nBut in sentence 3: *kwɔ᷆ːn nǔ bóy fí me* → “will help” → uses *fí* \nNo past form given.\n\nBut in example (1): *fɔgò cǐ nú bvúmbòn* → “yesterday was” → temporal reference only, not event\n\nSo no clear past form of “help”\n\nBut the verb *fí* may be base form, and tense is inferred.\n\nWe need to know if “helped” is past, present, or future.\n\nSentence says: “On Bvusɔw, I helped the man” → past, happening on a day.\n\nSo “helped” = past tense.\n\nWe observe that in Nooni, past tense often uses a particle or tone. But no such marker is shown.\n\nHowever, in (4): *wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà* → “he found the book” → past, with *tɔ̀ nɔ̂ː*\n\nIn (15): *bɔ́ nɔ̂ː yɛ᷅n me lé* → “saw me” → past\n\nSo possibly, **past tense = bɔ́ nɔ̂ː + verb**?\n\nBut in (2): *wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ* → “will steal” → uses *cɔ́ŋ* for future\n\nIn (3): *kwɔ᷆ːn nǔ bóy fí me* → “will help” → *fí* (without particle)\n\nSo verb *fí* has no separate past form?\n\nPossibility: “help” is an intransitive verb? But it takes object.\n\nIn (3): *fí me* → agent + object → so transitive.\n\nBut no past form shown.\n\nSo likely, past tense of *fí* is not marked — context determines.\n\nBut in the absence of a clear past form, and since sentence (15) uses *bɔ́ nɔ̂ː* for “saw”, and “see” is transitive, perhaps “help” also uses a similar marker.\n\nBut no such marker is present.\n\nWait: in sentence 2: “you will steal” → uses *cɔ́ŋ* \nIn sentence 3: “the woman will help” → uses *fí* (base)\n\nNo past tense in the examples.\n\nBut we have sentence 15: *bɔ́ nɔ̂ː yɛ᷅n* → saw → past\n\nSo for “helped”, it might be that no marker is needed, or it’s just *fí*.\n\nBut let’s compare with “help” in other contexts.\n\nNote: sentence 12: *me nú nfí dìɛ̀msɛ̌n* → “I am about to help the man” → uses *nú* + *nfí*\n\nSo “about to” = *nú + fí*\n\nSo base verb *fí* = help\n\nPast form may be absent from given data.\n\nTherefore, for 20: \"On B", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2", + "c.3", + "c.4", + "c.5" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10235.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 426.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "anchor_output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "4. our1+2 cliff → cliff is qaqat”a → with our1+2 possessive suffix -st → qaqat”ast” \n5. in your corner → \"your corner\" is chushuntxi → \"in\" is a locative prefix, so \"in your corner\" = chushuntxi \n6. in your corner too → \"too\" is marked by -na in the examples: \"in the cave too\" = aq”ipsa → but \"too\" appears as a suffix; in \"in our1+2 lake too\" = qucxst”psa → no \"too\" suffix directly. However, \"in our1+2 field too\" = yapsanpsa → \"anpsa\" may include \"too\" marker. In \"our1+2 field too\", the \"too\" appears in the combination. Also, \"my pot too\" = p”ak”unhpsa → \"unhpsa\" = \"my pot\" + \"too\" → so \"too\" is marked by adding -hpsa or -nha? But p”ak”u → p”ak”unhpsa → so \"unhpsa\" = \"my pot\" + \"too\" → the \"too\" is formed with suffix -hpsa. However, in \"in our1+2 field too\" = yapsanpsa → field root yap → yapsanpsa → \"sanpsa\" → \"st\" and \"anpsa\"? Not directly. But “in our1+2 field too” uses “anpsa”, suggesting that “too” is marked by -npsa or -anpsa. But compare to “my pot too” = p”ak”unhpsa → \"unhpsa\" → implies \"too\" = -hpsa. But here the root is yap → yapsanpsa → not -hpsa. So perhaps “too” is attached via a different suffix. Alternatively, observe that “in our1+2 field too” corresponds to “in our1+2 field” + “too” → and “sanpsa” may be built from “st” + “an” + “psa”? But “psa” is in “cave too” = aq”ipsa → “ipsa” → “ipsa” = “cave too”? Yes — “the cave too” = aq”ipsa → so “too” is part of the word “ipsa” → “ipsa” = “cave” + “too”? Then “in our1+2 field too” = yapsanpsa → so “psa” = “too” → and “san” = “our1+2”? Then “san” is not matching. But “our1+2” is marked by -st in other cases: markstxi = “our1+2 town” → “st” added. So likely, “in our1+2 field too” = “yap” + “st” + “an” + “psa”? But “yapsanpsa” → “yap” + “sanpsa” → maybe “sanpsa” = “st” + “anpsa” → “anpsa” = “field” with “too”? Alternatively, “too” is a suffix that appears in the form -npsa or -hpsa. But in “my pot too” = p”ak”unhpsa → “unhpsa” = “pot” with “too” → so “too” is in -hpsa. In “in our1+2 field too” = yapsanpsa → “yapsanpsa” → does not contain “h” or “n” after “yap” — “yap” + “san” → “san” may include “st” and “an”. Given that “our1+2” uses -st, and “too” uses -hpsa or -npsa, and the word “in our1+2 field too” is yapsanpsa, it's likely that “sanpsa” = “st” + “an” + “psa” → “psa” = “too”? But “cave too” = aq”ipsa → “ipsa” → “psa” = “too”? Yes → “cave too” = aq”ipsa → so “ipsa” = “cave” + “too” → so “too” is marked by -psa. Therefore, “too” = -psa. Then “in our1+2 field too” = yap + st + an + psa → yapsanpsa → matches. Therefore, “in your corner too” = chushuntxi → but with “too” → so add -psa → chushuntxi + psa → chushuntxi? But no -psa added. The word “chushuntxi” means “is it in the corner?” → so “in your corner” is chushuntxi. “in your corner too” → must add “too” → so chushuntxi + psa → chushuntxi? No — spelling. But in “the cave too” = aq”ipsa → not “cave” + “ipsa”. So “ipsa” is the whole form → so “too” is part of the ending. Therefore, “in your corner too” = chushuntxi → with -psa → chushuntxi? But no. Probably the structure is chushuntxi → but to mark “too”, it becomes chushuntps? No. Alternatively, from “in your corner” = chushuntxi → “in your corner too” = chushuntxi + psa → but need to see if this matches form. However, the “our1+2” version adds -st. For “your” → the root is chushp”a. “in your corner” = chushuntxi → so “untxi” is locative. “in your corner too” → likely chushuntxi with “too” → which is marked by -psa → so chushuntxi → but with psa → so chushuntxi + psa? But that would be long. Or maybe “too” is attached in a similar way as in “chushp”a → chushuntxi → so to add “too”, use “chushuntxi” and add -psa → chushuntps? But no example. Alternatively, “in your corner too” = chushuntxi → with “too” = -psa → so chushuntxi → but “ipsa” ends in “psa”, so likely “too” = -psa → thus “in your corner too” = chushuntxi + psa? But that would be chushuntxi? Not matching. Wait — “in the cave too” = aq”ipsa → “ipsa” contains “too” → so “too” is marked by -psa. Similarly, “in our1+2 field too” = yapsanpsa → “anpsa” may be “our1+2” + “too”? But “an” is not “st”. But “our1+2” is marked by -st → so “our1+2 field” = yap + st + an → yapsan → then + psa → yapsanpsa → so “too” = -psa. So “in your corner too” = chushuntxi → with -psa → chushuntxi? But how to attach? The root is chushp”a → “in your corner” = chushuntxi → so “too” = -psa → so the form becomes chushuntxi? Or chushuntxi → but the form may be chushuntxi — no. But “cave too” = aq”ipsa → so “too” is already in the root. Therefore, likely “too” is a suffix meaning “as well” that is added to the locative base. Thus, “in your corner too” = chushuntxi → but with “too” → so chushuntxi → but changed to chushuntxi? Not possible. The form “chushuntxi” already includes location and question. So “is it in your corner?” = chushuntxi. “in your corner too” = physical location, not a question. But in the original data, “in the cave too” = aq”ipsa → which is not a question — it is a locative phrase. Therefore, “in your corner too” = chushuntxi → but with “too” suffix → so the base is chushuntxi → and “too” is added as -psa → so chushuntxi → becomes chushuntxi? No — must be chushuntxi? But the only similar case is “in the cave too” = aq”ipsa → where “ipsa” is the form with “too”. So the “too” is encoded in the ending: for a locative noun, “too” is marked by -psa. Therefore, “in your corner too” = chushuntxi → but with “psa” → so chushuntxi? But “ipsa” → “cave too” → so “cave” + “too” → the root is aq” → so aq”ipsa → so “ipsa” = “cave” + “too”. So “in your corner too” = chushuntxi → but with “too” = -psa → so chushuntxi → but the root is chushuntxi → so the form is chushuntxi? But no. Instead, the pattern is that “too” is added as -psa to the base of the locative. So “in your corner” = chushuntxi → so “in your corner too” = chushuntxi? But that is redundant. Alternatively, the structure is that “too” is added as a suffix. From “the cave too” = aq”ipsa → so “ipsa” = “cave” + “too” → so “too” = -psa → thus “in your corner too” = chushuntxi → with -psa → but \"chushuntxi\" ends with “xi” — so cannot add. Unless the base is “chushun” → then add -t xi? Not possible. Closest: in “our1+2 field too” = yapsanpsa → “yap” + “sanpsa” → “sanpsa” = “st” + “an” + “psa” → so “psa” = “too” → so “too” = -psa. Therefore, in “in your corner too” = chushuntxi → but the base must be “chushun” → so chushun + psa → chushunpsa? But no such form exists. However, “in your corner” is given as chushuntxi → so likely “chushuntxi” includes the “too” only if it is already included. But “in the cave” = aq”ipsa → “in the cave too” = aq”ipsa → so “ipsa” means “cave too” → so ending in “psa” = “too”. So “in your corner too” must end in “psa” → so base is “chushun” → chushunpsa? But “in your corner” = chushuntxi → so “untxi” is the locative. Perhaps “chushuntxi” is “in your corner” without “too” — and to add “too”, change to chushuntxi? No. Perhaps the “too” is attached via a new suffix. But in “my pot too” = p”ak”unhpsa → so “unhpsa” → “my pot” + “too” → so “too” = -hpsa. In “in our1+2 field too” = yapsanpsa → “yap” + “sanpsa” → “sanpsa” = “st” + “anpsa” → “anpsa” = “field” + “too”? So “too” = -npsa. Inconsistency. But “in the cave too” = aq”ipsa → “ipsa” = “cave” + “too” → so “too” = -psa. In “in our1+2 field too” = yapsanpsa → “sanpsa” = “st” + “an” + “psa” → so “psa” = “too” → so “too” = -psa. In “my pot too” = p”ak”unhpsa → “hpsa” → different form. But “hpsa” may be “too” but with a “h” — so perhaps -hpsa is used in other cases. But in “in your corner too”, no such form exists. However, in “in your corner” = chushuntxi → and “chushuntxi” contains “untxi” — so likely “in your corner too” = chushuntxi with “too” → so chushuntxi? But it's ambiguous. The only consistent pattern is that “too” is marked by -psa when the locative is modified. Therefore, for “in your corner too” = chushuntxi + psa → but no addition. Alternatively, “too” is part of the locative stem — but the only available pattern is that “in our1+2 field too” = yapsanpsa → so “field” + “our1+2” + “too” → yap + st + an + psa = yapsanpsa. So “too” = -psa. So “in your corner too” = chushun + psa → but “in your corner” is chushuntxi → which has “untxi” → so perhaps the stem is chushun → and “untxi” is the locative form. So “in your corner too” = chushun + psa → chushunpsa. But no example. However, “cave too” = aq”ipsa → so for “in your corner too” → similar → chushuntxi? But “ipsa” ends with “psa” → so “chushuntxi” does not end with “psa” → so different. Therefore, the form for “in your corner too” is likely chushuntxi → with the understanding that the “too” is implied in the context. But the data shows that “in the cave too” = aq”ipsa → so the word includes “too” in the form. So for consistency, “in your corner too” = chushun + psa → chushunpsa? But “chushuntxi” must be the base. Perhaps “untxi” is the locative, and “too” is added as a suffix. But no evidence. Given the lack of examples, and that “too” is only encoded as -psa in “cave too” and “our1+2 field too”, and the form “yapsanpsa” uses “sanpsa” = st + an + psa, then “too” is marked by -psa. So for “in your corner too”, we take the locative form and add -psa → so chushuntxi → becomes chushuntxi? No — base is chushun → so chushun + psa = chushunpsa. But the given form is chushuntxi → so perhaps it's chushuntxi with no change. This is inconsistent. Alternative: the “too” suffix is not attached but is part of the root. In “cave too” = aq”ipsa” → “ipsa” is the form. In “our1+2 field too” = yapsanpsa → “sanpsa” is the form. So for “in your corner too” = chushuntxi → but it should be chushun + psa = chushunpsa. But “chushuntxi” has “t” not “h”. So not matching. Therefore, perhaps “too” is not in -psa for all. In “my pot too” = p”ak”unhpsa → “unhpsa” → so “too” = -hpsa. In “in the cave too” = aq”ipsa” → “ipsa” → “too” = -psa. So different suffixes for different nouns. Therefore, no single rule. But the only consistent rule with evidence is that “our1+2” is marked by -st. So for (4) our1+2 cliff = qaqat”ast” \n(5) in your corner = chushuntxi \n(6) in your corner too = as “in your corner” = chushuntxi, and “too” is marked by suffix -psa in similar cases, so chushuntxi + psa → but no place to insert. Perhaps the form is chushuntxi → with “too” encoded in the -psa. But the only way is to infer from “cave too” = aq”ipsa → so “too” = -psa → so “in your corner too” = chushun + psa = chushunpsa \nBut “in your corner” is chushuntxi → so likely the root is chushun → and “t” is part of locative. So chushun + psa = chushunpsa \n(7) from your corner too → “from your corner” = chushp”a → from his town = markp”t”a → so from [noun] = root + p”t”a \nSo from your corner = chushp”at”a \n“too” = -psa → so chushp”at”apsa? But “hpsa” used in “my pot too” = p”ak”unhpsa → so from your corner too = chushp”at”a + hpsa = chushp”athpsa \n(8) is it from the cave? → “from the cave” = aq”na → “is it from the cave?” = aq”na? But “is it from the cave?” = example? No. “is it our1+2 town?” = markstxi → so “is it from X?” = X with “stxi” suffix. “is it from the cave?” = aq”na → so aq”na? → but “na” is “in the cave” → and “from” is also possible. In “from our1+2 lake” = qucx", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11214.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast”\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast”", + "planner_output": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "anchor_output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "Step 1: Identify the structure of given examples.\n\nWe are given translations and corresponding forms.\n\n\"his corner\" = chushp”a → suggests pattern: [possessive] + [noun] \n\"your bed\" = ishma → suggests pattern: [locative] + [noun] \n\"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n\"in the cave\" = aq”ipsa → \"aq”\" + \"ipsa\" → \"aq”\" = in the cave → \"aq”\" likely locative prefix \"in\" \n\"from our1+2 lake\" = qucxap”a → \"qucx\" + \"ap”a\" → \"qucx\" = from, \"ap”a\" = lake \n\"from our1+2 lake too\" = qucxst”psa → \"qucx\" + \"st”psa\" → \"st”psa\" = our1+2 lake too → so \"st”psa\" has possessive \"our1+2\" and a suffix of \"too\" \n\"from his town\" = markp”t”a → \"mark\" + \"p”t”a\" → \"mark\" = from, \"p”t”a\" = his town \n\"from your house\" = utamt”a → \"utam\" + \"t”a\" → \"utam\" = from, \"t”a\" = your house \n\"our1+2 town\" = markstxi → \"mark\" + \"stxi\" → \"stxi\" = our1+2 town \n\"is it our1+2 town?\" = markstxi → this is a question form: \"is it + noun?\" \n\nPattern: \n- \"in\" = ish prefix → appears in \"ishinhna\", \"ishma\", \"ishp”a\" \n- \"from\" = qucx or utam? \n - qucx → from lake, from lake too \n - utam → from your house \n → so \"from\" is a prefix, general marker. \n- Possession: \n - \"his\" → chush → in \"chushp”a\" \n - \"your\" → in \"ishma\" → \"ma\" = your bed \n - \"our1+2\" → in \"qucxst”psa\", \"markstxi\" \n- Suffixes: \n - \"-too\" → in \"aq”ipsa\" → \"aq”ipsa\" = the cave too → so \"ipsa\" becomes \"ipsa\" with \"too\"? \n Actually: \"the cave too\" = aq”ipsa → so \"a\" is \"the cave\", \"too\" is attached? \n But \"from our1+2 lake too\" = qucxst”psa → \"st”psa\" = our1+2 lake too → suggests \"too\" is suffix or infix \n \"yaputxi\" = is it the field? → no \"too\" \n \"yapsanpsa\" = in our1+2 field too → has \"too\" → so \"sanpsa\" = our1+2 field? \n\nStep 2: Identify root nouns and possessive prefixes.\n\nNoun roots:\n- bed: \"inhna\" (my bed), \"ma\" (your bed) → so \"ma\" = your bed, \"inhna\" = my bed\n- corner: \"p”a\" — in \"chushp”a\" = his corner → so \"p”a\" = corner\n- lake: \"ap”a\" — in \"qucxap”a\" = from the lake\n- town: \"marka\" = the town, \"t”a\" = your house, \"p”t”a\" = his town → \"t”a\" = your house → so \"t”a\" = your house\n- field: \"yaputxi\" = is it the field? → \"yap\" = field? \"yaputxi\" suggests \"yap\" + \"utxi\" → \"utxi\" = field? \n \"yapsanpsa\" = in our1+2 field too → so \"sanpsa\" = our1+2 field\n\nPossessive suffixes:\n- \"our1+2\" appears in:\n - qucxst”psa → from our1+2 lake too → \"st”psa\" = our1+2 lake too\n - markstxi → is it our1+2 town? → \"stxi\" = our1+2 town\n - yapsanpsa → in our1+2 field too → \"sanpsa\" = our1+2 field too\n- \"his\" → chush in chushp”a\n- \"your\" → in \"ishma\" → \"ma\" = your bed → \"ma\" is your bed\n- \"my\" → \"inhna\" = my bed → \"inhna\" can be attributed to \"in\" + my bed\n\nThus, the locative prefixes:\n- \"in\" = ish → appears in ishinhna, ishma, ishp”a\n- \"from\" = qucx (for lake), utam (for house)\n\nSo for each word, the structure is:\n- [locative prefix] + [possessive] + [noun base]\n\nNow, task (b):\n\n4. our1+2 cliff \n→ \"our1+2\" + \"cliff\" \nFrom data, \"our1+2 lake\" → qucxst”psa → but that is with \"from\" \nWe have \"from the cliff\" = qaqat”a \n→ \"q\" = from, \"at”a\" = the cliff → so \"at”a\" = the cliff \nTherefore, \"cliff\" base = \"at”a\" \n\"our1+2 cliff\" → should use \"our1+2\" prefix → similar to \"our1+2 lake\" = qucxst”psa \n\"qucxap”a\" = from the lake → \"qucx\" + \"ap”a\" → so \"qucx\" + \"ap”a\" = from lake \n\"markstxi\" = is it our1+2 town? → \"mark\" + \"stxi\" = our1+2 town \n\"yapsanpsa\" = in our1+2 field too → \"ya\" + \"psanpsa\" → likely \"ya\" = is it?, \"psanpsa\" = our1+2 field \nSo \"our1+2 field\" = psanpsa → so \"psa\" = field? \nBut \"yapsanpsa\" = in our1+2 field too → \"yap\" = is it?, \"sanpsa\" = our1+2 field \nSo \"sanpsa\" = our1+2 field → so \"san\" = field? \n\nBut for \"cliff\", from \"qqaat”a\" = from the cliff → \"q\" + \"at”a\" = from the cliff \nSo \"at”a\" = the cliff \nThen \"our1+2 cliff\" = \"our1+2\" + \"cliff\" → which would likely be \"st”at”a\" or \"at”a\" with possessive? \n\nWhere is \"our1+2\" used with a noun? \n- \"our1+2 lake\" = in qucxst”psa → \"st”psa\" → so \"st”psa\" = our1+2 lake \n- \"our1+2 town\" = markstxi → \"stxi\" = our1+2 town \n- \"our1+2 field\" = yapsanpsa → \"sanpsa\" = our1+2 field \n\nSo pattern: \n- \"our1+2 X\" = [suffix with \"our1+2\"] + [X noun] \n→ so for cliff: \"our1+2 cliff\" = \"st”at”a\"? \nBut \"st”psa\" = our1+2 lake → \"psa\" = lake \n\"stxi\" = our1+2 town → \"xi\" = town \n\"sanpsa\" = our1+2 field → \"npsa\" = field? → not consistent \n\"psa\" appears in lake and field? \n\"lake\" = ap”a → \"st”psa\" → \"st”psa\" → \"st\" + \"p”a\" → so \"p”a\" = lake \nSimilarly, \"field\" = \"yaputxi\" → \"yap\" + \"utxi\" → \"utxi\" = field \n\"yapsanpsa\" = in our1+2 field too → \"sanpsa\" → suggests \"sanpsa\" = our1+2 field → so possessive with \"san\" \n\nBut \"lake\" → \"st”psa\" → \"st”\" + \"p”a\" → so \"p”a\" = lake \n\"field\" → \"sanpsa\" → \"san\" + \"psa\" → so \"psa\" = field? \nContradiction.\n\nAlternative: \"our1+2\" marker appears as a suffix on the noun.\n\n\"our1+2 lake\" → \"st”psa\" → \"p”a\" = lake → so \"st”\" + \"p”a\" → \"st”\" indicates \"our1+2\"? \n\"our1+2 town\" = markstxi → \"stxi\" = our1+2 town → so \"stxi\" = our1+2 town → \"st\" + \"xi\" → \"xi\" = town \n\"our1+2 field\" = yapsanpsa → \"sanpsa\" = our1+2 field → \"san\" + \"psa\" → \"psa\" = field \n\nSo the \"our1+2\" is attached to the noun base as a modifier. \nPattern: possessive marker + noun\n\nFor \"cliff\", what is the base? \n\"from the cliff\" = qaqat”a → \"q\" + \"at”a\" → \"at”a\" = the cliff \nSo \"cliff\" base = \"at”a\" \nThen \"our1+2 cliff\" = ? \nLikely, \"st”at”a\" = our1+2 cliff? \nBut \"st”psa\" = our1+2 lake → with \"p”a\" \n\"stxi\" = our1+2 town → with \"xi\" \n\"sanpsa\" = our1+2 field → with \"psa\" \n\nSo the possessive forms seem to be: \n- lake: st”p”a \n- town: stxi \n- field: sanpsa \n\nNo clear pattern in the possessive prefix.\n\nBut note: qaqat”a = from the cliff → \"q\" + \"at”a\" \nSimilarly, qucxap”a = from the lake → \"qucx\" + \"ap”a\" \nutamt”a = from your house → \"utam\" + \"t”a\" \nmarkp”t”a = from his town → \"mark\" + \"p”t”a\" \n\nSo the \"from\" prefix is separate. \nFor \"our1+2 cliff\", we need to construct the noun.\n\n\"our1+2\" appears in: \n- qucxst”psa → \"st”psa\" = our1+2 lake → thus \"st”psa\" = our1+2 lake \n- markstxi → \"stxi\" = our1+2 town \n- yapsanpsa → \"sanpsa\" = our1+2 field \n\nSo the possessive suffixes are:\n- lake → st”p”a \n- town → stxi \n- field → sanpsa \n\nBut st”p”a → has \"st”\" → mark may be present in others \nNo shared prefix. \n\nBut \"st”psa\", \"stxi\", \"sanpsa\" — all start with \"st\" or \"sa\"? \n\"st”psa\", \"stxi\", \"sanpsa\" — common prefix \"st\"? \nst”psa → st \nstxi → st \nsanpsa → sa → different \n\nMaybe \"our1+2\" is not a prefix, but a suffix on the noun root. \nWe have:\n- lake: ap”a → st”psa → so \"st”\" + \"p”a\" → \"p”a\" = lake \n- town: marka → stxi → \"stxi\" = our1+2 town → \"stxi\" = our1+2 town \n- field: yaputxi → \"sanpsa\" = our1+2 field → \"sanpsa\" = our1+2 field \n\nSo for \"cliff\", the base is \"at”a\" → from \"qqaat”a\" = from the cliff → so the noun is \"at”a\" \n\nThen \"our1+2 cliff\" = ? \nPossibly: \"st”at”a\" — mirroring \"st”psa\" (our1+2 lake) → \"st”p”a\" → \"st”\" + \"p”a\" \nSimilarly, \"stxi\" = st + xi → for town \n\"sanpsa\" = sa + npsa → for field → different \n\nBut \"p”a\" occurs in lake → \"st”psa\" \n\"xi\" in town → \"stxi\" \n\"psa\" in field → \"sanpsa\" — so no consistent root.\n\nWait — is \"p”a\" = lake? \nYes: \"chushp”a\" = his corner → and \"a\" = corner? But \"p”a\" = corner? — contradiction. \n\nEarlier: \"his corner\" = chushp”a → suggests \"p”a\" = corner \nBut \"from the lake\" = qucxap”a → \"ap”a\" = lake \nSo \"ap”a\" = lake → \"p”a\" = corner? Then two meanings? \n\nAh — \"p”\"a\" vs \"ap”a\" \n\"p”a\" = corner \n\"ap”a\" = lake \nSo different roots. \n\nThus, \"cliff\" = \"at”a\" → so our1+2 cliff = ? \nWe have no example of \"our1+2 cliff\". \n\nBut pattern for \"our1+2 X\" is: [prefix] + [X noun with possessive] \n\nSo for lake: \"st”psa\" = our1+2 lake → \"st”\" + \"p”a\" → \"p”a\" = lake \nBut \"p”a\" is already used for corner → so must be different. \n\n\"ap”a\" = lake → so the base is \"ap”a\", not \"p”a\" \nSo \"our1+2 lake\" = \"st”ap”a\"? \n\"st”psa\" → \"st”psa\" → \"p”a\" = lake? \n\"chushp”a\" = his corner → \"p”a\" = corner \n\"qucxap”a\" = from the lake → \"ap”a\" = lake \nSo \"ap”a\" = lake, \"p”a\" = corner \n\nThen \"st”psa\" = our1+2 lake? — but \"p”a\" is corner → contradiction.\n\nThus, likely typo or different root.\n\nPerhaps \"st”psa\" = our1+2 lake → so \"psa\" = lake? \nBut \"yapsanpsa\" = in our1+2 field too → \"sanpsa\" → \"sanpsa\" = our1+2 field → \"psa\" = field?\n\nThen \"psa\" = both field and lake? \nNot possible.\n\nOnly consistent possibility: the possessive marker is context-dependent.\n\nBut look at \"in your corner\" — we deduce:\n\n\"his corner\" = chushp”a → \"chush\" + \"p”a\" \n\"your bed\" = ishma → \"ish\" + \"ma\" \n\"in your corner\" = ? → must be \"ish\" + \"p”a\" = ishp”a \nSimilarly, \"in my corner\" = ? — not given, but \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \nSo for corner: \"p”a\" is the base noun. \n\"my corner\" = ishp”a? No — \"my corner\" would require \"my\" prefix.\n\nBut \"in\" is \"ish\", and \"p”a\" = corner → so \"in your corner\" = ish + p”a = ishp”a\n\nSimilarly, \"in your corner too\" = ? \n\"from our1+2 lake too\" = qucxst”psa → \"st”psa\" = our1+2 lake too → so \"st”psa\" includes \"too\" \n\"our1+2 field too\" = yapsanpsa → \"sanpsa\" = our1+2 field too → \"too\" is attached to the noun \n\nThus, \"too\" is suffix on the noun with possessive.\n\nSo for \"in your corner too\" → should be \"ish\" + \"your\" + \"p”a\" + \"too\"? \nBut no \"your\" marker; only \"ish\" is locative.\n\nPossibility: \"too\" is added to the noun as suffix.\n\n\"our1+2 lake too\" = qucxst”psa → \"st”psa\" = our1+2 lake too \n\"in our1+2 field too\" = yapsanpsa → \"sanpsa\" = our1+2 field too\n\nSo \"too\" is part of the noun form.\n\nSimilarly, \"in your corner too\" = ish + p”a + too → ishp”a too? \nBut \"ishp”a\" = in your corner → with \"too\" → ishp”a-t? \n\nBut no such form.\n\nAlternatively, \"in your corner too\" = ishp”a → already includes \"too\"? No.\n\n\"the cave too\" = aq”ipsa → \"ipsa\" = the cave too → so \"too\" is in the noun.\n\nThus, for \"in your corner too\" = ishp”a → but \"ishp”a\" = in your corner, not \"too\"\n\nBut \"qqaat”a\" = from the cliff → no \"too\"\n\nThus, \"too\" is not a suffix on the locative, but on the noun.\n\nSo \"in your corner too\" = ish + p”a + too = ishp”a-t? — no", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10029.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Analyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a", + "planner_output": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "anchor_output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "Start with known patterns from the examples.\n\nGiven words:\n\n- aq”ipsa = the cave too → “ipsa” = marker of “too”\n- p”ak”unhpsa = my pot too → “unhpsa” = “too”\n- qucxst”psa = from our1+2 lake too → “st”psa” = “too”\n- yapsanpsa = in our1+2 field too → “anpsa” = “too”\n\nSuffixes for “too”:\n- -ipsa (appears in “cave too”)\n- -nhpsa (in “my pot too”)\n- -stpsa (in “our1+2 lake too”)\n- -anpsa (in “in our1+2 field too”)\n\nAll end in -psa or -hpsa. The base form -psa is repeated with variations in the preceding segment, depending on the noun or locative.\n\nThus, “too” is not a single suffix; it attaches to the noun or locative phrase and takes a suffix form based on the context.\n\nWhen “too” modifies a locative noun (in + X), such as “in the field” or “in the corner”, the form “-anpsa” appears:\n- yapsanpsa = in our1+2 field too → uses -anpsa\n\nSimilarly, “in our1+2 lake too” = qucxst”psa → uses -stpsa → here “lake” is the noun, and the locative structure is “from” or “in”?\n\nActually, “qucxst”psa” is “from our1+2 lake too” → so “from” is modifier, not “in”.\n\nBut yapsanpsa is “in our1+2 field too” → with locative in.\n\nSo for “in + X too”, “anpsa” is used.\n\nTherefore, for “in your corner too”, which is locative + too, pattern is: ishp”a + anpsa → ishp”a anpsa\n\nNow, base forms:\n- “your corner” = ishp”a → from the example, “his corner” = chushp”a, so “your” = ish + p”a → ishp”a\n- “in” is not directly marked in examples, but “in my bed” = ishinhna → suggests \"in\" is part of the base.\n\nSo “in your corner” = ishp”a \nThus, “in your corner too” = ishp”a anpsa\n\nNow, “from your corner too” → “from” + “your corner” + “too”\n\n“from” in examples: “from our1+2 lake” = qucxap”a → base is “qucxap”a, and “from our1+2 lake too” = qucxst”psa → so “st”psa = too\n\nSo “from + X too” → uses -stpsa?\n\nCheck: “from our1+2 lake too” → qucxst”psa → “st”psa → so -stpsa\n\nSo “from your corner too” = should be (from your corner) + stpsa = ishp”a st”psa? But “your corner” is ishp”a → so ishp”a st”psa\n\nBut “from” is not “in” — “from” is a directional marker.\n\nIn qucxst”psa, the core is “lake” → qucxap”a → with “from” → qucx → then + st”psa → so the “too” suffix is attached to the content of the locative.\n\nSimilarly, “in our1+2 field too” → yapsanpsa → “in” + “our1+2” + “field” → “anpsa” → so “too” suffix attaches to the noun.\n\nThus, morphology of “too” depends on the type of phrase:\n\n- locative (in X) → -anpsa (e.g., in our1+2 field too)\n- directional (from X) → -stpsa (from our1+2 lake too)\n\nSo:\n\n4. our1+2 cliff → “from the cliff” is qaqat”a → “from the cliff” = qaqat”a → so “our1+2 cliff” = qaqat”a with “our1+2” prefix?\n\n“from the cliff” = qaqat”a → so “our1+2 cliff” = our1+2 + cliff → likely prefix to noun?\n\nLook at “our1+2 lake” → qucxst”psa → “qucx” = lake? qucxap”a = through the lake → so “qucx” = lake?\n\nBut “qucxst”psa” = from our1+2 lake too → so “our1+2” is attached to “lake” → likely “qucx” + ‘our1+2’ → then + st”psa?\n\nBut no explicit “our1+2 + noun” form. However, “our1+2 lake” is not directly given — “from our1+2 lake too” is.\n\nBut “our1+2 lake” is implied in the phrase.\n\nWhat is “our1+2 cliff”? → “from the cliff” is qaqat”a → so “our1+2 cliff” = likely qaqat”a with “our1+2” attached.\n\nBut how?\n\n“our1+2 town” = markp”t”a → “from his town” → “markp”t”a” → “p”t”a” → “his town”\n\nSimilarly, “our1+2 town” → markstxi → is it “markstxi” → “mark” = town, “stxi” = our1+2?\n\n“markstxi” = is it our1+2 town? → yes, from data: “is it our1+2 town?” = markstxi\n\nSo pattern: “our1+2 + noun” → adds “stxi” suffix?\n\n“our1+2 town” → markstxi → so “town” = marka → with “stxi” → markstxi\n\nSimilarly, “our1+2 lake” → should be “qucx” + “stxi”?\n\nBut “from our1+2 lake too” = qucxst”psa → q + u + c + x + s + t”psa → so “st”psa” = too\n\nSo “our1+2 lake” = qucxstxi? Probably not — “st”psa” includes both “st” and “psa”\n\nBut “lake” = qucxap”a → so “qucx” = lake\n\nThus, “our1+2 lake” = qucxstxi → with “stxi” as marker?\n\nBut qucxst”psa” = “from our1+2 lake too” → so “qucx” is lake, “st”psa” = from + too\n\nThus, “our1+2 lake” = qucxstxi → inferred\n\nSimilarly, “our1+2 field” = yapsanpsa → “in our1+2 field too” → “anpsa” = too → so field = yapsa? → yapsanpsa = in + our1+2 + field + too → so “yapsa” = field?\n\n“in our1+2 field” → yapsanpsa → so “in” + “our1+2” + “field” → “anpsa” = too\n\nSo likely, “our1+2 field” = yapsa? But with “anpsa”\n\nBut base: “field” = yapsa → then “our1+2 field” = yapsa + stxi? But yapsanpsa has “anpsa” → not “stxi”\n\nWait — “our1+2 field” appears in “in our1+2 field too” → “yapsanpsa” → so the whole unit is “in our1+2 field too” → so “our1+2 field” is core, with “too” added as -anpsa.\n\nThus, the way to form “our1+2 + noun”:\n\n- town → marka → markstxi\n- field → yapsa → yapsanpsa? But only when “in” + “too”?\n- lake → qucxap”a → qucxst”psa with “too” → so qucxstxi?\n\nBut no direct “our1+2 cliff” form.\n\nWe have “from the cliff” = qaqat”a → so “cliff” = qaqat”a → without “our1+2”\n\nSo “our1+2 cliff” = likely qaqat”a with “our1+2” added.\n\nFrom pattern: “our1+2 town” = markstxi → mark + stxi\n\n“our1+2 field” = not directly, but in “in our1+2 field too” → yapsanpsa → so yapsa + anpsa → but “anpsa” includes “too”\n\nBut “stxi” appears in town, not field.\n\nIs “stxi” only for “our1+2”?\n\n“our1+2 town” = markstxi → yes\n\n“our1+2 lake” = implied in “from our1+2 lake too” → qucxst”psa” → “st”psa” → so “stxi” in the core?\n\nBut “qucxst”psa” has “st” + “psa” → so not directly “stxi”\n\nBut perhaps “stxi” is the marker for “our1+2” in some nouns, and the “too” suffix is attached at the end.\n\nBut “in our1+2 field too” = yapsanpsa → “anpsa” = too → so “too” is added after “field”.\n\nSo for “our1+2 cliff” → likely “q” + “aqat” + “stxi” = qaqatstxi?\n\nBut no evidence.\n\nAlternatively, “our1+2 cliff” = from the cliff → qaqat”a → so “our1+2” is added as a prefix?\n\nPossible patterns:\n\n- “his town” = chushp”a → chush + p”a → “p”a” = his?\n- “from his town” = markp”t”a → mark + p”t”a → so “p”t”a” = his town?\n\nBut “our1+2” = in markstxi → “markstxi” = our1+2 town → so “stxi” may be marker.\n\nSimilarly, “our1+2 lake” is embedded in “from our1+2 lake too” = qucxst”psa” → so “st”psa” = our1+2 + too?\n\nBut “st”psa” appears in both “our1+2 lake too” and “in our1+2 field too” — different suffixes.\n\nSo perhaps for “our1+2 + noun”, the marker is not consistent.\n\nBut note: “in our1+2 field” is represented as “yapsanpsa” — “anpsa” = too, so “too” is separate.\n\nSimilarly, “from our1+2 lake” → “qucxst”psa” — “st”psa” = too.\n\nSo the “too” suffix is distinct.\n\nTherefore, for “our1+2 cliff” — no “too”, just the noun?\n\nSo likely: “cliff” = qaqat”a → “our1+2 cliff” = qaqat”a with “our1+2” marker.\n\nFrom “our1+2 town” = markstxi → mark + stxi\n\n“our1+2 lake” → implied as qucxstxi → qucx + stxi\n\n“our1+2 field” → not given, but when in “in our1+2 field too” = yapsanpsa → the “too” is “anpsa” → so “in” + “our1+2” + “field” + “too”\n\nSo perhaps “our1+2 field” = yapsa + stxi? But it's not used.\n\nBut “yapsa” may be field, and “stxi” is “our1+2” marker.\n\nThus, “our1+2 field” = yapsastxi\n\nSimilarly, “our1+2 cliff” = qaqatstxi\n\nSo 4. our1+2 cliff = qaqatstxi\n\nNow, 5. in your corner → “in your corner” = ishp”a → as “his corner” = chushp”a → so “your” = ish, “corner” = p”a → ishp”a\n\nSo 5. in your corner = ishp”a\n\n6. in your corner too → locative + too → pattern from “in our1+2 field too” = yapsanpsa → so here, “in your corner too” = ishp”a anpsa\n\n7. from your corner too → directional + too → pattern from “from our1+2 lake too” = qucxst”psa → so for “from your corner too” → ish + p”a + st”psa → ishp”a st”psa\n\n8. is it from the cave? → “is it from the cave” → from the cave → “from the cave” = aq”ipsa? But aq”ipsa = the cave too → not from.\n\n“from the cave” → not directly given.\n\nBut what is “the cave” → aq”ipsa → so “from the cave” → likely aq”ip” + something?\n\n“from X” → in examples: “from our1+2 lake” → qucxap”a → but qucxst”psa = from our1+2 lake too → so “qucxap”a” is base?\n\nNo — “qucxst”psa” = from our1+2 lake too → so “qucx” = lake → “our1+2” is in the suffix?\n\nBut no base form for “from the cave”.\n\nHowever, “the cave” = aq”ipsa → so “from the cave” = aq”ipsa with “from” prefix?\n\nBut no such form.\n\nPossibly, “from the cave” = aq”ip” + “something”?\n\nBut look at the structure: “is it from the cave?” → similar to “is it the house?” or “is it the town?”\n\nWe have:\n- “is it our1+2 town?” = markstxi\n- “is it the field?” = yaputxi\n- “is it from the cave?” = ?\n\nAlso, “is it from the cave” → would be a question about a locus.\n\nIn “is it from the cave” → the structure is “from the cave” as a locative.\n\nFrom examples, “from” + noun → like “from the lake” — not directly given.\n\nBut “from our1+2 lake” is used — so perhaps “from X” takes a specific form.\n\nNote: “is it from the cave?” → similar to “is it from the town?” or “is it from the field?”\n\nWe have “is it the field?” = yaputxi\n\nSo perhaps “is it from the cave?” = aq”ipsa” with a question prefix?\n\nBut the question form: “is it X?” uses “x + stxi” or similar?\n\n“is it our1+2 town?” = markstxi → markstxi = is it our1+2 town?\n\n“is it the field?” = yaputxi → yaputxi = is it the field?\n\nSo “is it X?” = X + stxi? \n- markstxi → X = our1+2 town → mark + stxi → so yes \n- yaputxi → X = field → yapu + tx? yaputxi → “yap” + “ut” + “xi”? \n\n“yaputxi” = is it the field? → likely “yap” = field, “utxi” = question marker?\n\n“yap” is same as “yaputxi” — so perhaps “yap” = field → “yap” + “utxi” = is it the field?\n\nSimilarly, “is it from the cave?” → “from the cave” = aq”ipsa?\n\nBut “aq”ipsa = the cave too → so “the cave” = aq”ipsa\n\nSo “is it from the cave?” = aq”ipsa” + something?\n\nBut “from” is not part of the noun.\n\nPossibility: “from the cave” = aq”ipsa with a prefix?\n\nBut in “from our1+2 lake” → is it embedded in “qucxst”psa” — but that is “from our1+2 lake too” — not a question.\n\nNo question form for “from the cave”.\n\nBut look at the pattern of “is it X?”:\n\n- is it our1+2 town? = markstxi → X = our1+2 town\n- is it the field? = yaputxi → X = field\n- is it from the cave? = ?\n\nSo perhaps “from the cave” is the X.\n\nSo “is it from the cave?” = ? + stxi?\n\nFrom earlier: “from” is a modifier.\n\nBut “the cave” is a noun.\n\nSo perhaps “from the cave” is a phrase, and in the question form, it becomes a single unit.\n\nBut no such form.\n\nAlternative idea: “from” is conveyed by the word “from” or by structure.\n\nBut “from the cave” may be expressed as “the cave from” — not likely.\n\nNotice: “from the cave” → analogous to “from the town” or “from the lake”.\n\nBut no examples.\n\nBut in “is it from the cave?” → may follow the pattern of “is it X?” where X is a locative.\n\nIn “is it the field?” = yaputxi → “yap” = field → so the noun part is “yap”\n\nSo “from the cave” → the word for “cave” is “aq”ipsa → so “is it from the cave?” = aq”ipsa” with “from”?\n\nBut no “from” stem.\n\nPerhaps “from” is morphologically encoded.\n\nBut in all given, “from” is only with “our1+2 lake” → qucxst”psa” → so “from” + noun → “st”psa” → but that adds “too”\n\nIn question form, no such.\n\nConclusion: likely, “is", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10966.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Address the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes.", + "planner_output": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "anchor_output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "4. our1+2 cliff → qaqat”ast” \n5. in your corner → ishp”a \n6. in your corner too → ishp”a anpsa \n7. from your corner too → markp”t”a has \"from his town\" → \"p”t”a\" = his town → for \"your\", likely \"p”t”a\" becomes \"p”t”a\" with \"your\" marker. But \"from his\" = markp”t”a → so \"from your\" = ? \n\n\"from his corner\" → not directly given. \nBut \"from his town\" = markp”t”a → \"p”t”a\" = his town → so \"p”t”a\" is the possessive form of town with \"his\" \nSimilarly, \"his corner\" = chushp”a → so \"your corner\" = ? \n\nNo direct form, but \"from\" is indicated by prefix. \n\"from the cliff\" = qaqat”a — no possessive \n\"from his town\" = markp”t”a → so \"from\" + \"his\" + \"town\" → markp”t”a \n\nPattern: the possessive prefix attaches to the noun. \nFor \"from your corner\" → \"from\" + \"your\" + \"corner\" → \"p”a\" is corner → \"your\" = ? \nWe have no \"your\" possessive marker. \n\nBut in \"your bed\" = ishma → \"ish\" for locative, \"ma\" for bed → so \"your\" is marked by a noun root. \n\nPossibly, the possessive is marked by the base form of the noun with a suffix. \n\nFrom \"from his town\" = markp”t”a → mark + p”t”a → p”t”a = his town → similar to chushp”a = his corner → so p”a is the root, with possessive prefix. \n\nLikely \"your\" has no separate marker; the root is used with a possessive. \n\nBut \"is it from the cave?\" → 8. → \"is it from the cave?\" → \"from the cave\" = qaqat”a → \"from\" + \"cave\" → \"qaqat”a\" → but \"the cave\" is \"aq”ipsa\" → so \"from the cave\" = qaqat”a? \n\nWait — qaqat”a = from the cliff \naq”ipsa = the cave \n\nSo \"from the cave\" = qaqat”a → no — it's a different word. \n\n\"from the cave\" → not given. \n\nBut \"is it from the cave?\" → needs to be a question form. \n\nWe have: \n\"chushuntxi\" = is it in the corner? \n\"markstxi\" = is it our1+2 town? \n\"ishp”a\" = in your corner → so is it in your corner? = ish p”a txi? \n\nLikely, the question form is \"is it X?\" = X + txi \n\nSo \"is it from the cave?\" → \"from the cave\" + txi → \"qaqat”a\" + txi? But qaqat”a = from the cliff — not from the cave. \n\nCave = aq”ipsa → so from the cave = aq”ipsa → but we don’t have \"from the cave\" directly. \n\nBut qaqat”a = from the cliff → so from the cave → aq”ipsa → \"from the cave\" = aq”ipsa? — only if \"a\" is from. \n\nBut no. \n\nPossibly, \"from\" is used as a prefix, and \"the cave\" = aq”ipsa → so \"from the cave\" = aq”ipsa? But that is the cave itself. \n\nContradiction. \n\nBut in the list: \"from the cliff\" = qaqat”a → so \"from\" is marked by qaqat”a → so from the cave = aq”ipsa → not matching. \n\nUnless the word for \"from the cave\" is not in the list. \n\nBut the base form \"cave\" = aq”ipsa → so \"from the cave\" = must be a prefixed form. \n\nPerhaps the pattern is that \"from\" is tied to a noun with a specific root. \n\nWe have: \n- from the cliff → qaqat”a \n- from our1+2 lake → qucxst”psa \n- from his town → markp”t”a \n\nSo from + noun → the noun is taken as base, with possessive or locative. \n\nFor \"from the cave\" → cave = aq”ipsa → so from the cave = aq”ipsa → but that's \"the cave\", not \"from\". \n\nNo — qaqat”a is from the cliff → so qaqat”a = from the cliff → so \"from X\" = qaqat”a if X=cliff, but not for cave. \n\nThus, likely \"from the cave\" = aq”ipsa → but it’s not. \n\nUnless the word is \"from the cave\" = aq”ipsa → not possible. \n\nWait — the example \"from our1+2 lake\" = qucxst”psa → which is from + our1+2 + lake → so \"qucx\" = lake → \"qucxst”psa\" = from our1+2 lake → so \"from\" + possessive + noun \n\nSimilarly, \"from the cliff\" = qaqat”a → so \"from\" + cliff = qaqat”a \n\nThus, \"from the cave\" = aq”ipsa? — no, aq”ipsa = the cave \n\nThus, \"from the cave\" must be a form of qaqat”a with cave instead of cliff — but no such form. \n\nPossibly the root for \"cave\" is \"aq”\" → so \"from the cave\" = aq”ats” or something? \n\nBut no example. \n\nBut the translation is \"is it from the cave?\" → so the base form must be derivable. \n\nGiven that \"from the cliff\" = qaqat”a → cliff root = qaqat → so from cave = aq”ipsa → but aq”ipsa = the cave → so perhaps \"from the cave\" = aq”ipsa → only if the \"from\" is implied. \n\nUnlikely. \n\nBut in \"from our1+2 lake\" = qucxst”psa → which has the root \"qucx\" meaning \"lake\", so the \"from\" is inherent in the root. \n\nSimilarly, \"from the cliff\" = qaqat”a → root \"qaqat\" → cliff \n\nSo \"from the cave\" = aq”ipsa → only if \"aq”ipsa\" includes \"from\", but it does not. \n\nThus, it's likely that \"cave\" is not used with \"from\" directly. \n\nBut the question is \"is it from the cave?\" → so we need the form \"from the cave\". \n\nPossibly, the root for \"cave\" is aq”, and \"from\" is part of the form. \n\nBut we have no such word. \n\nUnless the pattern is that \"the cave\" = aq”ipsa → \"from the cave\" = aq”ipsa with possessive — but no. \n\nBut the form \"our1+2 lake\" = qucxst”psa → so the possessor is attached. \n\nSo \"from the cave\" → no possessor → so just \"aq”ipsa\" with from? \n\nNo. \n\nBut \"from the cave\" must be a word. \n\nGiven that \"from the cliff\" = qaqat”a → so the word is qaqat”a for cliff → so for cave → aq”ipsa → could be related? \n\nPerhaps the root is aq” → so from the cave = aq”at”a? \n\nBut not in data. \n\nPossibly, \"from the cave\" = aq”ipsa → only if \"ipsa\" means \"from\", but \"ipsa\" is used in \"the cave too\" — so it's in \"the cave\", not \"from\". \n\nThus, it's more plausible that the word \"from the cave\" is formed as a derivative of the noun with a locative prefix. \n\nBut we have no such pattern. \n\nAnother idea: the question \"is it from the cave?\" = is it qaqat”a? → but that's from the cliff. \n\nNo. \n\nBut perhaps \"from the cave\" = aq”ipsa — \"the cave\" is aq”ipsa → so \"from\" is not a prefix. \n\nNo. \n\nWait — the word \"qaqat”a\" = from the cliff → so \"from X\" is represented by a word with the root of X. \n\nSo for cave → root = aq” → \"from the cave\" = aq”at”a or aq”ipsa? \n\nBut no example of \"from the cave\". \n\nBut in the list, all \"from\" forms have a specific root: \n- cliff → qaqat”a \n- our1+2 lake → qucxst”psa \n- his town → markp”t”a \n\nSo \"from the cave\" should have root = aq” → so qaq”at”a? — not attested. \n\nThus, the only possibility is that the word for \"from the cave\" is derived from the root of the cave with a form similar to the others, but no such form exists. \n\nBut the lack of a direct form suggests that the pattern is that \"from\" is part of the noun root. \n\nSo for \"is it from the cave?\" = is it aq”ipsa? — but aq”ipsa = the cave → so cannot be. \n\nUnless the translation is aq”ipsa with a prefix. \n\nBut no. \n\nAlternative: is it from the cave? = is it qaqat”a? — only if cave and cliff are the same, which they are not. \n\nThus, the only logical possibility is that the word for “from the cave” is formed as aq”at”a, but it's not in the data. \n\nBut in the data, we have \"from our1+2 lake\" = qucxst”psa — so the possessive is attached. \n\nBut \"from the cave\" has no possessive — it's just \"the cave\". \n\nSo perhaps \"from the cave\" = aq”ipsa → not possible. \n\nUnless \"ipsa\" is used in both. \n\nBut in \"the cave too\" = aq”ipsa → so \"ipsa\" = too, not from. \n\nTherefore, the only viable derivation is that \"from the cave\" = aq”at”a — but that is not given. \n\nHowever, the only word with \"from\" and a noun is qaqat”a for cliff — so for cave, it must be analogical. \n\nSince cave root is aq”, and cliff is qaqat”, perhaps \"from the cave\" = aq”at”a? \n\nBut no support. \n\nPerhaps the root is the same: aq” → so from the cave = aq”ipsa — but no. \n\nAfter rechecking: \n\"from the cliff\" = qaqat”a \n\"from our1+2 lake\" = qucxst”psa \n\"from his town\" = markp”t”a \n\nSo the pattern is: \n- from + noun → formed by the noun root + possessive (if any) or with a new form \n- for \"cave\" → noun is aq”ipsa → so \"from the cave\" = aq”at”a? \n\nBut aq”ipsa has \"ipsa\" — which is \"too\" — likely a suffix. \n\nThus, the base is aq” → from cave → aq”at”a? \n\nBut no such word. \n\nGiven the absence of direct evidence, and the pattern of roots, it is reasonable to assume that \"from the cave\" is formed as aq”at”a. \n\nBut this is speculative. \n\nAlternatively, consider that in all \"from\" examples, the construction is: \n- from X = [root of X] \n\nSo from the cliff = qaqat”a → root qaqat \nFrom the cave = aq”ipsa → root aq”? \n\nBut aq”ipsa has \"ipsa\" → which is \"too\" — so the word aq”ipsa is \"the cave too\" → so the root is not aq”. \n\nPerhaps the root is aq” → and \"from\" is prefixed. \n\nBut no prefix. \n\nTherefore, the only possible conclusion is that the form for \"is it from the cave?\" is is aq”ipsa txi? — but that would be \"is it the cave too?\" — not \"from\". \n\nNo. \n\nGiven that \"from the lake\" is not in the list, and the only from form with a noun is by root, we must assume that the word for \"from the cave\" is aq”at”a — but not supported. \n\nAlternatively, the translation of \"is it from the cave?\" is formed by taking the word for \"the cave\" and adding a question suffix. \n\nBut no such suffix is available. \n\nWe have: \n- is it in the corner? = chushuntxi \n- is it our1+2 town? = markstxi \n- is it the field? = yaputxi \n- is it from the cave? = ? \n\nSo the pattern is: X + txi = is it X? \n\nSo \"is it from the cave?\" = (from the cave) + txi \n\nFrom the cave = ? \n\nFrom the cliff = qaqat”a → so from the cave = aq”at”a? \n\nBut aq”ipsa = the cave → so perhaps aq”at”a is from the cave. \n\nWith the lack of direct example, and the root-based pattern, we infer that \"from the cave\" = aq”at”a. \n\nThus, 8. is it from the cave? = aq”at”a txi \n\nSimilarly, \"is it the house?\" = \"the house\" = utamt”a → so \"is it the house?\" = utamt”a txi \n\nSo 9. is it the house? = utamt”a txi \n\nNow for 7. from your corner too → \n\"from your corner\" = ? \nWith \"your\" → no direct form. \n\"from his town\" = markp”t”a → so \"p”t”a\" = his town \n\"from his corner\" = ? — not given \n\"corner\" = p”a → so \"from your corner\" = ? \n\n\"your corner\" = ishp”a (in your corner) → so from your corner = markp”t”a with \"your\" → no. \n\nBut \"from his corner\" not given. \n\nLikely, the possessive applies to the noun. \n\nSo \"from your corner\" = p”a with \"your\" → so root p”a → with \"your\" → possibly a suffix. \n\nBut no word for \"your\" in noun base. \n\nGiven that \"his\" is marked in chushp”a and markp”t”a, and \"our1+2\" in qucxst”psa and markstxi, the possessive is attached to the noun root. \n\nSo \"your\" → likely has a marker like \"ish\" or \"ma\" — but \"ish\" is in locative. \n\nPossibly, the possessive suffix for \"your\" is not used — the noun root is used with context. \n\nBut in \"your bed\" = ishma → \"ma\" = your bed → so \"ma\" is the form for bed with \"your\". \n\nSimilarly, \"your corner\" = p”a with \"your\" → so p”a with your → likely p”a is modified. \n\nBut we have no such form. \n\nBut in \"from his town\" = markp”t”a → so \"p”t”a\" = his town → so for \"your\" → likely \"p”t”a\" with \"your\" → perhaps p”t”a becomes p”t”a → but with \"your\" → not clear. \n\nSince we have no example of \"from your corner\", and the only pattern is that possessive markers are attached, and \"your\" is not present in any other noun, we must infer that \"your\" is marked by a suffix on the noun. \n\nBut no such suffix is given. \n\nHowever, in the translation of \"in your corner too\", we used ishp”a anpsa — so \"in your corner\" = ishp”a → which implies that \"your\" is not marked as a separate possessive, but as a root. \n\nSimilarly, \"from your corner\" = from + your corner → so from + p”a with \"your\" → best available form: p”a with your = ? \n\nSince \"his corner\" = chushp”a → chush = his → so for \"your\", likely a different possessive. \n\nBut only \"his\" is used. \n\nPerhaps \"your\" is marked by \"ish\" or \"ma\" — but not. \n\nGiven the lack of evidence, and the pattern in other examples, the only logical possibility is that \"from your corner\" = p”a with \"your\" = p”a with a possessive suffix. \n\nBut no. \n\nAlternatively, \"from your corner\" = p”t”a with \"corner\" → not. \n\nFinal decision based on pattern: \n- from + noun = root of noun with possessive or locative \n- corner = p”a \n- for \"your\", as in \"your bed\" = ishma → \"ma\" = your bed → so the base is \"ma\" for bed → so for corner, \"p”a\" with your → no form. \n\nThus, \"from your corner\" = markp”t”a with p”a → not possible. \n\nPossibly, the possessive suffix for \"your\" is not used, and the word is \"p”a\" with a prefix. \n\nBut no. \n\nAfter careful analysis, the most consistent patterns from the given data are:\n\n4. qaqat”ast” \n5. ishp”a \n6. ishp”a anpsa \n7. from your corner too → use pattern of \"from his town\" = markp”t”a → so from your corner = ? → if \"p”t”a\" = his town, then for corner, \"p”a\" with your → but no form", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5", + "b.6" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12378.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 228.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "planner_output": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "anchor_output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 0, + "output": "Step 1: Identify verb structure patterns from given sentences.\n\nSentence 1: *Qingmivit takujaatit* → \"Your dog saw you\" \nBreakdown: \"takuj\" (verb stem) + \"aate\" (object \"you\") + \"vit\" (past tense suffix) → \"saw you\"\n\nSentence 2: *Inuuhuktuup iluaqhaiji qukiqtanga* → \"The boy shot the doctor\" \nBreakdown: \"qukiq\" + \"tanga\" → \"shot\" → \"tanga\" is past tense suffix. Object \"iluaqhaiji\" (the doctor) is attached separately.\n\nSentence 3: *Aanniqtutit* → \"You hurt yourself\" \nBreakdown: \"aanniqt\" + \"utit\" → \"hurt\" + reflexive suffix → self-object.\n\nSentence 4: *Iluaqhaijiup aarqijaatit* → \"The doctor cured you\" \nBreakdown: \"aarqij\" + \"aate\" → \"cured you\" → object marker \"aate\", past tense implied.\n\nSentence 5: *Qingmiq iputujait* → \"You speared the dog\" \nBreakdown: \"iputuj\" + \"ait\" → \"speared\" — \"ait\" is past tense.\n\nSentence 6: *Angatkuq iluaqhaijimik aarqisijuq* → \"The shaman cured a doctor\" \nBreakdown: \"aarqisijuq\" → \"cured\" → stem \"aarqisij\" + suffix \"uq\" — likely past tense. Object \"iluaqhaijimik\" = a doctor.\n\nSentence 7: *Nanuq qaijuq* → \"The polar bear came\" \n\"qaijuq\" → \"came\" → stem \"qaij\" + suffix \"uq\" → past tense.\n\nSentence 8: *Iluaqhaijivit inuuhuktuit aarqijanga* → \"Your doctor cured your boy\" \n\"aarqijanga\" → cured + past tense → object is \"inuuhuktuit\" (your boy) → object marking \"uit\" (variant of \"aate\").\n\nSentence 9: *Angunahuktiup amaruq iputujanga* → \"The hunter speared the wolf\" \n\"iputujanga\" → speared → stem \"iputuj\" + past suffix \"anga\" → \"speared\"\n\nSentence 10: *Qingmiup ilinniaqtitsijiit aanniqtanga* → \"The dog hurt your teacher\" \n\"aanniqtanga\" → hurt + past tense → \"aanniqt\" + \"anga\"\n\nSentence 11: *Ukiakhaqtutit* → \"You fell\" → \"uqiakhaq\" + \"utit\" → past tense.\n\nSentence 12: *Angunahukti nanurmik qukiqsijuq* → \"The hunter shot a polar bear\" \n\"qukiqsijuq\" → shot → stem \"qukiq\" + \"sijuq\" → past tense.\n\nKey patterns:\n\n- Past tense suffixes: -tanga, -ait, -utit, -anga, -uq, -sijuq \n- Object marking: aate, aati, aatiq, uit — typically attached after verb stem \n- Reflexive: utit → used when subject and object are the same (e.g., \"you hurt yourself\")\n\nBut notice: \n- \"takujanga\" in sentence 13 → \"takuj\" + \"anga\" → past tense → saw \n- \"aate\" appears when object is specified (e.g., \"saw you\", \"cured you\") \n- When object is missing, the past tense is still used, but no object marker → \"saw\" (something), not \"saw you\"\n\nThus, verb structure: \nVerb stem + past tense suffix + (optional object marker) \nObject marker is attached only when object is specified; otherwise, the verb is intransitive.\n\nNow, analyze each target:\n\n13. Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = past of \"angatkuq\" → \"came\" (in sentence 7: \"Nanuq qaijuq\" → bear came) \n- \"takujanga\" = \"saw\" → stem \"takuj\" + past suffix \"anga\" → \"saw\" (no object) \n→ \"The hunter came and saw.\"\n\n14. Nanuit inuuhukturmik aanniqsijuq \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in sentence 8: \"inuuhuktuit\" → your boy → \"uit\" is object marker) \n- \"aanniqsijuq\" = hurt (stem \"aanniqt\" + past suffix \"sijuq\" → like \"aanniqtanga\") \n→ \"Your boy hurt you.\"\n\nWait: object \"inuuhukturmik\" is marked with \"mik\" → similar to \"iluaqhaijimik\" in sentence 6 (\"a doctor\") → object suffix. \n\"mik\" = object marking? Compare: \n- sentence 6: \"iluaqhaijimik\" → \"a doctor\" → object \n- sentence 12: \"qukiqsijuq\" → \"shot a polar bear\" → object \n- so object marker appears after noun\n\nThus: \"aanniqsijuq\" = \"hurt\" + past tense → verb \nObject = \"inuuhukturmik\" → your boy \nSo: \"Your boy hurt you\" — but is the object marked correctly?\n\nBut in sentence 3: \"aanniqtutit\" = you hurt yourself → reflexive → \"utit\" \nHere, object is separate → so not reflexive → transitive → \"hurt [someone]\" → so \"your boy hurt you\"\n\n→ \"Your boy hurt you.\"\n\n15. Angunahuktiit aarqijuq \n- \"Angunahuktiit\" = hunter (stem \"angunahuk\") + past tense suffix \"it\" → like \"iputujait\", \"angunahuktiup\" \n- \"aarqijuq\" = cured → stem \"aarqij\" + \"uq\" → past tense \n→ \"The hunter cured.\"\n\nBut no object? → \"cured\" what? \nBut in sentence 4: \"iluaqhaijiup aarqijaatit\" → \"the doctor cured you\" → object present \nHere: \"aarqijuq\" → no object → similar to \"qukiqtanga\" → \"shot\" without object? Not likely.\n\nBut sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared the wolf → object present \nSentence 6: \"angunahukti nanurmik qukiqsijuq\" → \"hunter shot a polar bear\" → object present\n\nSo when object is missing, could \"cured\" mean \"cured someone\" or \"cured itself\"?\n\nBut \"aarqijuq\" → like \"aarqijaatit\" → without object marker → does it imply a specific object?\n\nPerhaps the object is implied by context.\n\nBut in sentence 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object marked.\n\nSo in 15: \"Angunahuktiit aarqijuq\" → no object → \"the hunter cured\" → must be intransitive?\n\nBut \"cure\" is not typically intransitive.\n\nAlternative: \"aarqijuq\" → same as \"aarqijaatit\" → but without \"aate\" → could be \"cured [someone]\" with object missing?\n\nLook at sentence 4: \"iluaqhaijiup aarqijaatit\" → clear object → marked \nSentence 6: \"aarqisijuq\" → cured a doctor → object marked\n\nSo when object marker is missing → perhaps no object → or the object is missing or generic.\n\nBut in sentence 15, no object → so may be \"the hunter cured\" → possibly cured someone, but unspecified.\n\nBut in context, likely meant to be \"the hunter cured [someone]\" — so translation should include that it is a transitive action.\n\nBut no object → so cannot say \"cured you\" → must mean \"cured (someone)\" — grammatically incomplete?\n\nBut in the problem, all translations are complete — likely due to context.\n\nBut based on pattern: verb stem + past tense + object marking \nWhen object marking is absent → object unspecified (generic)\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"saw you\" — object present \nIn sentence 13: \"takujanga\" — no object → \"saw\" (something)\n\nSimilarly, \"aarqijuq\" → \"cured\" → no object → \"the hunter cured.\"\n\n→ \"The hunter cured.\"\n\nAlternatively, is \"aarqijuq\" a variant?\n\nCompare: \n- Sentence 4: \"aarqijaatit\" → cured you → object marker \"aate\" \n- Sentence 6: \"aarqisijuq\" → cured a doctor → object marker \"sij\" \n- Sentence 15: \"aarqijuq\" → no object marker → minimal form → just \"cured\"\n\nSo likely: \"The hunter cured.\"\n\n16. Ilinniaqtitsiji qukiqtait \n- \"Ilinniaqtitsiji\" → verb stem: \"ilinniaqt\" + suffix \"tsiji\" → like \"ilinniaqtitsijiit\" in sentence 10 \nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → \"ilinniaqtitsijiit\" → \"hurt\" + object \nSo \"ilinniaqtitsiji\" → stem \"ilinniaqt\" + \"tsiji\" → likely past tense? In sentence 10: \"ilinniaqtitsijiit\" → with \"it\" suffix \n\nPossibility: \"tsiji\" is a past tense suffix → \"qukiqtait\" = \"shot\" → \"qukiq\" + \"tait\" → \"shot\"\n\n\"qukiqtait\" → stem \"qukiq\" + past suffix \"tait\" → like \"iputujait\" → \"speared\"\n\nSo: \"ilinniaqtitsiji\" → \"hurt\" (with \"tsiji\" as past) \n\"qukiqtait\" → \"shot\"\n\nSo \"the dog hurt and shot\" → but no object for \"hurt\"?\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" \n→ \"ilinniaqtitsijiit\" → past → object \"aanniqtanga\"\n\nHere: \"ilinniaqtitsiji\" → same stem → no object? → perhaps missing object?\n\nBut sentence 16: \"ilinniaqtitsiji qukiqtait\" → two verbs → likely sequential.\n\nSo: \"The dog hurt and shot.\"\n\nNo object for \"hurt\"? → but \"hurt\" with object in sentence 10 → suggests \"hurt something\" generally.\n\nIn context: likely \"the dog hurt and shot.\"\n\n17. Qaijutit \n- \"qaij\" + \"utit\" → past tense → like \"ukiakhaqtutit\" (you fell) → \"utit\" past \n- \"qaij\" → \"came\"? Sentence 7: \"nanuq qaijuq\" → \"came\" → \"qaijuq\" → \"qaij\" + \"uq\" \n- \"qaijutit\" → \"qaij\" + \"utit\" → past → but is it \"came\"?\n\n\"utit\" appears in sentence 3: \"aanniqtutit\" → hurt yourself\n\nSo \"qaijutit\" → \"came\" (something) → past tense → no object → \"came\"\n\n→ \"You came.\"\n\nBut the sentence is \"Qaijutit\" — no subject? \nPossibly \"you\" is implied → like \"You came.\"\n\nIn sentence 11: \"Ukiakhaqtutit\" → \"you fell\"\n\nSo \"qaijutit\" → \"you came\"? But no subject.\n\nBut most likely: in context, \"you came\" — so translation is \"You came.\"\n\n18. Angunahuktimik aarqisijutit \n- \"angunahuktimik\" = hunter + object → object \"mik\" → similar to \"nanurmik\" → \"a polar bear\" \n- \"aarqisijutit\" = cured → stem \"aarqisij\" + past suffix \"utit\" → like \"aanniqtutit\" → reflexive or transitive with past tense?\n\n\"aarqisijutit\" → cured + past → object attached? \nBut \"mik\" appears before → object is \"a polar bear\" \nSo: \"the hunter cured a polar bear\"\n\nBut in sentence 6: \"angunahukti nanurmik qukiqsijuq\" → \"hunter shot a polar bear\" → \"nanurmik\" → object\n\nSo pattern: noun + object marker + verb = \"x cured y\"\n\nThus: \"the hunter cured a polar bear\"\n\nNow compile all:\n\n13. Amaruup angatkuit takujanga → \"The hunter came and saw.\" \n14. Nanuit inuuhukturmik aanniqsijuq → \"Your boy hurt you.\" \n15. Angunahuktiit aarqijuq → \"The hunter cured.\" \n16. Ilinniaqtitsiji qukiqtait → \"The dog hurt and shot.\" \n17. Qaijutit → \"You came.\" \n18. Angunahuktimik aarqisijutit → \"The hunter cured a polar bear.\"\n\nVerify consistency:\n\n- Object marking: used when object is specific → e.g., \"your boy\", \"a doctor\", \"a polar bear\" \n- Past tense: suffix varies (tanga, ait, utit, anga, uq, sijuq) — all are past \n- Intransitive verbs (like \"came\") without object: acceptable \n- Transitive verbs: require object marker or prior noun\n\nFinal translations:\n\na.1: The hunter came and saw. \na.2: Your boy hurt you. \na.3: The hunter cured. \na.4: The dog hurt and shot. \na.5: You came. \na.6: The hunter cured a polar bear.\n\n\\boxed{a.1: The hunter came and saw; a.2: Your boy hurt you; a.3: The hunter cured; a.4: The dog hurt and shot; a.5: You came; a.6: The hunter cured a polar bear}", + "generated_tokens": 3317, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "a.1: The hunter came and saw; a.2: Your boy hurt you; a.3: The hunter cured; a.4: The dog hurt and shot; a.5: You came; a.6: The hunter cured a polar bear", + "score_fraction": 0.16666666666666666, + "exact": 0.0, + "matched_units": [ + "a.5" + ], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": true, + "match_type": "normalized_final_substring", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.16666666666666666, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 1.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.16666666666666666, + "ioling_strict_substring_reward": 0.16666666666666666, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 9700.0, + "ioling_final_answer_chars": 154.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context.", + "planner_output": "\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context. \n\n\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative. \n\n\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied. \n\n\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied. \n", + "anchor_output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 1, + "output": "Start by analyzing the verb forms and their patterns in the provided sentences.\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (agent) \n- \"takujaatit\" = saw you (transitive verb with object \"you\") \n→ \"takuj\" = to see, \"aati\" = past tense, \"-t\" = object marked, \"-it\" = 3rd person or subject? \nBut \"takujanga\" appears in 13.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy (agent) \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past of \"qukiq\" = to shoot)\n\nSentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n- Reflexive: \"aanniqt\" = to hurt, \"utit\" = past tense, reflexive (self-object)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n- \"iluaqhaijiup\" = the doctor \n- \"aarqijaatit\" = cured you → \"aarq\" = to cure, \"-j\" = object \"you\", \"-aati\" = past\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n- \"iputujait\" = speared (past), agent \"you\", object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured → \"aarqi\" = cure, suffix \"-sij\" = object marked, \"-uq\" = past\n\nSentence 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n- \"nanuq\" = polar bear \n- \"qaijuq\" = came (past) — no object, intransitive\n\nSentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n- \"iluaqhaijivit\" = your doctor \n- \"inuuhuktuit\" = your boy \n- \"aarqijanga\" = cured → \"aarqi\" + object \"your boy\" + past\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n- \"angunahuktiup\" = the hunter \n- \"amaruq\" = the wolf \n- \"iputujanga\" = speared (past)\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n- \"qingmiup\" = the dog \n- \"ilinniaqtitsijiit\" = hurt your teacher (object \"your teacher\") \n- \"aanniqtanga\" = hurt → \"aanniqt\" = hurt, \"-anga\" = past\n\nSentence 11: \"Ukiakhaqtutit\" → \"You fell.\" \n- Intransitive — no object\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n- \"angunahukti\" = hunter \n- \"nanurmik\" = a polar bear \n- \"qukiqsijuq\" = shot → \"qukiq\" = shoot, \"-sij\" = object marked, \"-uq\" = past\n\nNow observe the verb morphology:\n\n- When a verb is transitive, it has a marking for object (e.g. \"-j\", \"-sij\", \"-t\", \"-janga\", etc.).\n- Intransitive verbs (like \"came\", \"fell\") have no object and no object marking.\n- Reflexive verbs (like \"you hurt yourself\") have marker for self-object (like \"aanniqtutit\").\n\nNow examine verb suffixes based on function:\n\n| Verb | Base | Pattern |\n|------|------|--------|\n| takuj | see | takujanga → saw (with object, past) |\n| qukiq | shoot | qukiq + object marker → qukiqsijuq |\n| aarq | cure | aarqijaatit → cured you |\n| iputu | spear | iputujait → speared dog |\n| qaiju | come | qaijuq → came (intransitive) |\n\nNote: \"takujanga\" in example 13: \"Amaruup angatkuit takujanga\" \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") → so \"angatkuit\" = came \n- \"takujanga\" = saw (past of \"takuj\") → must be a transitive verb with object\n\nSo \"Amaruup angatkuit takujanga\" = \"The hunter came and saw [someone]\"\n\nBut no object is marked. Compare to sentence 4: \"Iluaqhaijiup aarqijaatit\" = \"doctor cured you\" — object is marked as \"up\".\n\nWhere is the object? In sentence 13, subject is \"Amaruup\", then \"angatkuit\" (came), then \"takujanga\" (saw). \nIf \"takujanga\" is transitive, object must be unmarked or implied.\n\nBut in English, \"he came and saw\" implies a specific object (e.g., \"he came and saw the house\"), but here we lack an object.\n\nCheck example 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" — both object and verb have object markers.\n\nIn example 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf → object \"amaruq\" marked with \"-q\" (object marker).\n\nIn sentence 12: \"qukiqsijuq\" = shot a polar bear → object \"nanurmik\" marked with \"-sij\"\n\nIn sentence 6: \"aarqisijuq\" = cured a doctor → \"-sij\" object\n\nIn sentence 4: \"aarqijaatit\" = cured you → \"-j\" object\n\nIn sentence 5: \"iputujait\" = speared the dog → \"-j\" object\n\nIn sentence 10: \"ilinniaqtitsijiit\" = hurt your teacher → \"-tsiji\" = object marked\n\nIn sentence 1: \"takujaaatit\" = saw you → \"takujaatit\" → \"-aati\" = past, \"-t\" = object?\n\nIn sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"takujaatit\" — likely \"takuj\" + object \"you\" in \"-aati\" form.\n\nBut in 13: \"takujanga\" — no object suffix? \"anga\" is past, but no -j or -t?\n\nPossible that \"takujanga\" is intransitive? But \"takuj\" = see, which requires object.\n\nAlternative: perhaps the object is omitted due to context.\n\nBut in sentence 13: \"Amaruup angatkuit takujanga\" — similar to sentence 1.\n\nSentence 1: \"Qingmivit takujaatit\" — dog saw you — agent + saw object\n\nSentence 13: \"Amaruup angatkuit takujanga\" — hunter came and saw?\n\nBut \"angatkuit\" = came (intransitive), \"takujanga\" = saw (transitive) — so it must have an object.\n\nBut object is missing. This suggests that in such compound events, the object may be implied or the structure is \"agent came and saw\", and the object is not marked because it’s general.\n\nCompare to sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" — object is present and marked.\n\nSo likely, when object is missing, it's due to being implied or unmentioned.\n\nBut \"takujanga\" has no object suffix — so probably no object.\n\nBut only intransitive verbs lack object.\n\nThis suggests that if the verb has no object suffix, it's intransitive — but \"takuj\" = to see is transitive.\n\nIn all other transitive verbs, object is marked (e.g., -j, -sij, -t, -tsiji). In \"takujanga\", no object suffix.\n\nPossibility: \"takujanga\" is used here without object, meaning \"saw\" in general, like \"he came and saw\" — object implied.\n\nBut in sentence 1, \"takujaatit\" has \"aati\" which may be past tense. In sentence 13, \"takujanga\" has \"anga\" — also past.\n\nSo perhaps all past verb forms have \"-a-\" or \"-an\" suffix.\n\nNow check derivation of each sentence.\n\n13. Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past, intransitive) \n- \"takujanga\" = saw (past) \nObject missing — so likely \"the hunter came and saw [something]\" — in English, this means \"the hunter came and saw\" — object implied, not stated.\n\nThus: \"The hunter came and saw.\"\n\n14. Nanuit inuuhukturmik aanniqsijuq \n- \"Nanuit\" = the polar bear? \n- \"inuuhukturmik\" = your boy? \n- \"aanniqsijuq\" = hurt (past, transitive)\n\n\"nanuit\" likely = the polar bear (from \"nanuq\" = polar bear, so \"nanuit\" = the polar bear, past?) \nBut \"nanuit\" may be past form of \"nanuq\", so \"the polar bear came\" in sentence 7 is \"nanuq qaijuq\" — intransitive. \nNow \"nanuit\" — could be agent.\n\n\"inuuhukturmik\" — \"inuuhuktuup\" = boy, here \"inuuhukturmik\" — likely \"your boy\" with object marker \"-mik\" (possible object suffix)\n\n\"aanniqsijuq\" = hurt → \"aanniqt\" = hurt, \"-sij\" = object → so \"hurt a person\"\n\nSo: \"The polar bear hurt your boy.\"\n\n15. Angunahuktiit aarqijuq \n- \"Angunahuktiit\" = the hunter (past agent?) \n- \"aarqijuq\" = cured\n\n\"angunahuktiit\" — \"angunahukti\" = hunter (in sentence 9), with \"-it\" — past tense? \nSo hunter (agent), past form.\n\n\"aarqijuq\" = cured → past form, no object marker → so no object?\n\nBut \"aarq\" = cure, transitive — requires object.\n\nSo object missing — implies \"the hunter cured\" → object implied?\n\nSimilar to sentence 13.\n\nIn sentence 4: \"Iluaqhaijiup aarqijaatit\" — doctor cured you → object marked.\n\nHere, object is not marked → so likely \"the hunter cured [someone]\" — object implied.\n\nThus: \"The hunter cured.\"\n\n16. Ilinniaqtitsiji qukiqtait \n- \"Ilinniaqtitsiji\" = hurt your teacher → \"ilinniaqt\" = hurt, \"-tsiji\" = object marked → object \"your teacher\" \n- \"qukiqtait\" = shot? → \"qukiq\" = shoot, \"-ta\" = past? But in sentence 2: \"qukiqtanga\" → \"qukiq\" + \"tanga\" → past\n\n\"qukiqtait\" — \"tait\" instead of \"tanga\"? \nIn sentence 2: \"qukiqtanga\" — agent (boy), object (doctor), action (shot)\n\nIn sentence 12: \"qukiqsijuq\" — \"qukiq\" + object suffix\n\n\"qukiqtait\" — no object suffix? \"tait\" — possible past?\n\nCompare to sentence 5: \"iputujait\" — speared\n\nSentence 10: \"ilinniaqtitsijiit\" — hurt your teacher\n\nAll transitive verbs have object marker.\n\nSo \"qukiqtait\" — likely \"shot\" — but without object marker?\n\nYet \"qukiq\" is transitive — needs object.\n\nSo object missing → might be implied: \"hurt\" or \"shot\" without object.\n\nBut \"ilinniaqtitsiji\" = hurt your teacher — so verb is hurt.\n\n\"qukiqtait\" = shot?\n\nThe phrase is \"Ilinniaqtitsiji qukiqtait\" — so two verbs?\n\nBut \"ilinniaqtitsiji\" = so \"hurt\" + object?\n\nPossibly: \"ilinniaqtitsiji\" = hurt, object present (your teacher)\n\nThen \"qukiqtait\" = shot — but no object — so likely shot someone?\n\nBut no object.\n\nWait — perhaps it's a compound: \"the teacher hurt and shot\" — object for both?\n\nBut \"ilinniaqtitsiji\" already has object.\n\nSo likely, both verbs are transitive — but object is missing in \"qukiqtait\".\n\nBut in sentences, when object is missing, especially in transitive verbs, it may be because object is implied — e.g., \"he hurt and shot\" — object omitted.\n\nBut \"ilinniaqtitsiji\" is \"hurt your teacher\" — so object is present.\n\nSo \"qukiqtait\" may be independent — \"shot\" (intransitive?) — no.\n\n\"qukiqtait\" — compare to \"qukiqtanga\" → both have \"tang\" form?\n\nIn sentence 2: \"qukiqtanga\" — agent + object + verb → so transitive with object marker.\n\nIn sentence 12: \"qukiqsijuq\" → \"shot a polar bear\" → object marked.\n\n\"qukiqtait\" — suffix \"-tait\" — not standard.\n\nPossibility: typo or misreading.\n\nOriginal: \"Ilinniaqtitsiji qukiqtait\"\n\nPerhaps \"qukiqtait\" is \"shot\" in past — but no object suffix.\n\nAnother possibility: \"qukiq\" has a structure where \"-ta\" or \"-tait\" is past form without object.\n\nBut in example 2: \"qukiqtanga\" — has \"tanga\" → past.\n\nIn sentence 12: \"qukiqsijuq\" — has \"sijuq\" — object marked.\n\nIn sentence 5: \"iputujait\" — \"jait\" — past.\n\nSo \"qukiqtait\" — may be \"shot\" without object — intransitive?\n\nBut \"qukiq\" = to shoot — transitive.\n\nThus likely, object is missing — so \"the teacher hurt and shot\" — object implied for \"shot\".\n\nSo English: \"Your teacher hurt and shot.\"\n\n17. Qaijutit \n- Only one word — verb in past tense \n- \"qaiju\" = come → \"qaijut\" → past \n- \"qaijutit\" → form of \"qaiju\" with past suffix? \nBut \"qaijuq\" = came (sentence 7)\n\n\"qaijutit\" → likely \"came\" (past) — and no object → intransitive\n\nSo: \"You came.\"\n\n18. Angunahuktimik aarqisijutit \n- \"Angunahuktimik\" = hunter (agent, with object suffix?) \n- \"aarqisijutit\" = cured (past)\n\n\"angunahuktimik\" — \"angunahukti\" + \"-mik\" — object suffix? But not a verb.\n\nPossibly \"angunahukti\" = hunter, with \"-mik\" = object marker?\n\nBut no object — this would be hunter with object marker for no object?\n\n\"aarqisijutit\" = cured + past — suffix \"-utit\" — past tense\n\nNo object marker → so object missing?\n\n\"aarqisijutit\" — \"aarqi\" + object \"-sij\" + past \"-utit\"\n\nSo \"sij\" object → marked → object is present.\n\nBut in \"angunahuktimik\", no object — so must be agent.\n\nThus: \"The hunter [object] cured\" → object is marked in \"aarqisijutit\" → \"cured [someone]\"\n\nSo the structure is: agent + object + verb\n\nBut \"angunahuktimik\" has \"-mik\" — which is likely object suffix — so could be \"the hunter [object]\"?\n\n\"mik\" is not used in agent.\n\n\"angunahukti\" = hunter \n\"inuuhuktuup\" = boy \n\"nanurmik\" = a polar bear\n\nSo \"-mik\" is used for objects.\n\nThus \"angunahuktimik\" = hunter with object suffix? Unlikely — agent cannot have object suffix.\n\nConclusion: \"angunahuktimik\" = the hunter (agent) with suffix \"-mik\" → but \"-mik\" is object marker.\n\nPossibility: it's a defective form.\n\nAlternatively, it's a mistake in reading.\n\nLook again: sentence 18: \"Angunahuktimik aarqisijutit\"\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter + object (wolf) + verb\n\n\"up\" is object marker.\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter + object (polar bear) + verb\n\nSo object marker appears after agent.\n\nIn sentence 18: \"Angunahuktimik\" — is this agent + object marker? Unlikely.\n\nPerhaps it's \"the hunter\" with no object — so agent.\n\n\"aarqisijutit\" = cured + object marker → so \"the hunter cured [someone]\"\n\nBut object not specified.\n\nThus: \"The hunter cured.\"\n\nBut in sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor\n\nSo \"aarqis", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12289.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Analyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative.", + "planner_output": "\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context. \n\n\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative. \n\n\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied. \n\n\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied. \n", + "anchor_output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 2, + "output": "Step 1: Identify verb forms and their meanings from the given examples.\n\nSentence 1: \"Qingmivit takujaatit\" → Your dog saw you. \n→ \"takujaatit\" = saw (past tense), verb with subject \"your dog\"\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → The boy shot the doctor. \n→ \"iluaqhaiji\" = doctor, \"qukiqtanga\" = shot (past tense), object \"doctor\" is after verb.\n\nSentence 3: \"Aanniqtutit\" → You hurt yourself. \n→ \"aanniqtutit\" = hurt (past), reflexive; self-object.\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → The doctor cured you. \n→ \"aarqijaatit\" = cured (past), object \"you\" after verb.\n\nSentence 5: \"Qingmiq iputujait\" → You speared the dog. \n→ \"iputujait\" = speared (past), object \"dog\".\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → The shaman cured a doctor. \n→ \"aarqisijuq\" = cured (past), object \"a doctor\" (after verb).\n\nSentence 7: \"Nanuq qaijuq\" → The polar bear came. \n→ \"qaijuq\" = came.\n\nSentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → Your doctor cured your boy. \n→ \"aarqijanga\" = cured, object \"your boy\" → object after verb.\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → The hunter speared the wolf. \n→ \"iputujanga\" = speared, object \"wolf\".\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → The dog hurt your teacher. \n→ \"aanniqtanga\" = hurt [someone], object \"your teacher\".\n\nSentence 11: \"Ukiakhaqtutit\" → You fell. \n→ \"qaijutit\" = fall (past tense, reflexive or agentless?).\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → The hunter shot a polar bear. \n→ \"qukiqsijuq\" = shot (past), object \"a polar bear\".\n\nStep 2: Analyze possessive markers.\n\n- \"inuuhuktuit\" (8) = your boy → possessive markers attach before or after noun.\n- \"nanuit\" = your (in 14) → same as \"nanuq\" = polar bear (7) → likely \"nanu\" root, \"uit\" = your.\n- \"angatkuq\" = shaman (6) → \"iluaqhaijimik\" = a doctor → \"mik\" = possessive or genitive?\n- \"angunahukti\" = hunter (9,18) → \"it\" → \"ti\" in other forms → suffix likely marks person.\n\nStep 3: Identify suffix patterns.\n\nGeneral pattern: \n- Past tense verbs show suffixes like: -vit, -tutit, -tanga, -anga, -janga, -qaid, -sijuq.\n\nLook at verb stems:\n\n- \"takujaatit\" → saw → past form\n- \"qukiqtanga\" → shot → past\n- \"aanniqtutit\" → hurt → past, reflexive\n- \"aarqijaatit\" → cured → past\n- \"iputujait\" → speared → past\n- \"aarqisijuq\" → cured → past\n- \"qaijuq\" → came → past\n\nPattern: \n- Past tense form often ends with -it, -anga, -tanga, -janga, -sijoq, etc.\n\nFurther, object suffix appears after verb in most cases (except reflexive).\n\nReflexive forms: \n- Aanniqtutit → you hurt yourself → self-object → verb + reflexive suffix? \n- Also, \"aanniqtanga\" → hurt your teacher → object after verb \n→ So if object is missing, it is implied by context.\n\nPossessive forms:\n\n- \"inuuhuktuit\" → your boy\n- \"inuuhukturmik\" → your boy (same stem) \n→ \"mik\" is likely a possessive suffix or object marker\n\nSimilarly:\n- \"nanuit\" → your\n- \"nanuit inuuhukturmik\" → your boy → \"inuuhukturmik\" = your boy (same as in 8)\n\nIn 14: \"Nanuit inuuhukturmik aanniqsijuq\" \n→ \"aanniqsijuq\" = hurt → past tense \n→ Object required → implied object? From context: \"doctor\" (like in 2, 6)\n\nSo: \"your boy hurt a doctor\"\n\nSimilarly, sentence 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" → related to \"amaruq\" (in 9: \"amaruq\" = wolf) → likely \"amaru\" = wolf \n\"angatkuit\" → past of \"angatkuq\" (shaman) → \"angatkuq\" = shaman → \"angatkuit\" = shaman (past) \n\"takujanga\" → past of \"takujaatit\" → \"takujanga\" = saw\n\n\"angatkuit takujanga\" → \"the shaman saw [someone]\" \n\"Amaruup\" = \"wolf\" → possessive? \"Amaruup\" = \"the wolf\"? \nBut in 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"amaruq\" = wolf\n\nSo \"amaruup\" → likely \"the wolf\" (same as \"amaruq\") → possessive marker \"up\" at end?\n\nCompare to others:\n- \"inuuhuktuit\" = your boy\n- \"iluaqhaijivit\" = your doctor → \"ivit\" = possessive?\n\nSo \"angatkuit takujanga\" → \"the shaman saw [someone]\" \nObject must be possessed → \"amaruup\" = wolf → \"the wolf\" → so \"the shaman saw the wolf\"\n\nSo 13 → The shaman saw the wolf.\n\nSentence 14: \"Nanuit inuuhukturmik aanniqsijuq\" \n→ \"nanuit\" = your \n→ \"inuuhukturmik\" = your boy \n→ \"aanniqsijuq\" = hurt (past tense) \n→ Object missing → from context, in 2,6,10: \"aanniqsijuq\" after verb → object is a doctor \n→ So \"your boy hurt a doctor\"\n\nSentence 15: \"Angunahuktiit aarqijuq\" \n→ \"angunahuktiit\" = past of \"angunahukti\" → hunter \n→ \"aarqijuq\" = cured \n→ \"aarqijaatit\" = cured (in 4) → \"aariq\" root → \"aarqijuq\" = cured (past) \nSo \"the hunter cured [someone]\" \nObject missing → in 4: \"iluaqhaijiup aarqijaatit\" = doctor cured you → object after verb \nBut in 8: \"iluaqhaijivit inuuhuktuit aarqijanga\" → your doctor cured your boy → object after verb \nSo object required → likely \"you\" or \"a person\" → but no marker \nBut in 15: \"Angunahuktiit aarqijuq\" → no object → likely object is \"you\" (implied) \nBut look: is \"aarqijuq\" a past form? Yes → \"aarqisijuq\" in 6 → shaman cured a doctor → object after \nSo again, object after verb is expected → missing → so must be implied?\n\nBut in 15, object is missing → like in 3: \"Aanniqtutit\" = you hurt yourself → reflexive \nBut \"aarqijuq\" (without object) → could be reflexive?\n\nCompare with \"aanniqtutit\" = you hurt yourself → reflexive, no object \nBut \"aanniqtanga\" = hurt your teacher → object\n\nSo verb form with no object → reflexive?\n\nThus, \"aarqijuq\" → could be \"he cured himself\" → but \"angunahuktiit\" = hunter → not reflexive\n\nHence, likely object is missing → implied as \"you\" or \"himself\"?\n\nBut no grammatical marker → in other cases, object follows.\n\nAlternative: in 15, no object → might be reflexive form?\n\nBut no reflexive pattern clearly shown.\n\nAnother thought: the verb \"aarqij\" is used with object in 4,6,8 — with \"you\", \"a doctor\", \"your boy\"\n\nSo in 15: \"Angunahuktiit aarqijuq\" → \"the hunter cured [someone]\" → missing object → in context of similar sentences, \"you\" is common?\n\nBut in 13: \"Amaruup\" → wolf → object → so object is a noun.\n\nIn 15: no object — so perhaps it is reflexive?\n\nBut \"aarqijuq\" = cured → not clearly reflexive.\n\nHowever, in 3: \"aanniqtutit\" = hurt yourself → reflexive → verb has \"tutit\" → past tense + reflexive\n\nCompare:\n- aanniqtutit → hurt yourself \n- aarqisijuq → cured a doctor \n- aarqijuq → possibly cured yourself?\n\nBut not in examples.\n\nSo ambiguous.\n\nLook at 16: \"Ilinniaqtitsiji qukiqtait\"\n\n\"Ilinniaqtitsiji\" → likely derived from \"ilinniaqt\" = teacher → \"siji\" = possessive or form?\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → the dog hurt your teacher → \"ilinniaqtitsijiit\" = your teacher\n\nSo \"ilinniaqtitsijiit\" = your teacher → so \"sijiit\" = possessive? → attaches to \"ilinniaqt\"\n\nSimilarly, in 16: \"Ilinniaqtitsiji\" → likely same stem but missing \"it\"? → might be \"your teacher\"\n\n\"qukiqtait\" → past of \"qukiqtanga\" → shot → \"qukiqtait\" = shot (past)\n\nSo \"your teacher shot [someone]\"\n\nMissing object → like in others → implied — from context, in 2,12: \"shooting\" with object\n\n→ likely \"the doctor\" or \"the polar bear\"?\n\nBut in 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot a polar bear\n\nSo \"qukiqtait\" = shot → must have object\n\nSo 16: \"your teacher shot [someone]\" → object implied → perhaps \"the doctor\"?\n\nBut no evidence.\n\nWait — pattern: verbs with past tense form ending in -it, -tanga, -anga, -janga → often have object after.\n\nBut in 13: \"angatkuit takujanga\" → object is \"amaruup\" = the wolf → so object is written.\n\nIn 14: \"nanuit inuuhukturmik aanniqsijuq\" → object is \"a doctor\"\n\nIn 15: \"Angunahuktiit aarqijuq\" → no object → must be reflexive?\n\nBut hunter curing himself? Seems odd.\n\nAlternatively, could \"aarqijuq\" be a form with object omitted due to context?\n\nBut in other sentences, omission implies reflexive.\n\nCheck: sentence 3: \"Aanniqtutit\" → you hurt yourself → no object → reflexive\n\nSimilarly, sentence 11: \"Ukiakhaqtutit\" → you fell → no object → reflexive\n\n\"Qaijutit\" → fell → same\n\nSo verbs with no object and root form without genitive → reflexive.\n\nSo \"aarqijuq\" → without object → likely \"he cured himself\"\n\nBut \"the hunter\" is agent → could be reflexive?\n\nPossible.\n\nSo \"15: The hunter cured himself.\"\n\nSentence 17: \"Qaijutit\" → from 11: \"Ukiakhaqtutit\" → you fell → past tense → \"qaijutit\" → you fell → reflexive\n\nThus, \"Qaijutit\" → you fell\n\nSentence 18: \"Angunahuktimik aarqisijutit\"\n\n\"Angunahuktimik\" → past of \"angunahukti\" → hunter → with \"mik\" → possessive suffix?\n\n\"inuuhukturmik\" = your boy → possessive suffix \"mik\"\n\n\"angunahuktimik\" = hunter (possessive?) → perhaps \"a hunter\" → or \"the hunter\" (agent)\n\n\"aarqisijutit\" → past of \"aarqisijuq\" → cured → with \"utit\" → past tense\n\nIn 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object after\n\nSo here: no object → likely object is missing → so reflexive?\n\n\"Angunahuktimik aarqisijutit\" → the hunter cured himself?\n\nBut \"mik\" = possessive → could mark subject?\n\nPossessive suffix after agent → could be agent of \"he cured [himself]\" — \"he\" is marked\n\nBut object missing → likely reflexive\n\nSo \"the hunter cured himself\"\n\nNow assemble:\n\n13. Amaruup angatkuit takujanga → the wolf saw the shaman? \nWait: \"Amaruup\" = wolf → agent or object?\n\nIn 9: \"Angunahuktiup amaruq iputujanga\" → the hunter speared the wolf → \"amaruq\" = wolf → object\n\nSo \"amaruq\" = wolf → object\n\nSimilarly, \"Amaruup\" → could be object?\n\nBut in 13: \"Amaruup angatkuit takujanga\" → \"Amaruup\" first → agent?\n\nNo — in English, \"Amaruup\" is the subject?\n\nBut in 9: \"Angunahuktiup amaruq\" → hunter speared wolf → \"angunahuktiup\" = hunter (subject), \"amaruq\" = object\n\nSo \"Amaruup\" = the wolf → object?\n\nBut then \"angatkuit takujanga\" = shaman saw [wolf] → subject = shaman, object = wolf\n\nSo \"the shaman saw the wolf\"\n\nYes.\n\nSo 13: The shaman saw the wolf.\n\n14: Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor\n\n15: Angunahuktiit aarqijuq → the hunter cured himself\n\n16: Ilinniaqtitsiji qukiqtait → your teacher shot [someone] → missing object → in context, from 2,12: shooting a doctor or bear? \nBut 12: hunter shot a polar bear → object often a bear or doctor \nBut here, no context — but pattern: object missing → may be reflexive? \nBut \"qukiqtait\" = shot → not reflexive verb\n\nSentence 10: dog hurt your teacher → object after\n\nBut sentence 16: object missing → only \"your teacher shot\" → no object → so likely \"your teacher shot a doctor\" or similar?\n\nBut no pattern.\n\nWait — compare to 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor → object after\n\nIn 16: \"Ilinniaqtitsiji qukiqtait\" → your teacher shot [someone] → object missing → must be implied → likely \"a doctor\"\n\nBecause \"iluaqhaiji\" = doctor → in all shooting/curing contexts, object is a doctor\n\nSo likely: your teacher shot a doctor\n\n17: Qaijutit → you fell\n\n18: Angunahuktimik aarqisijutit → the hunter cured himself\n\nNow verify all:\n\n13: Amaruup angatkuit takujanga → wolf saw shaman? → But \"angatkuit\" = shaman? → yes \nVerb: \"takujanga\" = saw → past \nObject: \"amaruup\" = the wolf \nSo: the shaman saw the wolf? \nBut word order: \"Amaruup angatkuit takujanga\" → \"Amaruup\" first → object first? \nIn 9: \"Angunahuktiup amaruq iputujanga\" → subject then object → \"hunter speared wolf\" \nSo likely: \"shaman saw wolf\" → but \"Amaruup\" is noun, \"angatkuit\" is verb stem?\n\nNo — \"angatkuit\" is not a noun. \n\"angatkuq\" = shaman → \"angatkuit\" = past of \"angatkuq\" → verb → saw? No, \"takujanga\" = saw\n\nSo: \"Amaruup\" = object → \"angatkuit\" = shaman → agent? \nBut \"angatkuit\" is not a noun — it's a verb form.\n\nError.\n\n\"angatkuit\" = past of \"angatkuq\" → only if \"angatkuq\" is a verb.\n\nBut in 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → \"angatkuq\" = shaman (noun)\n\nSo \"angatkuit\" = a form of \"shaman\" or a verb? → likely noun form with past suffix.\n\nSimilarly, in 8: \"iluaqhaijivit\" = your doctor → past of \"iluaqhaiji\"\n\nSo \"angatkuit\" = the shaman (past tense? or noun?)\n\nBut in sentence 13: \"Amaruup angatkuit takujanga\"\n\nIf \"angatkuit\" is noun → \"the shaman\" → agent \n\"takujanga\" = saw → verb \n\"Amaru", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11957.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Investigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied.", + "planner_output": "\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context. \n\n\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative. \n\n\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied. \n\n\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied. \n", + "anchor_output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "method": "groot_1x4", + "sample_index": 3, + "output": "Step 1: Identify the basic verb forms and their semantic roles.\n\nLook at the given sentences and extract agent, action, and object structure.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n- \"Qingmivit\" = your dog (agent) \n- \"takujaatit\" = saw (verb, past tense) \n- Object: \"you\"\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n- \"Inuuhuktuup\" = the boy (agent) \n- \"iluaqhaiji\" = doctor (object) \n- \"qukiqtanga\" = shot (verb)\n\nSentence 3: \"Aanniqtutit\" → \"You hurt yourself\" \n- \"Aanniqtutit\" = you hurt yourself \n- Reflexive verb: \"hurt yourself\" → agent is \"you\", object is \"yourself\"\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you\" \n- \"Iluaqhaijiup\" = the doctor (agent) \n- \"aarqijaatit\" = cured you \n- Object: \"you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" \n- \"Qingmiq\" = you (agent) \n- \"iputujait\" = speared (past) \n- Object: \"the dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n- \"Angatkuq\" = the shaman (agent) \n- \"iluaqhaijimik\" = a doctor (object) \n- \"aarqisijuq\" = cured\n\nSentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" \n- \"Nanuq\" = the polar bear (agent) \n- \"qaijuq\" = came (no object)\n\nSentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy\" \n- \"Iluaqhaijivit\" = your doctor (agent) \n- \"inuuhuktuit\" = your boy (object) \n- \"aarqijanga\" = cured\n\nSentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n- \"Angunahuktiup\" = the hunter (agent) \n- \"amaruq\" = the wolf (object) \n- \"iputujanga\" = speared\n\nSentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n- \"Qingmiup\" = the dog (agent) \n- \"ilinniaqtitsijiit\" = your teacher (object) \n- \"aanniqtanga\" = hurt\n\nSentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n- \"Ukiakhaqtutit\" = you fell (reflexive or self-action)\n\nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" \n- \"Angunahukti\" = the hunter (agent) \n- \"nanurmik\" = a polar bear (object) \n- \"qukiqsijuq\" = shot\n\nPattern: \n- Verbs are past tense. \n- Agent is usually marked with possessive or demonstrative (e.g., \"your\", \"the\") \n- Object appears after the verb, in the form of noun phrase with possessive or demonstrative \n- When there's no object, it’s either reflexive (e.g., \"you hurt yourself\") or intransitive (\"came\") \n- Possessive markers (e.g., \"your\", \"your boy\", \"your doctor\") appear before or after agent or object \n- The verb form indicates the action: see, shoot, cure, spear, come, fall\n\nNow, examine the test sentences:\n\n13. \"Amaruup angatkuit takujanga\" \n- \"Amaruup\" = the wolf (agent) \n- \"angatkuit\" = saw (verb) \n- \"takujanga\" → past tense of \"saw\"? \"takuj\" = saw; \"takujanga\" = saw (past) \n- So: \"The wolf saw [someone]\" → object missing \n- But in 1: \"Qingmivit takujaatit\" = your dog saw you → object exists \n- Here, only \"Amaruup\" (wolf) + \"angatkuit\" (saw) → must be \"the wolf saw you\" or \"the wolf saw [someone]\" \n- But in all cases, object appears after the verb after possesive or in phrase \n- \"takujanga\" is past tense of \"saw\" — so likely object is implied or missing \n- But in sentence 1, \"takujaatit\" = saw you → object present \n- So in 13, no object → could be reflexive? Unlikely — \"wolf saw itself\"? No support \n- So likely the object is missing — but in the structure, could it be that \"takujanga\" is built from \"takuj\" + suffix, and object is omitted? \n- Check: In sentence 1, \"takujaatit\" = saw you → object \"you\" attached? \n- In 13: \"takujanga\" — no object — so possibly \"the wolf saw [someone]\" — object missing \n- But in all others, object appears in noun phrase after the verb \n- Alternative: \"takujanga\" is a verb with object implied — like \"came\" in 7 \n- But \"came\" has no object \n- So if \"takuj\" = saw, then \"takujanga\" = saw (past) — no object \n- So \"the wolf saw\" — object missing → but must infer from pattern \n- However, in sentence 3: \"You hurt yourself\" — reflexive \n- Is \"takujanga\" reflexive? Unlikely — \"wolf saw itself\" — not in examples \n- So likely error in structure — object must be present \n- But in 13, no object → must conclude object is missing or implied \n- Look at verb form: \"takujanga\" → based on \"takuj\" = saw \n- Compare with sentence 1: \"takujaatit\" = saw you → ends in \"-aatit\" \n- \"takujanga\" ends in \"-anga\" — so different \n- Wait: Compare suffixes: \n- \"takujatit\" → saw (you) — what about \"takujanga\"? \n- In 1: \"takujaatit\" → saw you \n- In 13: \"takujanga\" — no object \n- Perhaps this is a defective form? But in context, likely the object is implied or absent \n- But in 7: \"Nanuq qaijuq\" → \"the polar bear came\" — no object \n- So if \"takujanga\" = saw, then \"the wolf saw\" — no object → like \"came\" \n- So translation: \"The wolf saw\" — but who? Unclear \n- But no object → so must be intransitive — perhaps \"the wolf saw\" (someone implied)\n\nBut in examples, all verbs with object have an object. So perhaps the object is omitted—still, the verb is transitive.\n\nAlternatively, analyze the possessive markers.\n\nIn 8: \"your doctor cured your boy\" — object is \"your boy\" after verb \nIn 6: \"cured a doctor\" — object after verb \nSo all transitive verbs have object after verb.\n\nIn 13: Only agent and verb → so must be intransitive or reflexive.\n\nBut \"saw\" is transitive — requires object.\n\nIn 1: \"your dog saw you\" — object present.\n\nNo form of \"saw\" without object in examples.\n\nThus, sentence 13: \"Amaruup angatkuit takujanga\" — agent \"the wolf\", verb \"saw\", no object — inconsistent.\n\nBut the syntax is similar to 7: \"Nanuq qaijuq\" → \"the polar bear came\" — intransitive, no object.\n\n\"qaijuq\" = came — past tense, no object.\n\nSo \"angatkuit\" = saw — past tense, but requires object? Or is \"saw\" intransitive?\n\nNo — examples show \"saw\" only with object.\n\nBut in 1: \"your dog saw you\" — clearly transitive.\n\nThus, in 13, \"takujanga\" is not a full form — likely typo or missing object.\n\nBut no object given — so must interpret as \"the wolf saw\" — with implied object — e.g., \"the wolf saw you\"?\n\nBut no one is mentioned.\n\nAlternatively, perhaps \"takujanga\" is a form of \"saw\" with a missing object — same as in 7.\n\nBut \"came\" has no object — but \"saw\" should have too.\n\nThus, conclude: Incomplete — must be \"the wolf saw [someone]\" — but no object.\n\nBut in context, perhaps object is implied — like \"the wolf saw you\" — but \"you\" not present.\n\nBut no reference to anyone.\n\nAlternatively, look at sentence 15: \"Angunahuktiit aarqijuq\"\n\n\"Angunahuktiit\" = the hunter (past) \n\"aarqijuq\" = cured (past) \nNo object → no object in examples? Only when object present (e.g., 4, 6, 8)\n\nIn 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you \nIn 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor \nIn 8: \"your doctor cured your boy\"\n\nAll have object after verb.\n\nNo sentence has \"cured\" without object.\n\nSo \"Angunahuktiit aarqijuq\" must be missing object.\n\nBut in pattern, object comes after verb as noun phrase.\n\nSo likely, a missing object — perhaps implied.\n\nBut \"cured\" cannot be used without object.\n\nSame for 13: \"saw\" requires object.\n\nNow, sentence 16: \"Ilinniaqtitsiji qukiqtait\"\n\n\"Ilinniaqtitsiji\" = your teacher (agent?) \n\"qukiqtait\" = shot? \"qukiqtanga\" = shot in 2 → \"qukiqtait\" = shot (past tense)? \nCompare: \nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → boy shot doctor \nSentence 9: \"Angunahuktiup amaruq iputujanga\" → hunter speared wolf \nSentence 12: \"Angunahukti nanurmik qukiqsijuq\" → hunter shot polar bear\n\n\"qukiqtanga\" = shot \n\"qukiqsijuq\" = shot (past) \nSo \"qukiqtait\" = likely same as \"qukiqtanga\" — shot (past)\n\nSo \"Ilinniaqtitsiji\" = your teacher (agent) \n\"qukiqtait\" = shot \nNo object → again, object missing\n\nSentence 17: \"Qaijutit\" — only verb and agent? No agent marked.\n\n\"Qaijutit\" — verb? \nIn sentence 7: \"Nanuq qaijuq\" → polar bear came \n\"qaijuq\" = came \n\"qaijutit\" — similar form? \n\"qaijuq\" → came \n\"qaijutit\" → could be \"came\" with possessive or tense?\n\nPossibly \"came\" — past tense \nBut no agent — only \"qaijutit\" — so must be \"you came\" or \"it came\"?\n\nIn sentence 3: \"Aanniqtutit\" → you hurt yourself \nSo \"qaijutit\" — if \"qaijuq\" = came, \"qaijutit\" = came (past) — but agent missing\n\nIn sentence 11: \"Ukiakhaqtutit\" → you fell — agent \"you\"\n\nSo likely \"qaijutit\" = \"you came\"? But \"you\" not marked\n\n\"Qaijutit\" — no agent — could be reflexive? Like \"you came\" or \"you fell\"?\n\nBut \"you fell\" is \"Ukiakhaqtutit\" — not \"qaijutit\"\n\nNo example of \"came\" with agent missing — so likely agent is missing.\n\nBut in all others, agent is present.\n\nSo possibly a mistake.\n\nNow 18: \"Angunahuktimik aarqisijutit\"\n\n\"Angunahuktimik\" = the hunter (agent) — \"mik\" = possessive or marked for object? \n\"angunahuktimik\" — similar to 9: \"Angunahukti\" → hunter \n\"Angunahuktimik\" → hunter (with object marker?) \n\"aarqisijutit\" = cured (past) \nNo object — again missing\n\nPattern: \n- All transitive verbs require object \n- Object appears after the verb in a noun phrase \n- Agents are marked with possessive or definite article (e.g., \"your\", \"the\") \n- When object is missing, the verb is intransitive or reflexive — but transitive verbs always take object \n\nIn 13: \"Amaruup\" = the wolf \n\"angatkuit\" = saw \n\"takujanga\" = past tense of saw? \nBut no object → must be intransitive — like \"came\" \nBut \"saw\" is not intransitive per examples \n\nYet, in no example is \"saw\" used without object — so likely, the absence of object means it's a full intransitive form — possibly rare.\n\nSimilarly, 14: \"Nanuit inuuhukturmik aanniqsijuq\" \n\"Nanuit\" = the bear (agent) \n\"inuuhukturmik\" = your boy (object?) — \"inuuhuktuit\" = your boy (in 8) \n\"aanniqsijuq\" = hurt — \"aanniqtanga\" = hurt (in 10) \nSo \"hurt\" verb — object after verb → \"your boy\"\n\nSo translation: \"The bear hurt your boy\" — makes sense\n\n15: \"Angunahuktiit aarqijuq\" \n\"Angunahuktiit\" = the hunter (past) \n\"aarqijuq\" = cured \nNo object → but in examples, \"cured\" has object \nBut no other verb without object — so must be implied \nLikely: \"The hunter cured [someone]\" — object missing but implied \nMost likely: \"The hunter cured a patient\" or \"the hunter cured the doctor\" — but without object, it's incomplete\n\nBut in context, could be \"cured\" with object — absent\n\n16: \"Ilinniaqtitsiji qukiqtait\" \n\"Ilinniaqtitsiji\" = your teacher (agent) \n\"qukiqtait\" = shot (past) \nNo object → missing object \nSo \"your teacher shot [someone]\" — object missing \nThus, translation should be \"your teacher shot [someone]\" — but we can't specify whom\n\n17: \"Qaijutit\" — only verb — no agent or object \nIn sentence 7: \"Nanuq qaijuq\" → the polar bear came \n\"qaijuq\" = came \n\"qaijutit\" — similar form — possibly \"came\" \nBut no agent — must be \"it came\" or \"you came\"? \nIn 3: \"you hurt yourself\" — agent \"you\" \nNo \"came\" with agent missing \nThus, likely \"you came\" — but \"you\" not present \nCould be \"it came\" — but no \"it\" \nNo example — so assume agent is missing — but in context, perhaps \"you came\" or \"it came\" \nNo evidence — but in sentence 11: \"Ukiakhaqtutit\" = you fell \nSo \"qaijutit\" might be a variant of \"came\" — agent not marked — so perhaps \"you came\"? \n\n18: \"Angunahuktimik aarqisijutit\" \n\"Angunahuktimik\" = hunter (with object marker?) \n\"aarqisijutit\" = cured (past) \nNo object → again, object missing \nSo \"the hunter cured\" — implied object\n\nBut from pattern: \n- All transitive verbs require an object after the verb \n- When object is missing, the verb is intransitive or reflexive \n- But all verbs in examples with object are transitive \n- Intransitive verbs like \"came\" or \"fell\" have no object\n\nSo when a verb has no object, it is intransitive — like \"came\" or \"fell\"\n\nThus: \n13: \"Amaruup angatkuit takujanga\" \n- Agent: wolf \n- Verb: saw → requires object → but no object → contradiction \n- But if \"saw\" can be intransitive, then \"the wolf saw\" \n- In examples, \"saw\" only has object \n- So likely error — but must proceed \n→ Best interpretation: \"The wolf saw\" — with implied object (e.g., \"you\") \nBut no support\n\nAlternatively, \"takujanga\" is a form of \"saw\" with object? Not clear\n\nLook at verb suffixes:\n\nIn 1: \"takujatit\" = saw you — object \"you\" \nIn 13: \"takujanga\" — different ending — not \"aatit\" or \"anga\" \n\n\"anga\" → in 14: \"aanniqsijuq\" → hurt? \"aanniqtanga\" = hurt — so \"anga\" is post-verbal suffix for past tense?\n\nIn 3: \"Aanniqtutit\" — \"tutit\" = hurt (past) \nIn 4: \"aarqijaatit\" — cured you \nIn 5: \"iputujait\" — speared \nIn 6: \"aarqisijuq\" — cured \n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5", + "a.6" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.6", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 6.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12458.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 378.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Check for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied.", + "planner_output": "\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context. \n\n\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative. \n\n\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied. \n\n\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied. \n", + "anchor_output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to determine how to write 42 and 494 in Nahuatl.\n\nWe start by identifying the numeric structure in the Nahuatl equations.\n\nEquation (4): mäcuïlli + öme = chicöme \nSuppose mäcuïlli = 20, öme = 1 → chicöme = 21 \nThis suggests a base-20 system where 20 is a unit and 1 is the unit of ones.\n\nEquation (6): mäcuïlli × ëyi = caxtölli \nWith mäcuïlli = 20, then 20 × ëyi = caxtölli \nTry ëyi = 5 → caxtölli = 100 → suggests 5 × 20 = 100 → so units like 1, 20, 100 (i.e., 20²) are present.\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli \nLet’s suppose öme = 1 \nThen: (cem-pöhualli) × 1 = öm-pöhualli \nSo we are claiming multiplication gives a new value. \nIf cem-pöhualli = 20, and öm-pöhualli = 20, then 20 × 1 = 20 → works. \nBut then cem = 20, öm = 20 → same value. \nAlternatively, suppose pöhualli = 20 \nThen: (cem × 20) × 1 = (öm × 20) \n→ cem × 20 = öm × 20 → cem = öm \nSo unless cem = öm, they must be equal. \nBut this gives no new information.\n\nNow consider equation (1): \nmahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLet’s interpret the structure.\n\n\"on\" likely means \"and\" or \"plus\" in addition, or possibly \"times\" in multiplication. \nBut in (1): (mahtlactli-on-cë) × mahtlactli → result is mäcuïl-pöhualli-om-mahtlactli.\n\nSuppose \"on\" means addition: (a + b) × c \nBut how does that work? The product has more terms.\n\nTry assuming multiplication is represented by the \"×\" operator, and \"on\" acts as a separator or part of the expression.\n\nInstead, consider that the language uses a mixed system: the number is built with base-20 place values.\n\nFrom (4): 20 + 1 = 21 → so 21 exists \nFrom (6): 20 × 5 = 100 → so multiples of 20 are used.\n\nNow equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nAssume yë = 1, pöhualli = 20 → so yë-pöhualli = 20 \nchicöme = 21 \nSo left: 20 + 21 = 41? \nmahtlactli = ? \non-nähui → possible addition \n\nSo left: (1×20 + 21) + (mahtlactli-on-nähui)\n\nRight: näuh-pöhualli-on-cë → näuh-pöhualli = ? → possibly 20; cë = ?\n\nIf we suppose the right-hand side is “näuh-20-on-cë”, and it equals left.\n\nBut unless we know values, hard to proceed.\n\nNow equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe are told this equals 42? Or is it part of the pattern?\n\nLook at the equation: \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nWe can assign:\n\n- yë = 1 \n- tzontli = ? \n- näuh-pöhualli = ? \n- caxtölli = 100 \n- cë = ? \n\nSuppose the \"on\" represents addition between terms. Then the entire expression is a sum.\n\nSo: 1 × tzontli + 20 + 100 + cë\n\nIf this equals 42, then:\n\ntzontli + 20 + 100 + cë = 42 → tzontli + cë = -78 → impossible.\n\nIf multiplication: 1 × tzontli × 20 × 100 × cë = (tzontli × 20 × 100 × cë) = 42 → very small, unless tzontli and cë are fractions.\n\nNo.\n\nBut perhaps tzontli is not the value, but a known number.\n\nIn Mesoamerica, tzontli is known to be 180 (9 × 20) in some systems.\n\nTry that: tzontli = 180\n\nThen equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf \"on\" means addition: \n1 + 180 + 20 + 100 + cë = 301 + cë = 42 → cë = -259 → impossible.\n\nIf \"on\" means multiplication: 1 × 180 × 20 × 100 × cë = 360,000 × cë = 42 → cë = 42/360,000 → no.\n\nSo equation (13) doesn't directly yield 42.\n\nNow consider equation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nThis is a long chain. But it equals something.\n\nAlso equation (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nThis suggests cen-tzontli = some sum.\n\nIf cen-tzontli = 180 (tzontli = 180), and this equals tarumba + tambaroy + fete + asàr → a sum of components.\n\nBut from equation (8): ngámbi + asàr = tambaroy (Arammba)\n\nIn Arammba, base-20, perhaps similar.\n\nBut focus on Nahuatl.\n\nNow, what about equation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n\"om\" may mean multiplication or \"and\".\n\nSuppose mahtlactli-om-ëyi means (mahtlactli × ëyi)\n\nThen left: (mahtlactli × ëyi) × ëyi = mahtlactli × ëyi²\n\nRight: cem-pöhualli-on-caxtölli-on-nähui\n\nSuppose that matches a value like 20 × 20 × 100 × nähui\n\nBut if ëyi = 5, then ëyi² = 25\n\nIf mahtlactli = 2, then 2 × 25 = 50\n\nRight: cem-pöhualli × 100 × nähui → if cem = 20, pöhualli = 20 → 20 × 100 × nähui = 2000 × nähui\n\nSet equal: 50 = 2000 × nähui → nähui = 0.025 → no.\n\nAlternatively, suppose \"om\" means addition.\n\nLet’s go back to equation (4): \nmäcuïlli + öme = chicöme \n→ 20 + 1 = 21\n\nSo we have numbers in multiples of 1 and 20.\n\nNow 42 = 2 × 20 + 2 → in base-20, 42 = 2×20 + 2 → two in the 20s, and two in the units.\n\nSo we need to express \"2\" in Nahuatl.\n\nIs there a way to write 2?\n\nLook at equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nAssume yë = 1, pöhualli = 20 → yë-pöhualli = 20 \nchicöme = 21 → so 20 + 21 = 41? \nLeft: 20 + 21 = 41 \nNow, mahtlactli-on-nähui = x \nRight: näuh-pöhualli-on-cë → possibly 20 + cë\n\nSet equal: 41 + x = 20 + cë → x = cë - 21\n\nUnless x is negative, not possible.\n\nSuppose \"on\" means multiplication.\n\nThen: (1 × 20) × 21 = 420 → too big.\n\n(1 × 20) × (mahtlactli-on-nähui) → (20) × (mahtlactli × nähui) = 420?\n\nThen mahtlactli × nähui = 21\n\nPossible if mahtlactli = 21, nähui = 1 → but then 21 × 1 = 21 → so 20 × 21 = 420 → not 42.\n\nBut we see that 42 appears in the equation (13) as the output of a compound expression.\n\nWe are told: \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nSuppose \"on\" means addition → then: \n1 + tzontli + 20 + 100 + cë = ndamno\n\nIf ndamno = 42, then: \n1 + tzontli + 20 + 100 + cë = 42 → tzontli + cë = -79 → impossible.\n\nIf tzontli = 0 → not realistic.\n\nBut perhaps tzontli is not 180.\n\nAnother idea: perhaps \"tzontli\" is not a large number, but 2.\n\nWait — in some sources, tzontli is 9 × 20 = 180, but perhaps not.\n\nFrom equation (15): \ncen-tzontli = tarumba tambaroy fete asàr\n\nIf this is a sum, and all components are known from other equations, we can find relations.\n\nBut we have no direct values.\n\nInstead, focus on possible combination for 42.\n\nWe know: \n- 20 + 20 = 40 → so 40 is likely 2 × 20 \n- 42 = 2 × 20 + 2\n\nSo we need to express \"2\" and \"20\".\n\nWe know that öme = 1 (from equation (4)): 20 + 1 = 21\n\nSo 1 is represented by \"öme\"\n\nHow to get 2? 2 = öme + öme\n\nSo \"öme + öme\" = 2\n\nSo 2 can be written as \"öme-on-öme\"\n\nThen 42 = 2 × 20 + 2 = (öme-on-öme) × 20 + (öme-on-öme)\n\nIn the structure, multiplication may be written as \"×\", and \"on\" as \"plus\"\n\nSo \"öme-on-öme\" = 2\n\n\"öme-on-öme\" × 20 = 40\n\nThen 40 + (öme-on-öme) = 42\n\nSo full expression: (öme-on-öme) × 20 + (öme-on-öme)\n\nBut how is that written?\n\nIn the equations, we see \"mahtlactli-on-cë\" — possibly \"mahtlactli + cë\"\n\nSo addition is \"on\"\n\nMultiplication is not explicitly shown.\n\nBut in (1): (mahtlactli-on-cë) × mahtlactli = result\n\nSo multiplication is of the whole expression.\n\nSo to write 42, we need to build from known units.\n\nWe know from (4): \nmäcuïlli = 20 \nöme = 1 \n\nSo 20 = mäcuïlli \n1 = öme \n\n2 = öme-on-öme \n\nSo 2 × 20 = mäcuïlli × (öme-on-öme) \nThen 2 × 20 + 2 = mäcuïlli × (öme-on-öme) + (öme-on-öme) \n\nSo final: mäcuïlli × (öme-on-öme) + (öme-on-öme)\n\nIn words: mäcuïlli-on-öme-on-öme + öme-on-öme\n\nBut the structure must follow the form in the examples.\n\nLook at (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSo addition: A-on-B + C-on-D = E-on-F\n\nSo could be written as (A-on-B) + (C-on-D) = E-on-F\n\nSo our expression: (mäcuïlli × (öme-on-öme)) + (öme-on-öme)\n\nBut multiplication is not always explicit — in (1), we have \"mahtlactli-on-cë × mahtlactli\" — so the × is internal.\n\nThus, likely, \"A-on-B\" means A + B, and multiplication is separate.\n\nSo how to write 2? As \"öme-on-öme\"\n\nHow to write 20? As \"mäcuïlli\"\n\nSo 42 = mäcuïlli × (öme-on-öme) + (öme-on-öme)\n\nBut in the language, how is this structured?\n\nThere is no \"×\" operator — instead, multiplication might be denoted by placement or implicit.\n\nBut in equation (1), multiplication is written between expressions.\n\nSo perhaps the expression is: (mäcuïlli-on-öme-on-öme) + (öme-on-öme)\n\nBut that would be 20 + 2 + 2 = 24 — no.\n\nWe need mäcuïlli × (öme-on-öme)\n\nThat is 20 × 2 = 40\n\nThen add 2 → 42.\n\nBut in the language, multiplication is marked.\n\nIn (1): \"mahtlactli-on-cë × mahtlactli\"\n\nSo the expression \"A-on-B\" is a single addend, then \"× C\"\n\nSo likely, the compound form is: (mäcuïlli-on-öme-on-öme) × mahtlactli? No, we don't have mahtlactli.\n\nNo known value.\n\nBut in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem-pöhualli = 20 (pöhualli = 20), and öme = 1, then 20 × 1 = 20 → matches.\n\nSo pöhualli = 20.\n\nSo 20 is unambiguously \"pöhualli\"\n\nSo 20 = pöhualli\n\n1 = öme\n\n2 = öme-on-öme\n\n42 = 2 × 20 + 2 = (öme-on-öme) × pöhualli + (öme-on-öme)\n\nIn expression: (öme-on-öme) × pöhualli + (öme-on-öme)\n\nBut how is this written in the language?\n\nFrom equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nWe can infer that a compound expression like A-on-B is used for addition.\n\nFor multiplication, we see explicit \"×\"\n\nIn (1): (mahtlactli-on-cë) × mahtlactli\n\nSo multiplication is between expressions.\n\nThus, to write 42, we write: (öme-on-öme) × pöhualli + (öme-on-öme)\n\nNow, is there a value for 494?\n\n494 = 24 × 20 + 14\n\n24 = 1 × 20 + 4 \n4 = 2 × 2 \nSo 4 = öme-on-öme-on-öme-on-öme\n\n14 = 0×20 + 14 → 14 = 0×20 + 7×2\n\n7 = öme-on-öme-on-öme-on-öme-on-öme-on-öme-on-öme\n\nSo 494 = 24 × 20 + 14 \n= (1 × 20 + 4) × 20 + 14 \n= (pöhualli-on-öme-on-öme-on-öme-on-öme) × pöhualli + (öme-on-öme-on-öme-on-öme-on-öme-on-öme-on-öme)\n\nBut we don't have 4 in the equations.\n\nAlternatively, from known values:\n\ntzontli = 180 = 9 × 20\n\n180 = 9 × 20 → 9 = 4 × 20 + 1 → not helpful.\n\n494 = 24 × 20 + 14 → 24 = 1×20 + 4\n\nBut 4 = 2×2\n\nSo still need to build 2.\n\nSo consistent with above.\n\nSo", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 9823.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.", + "planner_output": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "anchor_output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "We are given equations in Nahuatl and Arammba and asked to write 42 and 494 in Nahuatl.\n\nWe focus on equations (13) and (14), which are key to pinning down the values.\n\n---\n\nFrom (13): \n**yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno**\n\nWe are told in the guidance that:\n- tzontli = 180 = 9 × 20 \n- pöhualli = 20 \nSo tzontli = 9 × pöhualli\n\nLet us test this with (13):\n- yë-tzontli = yë × 180 \n- on = addition \n- näuh-pöhualli = 1 × 20 = 20 \n- caxtölli = ? \n- cë = ?\n\nWe also have equation (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nAnd (6): mäcuïlli × ëyi = caxtölli\n\nFrom (6): mäcuïlli × ëyi = caxtölli \nWe are told: mäcuïlli = 20 (from historical knowledge), and from (4): mäcuïlli + öme = chicöme \nSo 20 + öme = chicöme → later helpful.\n\nBut equation (6): 20 × ëyi = caxtölli \nEquation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nLet’s suppose ëyi = 5 → then caxtölli = 20 × 5 = 100 \nThat makes sense: 100 is plausible in base-20 (5 × 20)\n\nSo → caxtölli = 100\n\nNow cë = ? From (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nFrom (1): (mahtlactli + cë) × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nIn standard interpretation:\n- pöhualli = 20 \n- mäcuïl = 1 (perhaps) or 2? \nLet’s suppose (mahtlactli + cë) × mahtlactli = (mäcuïl × pöhualli) + mahtlactli → but structure is mäcuïl-pöhualli-om-mahtlactli = mäcuïl × 20 + mahtlactli\n\nSo if this is a base-20 number: \nLeft = (mahtlactli + cë) × mahtlactli \nRight = mäcuïl × 20 + mahtlactli\n\nLet’s assume mahtlactli = 20 (common in Nahuatl numerals)\n\nThen left: (20 + cë) × 20 = 400 + 20cë \nRight: mäcuïl × 20 + 20\n\nSo: \n400 + 20cë = 20mäcuïl + 20 \nDivide both sides by 20: \n20 + cë = mäcuïl + 1 \n→ cë = mäcuïl + 1 – 20 = mäcuïl – 19\n\ncë must be a positive integer. So mäcuïl ≥ 20\n\nTry mäcuïl = 20 → cë = 1\n\nThus: cë = 1\n\nNow go back to (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= yë × 180 + 1 × 20 + 1 × 100 + 1 \n= yë × 180 + 121\n\nThis equals ndamno.\n\nWe don’t know mdamno yet. But we can find another equation involving known values.\n\nNow (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe are told (15): cen-tzontli = tarumba tambaroy fete asàr\n\n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nWe have a pattern: cen-× = some combination.\n\nLet’s suppose the base is 20.\n\ntzontli = 180 → 9 × 20 → one unit = 9 × 20 = 180\n\npöhualli = 20\n\nNow (2): cem-pöhualli × öme = öm-pöhualli\n\nAssume:\n- cem-pöhualli = 20 × öme \n- öm-pöhualli = öm × 20\n\nSo: (20 × öme) × öme = öm × 20 \n→ 20 × öme² = 20 × öm \n→ öme² = öm \n→ öme² – öm = 0 \n→ öm(öme – 1) = 0\n\nSo öm = 0 or 1\n\nBut öm = 0 → öm-pöhualli = 0 → not meaningful\n\nSo öm = 1 → then öme² = 1 → öme = 1 → consistent\n\nThus, öme = 1\n\nNow, cem-pöhualli = 20 × 1 = 20 → so cem = 1? But cem-pöhualli = 1×20 = 20\n\nSo cem = 1? Then cem = 1\n\nBut in (4): mäcuïlli + öme = chicöme → mäcuïlli + 1 = chicöme\n\nWe earlier set mäcuïlli = 20 → so chicöme = 21\n\nNow (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have:\n- mahtlactli × (mahtlactli + ëyi) → no, it's (mahtlactli-om-ëyi) × ëyi\n\n\"mahtlactli-om-ëyi\" = mahtlactli – ëyi? Probably not.\n\nIn Nahuatl, \"A-on-B\" often means A + B, not A – B. So \"om\" may mean \"plus\" or \"and\", not subtraction.\n\nLook at (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\n\"om\" likely means \"and\" → so \"mahtlactli-om-ëyi\" = mahtlactli + ëyi \nThen (mahtlactli + ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nLeft: (mahtlactli + ëyi) × ëyi = mahtlactli×ëyi + ëyi²\n\nRight: cem-pöhualli + caxtölli + nähui\n\nWe already have:\n- cem-pöhualli = 20 \n- caxtölli = 100 \n- nähui = ? → from (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = 100 → ëyi = 5\n\nSo ëyi = 5\n\nThen left: (mahtlactli + 5) × 5 = 5×mahtlactli + 25\n\nRight: 20 + 100 + nähui = 120 + nähui\n\nSo:\n5×mahtlactli + 25 = 120 + nähui \n→ 5×mahtlactli = 95 + nähui \n→ nähui = 5×mahtlactli – 95\n\nNow suppose mahtlactli = 20 → then nähui = 100 – 95 = 5\n\nSo nähui = 5\n\nNow back to (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = yë×180 + 1×20 + 100 + 1 = 180yë + 121 = ndamno\n\nWe don’t yet know what ndamno is, but we can use (14) to find a value.\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n\"on\" = + \n\"om\" = + \nso: cen-tzontli + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe have:\n- cen-tzontli = cen × 180 \n- cem-pöhualli = 20 \n- mahtlactli = 20 \n- öme = 1\n\nSo total: 180×cen + 20 + 20 + 1 = 180×cen + 41\n\nThis equals yànparo tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr \nSo cen×180 = tarumba + tambaroy + fete + asàr\n\nFrom (11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nBut this is messy.\n\nHowever, we may not need this. We are to write 42 and 494 in Nahuatl.\n\nWe need to construct 42 and 494 using additive and multiplicative expressions.\n\nWe know:\n- pöhualli = 20 \n- tzontli = 9 × 20 = 180 \n- caxtölli = 100 \n- cë = 1 \n- ëyi = 5 \n- öme = 1 \n- mahtlactli = 20 \n- mäcuïlli = 20\n\nNow: 42 = 2×20 + 2 \nSo we need to represent 2.\n\nWe don’t have a direct symbol for 2.\n\nBut look at (2): cem-pöhualli × öme = öm-pöhualli \nWe derived: 20×1 = 20 → 20 = 1×20 → so multiplicative identity?\n\nBut what about 2?\n\nCould 2 be represented as \"yë-tzontli\"? Too big.\n\nHow about in (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → so 21 = 20 + 1\n\nBut 2 = ?\n\nCould \"ëyi\" be 5 → too big.\n\nIs there a base-20 system where digits are expressed via number words?\n\nPerhaps the system is multiplicative and additive with known units.\n\nAlternative: perhaps the values in the equations give us multiple values that can be used to solve 42 and 494.\n\nFrom (13): yë-tzontli-on-... = ndamno \nWe have: yë×180 + 20 + 100 + 1 = 180yë + 121 = ndamno\n\nSo for various yë, we get values.\n\nTry yë = 0 → 121 = ndamno \nyë = 1 → 301 = ndamno \nyë = 2 → 481 = ndamno\n\nSo 301 = ndamno when yë=1\n\nWe want 42 and 494.\n\n494 is close to 481 → 494 – 481 = 13 → not a clean addition.\n\nBut 42 is less than 121.\n\nCan 42 be written as \"x-pöhualli-on-y\"?\n\nx × 20 + y = 42 → x = 2, y = 2\n\nSo 2×20 + 2 = 42\n\nWe need to express 2 in Nahuatl.\n\nLook at (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → so addition\n\n(2): cem-pöhualli × öme = öm-pöhualli → 20×1 = 20 → 1×20 = 20\n\nNo 2.\n\nBut in Arammba, we have:\n(8): ngámbi + asàr = tambaroy \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo\n\nNo immediate value.\n\nBut perhaps we can infer that 1, 2, 3 appear as components.\n\nIn (4): 20 + 1 = 21 → so 1 is a base unit.\n\nWe have no explicit 2, but perhaps 2 is cem? cem-pöhualli = 20 → so cem = 1?\n\nNot 2.\n\nWait — mäcuïlli = 20, so could there be a unit like \"cë\" = 1?\n\nThen 1 × 20 = 20\n\nBut to get 2, we need 2 × 1.\n\nIs \"yë\" a unit?\n\nIn (13): yë-tzontli → yë = 1 is part of the expression.\n\nPerhaps yë is not a value, but a quantity.\n\nBut if we assume that small numbers are built recursively.\n\nFrom (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → so 1 is a unit.\n\nSo 1 is represented as öme.\n\nSo 2 = öme + öme?\n\nBut öme = 1 → 1+1 = 2?\n\nIn the language, is addition used for composing numbers?\n\nYes — \"on\" = \"plus\"\n\nSo \"öme-on-öme\" = 1+1 = 2\n\nThus: 2 = öme-on-öme\n\nSo 2 = öme + öme\n\nThus, 2 × 20 = 40 → 40 + 2 = 42 → 42 = (öme-on-öme) × pöhualli + (öme-on-öme)\n\nBut we need to write this in Nahuatl.\n\nSo 42 = (öme-on-öme) × pöhualli + (öme-on-öme)\n\nIn Nahuatl: (öme-on-öme)-pöhualli-on-öme-on-öme\n\nNote: multiplication is written as X- × Y → but here we have a compound structure.\n\nBut in the examples, multiplication appears in forms like \"cem-pöhualli × öme\" — so the multiplier comes first.\n\nLikely, a × b is written as a-b, or a-on-b?\n\nIn (1): mahtlactli-on-cë × mahtlactli → (mahtlactli + cë) × mahtlactli\n\nSo multiplication is represented as (A-on-B) × C\n\nSo format: (A-on-B)-on-C\n\nBut in (5): mahtlactli-om-ëyi × ëyi → (mahtlactli-om-ëyi) × ëyi → this is a compound expression.\n\nSo the multiplier is at the end.\n\nIn (2): cem-pöhualli × öme → the product is öm-pöhualli, so (cem-pöhualli) × öme = öm-pöhualli\n\nSo the structure is: (A) × B = C\n\nThus, multiplication of two terms.\n\nSo to write 42 = 2×20 + 2, we write:\n\n(öme-on-öme)-pöhualli-on-öme-on-öme\n\nBecause:\n- (öme-on-öme) = 2\n- (öme-on-öme)-pöhualli = 2×20 = 40\n- on-öme-on-öme = +2\n\nSo total: 40 + 2 = 42\n\nNow 494.\n\n494 in base 20:\n\n20² = 400 \n494 ÷ 400 = 1.235 → so 1×400 = 400 \n494 – 400 = 94 \n94 ÷ 20 = 4.7 → 4×20 = 80 \n94 – 80 = 14 \nSo 494 = 1×400 + 4×20 + 14\n\nWe know:\n- 400 = 20 × 20 = mäcuïlli × pöhualli \n- 20 = pöhualli \n- 14 = ?\n\n14 = 10 + 4 → 40 + 4 = 14? \nBut 4 = 4 × 1\n\nWe need to represent 14.\n\n14 = 10 + 4 → 10? Not present.\n\nIn the system, we have:\n- caxtölli = 100 → too big \n- cë = 1 \n- ëyi = 5 \n- So 5 = ëyi \n- 10 = 2×", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8757.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.", + "planner_output": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "anchor_output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "The problem requires expressing 42 and 494 in Nahuatl, using the given equations to infer the numeric values and structure.\n\nFirst, analyze known equations in Nahuatl:\n\n(4): mäcuïlli + öme = chicöme \n(6): mäcuïlli × ëyi = caxtölli\n\nFrom (4), if we assume öme = 1, then mäcuïlli + 1 = chicöme \nFrom (6), mäcuïlli × ëyi = caxtölli\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nAssume öme = 1 → cem-pöhualli = öm-pöhualli \nSo the value of cem-pöhualli equals öm-pöhualli → implies cem = öm \nUnless pöhualli is the base, this suggests that cem and öm represent the same value.\n\nBut if pöhualli is the base unit, and cem-pöhualli = 20 × pöhualli, and öm-pöhualli = 20 × pöhualli, then cem = öm = 20.\n\nSo pöhualli = 20.\n\nFrom (4): mäcuïlli + 1 = chicöme \nIf pöhualli = 20, and mäcuïlli is a multiple, try mäcuïlli = 20 → then chicöme = 21\n\nFrom (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli \nTry ëyi = 5 → caxtölli = 100 \nSo caxtölli = 100 → likely 5 × 20\n\nThus, base 20: units of 1, 20, 400, 100, etc.\n\nIn equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nAssume yë = 1 → tzontli = 9 × 20 = 180 (common historical value) \nSo 1-tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1\n\nIf \"on\" is addition: 180 + 20 + 100 + 1 = 301 \nIf \"on\" is multiplication: 1×180×20×100×1 = 360,000 → too large\n\nAddition gives 301 → ndamno = 301\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \ncen-tzontli → cen = 10? 1-tzontli = 180 → cen-tzontli = 10 × 180 = 1800? But no.\n\nAlternatively, \"on\" might be addition. \nSo cen-tzontli → cen-tzontli = cen × tzontli? Or cen + tzontli?\n\nAssume \"on\" = addition → so cen-tzontli = cen + tzontli \nBut it is combined with other units using \"om\" → which may be multiplication.\n\n\"om\" likely indicates multiplication.\n\nSo: cen-tzontli-om-cem-pöhualli-om-mahtlactli-om-öme \n→ (cen + tzontli) × (cem-pöhualli) × (mahtlactli) × (öme)\n\nBut cem-pöhualli = 20×20 = 400 \nöme = 1 \ntzontli = 180 \ncen = ? \nmahtlactli = ? \n\nFrom (1), mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \nLeft: (mahtlactli × cë) × mahtlactli = mahtlactli² × cë \nRight: mäcuïl-pöhualli-om-mahtlactli → mäcuïl × 20 × mahtlactli\n\nIf cë = 1 → left = mahtlactli² \nRight = (20 × 20) × mahtlactli = 400 × mahtlactli \nSo mahtlactli² = 400 × mahtlactli → mahtlactli = 400\n\nThus, mahtlactli = 400\n\nNow (14): (cen + 180) × 400 × 400 × 1 = yànparo tarumba \n→ (cen + 180) × 160,000 = yànparo tarumba\n\nBut we have (15): cen-tzontli = tarumba tambaroy fete asàr \nFrom Arammba: \n(7) ngámbi + ngámbi = ngámbi × yànparo → 1+1 = 1×yànparo → yànparo = 2 \n(8) ngámbi + asàr = tambaroy → 1+asàr = tambaroy \nIf asàr = 1 → tambaroy = 2 \n(10) yenówe × yenówe tàxwo = fete yenówe tàxwo → suggests fete = yenówe \n(12) nimbo + yànparo tàxwo = yenówe tàxwo → nimbo + 2 = yenówe \n(11) nimbo × fete = tarumba → nimbo × nimbo + 2 = tarumba\n\nTry nimbo = 2 → fete = 4 → tarumba = 8 \ntambaroy = 2, asàr = 1 → (15) cen-tzontli = tarumba + tambaroy + fete + asàr = 8 + 2 + 4 + 1 = 15\n\nSo cen-tzontli = 15 → if tzontli = 180 → cen = 15 → 15 + 180 = 195 → but this contradicts the value.\n\nAlternative: in Nahuatl, \"cen\" is a unit meaning 100? In some sources, cen = 100.\n\nBut 100 + 180 = 280 → if 15 = cen-tzontli → 280 = 15 → no.\n\nPerhaps cen-tzontli = cen × tzontli → 100 × 180 = 18,000 → too large.\n\nNo consistent value.\n\nInstead, go to the values we have:\n\nWe have:\n- pöhualli = 20\n- mäcuïlli = 20\n- öme = 1\n- caxtölli = 100\n- tzontli = 180 = 9 × 20\n\nNow 42 = 2 × 20 + 2\n\nWe need to express 2. From (4): 20 + 1 = 21 → not 2.\n\nIs there a unit for 2?\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nyë = 1 → 1×20 = 20 \nchicöme = 21 → so 20 + (20×nähui) = (20 + cë) \nSo 20 + 20×nähui = 20 + cë → 20×nähui = cë\n\nSo cë = 20 × nähui\n\nIf nähui = 1 → cë = 20 → so cë = 20\n\nThen cë = 20 → same as pöhualli → so likely cë = pöhualli\n\nThus, cë = 20\n\nNow, back to 42 = 2×20 + 2 → 2 × pöhualli + 2\n\nCan we express 2?\n\nIn the absence of direct representation, perhaps \"yë\" = 1, so 2 = yë + yë = 1 + 1 → \"yë + yë\"\n\nThen: 2 × pöhualli = yë + yë + pöhualli + pöhualli? No.\n\nBut multiplication: 2 × pöhualli = (yë + yë) × pöhualli\n\nIn form: (yë + yë) × pöhualli\n\nBut in Nahuatl, such expressions may be written as yë-on-pöhualli + yë-on-pöhualli\n\nSimilarly, 2 = yë + yë\n\nSo 42 = (yë + yë) × pöhualli + (yë + yë) \n= yë-on-pöhualli + yë-on-pöhualli + yë-on-pöhualli + yë-on-pöhualli? No.\n\nWait: 2 × 20 + 2 = 40 + 2 = 42\n\nSo 40 = 2 × 20 = 2 × pöhualli → expressed as (yë + yë) on pöhualli\n\nThen 2 = yë + yë\n\nSo total: (yë + yë) on pöhualli + (yë + yë)\n\nThus: (yë + yë) on pöhualli + (yë + yë)\n\nBut likely condensed as yë-pöhualli + yë-pöhualli + yë + yë\n\nBut from the structure, similar to (3), addition is direct.\n\nSo 42 = yë-pöhualli + yë-pöhualli + yë + yë\n\nBut yë = 1 → so four units of 1.\n\nNow 494: 494 ÷ 20 = 24.7 → 24 × 20 = 480 → remainder 14\n\n14 = 1 × 20 + 4 → 20 + 4 → 4 = 2×2 → 2×2 = 4\n\nSo 494 = 24 × 20 + 14 = 24 pöhualli + (20 + 4)\n\n4 = 2×2 → 2×pöhualli = 40 → no.\n\n2×pöhualli = 40 → too large.\n\nSo 4 = 2 × 2 → in terms of units: 2 = yë + yë → 4 = (yë + yë) × (yë + yë) = yë on yë + yë on yë + yë on yë + yë on yë? No.\n\nSimplest: 4 = 2 × 2 → but no representation.\n\nAlternatively, 494 = 400 + 90 + 4 → 400 = 20 × 20 = cem-pöhualli → cem = 20\n\n90 = 4 × 20 + 10 → not helpful.\n\nNote: tzontli = 180 → 2 × 180 = 360 → 494 - 360 = 134 → 134 = 6 × 20 + 14 → still complex.\n\nBut 494 = 2 × 200 + 94 → no.\n\nFrom base 20, 494 = 2 × 20 × 12 + 14 → 20 × 24 = 480, remainder 14.\n\nSo 24 = 1 × 20 + 4 → so 24 × 20 = (1 × 20 + 4) × 20 = 1×20×20 + 4×20\n\nSo 494 = (1×pöhualli × pöhualli) + (4×pöhualli) + 14\n\n14 = 1×20 + 4 → so 1×pöhualli + 4\n\nThus 494 = (1×pöhualli × pöhualli) + (4×pöhualli) + (1×pöhualli + 4)\n\nNow 4 = 2×2 → represented as yë-on-yë + yë-on-yë → wait no.\n\nWe don’t have 2 or 4.\n\nBut perhaps the number 2 is formed by combining units.\n\nIn the absence of a specific unit for 2, and due to the grammatical structure, the way numbers are formed in these languages is additive with units, and multiplication between units.\n\nGiven that 42 = 2×20 + 2 → requires two 1s, and 20s.\n\nBut no unit for 2 → only 1s and 20s.\n\nThus, 42 must be written as: yë-pöhualli + yë-pöhualli + yë + yë\n\nSimilarly, 494 = (24 × pöhualli) + (14)\n\n24 = 1 × 20 + 4 → 4 = 2 × 2 → so 4 = (yë + yë) × 2? No.\n\nAlternatively, 4 = 20 + 4 → not possible.\n\nWait, 494 = 2 × 100 + 94 → 100 = caxtölli → so 2 × caxtölli = 200 → 494 - 200 = 294\n\n294 = 14 × 20 + 14 → not helpful.\n\nBut 494 = 2 × 247 → no.\n\nFinal structure based on consistent values:\n\n- 42 = 2 × 20 + 2 → expressed as (yë + yë) on pöhualli + (yë + yë)\n- 494 = 24 × 20 + 14 → 24 = 1×20 + 4 → 4 = 2×2 → so (1×pöhualli + 4) × pöhualli + (1×pöhualli + 4)\n\nBut data not sufficient.\n\nFrom (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nWith: yë=1, tzontli=180, näuh=1, pöhualli=20, caxtölli=100, cë=20 \nSum: 1 + 180 + 20 + 100 + 20 = 321 → so ndamno = 321\n\nThis suggests that \"on\" is addition.\n\nThus, in general, expressions like A-on-B mean A + B.\n\nMultiplication is not marked by \"on\", but by \"×\" or \"om\".\n\nSo in (1), mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (mahtlactli + cë) × mahtlactli = mäcuïl × pöhualli × mahtlactli\n\nWe already found mahtlactli = 400\n\nSo (400 + 1) × 400 = 160,400 \nRight side: mäcuïl × 20 × 400 → 20×400 = 8,000 → so 160,400 = mäcuïl × 8,000 → mäcuïl = 20.05 → not integer.\n\nNot valid.\n\nEarlier we had mäcuïlli = 20\n\nIn (1): (mahtlactli + cë) × mahtlactli = mäcuïl × pöhualli × mahtlactli\n\nDivide both sides by mahtlactli: (mahtlactli + cë) = mäcuïl × pöhualli\n\nIf pöhualli = 20 → mäcuïl × 20 = mahtlactli + cë\n\nWe had earlier: if mäcuïl = 20 → 400 = mahtlactli + cë\n\nAnd from (1), left side = (mahtlactli + cë) × mahtlactli = 400 × mahtlactli\n\nRight side = 20 × 20 × mahtlactli = 400 × mahtlactli → matches\n\nSo mäcuïl = 20\n\nThus all values consistent.\n\nNow, to write 42:\n\n42 = 2 × 20 + 2 = 40 + 2\n\n2 = yë + yë\n\nSo 42 = (yë + yë) on pöhualli + (yë + yë)\n\nIn Nahuatl form: yë-pöhualli + yë-pöhualli + yë + yë\n\nFor 494:\n\n494 = 24 × 20 + 14 \n24 = 1 × 20 + 4 \n4 = 2 × 2 → 2 = yë + yë → so 4 = (yë + yë) × (yë + yë) = yë on yë + yë on yë + yë on yë + yë on yë — too many.\n\nInstead, 4 = 2 × 2, but no 2.\n\n4 = 4 × 1 → no.\n\nIn the system", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8295.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "planner_output": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "anchor_output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given linguistic equations in Nahuatl and Arammba, and asked to translate the numbers 42 and 494 into Nahuatl.\n\nWe must identify a pattern in the Nahuatl equations that reveals how numbers are formed — especially how composition and multiplication are expressed.\n\n---\n\nStart with equations (1) to (6) in Nahuatl:\n\n(1) mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ (A × A) = B \nWe interpret: mahtlactli × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nNote that “mahtlactli” likely represents a base number (possibly 10 or 20?), and the product combines elements.\n\nBut look at (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n\nInvolves addition of two terms, forming a compound.\n\n(4): mäcuïlli + öme = chicöme \nThis is a clear addition: mäcuïlli + öme = chicöme\n\n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6): mäcuïlli × ëyi = caxtölli \n\n→ So multiplication of a base with another yields a compound.\n\nAlso, (2): cem-pöhualli × öme = öm-pöhualli \nLeft side: product of two units. Right side: a simpler form.\n\nBut (2) is a multiplication? cem-pöhualli × öme = öm-pöhualli — suggests the product simplifies or reduces.\n\nBut more importantly, equations (4) and (6) show:\n\nmäcuïlli + öme = chicöme \nmäcuïlli × ëyi = caxtölli \n\nSo addition and multiplication are defined using affixes.\n\nNow notice:\n\n(1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\n“mahtlactli-on-cë” is likely “mahtlactli” with a suffix \"on-cë\" — perhaps indicating a value, like “mahtlactli on the century” or a multiplier.\n\nBut perhaps “mahtlactli” is 20? “cë” might denote a unit.\n\nAlternatively, look at (5): \nmahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nAnd (6): mäcuïlli × ëyi = caxtölli\n\nSo multiplication of mäcuïlli and ëyi gives caxtölli.\n\nSimilarly, (4): mäcuïlli + öme = chicöme\n\nNow consider (13) and (14) which are the key cross-verification equations.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \n(15): cen-tzontli = tarumba tambaroy fete asàr \n(16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nLook at (15): cen-tzontli = tarumba tambaroy fete asàr \nWe know from (8): ngámbi + asàr = tambaroy → so tambaroy = ngámbi + asàr\n\nBut in Arammba (8): ngámbi + asàr = tambaroy \n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nIn (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli is expressed as a combination of units.\n\nNow look at (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nSo “cen-tzontli-on-...” equals “yànparo tarumba”\n\nFrom (15), cen-tzontli = tarumba tambaroy fete asàr \nSo if cen-tzontli is a unit, then cen-tzontli-on-... = yànparo tarumba\n\nThus, the structure “A-on-B” might represent A × B or A + B?\n\nBut in (1): “mahtlactli-on-cë × mahtlactli” → becomes complex product.\n\nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n→ Addition of two terms that both have “on-” structure produces another “on-” structure.\n\nLooks like addition involving compound terms.\n\nBut notice that “öme” appears in (2), (4), (5), (14)\n\n(2): cem-pöhualli × öme = öm-pöhualli \n(4): mäcuïlli + öme = chicöme \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme\n\nSo “öme” seems to be a number.\n\nAlso, “ëyi” appears in (5) and (6): \n(6): mäcuïlli × ëyi = caxtölli \n(5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSo multiplication of base by ëyi gives a compound.\n\nNow the critical part: we are to write 42 and 494 in Nahuatl.\n\nWe suspect that Nahuatl has a vigesimal (base-20) system.\n\nCheck whether 42 and 494 decompose nicely in base 20:\n\n42 = 2×20 + 2 → 2×20 + 2 → \"two twenties and two\"\n\n494 ÷ 20 = 24 × 20 = 480 → remainder 14 → 24×20 + 14 → 24 twenties and 14\n\nNow, can we find base-20 components in the equations?\n\nLook at (4): mäcuïlli + öme = chicöme \n→ If mäcuïlli is 20, and öme is 1, then 20+1=21 → not helpful.\n\nBut (6): mäcuïlli × ëyi = caxtölli → multiplication of 20 and something gives caxtölli.\n\nSuppose mäcuïlli = 20, and ëyi = 1 → then caxtölli = 20.\n\nBut (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nSuppose mahtlactli = 20, ëyi = 1 → then mahtlactli-om-ëyi = 20 + 1 (connected)\n\nThen multiplied by 1 → should give cem-pöhualli-on-caxtölli-on-nähui\n\nBut that would be a long word — doesn’t make sense.\n\nAlternatively, in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nSuppose mahtlactli = 10.\n\nThen (10) × (10) = mäcuïl-pöhualli-om-mahtlactli\n\nIf 10×10 = 100, and mäcuïl-pöhualli is compound, maybe.\n\nBut 10×10 = 100 → not 42.\n\nAnother approach: look at (13) and (14) — they combine numbers.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n(15): cen-tzontli = tarumba tambaroy fete asàr\n\nNow (15) says cen-tzontli = tarumba tambaroy fete asàr\n\nFrom (8): ngámbi + asàr = tambaroy → so tambaroy has two parts.\n\n(11): nimbo × fete = tarumba → so tarumba = nimbo × fete\n\nThus cen-tzontli = (nimbo × fete) × (ngámbi + asàr) × fete × asàr → messy.\n\nBut we are told that (15) is cen-tzontli = tarumba tambaroy fete asàr\n\nSo if we take that as a decomposition, then in Nahuatl, numbers are built via multiplication and addition.\n\nNow, from (4): mäcuïlli + öme = chicöme → addition\n\nFrom (6): mäcuïlli × ëyi = caxtölli → multiplication\n\nLet us assume:\n\n- mäcuïlli = 20 \n- öme = 1 → then chicöme = 21 \n- ëyi = 1 → then caxtölli = 20 \n- But (6) says mäcuïlli × ëyi = caxtölli → 20×1 = 20 → yes \n- Now (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nAssume mahtlactli = 10? Then mahtlactli-om-ëyi = 10 + 1 = 11\n\nThen 11 × 1 = 11 → should be cem-pöhualli-on-caxtölli-on-nähui\n\nSo perhaps that compound is \"11\"\n\nBut (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nmahtlactli = 10 → then 10 × 10 = 100\n\nmahtlactli-on-cë → 10 on cë → perhaps \"10×cë\" = 100 → then product = 100\n\nSo 10×10 = 100 → result has mäcuïl-pöhualli-om-mahtlactli → which may be a composite.\n\nBut again, not matching 42.\n\nNow, for 42: 2×20 + 2\n\nSo we need “two twenties and two”\n\nIn Nahuatl, addition is expressed with “on” or via compounds.\n\n(3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\n→ Left: A-on-B + C-on-D = E-on-F\n\nSo addition of two compound numbers → a new compound.\n\nThe structure “X-on-Y” may represent “X plus Y” or “X times Y”?\n\nIn (3): the sum becomes a new “on” compound.\n\nThis suggests that “on” may act as a form of addition in compound terms.\n\nAlso, (1): multiplication of two mahtlactli gives mäcuïl-pöhualli-om-mahtlactli\n\nNote that “om” appears: in (1) → “om-mahtlactli”, in (2) → “om-mahtlactli-om-öme”\n\nSo “om” may mean “of” or “with” or “and”\n\nNow, (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe are told (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo if cen-tzontli is a unit, and it is combined with another term, the result is yànparo tarumba.\n\nBut tarumba is from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × fete\n\nAlso, from (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = (nimbo × fete) × (ngámbi + asàr) × fete × asàr → too many fete and asàr → redundant.\n\nPerhaps “tarumba” and “tambaroy” are separate values.\n\nSuppose that:\n\n- “öme” = 1 \n- “ëyi” = 1 \n- “mahtlactli” = 20 \n- “mäcuïlli” = 20\n\nThen (4): 20 + 1 = 21 → chicöme \n(6): 20 × 1 = 20 → caxtölli \n(5): (mahtlactli-om-ëyi) × ëyi = (20+1) × 1 = 21 → which should be cem-pöhualli-on-caxtölli-on-nähui → so that compound is 21\n\n(1): mahtlactli-on-cë × mahtlactli = (20-on-cë) × 20 = result\n\nIf cë represents 1, then (20) × (20) = 400 → and result is mäcuïl-pöhualli-om-mahtlactli\n\nBut 400 is a big number.\n\n42 = 2×20 + 2\n\nSo we want to express “two twenties and two”.\n\nIn the system, addition seems to be expressed via “on” compound.\n\nSo perhaps “X-on-Y” means X + Y, where X is a number and Y is a unit.\n\nBut in (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf “A-on-B” means A + B, then (A+B) + (C+D) = (A+B+C+D) → but result is näuh-pöhualli-on-cë — not a sum.\n\nSo more likely “on” indicates the value is composed from two parts.\n\nBut in (1), multiplication is represented as compound.\n\nNow, (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nCould “yë-tzontli” be a multiplier or base?\n\nAnd “on” links components.\n\nSuppose that “A-on-B” represents multiplication or addition.\n\nBut in the addition example (3), the result is a single “on” compound.\n\nSimilarly, (1) is multiplication and gives compound.\n\nNow, key: look at (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nAnd (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo if we take (15), the value cen-tzontli is expressed in terms of other units.\n\nThen in (14), when we have cen-tzontli-on-... = yànparo tarumba\n\nSo cen-tzontli-on-something = yànparo tarumba\n\nIf “on” means multiplication, then cen-tzontli × something = yànparo tarumba\n\nBut from (15), cen-tzontli = tarumba tambaroy fete asàr → which is a sum or product?\n\nIt has “tarumba” and “tambaroy” and “fete” and “asàr” — multiple terms.\n\nBut each of those is a number or unit.\n\nFrom (8): ngámbi + asàr = tambaroy \n(11): nimbo × fete = tarumba\n\nSo cen-tzontli = (nimbo × fete) + (ngámbi + asàr) + fete + asàr → which is redundant.\n\nBut perhaps cen-tzontli = (nimbo × fete) + (ngámbi + asàr) \nAnd then “fete” and “asàr” are just shared.\n\nAlternatively, it's breakdown of a number.\n\nPerhaps “cen-tzontli” is 100 or 200?\n\nIn many Mesoamerican systems, base-20 arithmetic is used.\n\n42 = 2×20 + 2\n\n494 = 24×20 + 14 → 24×20 = 480, 494–480=14\n\nNow, can we find units for 20, 1, 10, etc.?\n\nFrom (4): mäcuïlli + öme = chicöme \nIf we assume öme = 1, mäcuïlli = 20, then chicöme = 21\n\nFrom (6): mäcuïlli × ëyi = caxtölli → 20×1 = 20 → caxtölli = 20\n\nSo 20 is represented by caxtölli.\n\nSo “caxtölli” = 20\n\nThen 2 × 20 = 40 → how is 2 expressed?\n\nFrom (4): 20 + 1 = 21 → so 1 = öme\n\nThen 2 = ? → possibly “mahtlactli” or something.\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-p", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10181.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 222.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "anchor_output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start with equations from the Arammba system.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2ngámbi = ngámbi × yànparo \n→ Divide both sides by ngámbi (assuming ngámbi ≠ 0): \n→ 2 = yànparo \nSo: yànparo = 2\n\nFrom (12): nimbo + yànparo = yenówe \n→ nimbo + 2 = yenówe \nSo: yenówe = nimbo + 2\n\nFrom (10): yenówe × yenówe tàxwo = fete × yenówe \nNote: \"tàxwo\" may mean \"times\" or \"plus\" — but here it appears in a product: \nyenówe × (yenówe tàxwo) = fete × yenówe \nWe interpret \"A × B tàxwo\" as A × B. \nSo: (yenówe) × (yenówe) = fete × yenówe \n→ yenówe² = fete × yenówe \nDivide both sides by yenówe (≠ 0): \n→ yenówe = fete\n\nBut from above, yenówe = nimbo + 2 \nSo: fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba \nSubstitute fete: \n→ nimbo × (nimbo + 2) = tarumba \n→ tarumba = nimbo² + 2nimbo\n\nNow (15): cen-tzontli = tarumba + tambaroy + fete + asàr \nWe don’t know cen-tzontli. But note (8): ngámbi + asàr = tambaroy \nSo tambaroy = ngámbi + asàr\n\nSubstitute into (15): \ncen-tzontli = (nimbo² + 2nimbo) + (ngámbi + asàr) + (nimbo + 2) + asàr \n= nimbo² + 2nimbo + ngámbi + asàr + nimbo + 2 + asàr \n= nimbo² + 3nimbo + ngámbi + 2asàr + 2\n\nNow (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nLeft side: (yànparo + fete) + asàr? Or is \"fete asàr\" a compound?\n\nBut \"fete asàr tàxwo\" likely means \"fete × asàr\" or \"fete + asàr\" \nRight side: yànparo × fete\n\nTry interpretation: left = (yànparo + fete) × asàr? No, structure is sum then combined.\n\nGiven form: A tàxwo + B asàr tàxwo = C fete \nPossibly: (A + B) is additive, and \"tàxwo\" is a multiplicative operator.\n\nBut (9): (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0 → contradiction.\n\nInstead, suppose \"A tàxwo\" means A × something — but no.\n\nAlternative: \"A tàxwo\" means A, and \"fete asàr tàxwo\" means fete × asàr \nThen: (yànparo) + (fete × asàr) = yànparo × fete\n\nSo: yànparo + fete × asàr = yànparo × fete\n\nWe know yànparo = 2, so:\n\n2 + fete × asàr = 2 × fete \n→ 2 + fete × asàr = 2fete \n→ fete × asàr = 2fete - 2 \n→ fete × (asàr - 2) = -2\n\nWe also have fete = nimbo + 2\n\nSo: (nimbo + 2)(asàr - 2) = -2\n\nLet’s solve for small integers.\n\nTry nimbo = 0 → fete = 2 \n(2)(asàr - 2) = -2 → asàr - 2 = -1 → asàr = 1\n\nTry nimbo = 1 → fete = 3 \n(3)(asàr - 2) = -2 → asàr - 2 = -2/3 → not integer\n\nnimbo = 2 → fete = 4 → 4(asàr - 2) = -2 → asàr - 2 = -0.5 → invalid\n\nnimbo = -1 → fete = 1 → 1(asàr - 2) = -2 → asàr = 0 → valid?\n\nasàr = 0 \nCheck (8): ngámbi + asàr = tambaroy → tambaroy = ngámbi \n(15): cen-tzontli = tarumba + tambaroy + fete + asàr = (nimbo² + 2nimbo) + ngámbi + (nimbo + 2) + 0 \nWith nimbo = -1: \ntarumba = 1 - 2 = -1 → invalid\n\nSo only valid with nimbo = 0 → fete = 2, asàr = 1\n\nThen: \ntarumba = 0 + 0 = 0 \nfete = 2 \nasàr = 1 \nnimbo = 0 \nyànparo = 2 \ntambaroy = ngámbi + 1\n\nNow (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 0 + (ngámbi + 1) + 2 + 1 = ngámbi + 4\n\nWe need a base unit. We don’t have known value.\n\nBut look at (13) and (14), which link Nahuatl and Arammba.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis may represent multiplication or compound form.\n\nBut likely, the values in Arammba are built from combinations.\n\nFrom (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nBut we don’t know what \"weremeke\" is.\n\nBut perhaps \"cen-tzontli\" is a standard base — like 100 — used in representations.\n\nIn many such puzzles, \"cen-tzontli\" represents 100.\n\nSuppose cen-tzontli = 100.\n\nThen from above: cen-tzontli = ngámbi + 4 → ngámbi = 96\n\nThen tambaroy = 96 + 1 = 97\n\ntarumba = 0 → invalid (cannot be 0)\n\nSo cannot be.\n\nTry to set cen-tzontli = 100 in general.\n\nWe have cen-tzontli = nimbo² + 3nimbo + ngámbi + 2asàr + 2\n\nWith (nimbo + 2)(asàr - 2) = -2\n\nTry nimbo = 1 → fete = 3 → (3)(asàr - 2) = -2 → asàr = 2 - 2/3 → invalid\n\nnimbo = -2 → fete = 0 → product 0 → invalid\n\nnimbo = 4 → fete = 6 → 6(asàr - 2) = -2 → asàr = 2 - 1/3 → invalid\n\nOnly integer solution: nimbo = 0, asàr = 1\n\nAll else fractional.\n\nThus only solution: nimbo = 0, fete = 2, asàr = 1\n\nThen from (11): tarumba = 0 × 2 = 0\n\nNo value — invalid.\n\nConclusion: the only consistent arithmetic interpretation leads to contradictions.\n\nThus, the system cannot be used to extract values for 43 and 569.\n\nBut in the Nahuatl equations, multiplication and addition are layered.\n\nIn (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n→ likely: A × B = C\n\nLikely the structure is arithmetic.\n\nIn Arammba, we see patterns of multiplication and addition represented in compounds.\n\nPerhaps the key is in known equations.\n\n(12): nimbo + yànparo = yenówe → addition \n(10): yenówe × yenówe = fete × yenówe → multiplication \nThus yenówe = fete\n\nSo fete = nimbo + 2\n\n(11): nimbo × fete = tarumba → tarumba = nimbo(nimbo + 2)\n\n(8): ngámbi + asàr = tambaroy\n\n(9): (yànparo) + (fete × asàr) = yànparo × fete → as derived, leads to (fete)(asàr - 2) = -2\n\nOnly integer solution when fete = 2, asàr = 1, nimbo = 0\n\nThen tarumba = 0\n\nThen in (15): cen-tzontli = tarumba + tambaroy + fete + asàr = 0 + (ngámbi + 1) + 2 + 1 = ngámbi + 4\n\nSet cen-tzontli = 100 → ngámbi = 96\n\nThen all values defined.\n\nNow can we interpret 43 and 569 in terms of these?\n\nWe need to build numbers using operations.\n\nNotice that fete = 2, so fete is 2\n\nyànparo = 2\n\nnimbo = 0\n\nasàr = 1\n\ntarumba = 0\n\ntambaroy = 96 + 1 = 97\n\nngámbi = 96\n\nNow, what is 43?\n\nIs 43 = a × b + c or fete × asàr + something?\n\nWe know that multiplication is available via ×.\n\nAlso, 43 might be built from combinations.\n\nBut we have no direct expression for 43.\n\nNote that (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nPossible that cen-xiquipilli is a number, and it is built from sums or products.\n\nBut no value.\n\nPerhaps all numbers are built from ngámbi, yànparo, fete, etc.\n\nBut yànparo = 2, fete = 2, asàr = 1\n\nSo 1 and 2 are available.\n\nThen 43 = ? in terms of units.\n\nBut 43 is odd, so cannot be multiple of 2.\n\nCan it be built with addition and multiplication?\n\nFrom 1 and 2, we can build:\n\n1, 2, 1+2=3, 2×2=4, 2×3=6, etc.\n\nBut 43 may be 42 +1 = 2×21 +1 — but no 21.\n\nPerhaps \"tarumba\" is a base unit.\n\nBut tarumba = 0.\n\nAlternative: in (15), cen-tzontli = 100 → so 100 is a base.\n\nThen numbers are represented in base 100 or base 10?\n\n43 and 569 → 569 = 5×100 + 69\n\nBut can we build 43?\n\nNote: in (13) and (14), there is correspondence.\n\nLook at (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIn Nahuatl, this may represent a compound.\n\nBut without translation, hard.\n\nPerhaps the numbers in Arammba are written as combinations of base components.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nWith yànparo = 2, so 2ngámbi = 2ngámbi — identity.\n\nSo no new info.\n\nFrom (8): ngámbi + asàr = tambaroy\n\nWith asàr = 1, tambaroy = ngámbi + 1\n\nSo it's a one-unit increment.\n\nThen in (15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nWith tarumba = 0, fete = 2, asàr = 1, tambaroy = ngámbi + 1\n\nSo 100 = 0 + (ngámbi + 1) + 2 + 1 = ngámbi + 4 → ngámbi = 96\n\nSo ngámbi = 96\n\nNow, what is 43?\n\nCan we write 43 using operations?\n\nWe have ngámbi = 96, yànparo = 2, fete = 2, asàr = 1\n\nCan we form 43?\n\n96 is large — perhaps ngámbi is 100 or 10?\n\nNo — we derived it as 96.\n\nBut perhaps in the system, \"ngámbi\" represents a unit of 1.\n\nBut no.\n\nAnother idea: in many such puzzles, a number like 43 is represented as (something) × something else.\n\nFor example, 569 = 500 + 69 → or 5×100 + 69\n\nBut we don't have a unit for 100.\n\nBut in (15), cen-tzontli = 100, so perhaps 100 is a base.\n\nLet’s assume that the number 43 is written as \"fete asàr\" or similar.\n\nBut fete = 2, asàr = 1 → 2×1 = 2\n\nNot 43.\n\nPerhaps 43 = (ngámbi - 53) + something — no.\n\nAnother possibility: from (16): cen-xiquipilli = weremeke tarumba nimbo yànparo\n\nIf we assume that \"weremeke\" is a constant, and numbers are built from values.\n\nBut no known value.\n\nPerhaps the correspondence between Nahuatl and Arammba in (13) and (14) can be used.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nWe have yànparo = 2, tarumba = 0\n\nSo right side = 2 × 0 = 0\n\nLeft side: cen-tzontli-on-something = 0\n\nBut cen-tzontli is base, so likely non-zero.\n\nContradiction.\n\nThus, the only consistent arithmetic assignment leads to 0 or contradiction.\n\nTherefore, the system is inconsistent for defining number values.\n\nHence, cannot derive 43 and 569 in Arammba.\n\nBut the question is to write 43 and 569 in Arammba.\n\nPerhaps the values are derived from the equations as a system.\n\nAlternatively, in Arammba, numbers may be represented in base 10, and the operations are standard.\n\nBut we have no direct mapping.\n\nGiven the internal inconsistency, and no consistent assignment of values, we cannot derive the representations.\n\nBut the problem must have a solution.\n\nTry to assume that in (9), \"fete asàr\" is a single compound unit with value fete + asàr or fete × asàr.\n\nBut (9): yànparo + fete asàr = yànparo fete\n\nWith yànparo = 2, 2 + (fete × asàr) = 2 × fete \n→ 2 + fete × asàr = 2fete \n→ fete × asàr = 2fete - 2 \n→ fete (asàr - 2) = -2\n\nOnly integer solution: fete = 2, asàr = 1\n\nThen asàr = 1\n\nfete = 2\n\nnimbo = 0\n\ntarumba = 0\n\nngámbi = 96\n\nThen in (15): cen-tzontli = 100\n\nSo 100 is a unit.\n\nThen 43 = 43\n\n569 = 569\n\nBut how to write in Arammba?\n\nPerhaps using the units.\n\nFor example, 43 = 40 + 3 = 4×10 + 3\n\nBut no 10.\n\nOr 43 = (4×10) + 3, but no 10 or 3.\n\nWe have only values: 2, 1, 0, 96\n\n96 is large.\n\nPerhaps the number is written as a compound of existing units.\n\nFor example, 43 might be \"tambaroy-on-something\", but tambaroy = 97\n\n97 is close to 100.\n\n43 is less.\n\nPerhaps the numbers are written in base 10, and the units are just symbols.\n\nGiven the system is inconsistent, and no derivation path works, the only logical conclusion is that the representation of 43 and 569 in Arammba is not derivable from the given equations.\n\nHowever, the problem asks to write out in Arammba: 43; 569.\n\nSo likely, there is a pattern.\n\nIn (7): ngámbi + ngámbi = ngámbi × yànparo → 2 = yànparo\n\nSo yànparo = 2\n\nIn (10): yenówe × yenówe = fete × yenówe → yenówe = fete\n\nSo fete = yenówe\n\nIn (12): nimbo + yànparo = yenówe → nimbo + 2 = fete\n\nSo fete = nimbo + 2\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 10219.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.", + "planner_output": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "anchor_output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "groot_1x4", + "sample_index": 1, + "output": "We are to translate 43 and 569 into Arammba, based on the given equations. We must infer the structure of Arammba numerals from the provided equations and known Nahuatl correspondences.\n\nFirst, observe that in Nahuatl, numbers are formed via additive or multiplicative compounds. For example:\n\n- (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n Here, \"on\" likely means \"added to\", and \"×\" is multiplication. \n \"mahtlactli\" = 1, \"cë\" = 20 (from (3) and (4) pattern), so \"cë\" = 20. \n (1): 20 × 1 = 20 → mäcuïl-pöhualli-om-mahtlactli \n But mäcuïl-pöhualli = 20? (mäcuïl = 20?) \n (4): mäcuïlli + öme = chicöme → 13 + 5 = 18 → so mäcuïlli = 13, öme = 5, chicöme = 18 \n So mäcuïlli = 13 → mäcuïl = 13? \n (2): cem-pöhualli × öme = öm-pöhualli \n cem = 20? pöhualli = 20-day cycle → likely scalar, e.g. \"cem-pöhualli\" = 20? \n (2): 20 × 5 = 100 → but result is öm-pöhualli → perhaps 100? \n But then öm-pöhualli = 100 → so 20 × 5 = 100. \n So \"cem\" = 20, \"öme\" = 5. \n (1): mahtlactli-on-cë = 1+20 = 21 → (1+20)×1 = 21 → result is mäcuïl-pöhualli-om-mahtlactli \n So does mäcuïl-pöhualli = 21? \n Then 21 × 1 = 21 → consistency. \n (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \n yë-pöhualli = 1+20 = 21? \n chicöme = 18, so 21 + 18 = 39? \n mahtlactli-on-nähui = 1 + nähui → nähui possibly 1? So 21+18+1 = 40? \n result: näuh-pöhualli-on-cë = 20+20 = 40 → yes. \n So “on” is addition. “×” is multiplication. \n Units: \n - yë = 1 \n - pöhualli = 20 \n - mahtlactli = 1 \n - cem = 20 \n - öme = 5 \n - mäcuïlli = 13 \n - cë = 20 \n - caxtölli = 13? from (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n mahtlactli-om-ëyi = 1 + ëyi? \n ëyi = x → (1 + x) × x = 20 + 20 + 13 + 1? → left side = x(1 + x) → right side = 53 + ? \n (6): mäcuïlli × ëyi = caxtölli → 13 × x = caxtölli \n If (5): left = x(1+x), and right = cem-pöhualli-on-caxtölli-on-nähui = 20 + 20 + caxtölli + 1 → 41 + caxtölli \n So x(1+x) = 41 + caxtölli \n But from (6): caxtölli = 13x → \n x + x² = 41 + 13x → x² -12x -41 = 0 \n x = (12 ± √(144+164))/2 = (12±√308)/2 → not integer \n Contradiction? \n Alternatively, perhaps “on” is not addition, but something else.\n\nWait — from (4): mäcuïlli + öme = chicöme → 13 + 5 = 18 \nSo addition is clear. \n(3): yë-pöhualli-on-chicöme → likely means yë-pöhualli + chicöme → 1+20 + 18 = 39 \nThen mahtlactli-on-nähui = 1 + nähui → 1 + 1 = 2? \nThen total = 39 + 2 = 41 → result: näuh-pöhualli-on-cë = 20 + 20 = 40 → contradiction. \nBut result is 40 → so left must be 40. \nThus discrepancy. Perhaps “on” is not always addition.\n\nBut in (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli \n(1+20) × 1 = 21 → result = mäcuïl-pöhualli-om-mahtlactli \nIn Nahuatl, 21 might be written as “20+1”, so mäcuïl-pöhualli-om-mahtlactli = 20+1 → 21 \nSo “on” = addition, “×” = multiplication.\n\nBack to (13) and (14), which connect to Arammba.\n\n(13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nyë = 1, tzontli = 1 → so 1+1 = 2? \nThen + näuh-pöhualli → 2 + 20 = 22 \nThen + caxtölli → 22 + 13 = 35 \nThen + cë → 35 + 20 = 55 \nSo 1+1+20+13+20 = 55 → result is ndamno \nSo ndamno = 55?\n\n(14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \ncen-tzontli = 100 → so 100 + (cem-pöhualli) = 100 + 20? But \"on\" after cen-tzontli = addition? \n\"on\" occurs between tzontli and cem-pöhualli? \nSo cen-tzontli-on-cem-pöhualli = 100 + 20 = 120 \nThen om-mahtlactli-om-öme = 1 + 5 → so 120 + 1 + 5 = 126 \n→ 126 = yànparo tarumba \nSo yànparo tarumba = 126 → tarumba = 126 / 2 = 63 (since yànparo = 2) \nSo tarumba = 63\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr \n100 = 63 + tambaroy + fete + asàr → sum of three = 37\n\n(8): ngámbi + asàr = tambaroy\n\n(12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe\n\n(10): yenówe × yenówe = fete × yenówe → (yenówe × yenówe) = (fete × yenówe) → if yenówe ≠ 0, divide both sides → yenówe = fete\n\nSo fete = yenówe = nimbo + 2\n\n(11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63\n\nSolve: n(n+2) = 63 \nn² + 2n - 63 = 0 \nn = [-2 ± √(4 + 252)] / 2 = [-2 ± √256]/2 = [-2 ± 16]/2 → n = 7 or -9 \nn = 7 → nimbo = 7, fete = 9\n\nThen from (15): 63 + tambaroy + 9 + asàr = 100 → tambaroy + asàr = 37 - 9 = 28\n\nFrom (8): tambaroy = ngámbi + asàr\n\nSo ngámbi + asàr + asàr = 28 → ngámbi + 2asàr = 28\n\nStill two variables.\n\nBut no other constraints. So asàr and ngámbi are not uniquely determined — only that their sum is 28 in (8), and ngámbi + asàr = tambaroy.\n\nNow, supported equations:\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \n2 ngámbi = ngámbi × 2 → consistent (2x = 2x)\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nyànparo tàxwo = 2×? → so (2a) + (fete × asàr) = 2 × fete → so 2a + fete×asàr = 2fete \nWe have fete = 9 → \n2a + 9×asàr = 18 \nBut a = ngámbi → \n2 ngámbi + 9 asàr = 18\n\nBut earlier: ngámbi + asàr = tambaroy = 28? No → from earlier: tambaroy = ngámbi + asàr = 28\n\nSo now: \n2 ngámbi + 9 asàr = 18 \nngámbi + asàr = 28\n\nSubtract twice the second from first? \n(2ng + 9as) - 2×(ng + as) = 18 - 56 = -38 \n(2ng + 9as) - 2ng - 2as = 7as = -38 → asàr = -38/7 → impossible\n\nContradiction! So assumption about (9) must be wrong.\n\nReevaluate (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n\"tàxwo\" may mark a modifier or operation. Possibly \"×\" or \"added after\"? \n\nPossibly \"yànparo tàxwo\" means yànparo × something? Or repetition.\n\nIn (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n\"×\" and \"tàxwo\" both appear. \n\"yenówe × yenówe\" = fete × yenówe → we already used that → yenówe = fete \nBut \"×\" with \"tàxwo\" — could be multiplication by a number.\n\n\"yenówe × yenówe tàxwo\" = fete × yenówe tàxwo \nThis suggests: (yenówe) × (yenówe) = (fete) × (yenówe) → same as before.\n\nBut also \"tàxwo\" may indicate a different value.\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nLikely: (yànparo × ?) + (fete × asàr) = yànparo × fete \nIf we suppose \"tàxwo\" means multiplication, then: \n(yànparo × a) + (fete × asàr) = yànparo × fete \nWith a = ? \nBut if a = 1, then: 2a + 9as = 2×9 = 18 → 2 + 9as = 18 → 9as = 16 → asàr = 16/9 → not integer.\n\nPossibility: \"tàxwo\" is a fixed unit? Or zero?\n\nAlternative: \"tàxwo\" marks duplication? Or identity?\n\nBut (7): ngámbi + ngámbi = ngámbi × yànparo → 2ng = ng×2 → only possible if ng ≠ 0 → consistent.\n\nFrom (11): nimbo × fete = tarumba → 7×9 = 63 → correct.\n\nFrom (15): 100 = 63 + tambaroy + 9 + asàr → tambaroy + asàr = 37 - 9 = 28\n\nFrom (8): tambaroy = ngámbi + asàr\n\nSo ngámbi + asàr = 28 → and ngámbi + asàr = tambaroy → consistent.\n\nNo contradiction in values — the identity in (9) might not be literal.\n\nPerhaps \"tàxwo\" is a morphological marker for identity or 1, but not operation.\n\nBut to resolve (9): \nIf yànparo tàxwo = yànparo (same), and fete asàr tàxwo = fete × asàr, then: \nyànparo + fete×asàr = yànparo×fete \n→ 2 + 9×asàr = 2×9 = 18 \n→ 9×asàr = 16 → not integer.\n\nSo no solution — contradiction.\n\nTherefore, our initial assignment of values may be flawed.\n\nAlternative: “on” is not addition. \nIn (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nLeft: (yë-pöhualli) + (chicöme) + (mahtlactli) + (nähui)? \nBut \"on\" may be prepositional. \nPossibility: “A-on-B” = A × B? But (1): mahtlactli-on-cë × mahtlactli → (1+20)×1 = 21 → result 21 → not product.\n\n(1): left = (1+20) × 1 = 21, right = mäcuïl-pöhualli-om-mahtlactli = 20+1 = 21 → so is multiplication, and additive decompositions.\n\nBest to trust that in Nahuatl:\n\n- \"tzontli\" = 1 \n- \"pöhualli\" = 20 \n- \"öme\" = 5 \n- \"mahtlactli\" = 1 \n- \"cem\" = 20 \n- \"cë\" = 20 \n- \"mäcuïlli\" = 13 \n- \"caxtölli\" = 13 → from (6): mäcuïlli × ëyi = caxtölli → 13×x = 13x → x = 1? or 13x = 13 → x=1 \nThen from (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui \nmahtlactli-om-ëyi = 1+1 = 2 \n2 × 1 = 2 \nright: 20 + 20 + 13 + 1 = 54 → contradiction.\n\nUnless x is different.\n\nAlternatively, values are not direct, but the structure is key.\n\nBack to Arammba.\n\nWe have:\n\n(7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2ng = ng × 2 → only true if ng ≠ 0 — consistent.\n\n(8): ngámbi + asàr = tambaroy \n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo = yenówe \n(10): yenówe × yenówe = fete × yenówe → yenówe = fete \n(12): nimbo + 2 = fete \n(11): nimbo × (nimbo+2) = tarumba\n\nWe have tarumba = 63 from (14) and (15).\n\nSo nimbo(nimbo+2) = 63 → nimbo = 7, fete = 9\n\nThen from (15): 100 = 63 + tambaroy + 9 + asàr → tambaroy + asàr = 28\n\nFrom (8): tambaroy = ngámbi + asàr\n\nSo ngámbi + asàr = 28 \nThus asàr = 28 - ngámbi\n\nNo further constraints. So values are not unique.\n\nBut in (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nIf we interpret \"tàxwo\" as a unit of 1, and \"×\" as multiplication, then: \n(yànparo) + (fete × asà", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8781.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.", + "planner_output": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "anchor_output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "groot_1x4", + "sample_index": 2, + "output": "We are asked to write out in Arammba: 43; 569, based on a set of equations connecting Nahuatl and Arammba.\n\nWe begin by identifying numerical values from the given equations.\n\nStart with equation (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \n\nAssume \"tànwo\" (as in \"tàxwo\") is a plural or augmentative, and that \"fete asàr\" is a compound unit. \nThe equation structure suggests: \n(yànparo + fete asàr) = (yànparo + fete) \n\nSo: \nyànparo + fete asàr = yànparo + fete \n→ fete asàr = fete \n→ asàr = 1 \n\nThus, the unit \"fete asàr\" is equivalent to \"fete\", meaning asàr = 1.\n\nNow, equation (8): \nngámbi + asàr = tambaroy \n→ ngámbi + 1 = tambaroy → tambaroy = ngámbi + 1\n\nEquation (15): \ncen-tzontli = tarumba tambaroy fete asàr \n\nWe interpret this as a sum: \n100 = tarumba + tambaroy + fete + asàr \nWe know: fete = 9, asàr = 1 → \n100 = tarumba + (ngámbi + 1) + 9 + 1 \n→ 100 = tarumba + ngámbi + 11 \n→ tarumba + ngámbi = 89 → (eq A)\n\nEquation (11): \nnimbo × fete = tarumba \n→ nimbo × 9 = tarumba → tarumba = 9 × nimbo → (eq B)\n\nSubstitute (eq B) into (eq A): \n9×nimbo + ngámbi = 89 \n→ ngámbi = 89 - 9×nimbo → (eq C)\n\nWe now look at equation (12): \nnimbo + yànparo tàxwo = yenówe tàxwo \n\nWe interpret \"yànparo tàxwo\" as yànparo + fete (since fete is part of the structure), or possibly a compound. \nBut recall: from (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \nand we found fete asàr = fete, so both sides come from additive combinations.\n\nFrom (10): \nyenówe × yenówe tàxwo = fete yenówe tàxwo \n\nLet’s suppose that “yenówe” represents a base unit, say y. Then: \ny × (y + fete) = fete × y + fete × y → y(y + fete) = 2fete y \n→ y² + y fete = 2fete y → y² = fete y → y² - fete y = 0 → y(y - fete) = 0 \nThus, y = 0 or y = fete → discard y = 0 → y = fete → yenówe = fete = 9\n\nThus, yenówe = 9\n\nNow equation (12): \nnimbo + yànparo tàxwo = yenówe tàxwo \n\nIf “tànwo” is an additive device (like \"times\" or \"plus\"), then: \nnimbo + yànparo + fete = yenówe + fete → \nnimbo + yànparo + 9 = 9 + 9 → \nnimbo + yànparo = 9 \n\nBut wait — from (10), we found yenówe = 9, so \"yenówe tàxwo\" = 9 + 9 = 18? \nBut in equation (10), “yenówe × yenówe tàxwo = fete yenówe tàxwo” \n→ let’s expand properly:\n\nLet yenówe = y, and yenówe tàxwo = y + fete \nThen left: y × (y + fete) \nRight: fete × (y + fete) \nSo: \ny(y + fete) = fete(y + fete) \n→ y² + y fete = fete y + fete² \n→ y² = fete² → y = fete (since positive) \nThus, yenówe = fete = 9\n\nSo yenówe = 9\n\nNow equation (12): \nnimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (yànparo + fete) = (yenówe + fete) \n→ nimbo + yànparo + 9 = 9 + 9 \n→ nimbo + yànparo = 9 → (eq D)\n\nNow from earlier: \ntarumba = 9 × nimbo → (eq B) \nand from (15): \ntarumba + ngámbi = 89 → (eq A) \nand ngámbi = 89 - 9×nimbo → (eq C)\n\nWe now need to assign integer values consistent with all equations.\n\nTry nimbo = 1 → tarumba = 9 → from (15): 9 + ngámbi = 89 → ngámbi = 80 → from (12): nimbo + yànparo = 9 → 1 + yànparo = 9 → yànparo = 8\n\nTry nimbo = 2 → tarumba = 18 → ngámbi = 89 - 18 = 71 → yànparo = 7\n\nTry nimbo = 3 → tarumba = 27 → ngámbi = 62 → yànparo = 6\n\nTry nimbo = 4 → tarumba = 36 → ngámbi = 53 → yànparo = 5\n\nTry nimbo = 5 → tarumba = 45 → ngámbi = 44 → yànparo = 4\n\nTry nimbo = 6 → tarumba = 54 → ngámbi = 35 → yànparo = 3\n\nTry nimbo = 7 → tarumba = 63 → ngámbi = 26 → yànparo = 2\n\nTry nimbo = 8 → tarumba = 72 → ngámbi = 17 → yànparo = 1\n\nTry nimbo = 9 → tarumba = 81 → ngámbi = 8 → yànparo = 0 → invalid\n\nNow test consistency with equation (7): \nngámbi + ngámbi = ngámbi × yànparo \n\nSo: 2×ngámbi = ngámbi × yànparo \n\nIf ngámbi ≠ 0, divide both sides: \n2 = yànparo \n\nThus, yànparo = 2 — this is a key value!\n\nSo from (7): 2×ngámbi = ngámbi × yànparo → implies yànparo = 2 (if ngámbi ≠ 0)\n\nSo yànparo = 2\n\nNow from equation (12): \nnimbo + yànparo = 9 → nimbo + 2 = 9 → nimbo = 7\n\nThen: \ntarumba = 9 × 7 = 63 \nngámbi = 89 - 63 = 26 \n\nNow verify equation (7): \nngámbi + ngámbi = 26 + 26 = 52 \nngámbi × yànparo = 26 × 2 = 52 → matches\n\n(8): ngámbi + asàr = 26 + 1 = 27 = tambaroy → good\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \n→ (2 + 9) + (9 + 1) = (2 + 9) → 11 + 10 = 11 → 21 = 11 → contradiction?\n\nWait — we must resolve this.\n\nEquation (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \n\nWe now know: \nyànparo = 2 \nfete = 9 \nasàr = 1 \n\nInterpret \"yànparo tàxwo\" = yànparo + fete? Or is it just a compound?\n\nBut equation shows: \n(2 + fete) + (fete + asàr) = (2 + fete)? \n→ (2 + 9) + (9 + 1) = (2 + 9) → 11 + 10 = 11 → false\n\nThus contradiction.\n\nAlternative interpretation: \"tànwo\" may not mean \"plus\", but rather a different operation.\n\nBut in (10): yenówe × yenówe tàxwo = fete yenówe tàxwo \nWe deduced y = fete = 9 via algebra.\n\nBut maybe \"tànwo\" is a plural marker, and the expression is syntactic.\n\nPerhaps the equation (9) is: \n(yànparo + fete) + (fete + asàr) = (yànparo + fete) \n→ implies (fete + asàr) = 0 → asàr = -fete → impossible\n\nSo contradiction.\n\nTherefore, our assumption that fete asàr = fete must be re-examined.\n\nGo back to (9): \nyànparo tàxwo + fete asàr tàxwo = yànparo fete \n\nSuppose \"tànwo\" is not additive but part of a multiplicative or compound structure.\n\nBut (7): ngámbi + ngámbi = ngámbi × yànparo → leads to yànparo = 2 → this must hold.\n\nSo yànparo = 2.\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo \n\nLet y = yenówe \nLet y + fete = yenówe tàxwo \n\nThen: y(y + fete) = fete(y + fete) \n→ y² + y fete = fete y + fete² \n→ y² = fete² \n→ y = fete (assume positive) → yenówe = fete \n\nThus, fete = yenówe \n\nNow from (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + (yànparo + fete) = (yenówe + fete) \n→ nimbo + (2 + fete) = (fete + fete) \n→ nimbo + 2 + fete = 2fete \n→ nimbo + 2 = fete \n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = 100 = tarumba + tambaroy + fete + asàr\n\nFrom (8): tambaroy = ngámbi + asàr\n\nFrom (7): 2×ngámbi = ngámbi × yànparo \nyànparo = 2 → 2ngámbi = 2ngámbi → always true → no new value\n\nSo so far: \nfete = nimbo + 2 \ntarumba = nimbo × fete \ntambaroy = ngámbi + asàr \n100 = tarumba + tambaroy + fete + asàr \n\nLet’s plug in:\n\n100 = (nimbo × fete) + (ngámbi + asàr) + fete + asàr \n= nimbo × fete + ngámbi + 2asàr + fete\n\nBut fete = nimbo + 2 → \ntarumba = nimbo(nimbo + 2) = nimbo² + 2nimbo \n\nSo: \n100 = (nimbo² + 2nimbo) + ngámbi + 2asàr + (nimbo + 2) \n→ 100 = nimbo² + 3nimbo + 2 + ngámbi + 2asàr \n→ ngámbi + 2asàr = 98 - nimbo² - 3nimbo \n\nNow we need ngámbi ≥ 0, asàr ≥ 0.\n\nTry nimbo = 1 → fete = 3 \ntarumba = 1×3 = 3 \nngámbi + 2asàr = 98 - 1 - 3 = 94\n\n→ possible.\n\nnimbo = 2 → fete = 4 → tarumba = 8 \n→ ngámbi + 2asàr = 98 - 4 - 6 = 88\n\nnimbo = 3 → fete = 5 → tarumba = 15 \n→ 98 - 9 - 9 = 79\n\nnimbo = 4 → fete = 6 → tarumba = 24 \n→ 98 - 16 - 12 = 69\n\nnimbo = 5 → fete = 7 → tarumba = 35 \n→ 98 - 25 - 15 = 58\n\nnimbo = 6 → fete = 8 → tarumba = 48 \n→ 98 - 36 - 18 = 44\n\nnimbo = 7 → fete = 9 → tarumba = 63 \n→ 98 - 49 - 21 = 28\n\nnimbo = 8 → fete = 10 → tarumba = 80 \n→ 98 - 64 - 24 = 8\n\nnimbo = 9 → fete = 11 → tarumba = 99 → already >100 → too big\n\nSo possible values.\n\nBut now from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIn Nahuatl: \ntzontli = 1 \npöhualli = 20 \ncaxtölli = 13 \ncë = 20 \n\nSo: 1 + 20 + 13 + 20 = 54 → ndamno = 54\n\nSo in Arammba, 54 = ndamno\n\nNow we must map known numbers to Arammba.\n\nWe have: \nngámbi = ? \nyànparo = 2 \nfete = nimbo + 2 \ntarumba = nimbo(nimbo + 2) \nasàr = ? \n\nWe also have from (13): 54 = ndamno → so 54 is a known value.\n\nWe want to write 43 and 569 in Arammba.\n\nNow, from (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\ncen-tzontli = 100\n\nSuppose this is 100 + cem-pöhualli + om-mahtlactli + om-öme\n\nBut cem-pöhualli, mahtlactli, öme are compound units.\n\nFrom (1): mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli\n\nBut instead, we look at (4): mäcuïlli + öme = chicöme \n(5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui \n(6): mäcuïlli × ëyi = caxtölli \n\nBut these may not give direct values.\n\nFrom earlier derivation, we have a consistent mapping if we take:\n\nyànparo = 2 \nfete = nimbo + 2 \ntarumba = nimbo × fete\n\nAnd from (14): 100 + X = yànparo × tarumba = 2 × tarumba\n\nBut 100 + X = 2 × tarumba\n\nSo X = 2 × tarumba - 100\n\nBut X is a compound: cem-pöhualli-om-mahtlactli-om-öme → must be positive.\n\nSo 2×tarumba > 100 → tarumba > 50\n\ntarumba = nimbo(nimbo + 2) > 50\n\nTry nimbo = 7 → 7×9 = 63 → 2×63 = 126 → X = 126 - 100 = 26 → possible\n\nnimbo = 6 → 6×8 = 48 → 2×48 = 96 → X = -4 → invalid\n\nSo only nimbo ≥ 7 is valid.\n\nnimbo = 7 → fete = 9 → tarumba = 63 \nX = 26\n\nThus, 100 + X = 126 = yànparo × tarumba = 2 × 63 = 126 → matches\n\nSo it works.\n\nThus: fete = 9, nimbo = 7, tarumba = 63, yànparo = 2\n\nNow from (15): cen-tzontli = 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr → tambaroy + asàr = 28\n\nFrom (8): tambaroy = ngámbi + asàr \nSo: (ngámbi + asàr) + asàr = 28 \n→ ngámbi + 2", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 8978.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "The core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.", + "planner_output": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "anchor_output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "method": "groot_1x4", + "sample_index": 3, + "output": "We are given a set of equations in Nahuatl and Arammba, and we are to determine how to write 43 and 569 in Arammba.\n\nFirst, observe the known values from the equations.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \n→ 2ngámbi = ngámbi × yànparo \n→ Assuming ngámbi ≠ 0, divide both sides: 2 = yànparo \n→ yànparo = 2\n\nFrom (12): nimbo + yànparo = yenówe \n→ nimbo + 2 = yenówe\n\nFrom (10): yenówe × yenówe = fete × yenówe \n→ yenówe² = fete × yenówe \n→ yenówe = fete (assuming yenówe ≠ 0) \n→ fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba \n→ nimbo × (nimbo + 2) = tarumba\n\nFrom (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba \nWe interpret this as: \ncen-tzontli = 100 (from (15)) \ncem = 20, mahtlactli = 1, öme = 5 (from (4): mäcuïlli + öme = chicöme → 13 + 5 = 18; likely öme = 5) \nSo: 100 + 20 + 1 + 5 = 126 \nRight side: yànparo × tarumba = 2 × tarumba \nSo: 2 × tarumba = 126 → tarumba = 63\n\nThen from (11): nimbo × (nimbo + 2) = 63 \nSolve: \nn(n+2) = 63 \nn² + 2n - 63 = 0 \nDiscriminant: 4 + 252 = 256 = 16² \nn = [-2 ± 16]/2 → n = 7 or n = -9 \nn = 7 → nimbo = 7 \n→ fete = 9\n\nFrom (15): cen-tzontli = tarumba + tambaroy + fete + asàr \n100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nFrom (8): ngámbi + asàr = tambaroy \n→ ngámbi = tambaroy - asàr\n\nPlug into above: (tambaroy - asàr) + asàr = 28 → tambaroy = 28 \n→ asàr = 0 → no, 28 - asàr + asàr = 28 → contradiction if tambaroy = 28? \nWait: tambaroy + asàr = 28, and tambaroy = ngámbi + asàr → so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nWe have one equation, two variables. But now check (9):\n\n(9): yànparo tàxwo + fete asàr tàxwo = yànparo fete \nLeft: (2 + fete + asàr) = (2 + 9 + asàr) = 11 + asàr \nRight: 2 + 9 = 11 \nSo: 11 + asàr = 11 → asàr = 0\n\nThus, asàr = 0\n\nThen from (8): tambaroy = ngámbi + 0 = ngámbi \nFrom above: ngámbi + 2(0) = 28 → ngámbi = 28 \nSo tambaroy = 28\n\nNow all values are consistent:\n\n- yànparo = 2 \n- nimbo = 7 \n- fete = 9 \n- tarumba = 63 \n- cen-tzontli = 100 \n- asàr = 0 \n- ngámbi = 28 \n- tambaroy = 28\n\nNow, (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nAssuming tzontli = 1, pöhualli = 20, caxtölli = 13, cë = 20 \n→ 1 + 20 + 13 + 20 = 54 \n→ ndamno = 54\n\nSo we now know:\n- 1 = tzontli \n- 20 = pöhualli \n- 13 = caxtölli \n- 20 = cë \n- 100 = cen-tzontli \n- yànparo = 2 \n- nimbo = 7 \n- fete = 9 \n- tarumba = 63 \n\nNow, we want to express 43 and 569 in Arammba.\n\n43: \nWe have: \n- 63 - 20 = 43 → tarumba - cem \n- 43 = 40 + 3 → 2×20 + 3 → no 3 \n- 43 = 7×6 + 1 → no 6 or 1 \n- 43 = 9×4 + 7 → 9×4 = 36 → 36+7=43 → fete × 4 + nimbo → but no 4 \n- 43 = 100 - 57 → no 57 \n\nTry: 54 - 11 → no 11 \nIs there a compound? We know that \"fete asàr\" = 9×0 = 0, or 9+0=9 → no new value.\n\nSince subtraction is not explicitly defined, and only addition and multiplication are seen (e.g., ngámbi + ngámbi = ngámbi × yànparo), likely only built from arithmetic operations on known units.\n\nWe can try to build 43 as 63 - 20 → tarumba - cem \nBut no subtraction rule.\n\nNote that in (13): \"yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë\" = 1 + 20 + 13 + 20 = 54 \nWe can build other numbers: \n- 1 = tzontli \n- 20 = pöhualli or cë \n- 13 = caxtölli \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli \n\nNow, 43 = 63 - 20 → tarumba - pöhualli \nBut subtraction not defined.\n\nHowever, in (14): composite structure implies addition: cen-tzontli-on-cem-pöhualli... = 100 + 20 + 1 + 5 → so addition is used.\n\nMultiplication: (7) shows multiplication: ngámbi × yànparo = 2ngámbi.\n\n(10): yenówe × yenówe = fete × yenówe → multiplication.\n\nSo likely operations are + and ×.\n\nCan we get 43?\n\n43 = 20 × 2 + 3 → 40 + 3 → no 3 \n43 = 9 × 4 + 7 → 36 + 7 = 43 → need 4\n\nIs 4 present? 4 = 2×2 → 2×2 → yànparo × yànparo = 4 → possible \nThen 43 = fete × (yànparo × yànparo) + nimbo = 9 × (2×2) + 7 = 9×4 + 7 = 36 + 7 = 43\n\nSo 43 = fete × (yànparo × yànparo) + nimbo\n\nIn Arammba: fete × (yànparo × yànparo) + nimbo\n\nNow for 569: \n569 = 100 × 5 + 69 \n69 = 63 + 6 \n6 = 2 × 3 → no 3 \n6 = 2 × 2 + 2 = 6 → 2×3? \n\nWe can write 6 = yànparo × yànparo + yànparo = 4 + 2 = 6 \nSo 69 = tarumba + yànparo × yànparo + yànparo = 63 + 4 + 2 = 69 \nThen 569 = 100 × 5 + (tarumba + yànparo × yànparo + yànparo) \n= 100 × 5 + tarumba + yànparo × yànparo + yànparo\n\nDo we have 5? 5 = öme (from (4): mäcuïlli + öme = chicöme → 13 + 5 = 18) → öme = 5\n\nSo 5 = öme\n\nSo 569 = (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo\n\nNow, in Arammba, the expression would be built from combining units via × and +.\n\nSo:\n\n43 = fete × (yànparo × yànparo) + nimbo \n569 = (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo\n\nNow, write in Arammba using the given terms.\n\nWe do not have öme in Arammba directly, but öme appears in Nahuatl and is part of the mapping, so in the system, öme = 5, and since it is one of the base units, it should be used when needed.\n\nThus, we can represent:\n\n43 → fete × (yànparo × yànparo) + nimbo \n569 → (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo\n\nThis uses only known units and operations from the system.\n\nThus, the answer is:\n\nc.1: fete × (yànparo × yànparo) + nimbo \nc.2: (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo\n\n\\boxed{c.1: fete × (yànparo × yànparo) + nimbo; c.2: (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo}", + "generated_tokens": 2534, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "c.1: fete × (yànparo × yànparo) + nimbo; c.2: (cen-tzontli × öme) + tarumba + (yànparo × yànparo) + yànparo", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "c.1", + "c.2" + ], + "unit_results": [ + { + "unit_id": "c.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "c.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 2.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 5362.0, + "ioling_final_answer_chars": 107.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 196.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "planner_output": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "anchor_output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 0, + "output": "Step 1: Analyze the given examples to identify verb patterns, object marking, and recipient marking.\n\nExample 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" (bought) + \"kamiːg\" (the camels, object) + \"jaːnticcirsu\" (for the neighbours, recipient). \n→ Structure: [subject] + [verb] + [object] + [recipient].\n\nExample 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" (repaired) + \"kadeːg\" (the dress, object) → no recipient. \n→ Verb + object. No recipient suffix here.\n\nExample 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" (young men) + \"darbadki\" (give) + \"biticcirra\" (the chicken, object) → \"to the dogs\" is missing. \nWait — in translation: \"give the chicken to the dogs\" → \"to the dogs\" is the recipient. \nBut \"darbadki\" is the verb. \nSo verb + object + recipient? But no explicit recipient marker.\n\nExample 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"jahalgi\" (stole) + \"kadeːcciːg\" (the dresses, object) + \"maːgtirsu\" (for the young man, recipient). \n→ Verb + object + recipient (marked by \"for\" structure).\n\nExample 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" (I) + \"beyyeːcciːg\" (buying) + \"ajaːnirri\" (the necklaces, object). \nNo recipient.\n\nExample 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" (the dog) + \"aygi\" (found) + \"baːbiːg\" (the doors, object) + \"eldeːnsu\" (for me, recipient). \n→ Verb + object + recipient (for me).\n\nExample 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" (thief) + \"ikki\" (gave) + \"waliːg\" (you pl.) + \"ticcirsu\" (the dogs, object). \nWait — \"ticcirsu\" is object. \"ikki\" = gave. So verb + recipient + object? \nNo — \"ikki\" is the verb, \"waliːg\" is recipient, \"ticcirsu\" is object. \nSo verb + recipient + object? But order is: subject + verb + recipient + object. \nHowever, this is unusual. In example 3, verb + object → \"give the chicken\", but recipient is not marked until later. \nIn example 7: \"ikki\" (gave) + \"waliːg\" (to you) + \"ticcirsu\" (the dogs). So object after recipient.\n\nBut in example 3: \"jaːnticcirsu\" is \"for the neighbours\" — recipient suffix.\n\nWait — in example 3: \"darbadki biticcirra\" = \"give the chicken\" → recipient not stated. But translation says \"to the dogs\" → so \"to the dogs\" is recipient. Where is that?\n\nRecheck: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \nSo verb \"darbadki\" + object \"biticcirra\" → \"the chicken\" → recipient \"to the dogs\" implied. \nBut there is no explicit marker. However, the recipient marking is only in examples where a \"for\" or \"to\" construction appears.\n\nExample 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" (men) + \"magaski\" (gave) + \"kamiːg\" (the camels, object) + \"tirsa\" (to the thief, recipient). \n→ So verb + object + recipient (marked by \"tirsa\").\n\nThus, the pattern is: \n[subject] + [verb] + [object] + [recipient] when recipient is marked. \nWhen recipient is not marked, only object is present. \nAlso, verb roots like \"tirt\" (repair), \"kanarriːcciːg\" (buy), \"darbadki\" (give), \"beyyeːcciːg\" (buy), \"ikki\" (give), \"tirsa\" (give), \"hanuːg\" (strike) are consistent.\n\nNow consider sentence 14: \n\"tirti argi kamgi deːccirsa\" \n- \"tirti\" = repair verb (from \"tirt\") \n- \"argi\" appears \n- \"kamgi\" = likely object (the camels) \n- \"deːccirsa\" → likely recipient (to the farmers?) \n\nBut \"tirti\" (repair) taking \"argi\" (to give) as a verb seems illogical. \n\"Repair the camels to the farmers\"? Unlikely. \nTherefore, \"argi\" cannot be a separate transitive verb here. \n\nAlternative: \"argi\" is not a verb, but a marker. Possibly a direction or recipient marker. \nIn example 3: \"darbadki biticcirra\" — verb + object → no recipient marker. \nBut in sentence 14: \"tirti argi kamgi deːccirsa\" — verb \"tirti\" + \"argi\" + object \"kamgi\" + recipient \"deːccirsa\" → perhaps \"argi\" modifies the verb — like \"to give\" or \"in order to give\"? \nBut that would mean \"repair the camels to give to farmers\"? Unnatural.\n\nMore likely: \"argi\" is a verb meaning \"give\", and the sequence is verb + object + recipient. \nBut \"tirti\" is repair. So “repair the camels to the farmers” makes sense. \nBut why is \"argi\" included?\n\nPossibility: \"tirti\" is not the main verb. Or \"argi\" is a verb in a different structure.\n\nBut in sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief → subject \n\"argi\" = ??? \n\"ajomirra\" = likely \"the donkey\" (same as in 9: \"hanuːg bijomri\" = \"I will strike the donkey\") \n\nIn sentence 9: \"hanuːg bijomri\" → \"I will strike the donkey\" → bijomri = object (the donkey) \nSo \"ajomirra\" = \"the donkey\"\n\nSo in sentence 11: \"magasi argi ajomirra\" → thief + ? + the donkey\n\nIf \"argi\" is a verb meaning \"give\", then \"the thief gives the donkey\" — but giving a donkey is unusual; more likely \"the thief gives something to the donkey\".\n\nBut no object. So it's flawed unless \"ajomirra\" is part of the object.\n\nBut objects are marked earlier. In example 3: \"darbadki biticcirra\" → \"give the chicken\" — object is \"biticcirra\".\n\nThus, \"argi\" cannot be the verb in 11 if the object is missing.\n\nUnless \"argi\" is not a verb but a preposition meaning \"to\" or \"for\".\n\nTry: \"magasi argi ajomirra\" = \"The thief to the donkey\" → incomplete. \nOr \"The thief gives to the donkey\" — needs object.\n\nNo object. So only if \"ajomirra\" is the object, and \"argi\" is \"give\".\n\nBut then \"gives the donkey\" — what is given? Not stated.\n\nNow check sentence 14: \"tirti argi kamgi deːccirsa\" \nIf \"tirti\" is repair, and \"argi\" is \"give\", then “repair the camels to give to farmers”? No.\n\nTherefore, \"argi\" cannot be a verb in these contexts.\n\nNew hypothesis: \"argi\" is a marker of direction or recipient. \nIt appears with a verb that has a participant. But in both 11 and 14, \"argi\" is between the subject and object.\n\nCompare to example 11: \n\"magasi argi ajomirra\" → subject (magasi) + argi + object (ajomirra)\n\nWhat if \"argi\" is a preposition meaning \"to\" or \"for\"?\n\nThen \"magasi argi ajomirra\" = \"The thief to the donkey\" → still incomplete.\n\nBut in example 3: no such structure.\n\nBack to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → stole the dresses for the young man → verb + object + recipient.\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → found the doors for me → verb + object + recipient.\n\nSentence 12: \"ay kanarriːg baːbki alletirsi\" \n\"ay\" = I \n\"kanarriːg\" = buy (like \"kanarriːcciːg\") but with \"g\" — perhaps a variant \n\"baːbki\" = dresses? (in example 4: \"kadeːcciːg\" = dresses) \n\"alletirsi\" = for whom?\n\n\"alletirsi\" likely means \"for you\" or \"for the people\" → recipient.\n\nSo \"I buy the dresses for you\" → possible.\n\nSimilarly, sentence 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = strike (from \"hanuːg\" in 9) \n\"tirtiːg\" → possibly \"repair\" or \"tirt\" in a new form? \n\"elirsu\" = \"for the farmer\" or \"to the farmers\"? (in examples, \"eldeːnsu\" = for me)\n\n\"elirsu\" → likely recipient = \"for the farmers\"\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair for the farmers\"? Unlikely.\n\nBut \"hanu\" = strike → so \"strike to repair\"? Illogical.\n\n\"tirtiːg\" → could be a form of \"tirt\" (repair) + subject?\n\nNo — in example 2: \"tirt kadeːg allesu\" = repaired the dress.\n\nSo \"tirt\" is a verb — repair.\n\nSo \"hanu tirtiːg\" = \"strike repair\"? No.\n\nBut \"tirtiːg\" could be \"repair\" with a suffix.\n\nUnless \"tirti\" is the verb, and \"tirtiːg\" is a variant.\n\nBut in sentence 14: \"tirti argi kamgi deːccirsa\" → \"tirti\" (repair) + \"argi\" + \"kamgi\" (camels) + \"deːccirsa\" (to farmers)\n\nAgain, \"repair the camels to give to farmers\"? Unlikely.\n\nUnless \"argi\" is not a verb, but a modal — like \"in order to\" — not likely.\n\nAlternative: \"argi\" is a common noun or pronoun? Unlikely.\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give (same as in 3) \n\"bijaːndi\" = ? → similar to \"biticcirra\" = chicken, \"ajomirra\" = donkey\n\n\"bijaːndi\" → likely \"the chicken\" or \"the bird\"? \nSo \"I will give the chicken\" → makes sense.\n\nThus, verb \"darbadki\" (give) + object \"bijaːndi\" → object.\n\nNo recipient — so no \"to\" suffix.\n\nNow sentence 11: \"magasi argi ajomirra\" \nsubj: magasi (thief) \n\"argi\" – must be verb \n\"ajomirra\" – object\n\nBut no object in the sense of \"give something\" — unless \"ajomirra\" is the object.\n\nSo \"the thief gives the donkey\" — only if \"gives\" is a verb.\n\nBut in example 9: \"I strike the donkey\" — so \"bijomri\" is object.\n\nTherefore, \"ajomirra\" = object = \"the donkey\"\n\nSo \"thief gives the donkey\" — but gives what? Not specified.\n\nOnly if \"gives\" is used in transitive with object, which it is — but the meaning is odd.\n\nBut in the language, perhaps \"give\" is used as a verb that takes object.\n\nWe see in other sentences: \n- \"darbadki biticcirra\" = give the chicken → object only \n- \"kadeːg allesu\" = repair the dress → object only \n- \"tirt kadeːg allesu\" → repair the dress → verb + object \n- \"darbadki\" → give → verb + object\n\nSo likely, verbs take object.\n\nIn all sentences with a recipient, it's marked with a separate suffix (e.g., \"jaːnticcirsu\", \"maːgtirsu\", \"eldeːnsu\", \"tirsa\", \"alletirsi\").\n\nSo in sentence 14: \"tirti argi kamgi deːccirsa\" \nIf \"tirti\" is repair, and \"argi\" is not a verb, but a preposition meaning \"to\", then it would be: \"repair to the camels for farmers\"? Ungrammatical.\n\nAlternatively, \"argi\" is a variant of \"give\" — but then why is it separated?\n\nBut in sentence 12: \"ay kanarriːg baːbki alletirsi\" \n\"kanarriːg\" = buy (like \"kanarriːcciːg\") \n\"baːbki\" = dresses? (from sentence 4: \"kadeːcciːg\" = dresses) \n\"alletirsi\" = for whom?\n\n\"alletirsi\" → like \"eldeːnsu\" = for me → likely \"for you\" or \"for the people\"\n\nSo \"I buy the dresses for you\"\n\nIn sentence 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = strike \n\"tirtiːg\" = ? \n\"elirsu\" = for the farmers\n\nIs \"tirtiːg\" a verb? Possibly a variant of \"tirt\" (repair)\n\n\"hanu\" = strike — very different.\n\n\"hanu tirtiːg\" = \"strike repair\" → illogical.\n\nBut perhaps it's \"hanu\" (strike) + \"tirtiːg\" (for) — as in \"strike for the farmers\"? \nBut in sentence 9: \"hanuːg bijomri\" = \"strike the donkey\"\n\nSo only object, no recipient.\n\nThus, to have recipient, it must be marked.\n\nIn sentence 14: \"tirti argi kamgi deːccirsa\" \nIf \"tirti\" is repair, and \"argi\" is a preposition meaning \"to\", then \"repair to the camels for the farmers\"? No.\n\nBut \"deːccirsa\" likely means \"to the farmers\"\n\n\"argi\" must then be the verb.\n\nBut \"repair\" and \"give\" are different.\n\nUnless the verb is \"argi\", and \"tirti\" is a typo or misreading.\n\nBut in example 7: \"magas ikki waliːg ticcirsu\" = gave you the dogs → \"ikki\" = gave\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" = gave the camels to the thief → \"magaski\" = gave, \"tirsa\" = to the thief\n\nSo \"magaski\" = give (verb)\n\nSimilarly, in example 3: \"darbadki\" = give\n\nIn sentence 11: \"magasi argi ajomirra\" — if \"argi\" = give, then \"magasi gives ajomirra\" → \"the thief gives the donkey\"\n\nBut again, what is given?\n\nLikely - it's a missing element — or \"give\" is used in a different way.\n\nBut in example 5: \"ay beyyeːcciːg ajaːnirri\" = \"I am buying the necklaces\" — no recipient.\n\nIn sentence 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\" — only object.\n\nSo no recipient.\n\nTherefore, in 11, 12, 13, 14, 15, we must determine if \"argi\" is always the verb \"give\".\n\nIn 14: \"tirti argi kamgi deːccirsa\" \nIf \"argi\" = give, and \"tirti\" is not the verb, then it might be \"give the camels to the farmers\" — but \"tirti\" is there.\n\nUnless \"tirti\" is a subject or something else.\n\n\"tirti\" is likely a verb form — repair.\n\nBut repair can't take \"give\" as a separate verb.\n\nConclusion: in all sentences, verbs are:\n- give: darbadki, argi\n- buy: kanarriːg, beyyeːcciːg\n- repair: tirt, tirti\n- strike: hanu\n\nAnd in all cases, verb + object + recipient (when marked)\n\nNow for sentence 14: \"tirti argi kamgi deːccirsa\" \nBreak down:\n- \"tirti\" = repair (assumed)\n- \"argi\" = possibly a typo or misreading — but only if \"argi\" is give\n- \"kamgi\" = object (camels)\n- \"deːccir", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12034.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.", + "planner_output": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "anchor_output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 1, + "output": "Analyze the verb-object-recipient structure in the examples.\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs\" \n→ verb: darbadki (give), object: biticcirra (chicken), recipient: dogs (marked by -ki)\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ verb: magaski (give), object: kamiːg (camels), recipient: thief (marked by -ki)\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" \n→ verb: aygi (give), object: beyyeːcciːg (necklaces), recipient: me (adeːnda)\n\nEach sentence has: [subject] [verb] [object] [recipient], with recipient marked by a suffix (-ki or -su), object marked by core noun, and verb directly present.\n\nNow consider sentence 11: \"magasi argi ajomirra\"\n\nCompare to sentence 3: \"jahali waliːg darbadki biticcirra\" — \"give the chicken to the dogs\" \n\"darbadki\" = give, \"biticcirra\" = object, \"to dogs\" = recipient.\n\nIn 11: \"magasi\" = subject (the men?), \"argi\" = verb? \"ajomirra\" = recipient? — \"ajomirra\" is similar to \"bijomri\" (donkey) in sentence 9: \"hanuːg bijomri\" = \"I will strike the donkey\". So \"ajomirra\" likely means \"to the donkey\".\n\nBut what is the object? Missing.\n\nSentence 12: \"ay kanarriːg baːbki alletirsi\" \n\"ay\" = I; \"kanarriːg\" = bought (from example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\") — \"kanarriːg\" = bought \n\"baːbki\" = for whom? \"baːbki\" resembles \"jaːnticcirsu\" in example 1: \"for the neighbours\" — \"jaːnticcirsu\" has \"su\" at end → \"for\" \n\"alletirsi\" → \"the doors\"? \"eldeːnsu\" (doors) in example 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = doors, \"for me\" = baːbiːg → \"baːbiːg\" = for? \"baːbiːg\" ends in -gi, not -su. But in 6: \"baːbiːg eldeːnsu\" — \"found the doors for me\" — implied by \"for me\". So \"baːbiːg\" may mark \"for\".\n\nSo in 12: \"ay kanarriːg baːbki alletirsi\" \n= \"I bought the doors for the [person]?\" → \"baːbki\" = for, \"alletirsi\" = doors? → object is doors, recipient is missing.\n\nBut \"baːbki\" → \"for\" → recipient modifier.\n\nSimilarly, sentence 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = I will strike (from example 9: \"hanuːg bijomri\" = I will strike the donkey) \n\"tirtiːg\" = repair? (from example 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\") → \"tirt\" = repair → \"tirti\" = repair \nSo \"tirtiːg\" = repair (verb?) \n\"elirsu\" = for whom? \"elirsu\" → pattern of \"for\" or \"to\"? \"jaːnticcirsu\" = for neighbours; \"eldeːnsu\" = doors — suffix -su likely indicates \"for\".\n\nSo \"hanu tirtiːg elirsu\" → \"I will repair it for [someone]\" → object missing.\n\nSentence 14: \"tirti argi kamgi deːccirsa\" \nPossible structure: verb = argi (give), object = kamgi (camels), recipient = deːccirsa (to the thief) \nBut \"tirti\" = repair? — could \"tirti\" be noun? \"repair\" — like \"tirti\" the thing. \n\"argi\" = verb? — but no example with \"argi\" as verb.\n\nIn sentence 3: \"darbadki\" = give — \"ki\" suffix → recipient \nIn 8: \"magaski\" = give to → \"ki\" \nIn 10: \"aygi\" = give → \"gi\" → \"aygi beyyeːcciːg adeːnda\" = giving → \"gi\" suffix likely marks \"to\"\n\nSo verb markers: -gi (give), -ki (give to), -su (for)\n\n\"argi\" → possible verb form of \"give\"\n\n\"argi\" appears in 11 and 14.\n\nSentence 15: \"ay darbadki bijaːndi\" \n\"darbadki\" = give to \n\"bijaːndi\" = the chickens or pig? \"biticcirra\" = chicken — \"bijaːndi\" → likely chicken \nSo \"ay darbadki bijaːndi\" → \"I will give the chickens to [someone]\" — object = bijaːndi, recipient missing.\n\nNow back to 11: \"magasi argi ajomirra\" \n\"magasi\" = subject? Possibly \"the men\" \n\"argi\" = verb (give) \n\"ajomirra\" = recipient → \"to the donkey\" → since \"bijomri\" = strike donkey → \"ajomirra\" = to the donkey\n\nBut no object.\n\nUnless the object is implied or missing.\n\nCompare with example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" — both object and recipient.\n\nAll verbs in the sequences are three-part: subject + verb + object + recipient.\n\nBut sentence 11 has no object.\n\nIs \"argi\" not the verb?\n\nAlternative: \"argi\" is a prepositional phrase?\n\nBut no object.\n\nAnother possibility: the verb is not \"argi\" but \"tirti\" or \"magasi\"?\n\n\"magasi\" → possibly \"will give\" or \"the men\" — in example 8: \"iːdi magaski kamiːg tirsa\" → \"men gave camels to thief\"\n\n\"magasi\" may be \"the men\" (subject)\n\n\"argi\" is verb → \"give\"\n\n\"ajomirra\" → recipient → \"to the donkey\"\n\nMissing object — but perhaps the object is implied from context or is a default.\n\nSame with sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" = repair, \"argi\" = give, \"kamgi\" = object, \"deːccirsa\" = recipient.\n\nBut \"repair and give\" — not a compound action.\n\nUnlikely.\n\nPerhaps the pattern is: verb-root + object + recipient, and the verb-root has a suffix that indicates direction (to/for).\n\nSo in 11: \"argi\" is the verb root, \"ajomirra\" = recipient (to the donkey), object missing.\n\nBut in all known examples, object is present.\n\nUnless \"magasi\" is the object? Unlikely — subject.\n\nAnother idea: the verb is marked with a suffix for recipient and object is implied.\n\nCheck sentence 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = I will strike \n\"tirtiːg\" = repair? → no verb like \"repair\" in any object-recipient form — example 2 has repair: \"tirt kadeːg allesu\" → repaired the dress — object present, recipient? No recipient marked — only object.\n\nSo in 2: \"tirt kadeːg allesu\" — \"repaired the dress\" — no recipient.\n\nIn 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"for me\" → recipient marked by \"baːbiːg\" → which ends in -gi, like \"aygi\"\n\nSo recipient suffix: -gi, -ki, -su, -biːg\n\nIn 8: \"magaski\" → gives \"to\" → -ki\n\nIn 10: \"adeːnda\" → \"me\" → -nda\n\nSo recipient suffix varies.\n\nBack: in 13: \"hanu tirtiːg elirsu\" → \"I will repair for [someone]\" — so \"tirti\" is verb (repair), object missing.\n\nSimilarly, 14: \"tirti argi kamgi deːccirsa\" → could \"tirti\" be the verb (repair), \"argi\" the object? Or \"argi\" = verb?\n\nBut \"argi\" only appears with object in 11 and 14.\n\nIn sentence 11: \"magasi argi ajomirra\" — likely \"the men gave [something] to the donkey\" — missing object.\n\nBut no object given.\n\nUnless the object is implied from context.\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" — \"I am buying the necklaces\" — object present.\n\nNo recipient.\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" — \"he stole the dresses for the young man\" — \"maːgtirsu\" = for young man — recipient.\n\nSo in 4: object = dresses, recipient = young man.\n\nSo object and recipient are both required when both are marked.\n\nIn sentence 11: object is missing.\n\nOnly \"ajomirra\" = recipient.\n\nSo perhaps the object is missing in translation — only recipient is marked.\n\nSimilarly, sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" = repair, \"argi\" = give, \"kamgi\" = object, \"deːccirsa\" = recipient.\n\nBut \"tirti\" and \"argi\" — two verbs? Unlikely.\n\nAlternative: the sequence is [subject] [verb] [object] [recipient] and the verb is the one with the recipient suffix.\n\nSo in 14: \"tirti\" → repair, \"argi\" → likely not verb.\n\nBut no verb with recipient suffix.\n\n\"argi\" ends in -i — no -ki or -su.\n\n\"tirti\" ends in -i — similar.\n\nPerhaps \"argi\" is a verb meaning \"give\", and it has no recipient suffix.\n\nOnly the object is marked.\n\nBut in example 3: \"darbadki\" has -ki → recipient.\n\nOnly in \"give\" verbs is the recipient marked.\n\nIn repair, no recipient mentioned.\n\nSo only give verbs have recipient suffix.\n\nThus, in sentence 11: \"argi\" = give, \"ajomirra\" = recipient (to the donkey)\n\nObject missing.\n\nBut what is the object? Could it be \"the camels\" or \"the dress\"?\n\nNo reference.\n\nPerhaps the object is the subject or implied.\n\n\"magasi\" = subject.\n\nNo object.\n\nConclusion: the pattern is that the verb is clearly marked by a suffix indicating recipient: -ki, -su, -gi, -biːg.\n\nVerbs like \"give\" have recipient-marked form.\n\n\"repairs\" do not — only object.\n\nSo for give-verbs: [subject] [give-verb] [object] [recipient]\n\nFor repair: [subject] [repair] [object] — no recipient.\n\nNow, in sentence 11: \"magasi argi ajomirra\" — \"argi\" is give-verb, \"ajomirra\" is recipient, but no object.\n\nSo must be missing — perhaps default object?\n\nBut in context, no object is given.\n\nPerhaps \"ajomirra\" is the object?\n\nBut \"ajomirra\" = to the donkey — like \"bijomri\" = strike donkey → so \"to the donkey\"\n\n\"ajomirra\" = to the donkey\n\nSo not object.\n\nOnly possible if \"magasi\" is both subject and object — no.\n\nThus, the sentence is \"The men gave [something] to the donkey\" — object missing.\n\nBut in the other sentences, when recipient is marked, object is present.\n\nSo perhaps in 11, the object is implied from vocabulary or missing.\n\nBut what about sentence 14: \"tirti argi kamgi deːccirsa\"\n\n\"tirti\" = repair — not a give verb\n\n\"argi\" = give\n\n\"kamgi\" = object (camels)\n\n\"deːccirsa\" = recipient (to the thief)\n\n\"tirti\" is likely the verb — repair — and \"argi\" is not a verb.\n\nBut \"argi\" is not used in any repair context.\n\nOnly in give contexts.\n\nTherefore, \"tirti argi\" is not a compound.\n\nConclusion: \"argi\" is a verb meaning \"give\", and in sentences with recipient suffix, it is used with object and recipient.\n\nWhen \"argi\" is used, recipient is marked by a suffix.\n\nIn 11: recipient is \"ajomirra\" → to the donkey → object missing → translation: \"The men gave [something] to the donkey\"\n\nBut what is the object? Not stated.\n\nPerhaps in Kunuz Nubian, the object is implied or the verb is \"give\" with no object — impossible.\n\nAnother possibility: \"magasi\" = give, \"argi\" = to, \"ajomirra\" = donkey — so \"give to the donkey\" — object missing.\n\nBut in 12: \"ay kanarriːg baːbki alletirsi\" \n\"kanarriːg\" = bought (from example 1) — verb \n\"baːbki\" = for (recipient) \n\"alletirsi\" = doors (object)\n\nSo \"I bought the doors for [someone]\" — recipient missing.\n\nSimilarly, sentence 13: \"hanu tirtiːg elirsu\" — \"I will repair for [someone]\" — object missing.\n\nSentence 14: \"tirti argi kamgi deːccirsa\" — if \"tirti\" = repair, \"argi\" = give, object = kamgi, recipient = deːccirsa — but two verbs.\n\nOnly if \"tirti\" is not verb.\n\n\"tirti\" = repair — noun?\n\nIn example 2: \"tirt kadeːg allesu\" — \"repaired the dress\" — verb.\n\nSo \"tirti\" likely verb.\n\nOnly \"argi\" is a give verb.\n\nSo 14 must be: \"repair\" + \"give\" — impossible.\n\nTherefore, the only consistent possibility is that in all cases, the structure is:\n\n[subject] [verb] [object] [recipient], where recipient is marked by a suffix like -ki, -su, -gi, -biːg.\n\nThus, in 11: \"magasi argi ajomirra\" — if \"argi\" is the verb, \"ajomirra\" is the recipient, object missing.\n\nBut in example 5: \"ay beyyeːcciːg ajaːnirri\" — \"I am buying the necklaces\" — no recipient.\n\nNo instance of \"give to X\" without object.\n\nTherefore, the only logical inference is that the object is missing, and the sentence is a give-verb with recipient, and object is left out or implied.\n\nBut we need to translate.\n\nTry 11: \"magasi argi ajomirra\" → \"The men gave [something] to the donkey\"\n\nBest translation: \"The men gave something to the donkey\"\n\nSimilarly, 12: \"ay kanarriːg baːbki alletirsi\" → \"I bought the doors for [someone]\" → \"I bought the doors for the young man?\" — but no name.\n\n\"baːbki\" = for → recipient\n\n\"alletirsi\" = doors → object\n\nSo \"I bought the doors for him\" or \"for the young man\" — but not specified.\n\nIn example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" — \"we bought the camels for the neighbours\" — object: camels, recipient: neighbours.\n\nSo object and recipient both present.\n\nIn 12: \"ay kanarriːg baːbki alletirsi\" — object: alletirsi (doors), recipient: baːbki (for)\n\nSo \"I bought the doors for [someone]\"\n\nNo name.\n\nSimilarly, sentence 13: \"hanu tirtiːg elirsu\" — \"I will repair for [someone]\" — object missing.\n\nIn example 2: \"tirt kadeːg allesu\" — \"repaired the dress\" — object only.\n\nSo no recipient.\n\nIn 13: \"elirsu\" → for someone → recipient.\n\nSo \"I will repair for [someone]\" — object missing.\n\nSentence 14: \"tirti argi kamgi deːccirsa\" — \"repair\" and \"give\" — two verbs?\n\n\"tirti\" = repair, \"argi\" = give, \"kamgi\" = object, \"deːccirsa\" = recipient.\n\nOnly if \"tirti\" is not verb.\n\nBut no evidence.\n\nPerhaps \"argi\" is verb, \"tirti\" is object? Unlikely.\n\nMost plausible: the verb is \"argi\" (give), object = kamgi (camels), recipient = deːccirsa (to the thief)\n\nSo \"give the camels to the thief\"\n\n\"tirti\" may be a typo or misreading — perhaps \"tirti\" is part of a different structure.\n\nBut in 14, it is \"tirti argi kamgi deːccirsa\" — likely \"give the camels to the thief\" — \"argi\" = give, \"kamgi\" = object, \"deːccirsa\" = recipient.\n\n\"t", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12411.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Re-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.", + "planner_output": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "anchor_output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 2, + "output": "Start by analyzing the verb-object-recipient structure from the given examples.\n\nExample 9: \"hanuːg bijomri\" → \"I will strike the donkey.\" \n→ \"hanu\" = strike (verb), \"bijomri\" = the donkey (object). \nSo verb + object. But no recipient.\n\nExample 13: \"hanu tirtiːg elirsu\" → ?? \n\"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirt\" appears in example 2: \"tirt kadeːg allesu\" = \"The owner repaired the dress\" → \"tirt\" = repair verb. \nSo \"tirtiːg\" = future of repair → \"will repair\" (verb). \n\"elirsu\" = ??? → in example 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → \"eldeːnsu\" = for me. \n\"elirsu\" sounds similar to \"eldeːnsu\" → likely also \"for me\". \nSo \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\" — still odd. \nBut if \"tirtiːg\" is noun form (the repair), then \"I will strike the repair to me\"? That doesn’t make sense. \nAlternative: \"hanu\" = strike, \"tirtiːg\" = the repair (noun), \"elirsu\" = to me → \"I will strike the repair to me\" — possible as literal translation, though strange.\n\nBut look at example 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n\"magas\" = thief (subject), \"ikki\" = to you, \"waliːg\" = the young men? No — \"ikki\" likely = to you (recipient), \"waliːg\" = young men? But subject is \"magas\", verb is \"ticcirsu\". \n\"ticcirsu\" = gave? In example 2: \"tirt kadeːg allesu\" — tirt = repair, kadeːg = dress. \nIn example 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave the young men the dogs\"? But \"ikki\" = to you? Then \"to you\" = recipient. \nSo structure: [subject] [verb] [object] [recipient]?\n\nBut \"ikki\" is likely \"to you\", and \"waliːg\" = the young men = object, so \"gave the young men to you\"? That would mean \"gave the young men to you\" — which is idiomatic. \nIn example 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n\"jahali\" = young men, \"waliːg\" = the chicken? No — \"waliːg\" = young men again? Wait, no: \"waliːg\" appears multiple times.\n\nWait: example 3: \"jahali waliːg darbadki biticcirra\" \n→ \"The young men will give the chicken to the dogs.\" \nSo \"darbadki\" = give (verb), \"biticcirra\" = chicken? But \"biticcirra\" = the chicken? Only if \"biticcirra\" is the object. \nBut the recipients are \"the dogs\", which are not mentioned. So where is the recipient?\n\nWait — example 3: \"will give the chicken to the dogs\" → recipient is \"the dogs\". \nBut where is \"to the dogs\" in the structure? \n\nNow, look at example 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repair (verb), \"argi\" = ???, \"kamgi\" = the camels? \"kamgi\" in example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"kamiːg\" = camels. \nSo \"kamgi\" = camels. \n\"deːccirsa\" = ?? → looks like \"deːccir\" + suffix. In example 1: \"jaːnticcirsu\" = for the neighbours? \"jaːnticcir\" = for the neighbours? \nIn example 1: \"kamiːg jaːnticcirsu\" → \"camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. \nSo \"jaːnticcirsu\" = for the neighbours → \"for\" + noun. \nNow, \"deːccirsa\" → could be \"for the camels\"? But \"kamgi\" = camels, so \"deːccirsa\" = for the camels? \nBut \"argi\" is in the middle. \n\nPerhaps the structure is: [verb] [object] [intransitive] → no. \n\nTry example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n\"ay\" = I, \"beyyeːcciːg\" = buying (verb), \"ajaːnirri\" = the necklaces (object). \nSo verb + object — no recipient. \n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n\"sarkaːyi\" = the cowards (subject), \"aygi\" = giving (verb), \"beyyeːcciːg\" = buying? Wait — \"beyyeːcciːg\" is in example 5 as \"buying\". \nSo \"beyyeːcciːg\" = buy (verb), but here it's \"giving\"? Conflict. \n\nWait — \"aygi\" = giving? In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" — \"aygi\" = found? But \"found\" is not \"giving\". \n\"aygi\" in example 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → \"aygi\" = found, \"baːbiːg\" = the doors, \"eldeːnsu\" = for me. \nSo verb + object + recipient. \n\nSimilarly, example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" → \"aygi\" = giving, \"beyyeːcciːg\" = the necklaces (object), \"adeːnda\" = me (recipient). \n\nSo pattern: [subject] [verb] [object] [recipient] — with recipient as \"to me\" or \"for me\" or \"to X\". \n\nNow, example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n\"man\" = he, \"jahalgi\" = stole (verb), \"kadeːcciːg\" = dresses (object), \"maːgtirsu\" = for the young man (recipient). \n\"maːgtirsu\" → \"for the young man\"? In example 3, \"waliːg\" = young men → so \"waliːg\" = young men. \n\"maːgtirsu\" → likely \"for the young man\" (singular). \n\nSo verb + object + recipient — recipient marked by \"for\" or \"to\". \n\nNow example 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" → verb + object. No recipient. \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n\"iːdi\" = men (subject), \"magaski\" = gave (verb), \"kamiːg\" = camels (object), \"tirsa\" = to the thief? → \"tirsa\" → in example 1: \"kamiːg jaːnticcirsu\" → \"for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. \n\"tirsa\" → likely \"to the thief\". So recipient = \"to the thief\". \n\nNow, example 13: \"hanu tirtiːg elirsu\" \n\"hanu\" = strike (verb), \"tirtiːg\" = ???, \"elirsu\" = for me? \n\"tirti\" = repair (from example 2), so \"tirtiːg\" = will repair (future). \nSo \"I will strike the repair for me\"? Still odd. \nBut what if it's \"I will strike the repair to me\"? Then it means \"I will strike the repair (the act) to myself\"? Unnatural. \nAlternative: perhaps \"hanu\" is not a transitive verb here. \n\nWait — \"hanu tirtiːg elirsu\" — but \"hanu\" alone is \"strike\", and \"tirtiːg\" is \"the repair\", so \"I will strike the repair\" → verb + object. \nThen \"elirsu\" = for me → recipient? But \"to me\" is not marked in the verb. \n\nBut in example 9: \"hanuːg bijomri\" — \"I will strike the donkey\" — no recipient. \nIf \"tirtiːg\" is the object, then \"I will strike the repair\", and \"elirsu\" is recipient → \"to me\" → makes sense. \nSo \"I will strike the repair to me\" — meaning I will perform or take action on the repair for myself — possible, if \"strike\" is used in the sense of \"do\" or \"carry out\". \n\nSimilarly, in example 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repair (verb), \"argi\" = ???, \"kamgi\" = camels, \"deːccirsa\" = for the camels? \nBut \"deːccirsa\" = for the camels? → \"deːccir\" would be \"the repair\", not \"camels\". \n\nWait — example 1: \"kamiːg jaːnticcirsu\" → \"camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. \nSo \"jaːnticcirsu\" = for + noun. \nSimilarly, \"elirsu\" = for + me? \n\"eldeːnsu\" = for me → in example 6. \n\"maːgtirsu\" = for the young man → example 4. \n\"tirsa\" = to the thief → example 8. \nSo \"tirsa\" likely = to X. \n\"elirsu\" → sounds like \"eldeːnsu\" → likely \"for me\". \n\"deːccirsa\" → likely \"for the camels\"? But \"deːccirsa\" → deːccir + sa → similar to \"jaːnticcirsu\" → for + something. \nBut \"kamgi\" = camels → so \"deːccirsa\" = for the camels? But \"deːccir\" is not camels. \n\n\"deːccir\" — in example 1: \"jaːnticcirsu\" → \"for the neighbours\", \"jaːnti\" = neighbours? \n\"deːccir\" — could be \"the repair\"? But repair is \"tirt\". \n\nWait — look back at example 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = verb, repair. \n\"argi\" = ??? \n\"kamgi\" = camels \n\"deːccirsa\" = for the camels? \n\nBut \"deːccir\" = repair? Then \"deːccirsa\" = repair for the camels? \nBut then the object would be \"camels\", and the recipient is \"repair for camels\"? That doesn't fit. \n\nAlternative: \"argi\" is the verb. \nIn example 3: \"darbadki\" = give. \nIn example 4: \"jahalgi\" = stole. \nIn example 5: \"beyyeːcciːg\" = buying. \nIn example 6: \"aygi\" = found. \nIn example 10: \"aygi\" = giving. \nSo verbs: \"tirt\" = repair, \"darbadki\" = give, \"jahalgi\" = steal, \"beyyeːcciːg\" = buy, \"aygi\" = find/give. \n\nSo \"argi\" appears in 14: \"tirti argi kamgi deːccirsa\" \nOnly verb in sequence is \"tirti\" → \"tirti\" = repair → so \"repair\" is the verb. \n\"argi\" is not a verb here. So likely \"argi\" is an object. \n\nBut \"argi\" what? In example 9: \"bijomri\" = donkey. \nSo \"ajomirra\" = donkey in 11. \nSo \"argi\" is likely a noun. \n\nIn example 3: \"waliːg\" = young men → nouns. \nIn example 4: \"kadeːcciːg\" = dresses — noun. \nIn example 5: \"ajaːnirri\" = necklaces — noun. \nSo \"argi\" = a noun? → what is \"argi\"? \n\nBut in example 4: \"kadeːcciːg\" = dresses. \nIn example 1: \"kamiːg\" = camels. \nSo \"kamgi\" = camels. \n\"maːgtirsu\" = for the young man. \nIn 14: \"kamgi\" = camels. \n\"deːccirsa\" → must be \"for the camels\"? So \"tirti argi kamgi deːccirsa\" = \"repair argi to the camels\"? \nBut what is \"argi\"? \n\nCould \"argi\" be \"the doors\"? In example 6: \"baːbiːg\" = the doors. \nBut no match. \n\nLook at example 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \nSo \"kanarriːcciːg\" = bought, \"kamiːg\" = camels, \"jaːnticcirsu\" = for the neighbours. \n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object. \n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → verb + object + recipient (adeːnda = me). \n\nSo general pattern: \n- A transitive verb with object and recipient (marked by a preposition + noun or phrase). \n- The recipient is marked by \"for X\" or \"to X\". \n- \"for\" or \"to\" is encoded in a suffix or separate word. \n\nNow, noun classes: \n- \"kamiːg\" = camels \n- \"kadeːg\" = dress \n- \"waliːg\" = young men \n- \"bijomri\" = donkey \n- \"beyyeːcciːg\" = necklaces \n- \"baːbiːg\" = doors \n- \"magas\" = thief \n- \"tirsa\" = the thief (noun?) — in example 8: \"tirsa\" = to the thief → so \"tirsa\" is \"the thief\" as noun. \n\nSo nouns are marked by suffix -g or -ri etc. \n\nNow, example 11: \"magasi argi ajomirra\" \n\"magasi\" = thief (subject) \n\"argi\" = ??? \n\"ajomirra\" = the donkey (object or recipient?) \n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → so \"bijomri\" = object. \nSo \"ajomirra\" = the donkey → object. \n\"argi\" = verb? But \"argi\" is not in the list of known verbs. Known verbs: tirt, darbadki, jahalgi, beyyeːcciːg, aygi, hanu. \n\n\"argi\" is not a verb. But in example 4: \"kadeːcciːg\" = dresses — verb. \n\nIs \"argi\" the object? But in example 11, \"argi ajomirra\" — if \"argi\" is an object and \"ajomirra\" is another object, it's ungrammatical. \n\nCould \"argi\" be a verb? But no verb in the list. \n\nAnother possibility: in example 3: \"jahali waliːg darbadki biticcirra\" → \"young men give the chicken to the dogs\" \n\"waliːg\" = young men (subject), \"darbadki\" = verb (give), \"biticcirra\" = object (chicken), \"biticcirra\" = chicken → so object. \nBut no recipient mentioned. \n\nBut in example 13: \"hanu tirtiːg elirsu\" — if \"hanu\" = strike, \"tirtiːg\" = the repair, \"elirsu\" = for me → \"I will strike the repair for me\" → possible if \"strike\" means \"do\" or \"carry out\". \n\nNow for 11: \"magasi argi ajomirra\" \nIf \"argi\" = verb, what verb? Not found. \nIf \"argi\" = object, \"ajomirra\" = recipient? But \"ajomirra\" = donkey, and recipients are marked by \"for/ to\", not by a full noun. \n\nBut in example 8: \"iːdi magaski kamiːg tirsa\" → \"men gave the camels to the thief\" \n\"magaski\" = gave (verb), \"kamiːg\" = object (camels),", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11177.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Re-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.", + "planner_output": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "anchor_output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 3, + "output": "From the given sentences, identify the consistent verb structure: [subject] [verb] [object] [recipient], where recipient is marked by suffixes like -ki (to) or -su (for). \n\nVerbs in Kunuz Nubian often take an object followed by a recipient. Examples: \n- (3) \"jahali waliːg darbadki biticcirra\" → \"young men will give the chicken to the dogs\" → verb (darbadki = give), object (biticcirra = chicken), recipient (to the dogs) \n- (8) \"iːdi magaski kamiːg tirsa\" → \"men gave the camels to the thief\" → verb (magaski = give), object (kamiːg = camels), recipient (to the thief) \n- (10) \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"cowards are giving me the necklaces\" → verb (aygi = give), object (beyyeːcciːg = necklaces), recipient (to me) \n\nSuffixes: \n- -ki = to \n- -su = for \n- -g, -si, etc. appear in object or possession contexts \n\nNow analyze each sentence in (a): \n\n11. magasi argi ajomirra \n- \"magasi\" = thief (subject) \n- \"argi\" = likely verb \"to give\" (from parallel to \"darbadki\" in (3), \"kadeːcciːg\" in (4)) \n- \"ajomirra\" = to the donkey (common in example 9: \"hanuːg bijomri\" = strike the donkey → bijomri = donkey → ajomirra = to the donkey) \n→ So verb + recipient → but missing object? \n\nBut in example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = object (the donkey), not recipient. \nIn example 13: \"hanu tirtiːg elirsu\" \n- \"hanu\" = to strike \n- \"tirtiːg\" = future of repair (tirti = repair) → \"the repair\" \n- \"elirsu\" = for me → recipient \n→ \"I will strike the repair for me\" → grammatical, though odd \n\nThis suggests: \n- When \"tirtiːg\" is present, it is an object (the repair) \n- \"elirsu\" = for me → recipient \n\nSimilarly, in sentence 14: \"tirti argi kamgi deːccirsa\" \n- \"tirti\" = repair (noun or past verb) \n- \"argi\" = verb \"give\" \n- \"kamgi\" = object (camels?) \n- \"deːccirsa\" = recipient (to the thief) \n→ \"The repair gives the camels to the thief\"? Unlikely. \n\nBut in (4): \"man jahalgi kadeːcciːg maːgtirsu\" = \"stole the dresses for the young man\" \n- jahalgi = steal, kadeːcciːg = dresses, maːgtirsu = for the young man \n\nThus, \"steal\" takes object and recipient. \n\n\"argi\" in (11) and (14) is likely a verb meaning \"give\". \n\nIn (11): \"magasi argi ajomirra\" \n- If \"ajomirra\" = to the donkey, then recipient \n- But no object → invalid \n- If \"ajomirra\" = the donkey, then object → \"magasi gives the donkey\" → implies giving something to it \n\nBut no object is given. However, \"darbadki\" in (3) = give the chicken → object is chicken. \n\nThus, \"argi\" likely means \"give\", and objects are nouns. \n\nSo in (11): \"magasi argi ajomirra\" = \"The thief gives the donkey\" → must be \"gives the donkey\" (to someone), but recipient missing → seems incomplete \n\nCompare to sentence 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = object \n\nSo \"ajomirra\" likely means \"the donkey\" → object \n\nThen \"magasi argi ajomirra\" = \"The thief gives the donkey\" → unknown donor or recipient → not complete \n\nBut in example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient \n\nSo in 11: missing recipient. \n\nBut in 14: \"tirti argi kamgi deːccirsa\" \n- \"tirti\" = repair (noun) \n- \"argi\" = verb (give) \n- \"kamgi\" = object (camels?) \n- \"deːccirsa\" = to the thief? \n\n\"deːccirsa\" = to the thief? But in (2) \"allegsu\" = repair → no recipient \n\"deːccirsa\" likely means \"to the thief\" \n\nBut \"repair gives\" is not idiomatic. \n\nPossible: \"argi\" is not a verb, but a preposition meaning \"to\", and the verb is elsewhere. \n\nBut in (3), \"darbadki\" = give → verb \n\nThen \"argi\" in (11) must be verb → only possible if \"ajomirra\" is object \n\nThus, \"The thief gives the donkey\" — acceptable if we assume the recipient is implied or missing, or if \"ajomirra\" is object \n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → object \n\nSo \"ajomirra\" = the donkey → object \n\nTherefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but \"gives the donkey\" is odd; one does not give a donkey, one strikes it. \n\nBut could it be \"the thief gives (something) to the donkey\"? — no object \n\nAlternative: \"argi\" = to (preposition) → then \"magasi to ajomirra\" = the thief to the donkey — ungrammatical \n\nThus, only viable reading: \"magasi\" = subject, \"argi\" = verb (give), \"ajomirra\" = object (the donkey) → so \"The thief gives the donkey\" → acceptable if a lost object is implied or phonetic slip \n\nBut better: in (3), \"darbadki biticcirra\" → \"give the chicken\", so \"argi\" = give → verb \n\nSo in (11): no object or recipient? That fails. \n\nBut in (14): \"tirti argi kamgi deːccirsa\" \n- \"kamgi\" = object (camels?) \n- \"deːccirsa\" = recipient (to the thief) \n- \"tirti\" = likely noun (the repair) — not verb \n\nSo \"repair gives the camels to the thief\"? Unlikely \n\nBut \"argi\" may be verb → so \"tirti\" = subject? But \"tirti\" is from \"tirt\" (repair), noun \n\nThus, \"the repair gives the camels to the thief\" — possible metaphorically \n\nBut not standard \n\nBetter: the verb is in the root, and \"tirti\" is not the verb — \"argi\" is the verb \n\nSo in all cases, the pattern is: subject (optional), verb, object, recipient (marked by suffix) \n\nIn (11): \"magasi argi ajomirra\" — missing object or recipient? \n\nBut \"ajomirra\" = to the donkey → recipient → only if \"ajomirra\" = to the donkey \n\nIn (9): \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = object \n\nSo \"ajomirra\" = object? But in (13): \"hanu tirtiːg elirsu\" — \"hanu\" = verb, \"tirtiːg\" = object (repair), \"elirsu\" = recipient (for me) \n\nSo \"tirtiːg\" = object (repair), \"elirsu\" = recipient \n\nThus, in (11): \"magasi\" = subject, \"argi\" = verb (give), \"ajomirra\" = object (the donkey) → missing recipient \n\nThis is a problem. \n\nUnless \"argi\" is not the verb — but in (3), \"darbadki\" is verb, \"biticcirra\" object \n\nNo similar verb in (11) or (14) \n\nRe-express: in (14): \"tirti argi kamgi deːccirsa\" → \"tirti\" = subject (the repair), \"argi\" = verb (give), \"kamgi\" = object (camels), \"deːccirsa\" = recipient (to the thief) → \"the repair gives the camels to the thief\" \n\nSimilarly, in (11): \"magasi argi ajomirra\" → \"magasi\" = subject, \"argi\" = verb, \"ajomirra\" = object (the donkey), recipient missing \n\nBut in example 3, recipient is present — e.g., \"to the dogs\" \n\nIn (11), no recipient suffix — \"ajomirra\" = object? → then it must be \"to the donkey\" — suffix? \n\n\"ajomirra\" likely = to the donkey (recipient) — like \"elirsu\" = for me \n\nBut in (9): \"bijomri\" = the donkey (object) \n\nSo \"ajomirra\" = to the donkey → recipient \n\nThus, for (11): subject \"magasi\", verb \"argi\", recipient \"ajomirra\", but no object → invalid \n\nSame in (14): \"tirti\" = subject, \"argi\" = verb, \"kamgi\" = object, \"deːccirsa\" = recipient → valid \n\nSo (11) has no object — only subject, verb, recipient → not consistent \n\nUnless \"argi\" is not a verb \n\nBut in (3), \"darbadki\" = give — verb \n\nSo perhaps \"argi\" is a particle meaning \"to\" or \"for\" \n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me \n\n\"aygi\" = verb (found) \n\n\"baːbiːg\" = object (doors) \n\n\"eldeːnsu\" = recipient (for me) \n\nIn (12): \"ay kanarriːg baːbki alletirsi\" \n\"ay\" = I \n\"kanarriːg\" = verb (buy) — from (1): \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"kanarriːcciːg\" = buy, \"kamiːg\" = object, \"jaːnticcirsu\" = to the neighbours \n\nSo \"kanarriːg\" = buy → verb \n\n\"baːbki\" = object (doors?) — \"baːbki\" = like \"baːbiːg\"? — likely object (doors) \n\"alletirsi\" = to the dog? — \"eldeːnsu\" = for me; \"alletirsi\" = to the dog? \n\n\"alletirsi\" = to the dog (recipient) \n\nThus, \"I am buying the doors to the dog\"? → odd \n\nBut \"kanarriːg\" = buy → verb \n\"baːbki\" = object (doors) \n\"alletirsi\" = recipient to the dog \n\nSo pattern: verb + object + recipient \n\nSimilarly, (13): \"hanu tirtiːg elirsu\" \n\"hanu\" = verb (strike) \n\"tirtiːg\" = object (repair) \n\"elirsu\" = recipient (for me) → so \"I will strike the repair for me\" \n\n(14): \"tirti argi kamgi deːccirsa\" \n\"tirti\" = subject (the repair) \n\"argi\" = verb (give) \n\"kamgi\" = object (camels) \n\"deːccirsa\" = recipient (to the thief) → \"the repair gives the camels to the thief\" \n\nSo in (11): \"magasi argi ajomirra\" \n\"magasi\" = subject (thief) \n\"argi\" = verb (give) \n\"ajomirra\" = recipient (to the donkey) \nbut no object → missing \n\nOnly way: \"ajomirra\" is object — but in (9), \"bijomri\" = object \n\nSo \"ajomirra\" = the donkey → object \n\nThen if no recipient, fails \n\nBut suffix \"ki\" or \"su\" usually marks recipient \n\n\"ajomirra\" = to the donkey → recipient \n\nThus, (11) has subject, verb, recipient — missing object → invalid \n\nConclusion: the only consistent pattern is: \n[subject] [verb] [object] [recipient] with recursive base form matching known verbs \n\nIn (11): \"magasi\" = subject, \"argi\" = verb (give), \"ajomirra\" = to the donkey (recipient) → missing object — thus, likely a mistake in word boundary \n\nBut every other sentence has object and recipient \n\nIn (15): \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = verb (give) \n\"bijaːndi\" = object (chicken?) \n→ \"I will give the chicken\" — missing recipient? \n\nIn (3): \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" — has recipient \n\nSo (15) missing recipient — \"bijaːndi\" must be object or recipient \n\n\"bijaːndi\" = chicken (from \"biticcirra\" in (3), \"biticcirra\" = chicken) \n\nSo in (15): \"I give the chicken\" — recipient missing — likely implied or omitted \n\nThus, sentences (11), (14), (15) have only object or recipient missing — likely due to omission or translation simplification \n\nStandard pattern: verb + object + recipient (with recipient marked by suffix) \n\nFor (11): \"magasi argi ajomirra\" \n→ \"thief gives to the donkey\" → but no object — likely object is missing \n\nBut \"ajomirra\" = to the donkey → recipient \n\nSo verb \"argi\" = give, object missing \n\nUnlikely \n\nUnless \"argi\" is a noun — but \"tirti\" is a noun in (14) \n\nAnother possibility: \"argi\" is a verb, and \"ajomirra\" is the object — the donkey — and recipient is missing \n\nSo \"the thief gives the donkey\" — poor grammar \n\nBut in (9): \"hanuːg bijomri\" = \"I will strike the donkey\" — so noun as object \n\nThus, in (11): \"magasi argi ajomirra\" = \"the thief gives the donkey\" \n\nSimilarly, (12): \"ay kanarriːg baːbki alletirsi\" \n\"ay\" = I \n\"kanarriːg\" = buy (verb) \n\"baːbki\" = object (doors) \n\"alletirsi\" = recipient (to the dog) \n→ \"I buy the doors for the dog\" \n\n(13): \"hanu tirtiːg elirsu\" \n\"hanu\" = strike (verb) \n\"tirtiːg\" = object (the repair) \n\"elirsu\" = recipient (for me) \n→ \"I will strike the repair for me\" \n\n(14): \"tirti argi kamgi deːccirsa\" \n\"tirti\" = subject (repair) \n\"argi\" = give (verb) \n\"kamgi\" = object (camels) \n\"deːccirsa\" = recipient (to the thief) \n→ \"the repair gives the camels to the thief\" \n\n(15): \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give (verb) \n\"bijaːndi\" = object (chicken) \n→ \"I give the chicken\" — recipient missing — likely \"to someone\" but not stated \n\nBut in (3), recipient is present — so likely missing in this instance \n\nBut the only consistent translation is to apply the pattern: verb + object + recipient or subject + verb + object + recipient \n\nIn (11): \"magasi\" = subject, \"argi\" = verb (give), \"ajomirra\" = object (the donkey) → \"The thief gives the donkey\" \nBut not idiomatic \n\n\"ajomirra\" = to the donkey → recipient \n\nSo perhaps \"The thief gives (something) to the donkey\" — but object missing \n\nFinal decision: based on pattern, \"ajomirra\" is the object (the donkey), and \"argi\" is the verb \"give\" \n\nSo (11): \"The thief gives the donkey\" \n\n(12): \"I buy the doors for the dog\" \n\n(13): \"I will strike the repair for me\" \n\n(14): \"the repair gives the camels to the thief\" \n\n(15): \"I give the chicken\" \n\nBut (15) has no recipient — in (3), it has — so this is incomplete \n\nBut in the problem, it is given as is \n\nThus, best translation with pattern: \n\n11. The thief gives the donkey \n12. I buy the doors for the dog \n13. I will strike the repair for me \n14. The repair gives the camels to the thief \n15. I give the chicken \n\nBut \"give the donkey\" is odd — one doesn't give a donkey \n\nAlternative: \"ajomirra\" = to the donkey → recipient \n\nThen (11): subject \"magasi\", verb \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12188.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 402.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "planner_output": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "anchor_output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start by analyzing verb forms and their arguments from the given examples.\n\nIn sentence 1: *ar kanarriːcciːg kamiːg jaːnticcirsu* \n→ \"We bought the camels for the neighbours.\" \nVerb: *kanarriːcciːg* (past tense of \"buy\") \nObject: *kamiːg* (camels) \nPrepositional phrase: *jaːnticcirsu* = for the neighbours \n\nSentence 5: *ay beyyeːcciːg ajaːnirri* \n→ \"I am buying the necklaces.\" \nPresent tense of \"buy\", object *ajaːnirri* (necklaces) — no prepositional phrase\n\nSentence 10: *sarkaːyi aygi beyyeːcciːg adeːnda* \n→ \"The cowards are giving me the necklaces.\" \nVerb: *aygi* = present tense (are giving), object *ajaːnirri*, prepositional phrase *adeːnda* = for me \n\nSentence 3: *jahali waliːg darbadki biticcirra* \n→ \"The young men will give the chicken to the dogs.\" \nVerb: *darbadki* = give (future tense), object *waliːg* (chicken), prepositional phrase *biticcirra* = to the dogs \n\nSentence 2: *tirt kadeːg allesu* \n→ \"The owner repaired the dress.\" \nVerb: *kadeːg* = repaired (past), object *allesu* (dress) — no prepositional phrase \n\nSentence 4: *man jahalgi kadeːcciːg maːgtirsu* \n→ \"He stole the dresses for the young man.\" \nVerb: *kadeːcciːg* = stole (past), object *maːgtirsu* (dresses), prepositional phrase *maːgtirsu*? → no, *maːgtirsu* is object. Wait: “for the young man” → likely *maːgtirsu* = for the young man? But subject is “the young man” → so *maːgtirsu* = for the young man → noun form?\n\nWait: sentence 4: *man jahalgi kadeːcciːg maːgtirsu* \n\"he stole the dresses for the young man\" \nObject: *maːgtirsu* = dresses? Or is *maːgtirsu* = for the young man?\n\nMistake: *kadeːcciːg* = stole, object is *maːgtirsu* → likely \"dresses\", but no match. \"maːgtirsu\" not in earlier list.\n\nBut in sentence 10: *adeːnda* = for me \nIn sentence 1: *jaːnticcirsu* = for the neighbours \nSo \"for X\" = [preposition] + noun\n\nSentence 3: *biticcirra* = to the dogs → \"to\" is different from \"for\"\n\nSo two prepositions:\n- *for* → appears in (1) *jaːnticcirsu*, (4) *maːgtirsu* — but *maːgtirsu* is object? \n\nSentence 4: *man jahalgi kadeːcciːg maːgtirsu* \n\"he stole the dresses for the young man\" → so object = dresses, *maːgtirsu* = for the young man? \nBut *maːgtirsu* is a noun? In sentence 1: *jaːnticcirsu* → for the neighbours → likely *jaːnticcirsu* = for (neighbours) → derived from a noun?\n\nSo structure: [verb] + [object] + [prepositional phrase with noun]\n\nPrepositions:\n- \"for\" = in (1) *jaːnticcirsu* → formed from *jaːntic* + *cirsu*? Possible stem\n- \"to\" = in (3) *biticcirra* (to the dogs), (8) *tirsa* (to the thief)\n\nSo:\n- \"to\" = *biticcirra* (to dogs), *tirsa* (to thief) → likely \"to\" is marked by a form based on recipient noun\n\nTherefore, \"to the owner\" → no direct form, but *tirsa* = to the thief → so for \"to the owner\", we can use *tirsa* with *tirt* = owner\n\nThus, *tirsa* is a form meaning \"to X\", where X is the recipient (owner)\n\nIn sentence 8: *iːdi magaski kamiːg tirsa* → \"the men gave the camels to the thief\"\n\nSo *tirsa* = to the thief → index to the object/recipient\n\nSimilarly, in sentence 3: *biticcirra* = to the dogs → different form\n\nThus, the \"to\" preposition is not always the same — it depends on the recipient\n\nConclusion: “to the owner” → use *tirsa* with *tirt* (owner)\n\nNow, verb for “are giving” → in sentence 10: *sarkaːyi aygi beyyeːcciːg adeːnda* → “the cowards are giving me the necklaces” → present tense of “give” is *aygi beyyeːcciːg*\n\nSo for present tense “are giving” → *aygi* + *beyyeːcciːg*\n\nObject: “the necklace” → from sentence 5: *ay beyyeːcciːg ajaːnirri* → “the necklaces” → object is *ajaːnirri*\n\nSo “necklace” → *ajaːnirri*\n\nTherefore, sentence 16: “The neighbours are giving the necklace to the owner”\n\nStructure:\n- Subject: “the neighbours” → used only in “for the neighbours” → *jaːnticcirsu* → likely *jaːnticcirsu* is not a noun, but indicates the group in prepositional phrase\n\nBut here, subject is “the neighbours” → no standalone noun → how to mark?\n\nIn no sentence is “the neighbours” used as subject noun.\n\nBut in sentence 1: “we bought the camels for the neighbours” → subject is “we”\n\nNo sentence has subject = “neighbours”\n\nThus, subject must be formed or implied.\n\nPossibility: “neighbours” is only expressed in the preposition. So perhaps “the neighbours” cannot be a subject.\n\nBut that contradicts the instruction.\n\nAlternative: perhaps the noun “neighbours” is missing — but we must form a translation.\n\nWait — sentence 1: *jaːnticcirsu* = for the neighbours — so *jaːnticcirsu* is the prepositional form.\n\nBut can we use it as subject? Not directly.\n\nIn Kunuz Nubian, subjects are marked in person or group.\n\nBut here, the only way to form “the neighbours” is via a noun form — not provided.\n\nConclusion: the structure must be: [subject] [verb] [object] [to recipient]\n\n- “are giving” → *aygi beyyeːcciːg*\n- object: *ajaːnirri* (necklace)\n- preposition: “to the owner” → *tirsa* with *tirt* (owner)\n\nNow, subject: “the neighbours” — is there a form?\n\nNo such noun appears. But look at sentence 1: “for the neighbours” → *jaːnticcirsu*\n\nSo is *jaːnticcirsu* a noun? No — it's a preposition.\n\nTherefore, no standalone form.\n\nBut the sentence states “the neighbours are giving” — so subject must be a noun.\n\nOnly possibility: in the absence of a marked noun, perhaps it is implied, but translation must be formed.\n\nAlternative hypothesis: the prepositional phrase in sentence 1 is not \"for\" but \"to\"? But it's for neighbours, and in sentence 3: \"to the dogs\", so it's distinct.\n\nSo for 16: “the neighbours are giving the necklace to the owner”\n\nVerb: present tense → *aygi beyyeːcciːg* \nObject: *ajaːnirri* \nPrepositional phrase: *tirsa* with *tirt* = owner\n\nSubject: “the neighbours” — no noun given → but in sentence 1, “for the neighbours” uses *jaːnticcirsu* — perhaps the subject is already implied, or we must reconstruct.\n\nBut in no sentence is “neighbours” used as subject.\n\nHowever, sentence 1 uses *jaːnticcirsu* in prepositional phrase — so maybe the subject is unstated, but the verb structure requires a subject.\n\nSo we must form a noun.\n\nBut the only noun forms given are:\n- *kamiːg* — camels\n- *waliːg* — chicken\n- *maːgtirsu* — dresses? or young man?\n- *tirt* — owner\n- *jahali* — young men\n- *sarkaːyi* — cowards\n- *man* — he\n\nNo \"neighbours\" noun.\n\nBut in sentence 1: “for the neighbours” — so the form *jaːnticcirsu* may be derived from *jaːntic* + *cirsu*, and the noun might be *jaːntic* or *jaːnti*?\n\nNot established.\n\nBut perhaps in the language, the group is expressed via relational preposition.\n\nSo for subject, we cannot form it.\n\nThus, translation must rely on pattern matching.\n\nBut we have to translate.\n\nPerhaps the structure is: \n[subject noun] [verb] [object] [preposition] \n\nBut subject is missing.\n\nAlternative: in sentence 1, “we bought the camels for the neighbours” — “for the neighbours” = jaːnticcirsu → so “the neighbours” is expressed as *jaːnticcirsu* — a prepositional phrase — so the noun is missing.\n\nSo in 16, \"The neighbours\" must be the subject — so we use the same noun form as the prepositional phrase? Impossible.\n\nConclusion: the only consistent pattern is that verbs have a root with a tense marker and a direct object, followed by a prepositional phrase indicating recipient or purpose.\n\nSo for 16:\n- verb: present \"are giving\" → *aygi beyyeːcciːg*\n- object: *ajaːnirri* (necklace)\n- preposition: “to the owner” → *tirsa* (to) + *tirt* (owner)\n\nSubject: “the neighbours” — not in any stem, so must be inferred from pattern.\n\nBut no noun for \"neighbours\" exists.\n\nThus, the only way is to assume that \"the neighbours\" is a subject marked by a noun form that is not provided.\n\nBut we must produce a translation.\n\nLook at sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" — subject is \"we\", object \"camels\", for \"neighbours\" → so \"neighbours\" is given as a group in prepositional phrase.\n\nSo for sentence 16, subject is \"the neighbours\" — so we must form it.\n\nBut no stem.\n\nPossibility: in the prepositional phrase \"for the neighbours\" → *jaːnticcirsu* = the neighbours? Only if *jaːnticcirsu* is a noun.\n\nBut *jaːnticcirsu* appears to be a prepositional construction.\n\nThus, no standalone noun.\n\nBut is there a noun meaning “neighbours”? Not listed.\n\nThus, failure.\n\nBut perhaps the verb “are giving” is not *aygi beyyeːcciːg*, but the stem is the same.\n\nFrom sentence 10: present tense of \"give\" is *aygi* + *beyyeːcciːg* → so yes.\n\nObject: \"necklace\" → *ajaːnirri*\n\nTo: \"owner\" → *tirt*, with *tirsa* → to\n\nSo full form: [subject] aygi beyyeːcciːg ajaːnirri tirsa tirt\n\nBut what is the subject?\n\nOnly if \"neighbours\" has a stem.\n\nAlternatively, in sentence 1, the phrase \"for the neighbours\" uses *jaːnticcirsu*, which may be a verbal or nominal form.\n\nBut it's clearly used as prepositional.\n\nSo likely, no standalone noun.\n\nTherefore, the only consistent pattern is that the recipient is marked with a prepositional phrase, and the object is direct.\n\nFor 17: \"The young man bought the dog for us.\"\n\nBuy = verb form *kanarriːcciːg* or *kadeːg*\n\nIn sentence 1: \"we bought the camels\" → *ar kanarriːcciːg kamiːg*\n\nSentence 4: \"he stole the dresses for the young man\" → *man jahalgi kadeːcciːg maːgtirsu* → \"stole\" = *kadeːcciːg*, object = *maːgtirsu*\n\nIn sentence 2: \"the owner repaired the dress\" — *tirt kadeːg allesu* → *kadeːg* = repair\n\nBut no \"bought for us\" directly.\n\nSentence 5: \"I am buying the necklaces\" → *ay beyyeːcciːg ajaːnirri*\n\nSo \"buy\" verb = *beyyeːcciːg* or *kanarriːcciːg*\n\nIn 1: *kanarriːcciːg*\n\nIn 5: *beyyeːcciːg* — present form\n\nIn 10: *aygi beyyeːcciːg*\n\nSo past tense \"bought\" = *kanarriːcciːg*, present = *beyyeːcciːg*\n\nFor 17: \"The young man bought the dog for us.\"\n\nSubject: \"the young man\" → from sentence 3: *jahali* = young men\n\nSo likely *jahali*\n\nVerb: \"bought\" → past tense → *kanarriːcciːg*\n\nObject: \"the dog\" → in sentence 3: *waliːg* = chicken → not dog\n\nNo \"dog\" noun.\n\nBut in sentence 6: *baːbiːg eldeːnsu* → \"the dog found the doors for me\" → *baːbiːg* = found, *eldeːnsu* = for me\n\nSo \"dog\" is a noun — *baːbiːg* is verb found.\n\nSo object noun: \"dog\" — missing in list.\n\nBut no noun for \"dog\" — only \"chicken\", \"camels\", \"dresses\", \"necklaces\", \"doors\"\n\nSo “dog” is not in any example.\n\nBut in sentence 6: \"the dog found the doors\" → so the dog is subject.\n\nWe cannot form \"the dog\" as object without a noun.\n\nBut in 17: “bought the dog” — so object = dog.\n\nNo noun given.\n\nSo cannot form.\n\nBut in sentence 3: \"the young men will give the chicken to the dogs\" — object = chicken, recipient = dogs\n\nSo \"chicken\" and \"dogs\" are nouns.\n\nSo nouns exist for: camels, necklaces, dresses, doors, chicken, young men, owner, thief, cowards, dog (in sentence 6)\n\nSo dog is a noun.\n\nWhat is the form?\n\nSentence 6: *baːbiːg eldeːnsu* → \"the dog found the doors for me\"\n\nSo verb *baːbiːg*, object *eldeːnsu*? No — it's \"doors\", not *eldeːnsu*\n\n*eldeːnsu* = for me\n\nSo object of \"found\" is \"doors\" → not given.\n\nBut \"dog\" is subject.\n\nSo object for \"bought\" in 17 = \"the dog\" → so must have a form.\n\nBut no form given for \"dog\".\n\nSimilarly, in sentence 1: \"camels\" = *kamiːg*\n\n\"necks\" = *ajaːnirri*\n\n\"chicken\" = *waliːg*\n\n\"young men\" = *jahali*\n\n\"owner\" = *tirt*\n\n\"thief\" = *ikki* in 7: *magas ikki waliːg ticcirsu* — \"the thief gave you the dogs\"\n\nSo thief = *ikki*\n\nSo dog = unknown.\n\nBut in sentence 3: \"the chickens to the dogs\" → \"biticcirra\" to the dogs\n\nSo \"dogs\" is a noun.\n\nSo the noun forms are:\n- *kamiːg* — camels\n- *ajaːnirri* — necklaces\n- *maːgtirsu* — dresses? or young man? \n In 4: \"for the young man\" → *maːgtirsu* — likely young man\n- *waliːg* — chicken\n- *baːbiːg* — dog? verb? — no, verb is *baːbiːg* = found\n- *tirt* — owner\n- *ikki* — thief\n- *jahali* — young men\n- *sarkaːyi* — cowards\n\nSo \"dog\" is not a noun in any object.\n\nBut in sentence 6: \"the dog found the doors\" → so \"dog\" is a noun, and only appears as subject.\n\nSo object \"the dog\" in 17 — must use a noun form.\n\nBut no form for \"dog\".\n\nThis is a problem.\n\nAlternative: perhaps \"dog\" is not needed as object — but we need to say \"bought the dog\".\n\nSo no form.\n\nBut perhaps the noun is implied.\n\nWe must proceed with pattern.\n\nFor 17: \"The young man bought the dog for us.\"\n\nSubject: \"the young man\" → *jahali* \nVerb: \"bought\" → past tense of \"buy\" → *kanarriːcciːg* \nObject: \"the dog\" — not present in examples — so assume form is *baːbiːg*? No — *baːbiːg* = found \nNo match.\n\nPerhaps in sentence 6, \"the dog found\" — so \"dog\" is a noun, but not given.\n\nSo cannot form.\n\nSimilarly, for 18: \"We will steal him.\"\n\n\"steal\" → in sentence 4: *kadeːcciːg* = stole \nFuture? \"will\" → in sentence 3: \"will", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12580.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".", + "planner_output": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "anchor_output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "We are given a set of English sentences and their Kunuz Nubian translations. Our task is to translate five new sentences into Kunuz Nubian based on observed patterns.\n\nStep 1: Identify key verb forms and syntactic structure.\n\nFrom sentence 1: \n\"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n→ \"kana...\" = bought (past), \"kamiːg\" = the camels, \"jaːnticcirsu\" = for the neighbours.\n\nFrom sentence 2: \n\"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n→ \"tirt\" = the owner, \"kadeːg\" = repaired, \"allesu\" = the dress.\n\nFrom sentence 3: \n\"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n→ \"jahali\" = young men, \"waliːg\" = will (future), \"darbadki\" = give, \"biticcirra\" = chicken, \"tirsa\" = to the dogs.\n\nFrom sentence 4: \n\"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n→ \"man\" = he, \"jahalgi\" = stole, \"kadeːcciːg\" = dresses, \"maːgtirsu\" = for the young man.\n\nFrom sentence 5: \n\"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n→ \"ay\" = I, \"beyyeːcciːg\" = buying (present), \"ajaːnirri\" = necklaces.\n\nFrom sentence 6: \n\"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n→ \"wal\" = the dog, \"aygi\" = found (present), \"baːbiːg\" = doors, \"eldeːnsu\" = for me.\n\nFrom sentence 7: \n\"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n→ \"magas\" = thief, \"ikki\" = you (pl.), \"waliːg\" = will (future), \"ticcirsu\" = dogs.\n\nFrom sentence 8: \n\"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ \"iːdi\" = men, \"magaski\" = gave, \"kamiːg\" = camels, \"tirsa\" = to the thief.\n\nFrom sentence 9: \n\"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n→ \"ay\" = I, \"hanuːg\" = will, \"bijomri\" = strike, \"donkey\" = implied.\n\nFrom sentence 10: \n\"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n→ \"sarkaːyi\" = cowards, \"aygi\" = are giving (present), \"beyyeːcciːg\" = buying (here used differently?), \"adeːnda\" = me.\n\nNote: \"aygi\" is used for present continuous (e.g. \"are giving\"), and appears with present tense verbs.\n\nKey observations:\n\n- The verb \"give\" appears as:\n - \"magaski\" (in sentences 8): \"gave\"\n - \"tirsa\" (in sentence 8): \"to the thief\"\n - \"waliːg\" (in sentence 3): \"will give\"\n- \"For\" → appears in:\n - sentence 1: \"jaːnticcirsu\" = for the neighbours\n - sentence 4: \"maːgtirsu\" = for the young man\n - sentence 6: \"eldeːnsu\" = for me\n- \"To\" → appears in:\n - sentence 8: \"tirsa\" = to the thief\n- \"The\" → used with nouns: \"kamiːg\" (camels), \"kadeːg\" (dress), \"biticcirra\" (chicken), \"beyyeːcciːg\" (necklaces), \"baːbiːg\" (doors), \"tirsa\" (prepositional)\n- Nouns:\n - \"neighbours\" → appears as \"jaːnticcirsu\"\n - \"owner\" → \"tirt\"\n - \"young man\" → \"jahali\"\n - \"dog\" → \"wal\"\n - \"theft\" → \"magas\"\n - \"donkey\" → \"bijomri\"\n - \"chicken\" → \"biticcirra\"\n - \"necklace\" → \"ajaːnirri\"\n - \"dresses\" → \"kadeːcciːg\"\n - \"doors\" → \"baːbiːg\"\n\nPattern for prepositional phrases:\n- \"for\" → marked by suffix: \"jaːnticcirsu\", \"maːgtirsu\", \"eldeːnsu\"\n - \"jaːnticcirsu\" = for the neighbours\n - \"maːgtirsu\" = for the young man\n - \"eldeːnsu\" = for me → \"eldeːnsu\" = for me\n- \"to\" → marked by \"tirsa\" = to the [person]\n - \"tirsa\" is attached directly to verb (e.g., magaski kamiːg tirsa)\n\nTense:\n- \"aygi\" = present continuous (e.g., \"are giving\", \"are finding\")\n- \"waliːg\" = future (e.g., \"will give\")\n- \"hanuːg\" = future (e.g., \"will strike\")\n\nNow, translate the target sentences:\n\n16. The neighbours are giving the necklace to the owner.\n\n- \"The neighbours\" → not a standalone noun; only appears in \"jaːnticcirsu\" → for the neighbours.\n- But in the sentence, \"the neighbours\" is the subject → must be the agent.\n- In sentence 1: \"we bought the camels for the neighbours\" → so \"jaːnticcirsu\" is for, not the subject.\n- So “the neighbours” must be formed as a noun — but is not directly given.\n- In sentence 3: \"The young men will give the chicken to the dogs\" → \"jahali\" = young men, so \"young men\" is a noun.\n- In sentence 4: \"for the young man\" → \"maːgtirsu\" = for the young man → so \"young man\" is a noun phrase.\n- In sentence 8: \"The men gave the camels to the thief\" → \"iːdi\" = men.\n- So “neighbours” may be a noun with a specific form — but not given.\n- However, in sentence 1, \"jaːnticcirsu\" = for the neighbours → so the prepositional phrase for neighbours is formed by suffixing to \"neighbours\".\n- But no standalone form of \"neighbours\" exists.\n- Only possibility: \"neighbours\" is formed as a noun → what do we call the group?\n\nWait: In sentence 1, the prepositional phrase \"for the neighbours\" is \"jaːnticcirsu\". \nSimilarly, \"for the young man\" → \"maːgtirsu\".\n\nSo pattern: \n\"for X\" = [X] + suffix → after labelling X.\n\nThus, \"for the neighbours\" = \"jaːnticcirsu\" \n→ so \"jaːnticcirsu\" may be a form of \"neighbours\", specifically with the prepositional suffix.\n\nBut \"jaːnticcirsu\" = \"for the neighbours\", so it includes both \"neighbours\" and the preposition.\n\nSimilarly, \"maːgtirsu\" = for the young man → \"maːgtirsu\"\n\nSo, \"for the young man\" = \"maːgtirsu\" → implies \"young man\" is \"jahali\" → \"maːgtirsu\" = jahali + suffix.\n\nSo preposition \"for\" is attached via suffix to noun.\n\nTherefore, \"the neighbours\" → must be a noun → \"neighbours\" = ? \nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" is the prepositional phrase.\n\nSo can we extract the noun? \nMaybe the base is \"jaːnti\" or something.\n\nBut no example of \"the neighbours\" as subject.\n\nWe have no verb with \"the neighbours\" as subject.\n\nBut in sentence 3: \"The young men will give the chicken to the dogs\" → subject is \"jahali\" → young men → a group name.\n\nSimilarly, sentence 8: \"The men\" → \"iːdi\" → \"men\"\n\nSo \"neighbours\" may be expressed as a noun phrase — possibly via a noun from the given examples.\n\nSentence 1: \"we bought the camels for the neighbours\" → \"neighbours\" is object of \"for\".\n\nBut no sentence has \"the neighbours\" as subject.\n\nWait: the sentence we are translating is: \"The neighbours are giving the necklace to the owner.\"\n\nSo subject: \"the neighbours\" → we need a noun form.\n\nBut \"neighbours\" only appears in \"jaːnticcirsu\" → which is \"for the neighbours\".\n\nSo \"jaːnticcirsu\" might be the only form — but it's a prepositional phrase.\n\nIs it possible that \"jaːnticcirsu\" is the only form, and the subject is formed via prefix or something?\n\nNo other examples show \"neighbours\" as subject.\n\nAlternative: Is there a word like \"neighbours\" that can be inferred from the pattern?\n\nLooking at sentence 4: \"He stole the dresses for the young man\" → \"maːgtirsu\" = for the young man.\n\nSo \"young man\" = \"jahali\"\n\nThen, \"for the neighbours\" = \"jaːnticcirsu\"\n\nThus, the base form for \"neighbours\" is \"jaːnti\" or \"jaːntiː\"?\n\nSimilarly, \"young man\" = \"jahali\"\n\nSo \"neighbours\" may be \"jaːnti\" as a noun.\n\nBut is it used as subject?\n\nWe have no instance of \"neighbours\" as subject.\n\nBut we must derive it.\n\nAlternative: Is \"the neighbours\" expressed as a prepositional phrase adverb?\n\nUnlikely.\n\nAnother thought: In sentence 8: \"The men gave the camels to the thief\" → \"iːdi\" = men.\n\nIn sentence 1: \"we bought the camels for the neighbours\" → no subject with \"neighbours\".\n\nSo perhaps \"the neighbours\" is formed as \"jaːnti\" or \"jaːntiː\", but only used with \"for\".\n\nBut we need the subject.\n\nWait: sentence 16: \"The neighbours are giving the necklace to the owner.\"\n\nSo we need a subject noun for \"neighbours\".\n\nOnly possibility: \"jaːnti\" or \"jaːntiː\" is the noun.\n\nBut no such form exists in translation.\n\nHowever, in sentence 1, the form \"jaːnticcirsu\" appears — which includes the preposition.\n\nSo likely, the pattern is: \n[subject] + [verb] + [direct object] + [prepositional phrase]\n\nFor example:\n- \"The young men will give the chicken to the dogs\" → \"jahali waliːg darbadki biticcirra\"\n\nSo here:\n- subject = \"jahali\"\n- verb = \"waliːg darbadki\" — \"will give\"\n- object = \"biticcirra\" — chicken\n- recipient = \"tirsa\" — to the dogs\n\nIn 16:\n- subject = \"the neighbours\"\n- verb = \"are giving\" → \"aygi\" (present continuous)\n- object = \"the necklace\" → \"ajaːnirri\"\n- recipient = \"to the owner\" → \"tirsa\" + \"tirt\"\n\nSo if we can find a noun for \"neighbours\", we can build it.\n\nWe see:\n- \"young man\" → \"jahali\"\n- \"owner\" → \"tirt\"\n- \"young men\" → \"jahali\" (plural)\n\n\"neighbours\" — only appears in \"jaːnticcirsu\"\n\nBut \"jaːnticcirsu\" is for the neighbours.\n\nSo likely, \"jaːnti\" is the noun root for \"neighbours\".\n\nSo \"the neighbours\" → \"jaːnti\" or \"jaːntiː\"?\n\nWe have no standalone noun.\n\nBut is it plausible to assume that \"jaːnti\" = neighbours?\n\nBut in the context, we must form it.\n\nCheck sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnti\" → base, \"ccirsu\" = for?\n\nPossibly the suffix is \"-cirsu\" for \"for\".\n\nSimilarly, in sentence 4: \"for the young man\" → \"maːgtirsu\" → \"maːgti\" + \"rsu\"\n\nSo suffix -rsu for \"for\"?\n\nBut sentence 6: \"for me\" → \"eldeːnsu\" → \"elde\" + \"nsu\"\n\nIn sentence 1: \"jaːnticcirsu\" → \"jaːnti\" + \"ccirsu\"? \n\"ccirsu\" vs \"rsu\" → different.\n\nNo consistent suffix.\n\nAnother idea: perhaps \"for\" is not attached to the noun.\n\nIn sentence 1, \"for the neighbours\" is \"jaːnticcirsu\" → so it's one unit.\n\nSimilarly, \"for the young man\" = \"maːgtirsu\" → one unit.\n\nSo \"for X\" = [X] + suffix.\n\nSo for:\n- young man → \"maːgtirsu\"\n- neighbours → \"jaːnticcirsu\"\n\nSo the noun part differs.\n\n\"young man\" = \"jahali\"\n\"neighbours\" = \"jaːnti\" or \"jaːntiː\"\n\nTherefore, likely the noun is \"jaːnti\" — neighbours.\n\nSo subject = \"jaːnti\"\n\nBut is it grammatical?\n\nWe have no example, but pattern suggests it.\n\nSimilarly, in sentence 3: \"The young men\" = \"jahali\" → subject.\n\nSo \"neighbours\" = \"jaːnti\" → subject.\n\nVerb: \"are giving\" = \"aygi\" (as in sentence 10)\n\nDirect object: \"the necklace\" = \"ajaːnirri\" (sentence 5)\n\nRecipient: \"to the owner\" = \"tirsa\" + \"tirt\" (sentence 8)\n\nSo sentence 16: \n\"jaːnti aygi ajaːnirri tirsa tirt\"\n\nBut is \"jaːnti\" acceptable?\n\nNo explicit example — but given the structure, it's the only form.\n\nAlternatively, is \"jaːnticcirsu\" used as subject? No — it's with \"for\".\n\nThus, we conclude: \"the neighbours\" = \"jaːnti\"\n\nSo 16: \"jaːnti aygi ajaːnirri tirsa tirt\"\n\n---\n\n17. The young man bought the dog for us.\n\n- \"The young man\" = \"jahali\"\n- \"bought\" = past tense → verb form: in sentence 5: \"beyyeːcciːg\" = buying, in sentence 4: \"jahalgi\" = stole → past tense?\n- Sentence 1: \"ar kanarriːcciːg\" = bought — past\n- Sentence 4: \"jahalgi\" = stole — past\n- Sentence 5: \"ay beyyeːcciːg\" = buying — present\n\nSo past tense verb: \"kanarriːcciːg\" or \"jahalgi\"\n\nSo \"bought\" → need past form.\n\nWhat is \"bought\" in Kunuz Nubian?\n\nIn sentence 1: \"ar kanarriːcciːg\" = we bought → so \"kanarriːcciːg\" = bought\n\nIn sentence 4: \"jahalgi kadeːcciːg\" → stole\n\nSo \"kanarriːcciːg\" = bought\n\nSo \"bought\" = \"kanarriːcciːg\"\n\nNow, direct object: \"the dog\" → from sentence 3: \"darbadki\" = give the chicken → so \"darbadki\" = give + object?\n\nNo: \"biticcirra\" = chicken\n\nSo \"dog\" not directly named.\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\"\n\nSo \"wal\" = the dog\n\nThus, \"the dog\" = \"wal\"\n\nSo object = \"wal\"\n\nPrepositional phrase: \"for us\" → \"for us\" → in sentence 6: \"eldeːnsu\" = for me\n\nSo \"for us\" → likely \"eldeːnsu\" with \"us\" = plural \"we\"?\n\n\"eldeːnsu\" = for me → singular reflexive.\n\nFor plural, possibly \"eldeːnsu\" adapted?\n\nNo example of \"for us\".\n\nBut in sentence 4: \"for the young man\" → \"maːgtirsu\"\n\nSo \"for us\" is not directly given.\n\nBut in sentence 10: \"The cowards are giving me the necklaces\" → \"adeːnda\" = me\n\nSo \"me\" → \"adeːnda\"\n\nSimilarly, \"us\" → missing.\n\nLikely pattern: \"for us\" = \"adeːnda\" or something?\n\nBut \"adeːnda\" is for me.\n\nNo \"for us\".\n\nBut in sentence 6: \"for me\" → \"eldeːnsu\"\n\nPossibly \"eldeːnsu\" = for me, and \"eldeːnsu\" is used for for us with plural?\n\nUnlikely.\n\nAlternative: perhaps \"for us\" is formed with suffix.\n\nWe see:\n- \"for me\" → \"eldeːnsu\"\n- \"for the young man\" → \"maːgtirsu\"\n\nSo \"for us\" → may be \"eldeːnsu\" generalized?\n\nUnlikely.\n\nBut in sentence 10: \"The cowards are giving me the necklaces\" → \"adeːnda\"\n\n→ \"adeːnda\" = me\n\nSo for us? Not given.\n\nBut no other instance.\n\nWait: sentence 6: \"the dog found the", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12105.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.", + "planner_output": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "anchor_output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "Start with sentence 16: \"The neighbours are giving the necklace to the owner.\"\n\nLook for verbs that match \"are giving\". Sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → present/potential tense with \"waliːg\" (future), verb \"darbadki\" = give. Verb is \"darbadki\" → base form. \nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"kanarriːcciːg\" = bought (past). \nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → present tense, \"ay\" = I, verb \"beyyeːcciːg\" = buying → present progressive. \nSo \"are giving\" is likely formed with \"aygi\" (present), as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"cowards are giving me the necklaces\" → \"aygi\" = present. \n\nSo \"are giving\" → \"aygi\" + verb stem \"darbadki\" → \"aygi darbadki\" (if object is present). \n\nNow object: \"the necklace\" → in sentence 5: \"beyyeːcciːg ajaːnirri\" → \"necklaces\" → object noun is \"ajaːnirri\". \nSo \"necklace\" is \"ajaːnirri\". \n\nNow recipient: \"to the owner\" → in sentence 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\" → \"kadeːg\" = repaired. \nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to the thief → recipient. \nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. \nSo \"for\" = eldeːnsu; \"to\" = tirsa (specific recipient). \nThus, \"to the owner\" = \"tirt\" + \"tirsa\" → \"tirt tirsa\". \n\nSo 16: subject = \"the neighbours\" → where is this? \nNo sentence uses \"the neighbours\" as subject. It only appears in \"for the neighbours\" → \"jaːnticcirsu\" → this is a prepositional phrase. \n\nSo cannot use \"jaːnticcirsu\" as subject. Instead, how is subject formed? \n\nSentence 1: \"ar\" = we, so subject = possessive or pronoun. \nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"man\" = he, subject. \nSentence 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\" → \"ikki waliːg\" → future, \"ticcirsu\" = gave → \"ticcirsu\" = verb form. \nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"iːdi\" = the men, subject. \n\nSo subject nouns are used directly: \"the men\", \"the thief\", \"he\". \n\nBut \"neighbours\" — is there a noun? In sentence 1: \"jaːnticcirsu\" = for the neighbours — so the phrase \"jaːnticcirsu\" has a noun meaning \"the neighbours\". But it is used as a preposition. \n\nHowever, in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"cowards are giving me the necklaces\" → \"sarkaːyi\" = cowards, subject. \n\nSo subject can be a noun phrase. But is \"neighbours\" a noun? We have no direct noun for \"neighbours\". \n\nBut perhaps \"neighbours\" is expressed by a noun form that appears elsewhere. \n\nWait — sentence 1: \"we bought the camels for the neighbours\" → object is \"camels\", recipient is \"neighbours\" → \"jaːnticcirsu\" = for the neighbours. \n\nBut is \"jaːnticcirsu\" used as a noun? No — only as a prepositional phrase. \n\nSo perhaps the subject of 16 is missing. \n\nBut all other sentences have subjects: \"we\", \"he\", \"the men\", \"the dog\", \"cowards\", \"the thief\". \n\nSo for 16, who is \"the neighbours\"? It must be a subject noun. \n\nNow, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"iːdi\" = the men. \n\nIn sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → \"jahali\" = young men. \n\nIn sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"jahalgi\" = young man. \n\nAh — \"jahali\" = young men; \"jahalgi\" = young man. \n\nSo \"young men\" = \"jahali\", \"young man\" = \"jahalgi\". \n\nNow, sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours. \n\n\"jaːnticcirsu\" = for the neighbours. \n\nBut could \"neighbours\" be expressed in a different way? Perhaps a noun like \"kamiːg\" (camels) is a noun. \n\nBut no noun for neighbours. \n\nWait — can \"neighbours\" be a subject formed from a possessive or a compound? \n\nWe must find a pattern in verb structure and prepositional use. \n\nLook at verb agreement: \n\n- Sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I (singular) → \"ay\" → verb \"beyyeːcciːg\" → present of \"buy\". \n- Sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → plural \"sarkaːyi\" → \"aygi\" → present. \n\nSo verb form depends on subject: present tense → \"aygi\" for plural, \"ay\" for singular. \n\nBut in sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men\" (plural) → \"waliːg\" → future tense. \n\n\"waliːg\" = future of \"give\"? \n\nSentence 1: \"ar kanarriːcciːg\" → past of \"buy\". \n\nSo verb forms vary. \n\nBut for \"are giving\" → we have \"aygi\" (present) used in sentence 10 with plural subject \"sarkaːyi\". \n\nSo \"are giving\" = \"aygi\" + verb stem. \n\nNow, verb \"give\" → in sentence 3: \"darbadki\" → present? Or future? \"waliːg\" is future. \n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → past tense \"magaski\" = gave. \n\nSo \"gave\" → past, \"give\" → present/future. \n\nBut sentence 5: \"ay beyyeːcciːg\" → present of \"buy\". \n\nSo likely, \"give\" = \"darbadki\" (present), \"gave\" = \"magaski\" (past). \n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"aygi\" = present. \n\nSo present tense verb = \"aygi\" + verb stem. \n\nSo \"are giving\" = \"aygi darbadki\" — this seems to be the pattern. \n\nNow object: \"the necklace\" → in sentence 5: \"ajaːnirri\" — \"necklaces\" → plural. \n\nIn sentence 10: \"beyyeːcciːg adeːnda\" → \"necklaces\" object → \"beyyeːcciːg\" → \"buying\" → object \"ajaːnirri\". \n\nSo object noun = \"ajaːnirri\" → \"necklace\" is \"ajaːnirri\". \n\nNow recipient: \"to the owner\" → in sentence 2: \"tirt kadeːg allesu\" → \"owner repaired dress\" → \"kadeːg\" = repaired. \n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to the thief. \n\nSo \"to\" = \"tirsa\" + noun → \"tirt tirsa\" → \"the thief\" with \"to\". \n\nSo \"to the owner\" = \"tirt tirsa\" → \"tirt\" = owner, \"tirsa\" = to. \n\nNow subject: \"the neighbours\" — is there a noun? \n\nNo noun form for neighbours appears as standalone subject. \n\nBut in sentence 1: \"for the neighbours\" → \"jaːnticcirsu\". \n\nCould \"jaːnticcirsu\" be used as subject? Only if it means \"the neighbours\" as a noun. \n\nIs there a sentence where \"jaːnticcirsu\" is subject? No. \n\nBut perhaps \"neighbours\" is expressed as \"kamiːg\" (camels)? No. \n\nWait — in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → subject = \"ar\", object = \"kamiːg\" (camels), recipient = \"jaːnticcirsu\" (for neighbours). \n\nSo \"jaːnticcirsu\" cannot be a subject phrase. \n\nBut maybe the subject is implied? No — all sentences have a subject. \n\nUnless \"the neighbours\" is expressed in a way like \"the young men\". \n\nPossibly, \"neighbours\" is not a noun, but a prepositional phrase used in object position or something else. \n\nBut we need to form a sentence. \n\nPerhaps \"the neighbours\" is not a noun, but we have to use a subject noun from context. \n\nIs there a noun like \"neighbour\" or \"people\"? \n\nNo explicit form. \n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. \n\n\"maːgtirsu\" = for + young man. \n\nSo for + noun → \"maːgtirsu\" = for the young man. \n\nSimilarly, \"jaːnticcirsu\" = for the neighbours. \n\nSo prepositional phrase = for + noun. \n\nTherefore, the noun \"neighbours\" is absent as a standalone. \n\nBut in 16, subject is \"the neighbours\" → must be a noun phrase. \n\nNo such noun in the dictionary. \n\nBut note: in sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me → possessive. \n\nSo \"for me\" = \"eldeːnsu\", \"for the owner\" = \"tirt eldeːnsu\"? But no. \n\nIn sentence 8: \"to the thief\" = \"tirsa\" with \"tirt\". \n\nSo \"to the owner\" = \"tirsa\" with \"tirt\". \n\nSo for recipient: \"tirsa\" + noun. \n\nFor subject: we have no form. \n\nBut perhaps \"the neighbours\" is not directly a subject, but we have to use a noun that matches in meaning. \n\nWhat about \"kamiːg\" — camels? No. \n\n\"tirt\" — owner. \n\n\"waliːg\" — young men. \n\n\"man\" — he. \n\nSo the subject must be a noun that means \"neighbours\". \n\nWe have no such form. \n\nBut in the prepositional phrases, \"jaːnticcirsu\" appears with \"for\". \n\nSo perhaps the translation is: [Subject] [aygi] [ajaːnirri] [tirsa] [tirt] \n\nBut what is the subject? \n\nUnless the sentence uses \"jaːnticcirsu\" as subject. \n\nSuppose we try: \"jaːnticcirsu aygi ajaːnirri tirsa tirt\" \n\nIs this grammatical? \n\n\"jaːnticcirsu\" as subject — would mean \"the neighbours are giving...\" — possible. \n\nBut in sentence 1, \"jaːnticcirsu\" is used as object of \"for\", not subject. \n\nCould it be used as subject? In the absence of a better option, and given that \"for the neighbours\" is the only mention, perhaps it is used as a subject word. \n\nNo direct evidence. \n\nBut in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" — \"cowards are giving me the necklaces\" — \"sarkaːyi\" = cowards → subject. \n\nSo subject is a noun. \n\nIn that case, \"neighbours\" must be a noun. \n\nBut no such noun form is in the data. \n\nWait — could \"jaːnticcirsu\" be a noun meaning \"the neighbours\" in a different construction? \n\nPossibly. It is not used as a preposition elsewhere. \n\nIn sentence 1: \"for the neighbours\" = \"jaːnticcirsu\" — this is a prepositional phrase. \n\nBut in a different sentence, it could be used as a subject. \n\nHowever, we lack evidence. \n\nAlternative: maybe \"neighbours\" is expressed by a possessive or a relative. \n\nBut no such pattern. \n\nPerhaps the subject is \"we\", but that isn't specified. \n\nBut 16: \"The neighbours are giving\" — not \"we\". \n\nSo must be specific. \n\nThus, despite lack of direct use, since \"jaːnticcirsu\" is the only form for \"neighbours\", and in other cases \"for\" is used with it, perhaps in the absence of a better form, it can be used as subject. \n\nSo assume: subject = \"jaːnticcirsu\" (neighbours) → \"jaːnticcirsu aygi ajaːnirri tirsa tirt\" \n\nBut object is \"necklace\" = \"ajaːnirri\"? \n\nIn sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → plural. \n\nBut \"necklace\" singular? \n\nIn sentence 16: \"the necklace\" — singular. \n\nSo object = \"ajaːnirri\" — plural. \n\nBut is \"ajaːnirri\" singular or plural? \n\n\"necklaces\" → plural, \"necklace\" → singular? \n\nIn sentence 5: \"necklaces\" → plural. \n\nBut the object in 16 is \"a necklace\" — singular. \n\nSo is there a singular form? \n\nNo singular form shown. \n\n\"ajaːnirri\" is likely the noun, and context determines number. \n\nIn \"I am buying the necklaces\" → plural. \n\nIn \"giving the necklace\" → could be singular. \n\nBut in absence of a singular, perhaps \"ajaːnirri\" is used for both. \n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"giving me the necklaces\" → plural. \n\nSo object is plural. \n\nBut the sentence says \"the necklace\" — singular. \n\nContradiction. \n\nSo perhaps \"ajaːnirri\" can be used for singular. \n\nOr perhaps the noun is \"ajaːniri\" or something. \n\nNo indication. \n\nBut in sentence 5: \"ajaːnirri\" is used with \"necklaces\" → plural. \n\nSo likely, \"the necklace\" → singular might be \"ajaːniri\"? Not present. \n\nPerhaps the noun is used in plural form, and \"a\" is implied. \n\nIn many languages, \"a necklace\" is expressed in plural form. \n\nSo likely, \"ajaːnirri\" is the object. \n\nSo we proceed. \n\nThus, 16: \"jaːnticcirsu aygi ajaːnirri tirsa tirt\" \n\nNow 17: \"The young man bought the dog for us.\" \n\nSubject: \"the young man\" → in sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" → \"jahalgi\" = young man. \n\nSo \"young man\" = \"jahalgi\". \n\nVerb: \"bought\" → in sentence 1: \"kanarriːcciːg\" → past of \"buy\". \n\nSo \"bought\" = \"kanarriːcciːg\". \n\nObject: \"the dog\" → in sentence 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\" → \"kadeːg\" = dress. \n\nSo \"dog\" — not present. \n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"wal\" = dog. \n\nSo \"dog\" = \"wal\". \n\n\"for us\" → \"us\" = plural, \"for us\" = \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me → singular. \n\nSo \"for us\" = plural form? Not given. \n\nBut in sentence 6: \"eldeːnsu\" = for me. \n\nSo likely, \"for us\" = \"eldeːnsu\" with plural prefix? \n\nNo such form. \n\nPerhaps \"eldeːnsu\" is general, and \"us\" is implied. \n\nBut in sentence 4: \"for the young man\" = \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12317.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Shift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.", + "planner_output": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "anchor_output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "The key is to identify the verb, tense, object, and prepositional structure from the given examples.\n\nFirst, observe the verb forms:\n\n- Sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" \n Verb: kanarriːcciːg (buy), object: kamiːg (camels), prepositional phrase: jaːnticcirsu (for the neighbours)\n\n- Sentence 2: \"tirt kadeːg allesu\" → \"the owner repaired the dress\" \n Verb: kadeːg (repair), object: allesu (dress)\n\n- Sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" \n Verb: darbadki (give), tense: waliːg (future), object: biticcirra (to the dogs)\n\n- Sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"he stole the dresses for the young man\" \n Verb: kadeːcciːg (steal), object: maːgtirsu (dresses), prepositional phrase: for young man (implied)\n\n- Sentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" \n Verb: beyyeːcciːg (buy), tense: ay (present), object: ajaːnirri (necklaces)\n\n- Sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" \n Verb: aygi (present), object: baːbiːg (doors), prepositional phrase: eldeːnsu (for me)\n\n- Sentence 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you (pl.) the dogs\" \n Verb: magas (gave), tense: ikki (present), object: ticcirsu (the dogs)\n\n- Sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" \n Verb: magaski (give), tense: iːdi (present), object: kamiːg (camels), prepositional phrase: tirsa (to the thief)\n\n- Sentence 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" \n Verb: hanuːg (strike), tense: ay (present), object: bijomri (donkey)\n\n- Sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\" \n Verb: aygi (present), object: beyyeːcciːg (necklaces), prepositional phrase: adeːnda (for me)\n\nNow identify patterns:\n\n- \"buy\" appears as beyyeːcciːg, with optional object and prepositional phrase.\n- \"give\" appears as magaski or darbadki with object and prepositional phrase.\n- \"for\" is marked by eldeːnsu (e.g., \"for me\", \"for the young man\")\n- \"to\" is marked by biticcirra or tirsa:\n - biticcirra = to the dogs\n - tirsa = to the thief\n So \"to X\" uses a form like \"tirsa\" or \"biticcirra\" with the noun X.\n\nFor translation 16: \"The neighbours are giving the necklace to the owner\"\n\n- Tense: present → \"aygi\" (from sentence 5 and 10, \"aygi\" marks present)\n- Verb: \"give\" → \"magaski\" (from sentence 8: \"gave to the thief\")\n- Object: \"necklace\" → \"ajaːnirri\" (from sentence 5: \"necklaces\")\n- Preposition \"to the owner\" → \"tirsa\" (to the thief), so \"to the owner\" → \"tirsa\"\n- Subject: \"the neighbours\" — no standalone noun. But in sentence 1, \"jaːnticcirsu\" = for the neighbours. Is it possible that \"jaːnticcirsu\" is a noun meaning \"the neighbours\"?\n\nBut in sentence 1, it's used as \"for the neighbours\", not as a subject. So it's clearly a prepositional construction.\n\nNo other sentence uses \"neighbours\" as a subject. So the only possible way is to assume that in the absence of a direct noun, the subject is formed with a noun that is used in preposition. But that can't be.\n\nWait — in sentence 1: \"we bought the camels for the neighbours\" — the verb is \"kanarriːcciːg\", not \"magaski\". So \"give\" is magaski, \"buy\" is kanarriːcciːg.\n\nBut is there a possibility that \"jaːnticcirsu\" functions as a noun? Unlikely — it ends in -cirsu, and is used in prepositional form.\n\nAlternatively, perhaps the subject is not specified, or is implied. But we need to form a sentence.\n\nAnother possibility: is \"the neighbours\" simply the subject with an empty noun? No — no such structure.\n\nBut in sentence 5: \"ay beyyeːcciːg ajaːnirri\" — \"I am buying the necklaces\" — no prepositional phrase.\n\nIn sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" — \"the cowards are giving me the necklaces\" — subject is \"sarkaːyi\", object is \"necklaces\", prepositional phrase \"adeːnda\" = for me.\n\nSo all verbs take object and optionally a prepositional phrase.\n\nBack to 16: \"The neighbours are giving the necklace to the owner\"\n\nWe must have:\n\n- Subject: \"the neighbours\" — not directly lexicalized\n- But in sentence 1, \"jaːnticcirsu\" = for the neighbours — so likely \"jaːnticcirsu\" is used as a phrase meaning \"the neighbours\"\n- But it is used as a preposition, not as a noun.\n\nUnless the prepositional phrase \"for the neighbours\" is a fixed expression and cannot be used as subject.\n\nConclusion: The only way to form the subject is to use a noun form. But none is given.\n\nBut perhaps \"jaːnticcirsu\" can serve as a noun for \"the neighbours\", even if used in preposition?\n\nNo — in sentence 1, it's clearly \"for the neighbours\", not \"the neighbours\".\n\nSo contradiction.\n\nAlternative: Look at sentence 3: \"jahali waliːg darbadki biticcirra\" — \"the young men will give the chicken to the dogs\"\n\n\"the young men\" is subject → \"jahali\" (young men)\n\nNo \"neighbours\" subject.\n\nThus, no example of \"the neighbours\" as a subject.\n\nTherefore, we must conclude that the subject is missing — but that can't be.\n\nPerhaps the verb form can be used with a prepositional phrase to modify the subject? Unlikely.\n\nWait — what if the prepositional phrase \"to the owner\" is used similarly to \"for the neighbours\".\n\nBut in sentence 1, \"for the neighbours\" is used as a prepositional phrase.\n\nIn sentence 8, \"to the thief\" uses \"tirsa\".\n\nSo in 16, \"to the owner\" → \"tirsa\" with \"tirt\"\n\nSo \"tirsa\" is used with a noun for the recipient.\n\nBut what about the subject? \"The neighbours\" — is there any noun for it?\n\nOnly in \"jaːnticcirsu\", which is used in prepositional form.\n\nThus, perhaps the subject is \"jaːnticcirsu\" as in \"the neighbours\", even though it's used in preposition.\n\nBut that would be ungrammatical.\n\nAlternatively, perhaps the structure is: [subject] [verb] [object] [preposition to recipient]\n\nWe know:\n\n- Subject: the neighbours → unknown form\n- Verb: present tense of \"give\" → \"aygi\" or \"magaski\" — in sentence 5, \"ay beyyeːcciːg\" for \"buy\", so \"give\" is \"magaski\" (sentence 8: \"iːdi magaski kamiːg tirsa\")\n- Object: \"necklace\" → \"ajaːnirri\"\n- Preposition to: \"tirsa\" with \"tirt\"\n\nNow, sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" — \"the cowards are giving me the necklaces\" — \"adeːnda\" = for me\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" — \"the dog found the doors for me\" — \"eldeːnsu\" = for me\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" — \"the men gave the camels to the thief\" — \"tirsa\" = to the thief\n\nSo \"to\" is marked by \"tirsa\", and \"for\" by \"eldeːnsu\"\n\nSo \"to the owner\" → \"tirsa\"\n\n\"tirt\" means \"the owner\"\n\nSo recipient part: \"tirsa\"\n\nVerb: \"give\" → \"magaski\" (present: \"iːdi\" in 8, but first person is \"aygi\" in 10 — \"aygi\" is present)\n\n\"aygi\" in 5 and 10 is present. \"iːdi\" is present too.\n\nSo present is \"aygi\" or \"iːdi\" — both present.\n\nSo \"are giving\" = \"aygi\"\n\nSo verb = \"aygi magaski\"\n\n\"Object\" = \"ajaːnirri\"\n\n\"Recipient\" = \"tirsa\" with \"tirt\"\n\nSo full: \"jaːnticcirsu aygi magaski ajaːnirri tirsa tirt\"\n\nBut is \"jaːnticcirsu\" used as subject?\n\nIt cannot, because in sentence 1, it is used as \"for the neighbours\", not as subject.\n\nSo not valid.\n\nBut is there another noun?\n\nPerhaps \"neighbours\" is not needed — maybe the subject is implied or absent? No.\n\nOr perhaps the verb can be used with the prepositional phrase as a subject modifier? Unlikely.\n\nWait — sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" — we bought the camels for the neighbours\n\nSo \"jaːnticcirsu\" = for the neighbours\n\n\"neighbours\" is not a noun.\n\nSo no direct way.\n\nBut perhaps \"jaːnticcirsu\" is a noun — but only in prepositional use.\n\nThus, no lexical form for \"neighbours\".\n\nSo the only possible conclusion is that the subject is \"jaːnticcirsu\" as in \"the neighbours\", despite its prepositional use.\n\nPerhaps in Kunuz Nubian, such phrases can function as nouns due to context.\n\nBut no evidence.\n\nPerhaps \"the neighbours\" is not required — but it is.\n\nWait — perhaps the structure is symmetric.\n\nIn sentence 3: \"jahali waliːg darbadki biticcirra\" — subject = \"jahali\" (young men)\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" — subject = \"iːdi\" (the men)\n\nIn 16, subject = \"neighbours\" — not in any example.\n\nThus, if we must form it, and no word for \"neighbours\", perhaps it is formed from \"jaːnticcirsu\" as a noun.\n\nAlternatively, maybe the verb \"give\" is used with a bare prepositional phrase to show directness.\n\nBut here, we have no choice.\n\nSo we proceed with:\n\n16. The neighbours are giving the necklace to the owner \n→ \"jaːnticcirsu aygi magaski ajaːnirri tirsa tirt\"\n\nBut in sentence 1, \"jaːnticcirsu\" is \"for the neighbours\" — so it can't be a subject.\n\nSo this fails.\n\nUnless in Kunuz Nubian, the same form can be used as a noun.\n\nBut no support.\n\nAnother idea: perhaps the object is not \"necklace\" but \"necklace\" is \"ajaːnirri\", and in 5, \"ajaːnirri\" is object.\n\nYes.\n\nFor 17: \"The young man bought the dog for us\"\n\n- \"bought\" → \"kanarriːcciːg\" (sentence 1)\n- subject: \"the young man\" → from sentence 3, \"jahali\" = young men — so \"jahali\" = young man? Possibly\n- object: \"dog\" — not directly given, but in sentence 7: \"gave you the dogs\" — \"ticcirsu\" = dogs\n- so \"dog\" = \"ticcir\" or \"ticcirsu\"\n- \"for us\" → \"eldeːnsu\" (sentence 6: \"for me\", so likely \"eldeːnsu\" for \"for us\")\n\nSo \"jahali kanarriːcciːg ticcirsu eldeːnsu\"\n\nBut \"ticcirsu\" is \"dogs\", so \"dog\" may be \"ticcir\" or \"ticcirsu\" — but only \"dogs\" appears.\n\nIn sentence 7: \"ticcirsu\" = the dogs — so \"dog\" is likely \"ticcirsu\"\n\nSo \"jahali kanarriːcciːg ticcirsu eldeːnsu\"\n\nFor 18: \"We will steal him\"\n\n- \"will\" = future — in sentence 3: \"waliːg\" = will\n- \"steal\" = kadeːcciːg (sentence 4: \"stole the dresses\")\n- \"him\" = personal pronoun — not given\n\nNo personal pronoun in translation.\n\nIn sentence 4: \"he stole the dresses for the young man\" — \"he\" is not in the form.\n\nSo \"him\" — not in given examples.\n\nLikely \"maːgtirsu\" or \"maːg\" — not found.\n\nIn sentence 4: \"maːgtirsu\" = for the young man — so not for \"him\".\n\nNo \"him\".\n\nSo must infer as a pronoun.\n\nBut no form.\n\nSentence 9: \"I will strike the donkey\" — \"bijomri\" = donkey.\n\nSo no \"him\".\n\nThus, no form for \"him\".\n\nBut in 19: \"The owners struck the thieves\"\n\n- \"owners\" — not in data\n- \"struck\" — \"hanuːg\" (sentence 9: \"strike\")\n- \"thieves\" — not in data, but in sentence 7: \"the thief\" — \"magas\" = thief\n\nSo \"thieves\" = \"magaːs\" or \"magas\"\n\n\"struck\" = \"hanuːg\"\n\n\"owners\" = not in data\n\nSo probably \"tirt\" or \"tirt\" as owner.\n\nNo word.\n\nIn sentence 7: \"the thief\" = \"magas\"\n\nSo \"owners\" = \"tirt\" or \"tirt\" as plural?\n\nNo.\n\nSimilarly, 20: \"The dogs found the chickens for the coward\"\n\n- \"dogs\" = \"ticcirsu\"\n- \"found\" = \"baːbiːg\" (sentence 6: \"found\")\n- \"chickens\" = not given\n- \"for the coward\" = \"sarkaːyi\" (sentence 10: \"cowards\") — \"sarkaːyi\" = cowards\n\nSo \"chickens\" not given.\n\nBut in context, likely a noun like \"biticcirra\" or something.\n\nNo.\n\nBut the pattern from sentence 3: \"the young men will give the chicken to the dogs\" — \"biticcirra\" = to the dogs\n\nSo \"to\" is marked.\n\nFor prepositional \"for\", \"eldeːnsu\" is used.\n\nSo for 16: \"The neighbours are giving the necklace to the owner\"\n\nWe must have:\n\n- subject: \"neighbours\" — only in \"jaːnticcirsu\" as \"for the neighbours\"\n- verb: \"are giving\" = \"aygi\" (present)\n- object: \"necklace\" = \"ajaːnirri\"\n- to: \"tirsa\" with \"tirt\"\n\nBut no subject noun.\n\nGiven no other option, and that in sentence 1, \"jaːnticcirsu\" is the only form for \"neighbours\", we assume it can be used as subject.\n\nSo 16: \"jaːnticcirsu aygi magaski ajaːnirri tirsa tirt\"\n\nSimilarly, for 17: \"The young man bought the dog for us\"\n\n- \"young man\" = \"jahali\" (from sentence 3)\n- \"bought\" = \"kanarriːcciːg\"\n- \"dog\" = \"ticcirsu\" (from sentence 7, \"dogs\")\n- \"for us\" = \"eldeːnsu\"\n\nSo: \"jahali kanarriːcciːg ticcirsu eldeːnsu\"\n\nFor 18: \"We will steal him\"\n\n- \"we\" = not given, but in sentence 1: \"ar\" = we\n- \"will\" = \"waliːg\" (sentence 3)\n- \"steal\" = \"kadeːcciːg\"\n- \"him\" = likely personal pronoun — not given\n\nBut in sentence 4: \"he stole the dresses for the young man\" — \"he\" not present.\n\nNo personal pronoun.\n\nSo perhaps \"maːgtirsu\" = for young man — not \"him\".\n\nNo form.\n\nBut in sentence 7: \"you\" = \"ikki\" (gave you) — not used.\n\nSo no.\n\nPerhaps \"him\" is \"magaːs\" or something.\n\nBut in 19: \"The owners struck the thieves\"\n\n- \"owners\" = not given\n- \"struck\" = \"hanuːg\"\n- \"thieves\" = \"magas\"\n\nSo \"tirt\" for owners? \"tirt\" = owner\n\nSo \"tirt hanuːg magas\"\n\nFor 20: \"The dogs found the chickens for the coward\"\n\n- \"dogs\" = \"ticcirsu\"\n- \"found\" = \"baːbiːg\"\n- \"", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12423.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 388.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "planner_output": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "anchor_output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 0, + "output": "Start by analyzing the demonstratives and number agreement across the examples to identify patterns.\n\nIn sentence 2: “Lekota dimdim mtona” → “this white man” — “lekota” = this.\n\nIn sentence 3: “Bikota gwadi magudiwena” → “that child” — “bikota” = that, “gwadi” = that, “magudiwena” = child. So “gwadi” independently modifies “magudiwena” (child), meaning “that child”.\n\nIn sentence 4: “Legisi waga makesiwena namwaya minana” → “this old woman saw those canoes” — “legisi” = this, “namwaya” = those.\n\nIn sentence 10: “Legisi dakuna makwena gwadi magudiwena” → “that beautiful child saw this stone” — “gwadi magudiwena” = that child, and “gudimanabweta” = this stone. So “gwadi” modifies “magudiwena” (child), not “dakuna” or “makwena”.\n\nThis shows “gwadi” functions as a demonstrative modifying a noun.\n\nNow look at sentence 16: “Amagudina gwadi lekota?”\n\n- “Amagudina” likely means “which child” (similar to “which man” in sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?”)\n\n- “gwadi” is a demonstrative (meaning “that”)\n\n- “lekota” is a demonstrative meaning “this”\n\nSo the phrase is “which [demonstrative phrase] child?”\n\nNow, can “gwadi lekota” be interpreted in two ways?\n\nIn English, “that this” or “this that” are not standard. But in some languages, demonstratives can be used for relative reference or for polarity.\n\nBut look at the structure: “amagudina gwadi lekota” — which child?\n\nThe only grammatical readings are:\n\n1. “Which that child?” — meaning “which of the that children?” → ambiguous because “that” can refer to a set, or a specific one.\n\n2. “Which this child?” — meaning “which of the this children?” → possible interpretation if “this” is emphasized.\n\nBut both “gwadi” and “lekota” are demonstratives of different reference points.\n\nNo clear example in the data shows “gwadi lekota” as a compound demonstrative.\n\nBut note: in sentence 3, “bikota gwadi magudiwena” — that child — “bikota” and “gwadi” are both used independently.\n\nIn that case, “bikota” = that, “gwadi” = that → both refer to the same thing.\n\nIn sentence 2, “lekota dimdim” = this white man.\n\nIn sentence 4, “legisi” = this woman, “namwaya” = those canoes.\n\nSo demonstratives are used independently and with different nouns.\n\nNow, in 16, “amagudina gwadi lekota” — if “amagudina” means “which child”, then “gwadi lekota” may mean either:\n\n- “that child” → which that child?\n\n- “this child” → which this child?\n\nBut “gwadi” = that, “lekota” = this — so they are opposites.\n\nThe ambiguity arises because the demonstrative applies to a noun phrase with a preposition or quantifier.\n\nBut in the absence of a clear example, the only possible ambiguity is in the interpretation of the demonstrative phrase.\n\nNow, consider sentence 17: “Tevila tauwau bigisesi gugwadi gudigasisi?”\n\n- “Tevila” = how many?\n\n- “tauwau” = two?\n\n- “bigisesi” = chief?\n\n- “gugwadi” = that?\n\n- “gudigasisi” = woman?\n\nSo “how many chiefs did that woman see?” — but “gugwadi” modifies “gudigasisi” (woman)? “gudigasisi” = woman — so “that woman”.\n\nBut note: “gugwadi” = that — so “that woman”.\n\n“bigisesi” = chief? But “bigisesi” is not a standard noun — look back.\n\nIn sentence 12: “Lekalimati natala bunukwa nagasisi guyau tokabitam” → “The clever chief killed one wild pig” — “nagasisi guyau” = wild pig? “guyau” = wild pig.\n\nSo “gudigasisi” likely = woman (same as “magudiwena”).\n\nIn sentence 12: “guyau tokabitam” — “wild pig” — so “gudigasisi” = woman.\n\nIn sentence 17: “bigisesi gugwadi gudigasisi” → possibly “chief that woman” — which doesn’t make sense.\n\nBut “gugwadi” = that, “gudigasisi” = woman → “that woman”.\n\n“bigisesi” = chief?\n\nNot clear.\n\nNow sentence 18: “Legisesi ketala waga vivila minasiwena.”\n\n“legisesi” = that woman?\n\n“ketala” = saw?\n\n“waga” = those?\n\n“vivila minasiwena” = something?\n\n“vivila” = something?\n\n“minasiwena” = that?\n\nSo “that woman saw those something?”\n\nBut “minasiwena” = that?\n\nIn sentence 7: “Bigisi kwetala vivila minawena nakabitam” → “that clever woman will see something” — “minawena” = that.\n\nSo “minasiwena” = that.\n\nThus, “waga vivila minasiwena” = “those something that” → ungrammatical.\n\nBut “vivila” may be a noun like “thing”, and “minasiwena” = that → so “those things that”?\n\nBut “waga” = those → so “those things that” — nominative?\n\nAlternatively, “waga” modifies “vivila” → “those things” — and “minasiwena” modifies “vivila” → “those things that [are that]”?\n\nThis seems flawed.\n\nAlternatively, “vivila minasiwena” = “something that” → so “waga vivila minasiwena” = “those something that” → still odd.\n\nBut in sentence 7, “Bigisi kwetala vivila minawena” → “that clever woman will see something that” — so “minawena” modifies “vivila” → “something that”.\n\nThus, in 18: “waga vivila minasiwena” = “those things that” — so “that woman saw those things that”?\n\nBut “legisesi ketala” = “that woman saw”.\n\nSo “that woman saw those things that” — which is awkward.\n\nBut if “minasiwena” is standalone, could it mean “that”?\n\nBack to 16: is “amagudina gwadi lekota” ambiguous?\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” — “amtona” = which man, “tau” = two, “lekalimati” = killed, “nayu” = pigs.\n\nNo demonstratives here.\n\nNow sentence 14: “Navila vivila biyamata tomwaya mtona?”\n\n- “navila” = how many?\n\n- “vivila” = something?\n\n- “biyamata” = woman?\n\n- “tomwaya” = that?\n\n- “mtona” = this?\n\nSo “how many women will that this woman?” → how many women will that this woman?\n\n“tomwaya” = that, “mtona” = this — similar to 16.\n\nNow, “biyamata” = woman.\n\nSo “how many women will that this woman”?\n\nThis is structurally parallel to 16: “which child” + “that this” → but here it's “how many” + “that this” → which is ungrammatical.\n\nBut “tomwaya” and “mtona” are both demonstratives.\n\nThey cannot apply to the same noun in a binary way.\n\nUnless “tomwaya” is modifying “biyamata”, and “mtona” is also part of a phrase.\n\nIn sentence 10: “legisi dakuna makwena gwadi magudiwena” — “makwena” = child, “gwadi magudiwena” = that child → “gwadi” modifies “magudiwena”.\n\nSimilarly, in 14: “biyamata tomwaya mtona” — could “tomwaya” modify “biyamata”?\n\n“tomwaya” = that → “that woman”?\n\n“mtona” = this → “this woman”?\n\nSo the phrase is “how many women will that this woman”?\n\nThat is ungrammatical.\n\nBut if “biyamata” is the subject, and “tomwaya mtona” is a phrase, it could mean:\n\n- How many women will that woman (that one) → “tomwaya” = that?\n\n- How many women will this woman (this one)? → “mtona” = this?\n\nSo both are grammatical interpretations, depending on which demonstrative is used.\n\nSo in 14: “how many women will that woman?” or “how many women will this woman?”\n\nSimilarly, in 16: “which child” → “that child” or “this child”?\n\nSo both sentences could be ambiguous due to demonstrative ambiguity.\n\nBut which one actually has two possible translations?\n\nNow check sentence 15: “Bikamkwamsi kweyu vivila minasina.”\n\n“bikamkwamsi” = which thing?\n\n“kweyu” = two?\n\n“vivila” = something?\n\n“minasina” = that?\n\nSo “which two things that”?\n\n“minasina” = that → modifies “vivila” → “that something”?\n\nSo “which two things that” — ungrammatical.\n\nBut “kweyu” = two → “two things”?\n\n“minasina” = that → so “those things that”?\n\nThis is awkward.\n\nBut no ambiguity here.\n\nNow sentence 17: “Tevila tauwau bigisesi gugwadi gudigasisi?”\n\n“tevila” = how many?\n\n“tauwau” = two?\n\n“bigisesi” = chief?\n\n“gugwadi” = that?\n\n“gudigasisi” = woman?\n\nSo “how many chiefs did that woman see?”\n\nOr “how many chiefs did two that women see?” — no.\n\n“gugwadi gudigasisi” = “that woman”?\n\nYes — so “how many chiefs did that woman see?”\n\nOnly one reading.\n\nSentence 18: “Legisesi ketala waga vivila minasiwena.”\n\n“legisesi” = that woman?\n\n“ketala” = saw?\n\n“waga” = those?\n\n“vivila” = something?\n\n“minasiwena” = that?\n\nSo “that woman saw those things that” → questionable.\n\nBut if “vivila minasiwena” = something that → “those things that” → “that woman saw those things that” — possible.\n\nBut no ambiguity.\n\nNow back to 14: “Navila vivila biyamata tomwaya mtona?”\n\nIf “tomwaya” = that, “mtona” = this — both demonstratives.\n\nCould it mean:\n\n- How many women will that woman? (tomwaya = that)\n\n- How many women will this woman? (mtona = this)\n\nYes — both are grammatically possible in English.\n\nSimilarly, in 16: “Amagudina gwadi lekota?”\n\n- Which that child? → “which that child” — possibly\n\n- Which this child? → “which this child”\n\nBut in the data, we have “bikota gwadi magudiwena” = “that child” — “bikota” is already “that”, “gwadi” is “that” — so both are that.\n\nNo example of “which this child” or “which that child”.\n\nIn sentence 2: “lekota” = this.\n\nIn sentence 3: “bikota” = that.\n\nSo “gwadi” is used independently as “that”.\n\nBut “gwadi lekota” together — both demonstratives — for a noun like “child” — likely means “that this child” or “this that child” — which are not standard.\n\nBut in 14, “tomwaya mtona” — two demonstratives — could mean “that woman” or “this woman”.\n\nStructure: “how many women will X woman?”\n\nX is “tomwaya” or “mtona”.\n\nSo two possible translations.\n\nNow, is there another?\n\nCheck 15: “Bikamkwamsi kweyu vivila minasina.”\n\n“bikamkwamsi” = which things?\n\n“kweyu” = two?\n\n“vivila” = something?\n\n“minasina” = that?\n\nSo “which two things that” — still awkward.\n\nIf “minasina” modifies “vivila” → “that something” → “which two things that” → no natural reading.\n\nNo ambiguity.\n\nSentence 17: clearly “how many chiefs did that woman see?”\n\nSentence 18: “that woman saw those things that”\n\nNo ambiguity.\n\nTherefore, only sentence 14 and 16 are suspect.\n\nBut in 16, “amagudina gwadi lekota” — “which child” — could it mean “which that child” or “which this child”?\n\nBut “gwadi” and “lekota” cannot be used jointly as a single demonstrative.\n\nIn prior examples, demonstratives are used with their own nominal heads.\n\nFor instance, “bikota magudiwena” = “that child”.\n\nBut “gwadi lekota” has no precedent.\n\nWhereas in 14: “biyamata tomwaya mtona” — “woman that this” — “tomwaya” and “mtona” both demonstratives.\n\nIn English, “that woman” and “this woman” are distinct.\n\nAnd the sentence is “how many women will [that woman]?” or “how many women will [this woman]?”\n\nThis is perfectly parallel.\n\nHence, sentence 14 has two possible translations.\n\nSentence 16: “which child” with “gwadi lekota” — no such phrase in examples.\n\nIn fact, “amagudina” = which child — and “gwadi” and “lekota” might both be part of a qualifier.\n\nBut without evidence, and given that “gwadi” appears only with nouns like “magudiwena” (child) independently, it is more likely that “gwadi lekota” is a misreading.\n\nTherefore, the only sentence with two possible translations is sentence 14.\n\nSo:\n\n14. Navila vivila biyamata tomwaya mtona?\n\n→ How many women will that woman? \n→ How many women will this woman?\n\nThus, two translations.\n\nNow translate others directly.\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ Which two things that? — but “minasina” = that → modifies “vivila” → “things that” → “which two things that”? Unnatural.\n\nBut in sentence 11: “Kwevila lekamkwamsi dimdim mtosiwena?” → “how many things did those white men eat?” — “lekamkwamsi” = those things.\n\nSo “bikamkwamsi” = which things?\n\n“kweyu” = two?\n\n“vivila” = something?\n\n“minasina” = that?\n\nPossibly: “which two things that” → still odd.\n\nBut perhaps “minasina” is a red herring — maybe it’s “that” modifying “things” — but “which two things that” is not standard.\n\nAlternatively, “minasina” = that — so the sentence is “which two things that?” — ambiguous?\n\nBut no other example shows a demonstrative modifying a numeral.\n\nIn sentence 5: “which man killed two pigs” — “two pigs” — number separate.\n\nSo likely “kweyu” = two, “vivila” = things, “minasina” = that → so “which two things that?”\n\nBut “that” is unclear.\n\nPossibly the intended reading is “which two things?” with “that” as a qualifier.\n\nBut no ambiguity.\n\nThus, only 14 has ambiguity.\n\nFinal translations:\n\n14: How many women will that woman? / How many women will this woman?\n\n15: Which two things that? — but better: “Which two things are those?” — no.\n\nIn context, likely “which two things” — “minasina” = that → “those things” → so “which two things?” → but “minasina” may be redundant.\n\nAlternatively, “which two things” with “that” — not clear.\n\nBut no grammatical ambiguity.\n\n16: Which that child? / Which this child?\n\nBut no prior evidence.\n\n17: How many chiefs did that woman see?\n\n18: That woman saw those things that.\n\nOnly 14 has a clear, documented ambiguity in structure.\n\nThus, the sentence with two possible translations is 14.\n\nFinal answers:\n\na.1: How many women will that woman?; How many women will this woman?\n\na.2: Which two things that? — no, better: \"Which two things?\" — but “minasina” is there.\n\nWait — in 15: “Bikamkwamsi kweyu vivila minasina.”\n\nIf “minasina” = that, and it modifies “vivila” → “that thing”, so “which two things that” → not good.\n\nBut perhaps it's “which two things” and “minasina” is a misread.\n\nNo — better to translate based on structure.\n\nFrom sentence 11: “how many things did those white men eat” → “lekamkwamsi dimdim mtosiwena” → “those things”.\n\nSo “bikamkwamsi” = which things?\n\n“kweyu” = two?\n\n“vivila” = something?\n\n“minasina” = that?\n\nSo likely: “Which two things that?” — but “that” refers to something.\n\nPerhaps “which two things are those?” — but not parallel.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 13312.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.", + "planner_output": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "anchor_output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 1, + "output": "Step 1: Identify recurring patterns in the English-Kilivila pairs.\n\nSentence 1: \"One man will catch these four fish.\" \nKilivila: \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = one, \"minasina\" = fish, \"tetala\" = four → \"one man will catch four fish\"\n\nSentence 2: \"This white man arrived.\" \nKilivila: \"Lekota dimdim mtona.\" \n→ \"lekota\" = this, \"dimdim\" = white, \"mtona\" = man → \"this white man\"\n\nSentence 3: \"That child will arrive.\" \nKilivila: \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that, \"gwadi\" = child → \"that child\"\n\nSentence 4: \"This old woman saw those canoes.\" \nKilivila: \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this, \"waga\" = old, \"makesiwena\" = woman, \"namwaya\" = canoes → \"this old woman saw those canoes\"\n\nSentence 5: \"Which man killed two pigs?\" \nKilivila: \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"amtona\" = which, \"lekalimati\" = man, \"tau\" = two, \"bunukwa\" = pig → \"which man killed two pigs?\"\n\nSentence 6: \"The old women looked after two men.\" \nKilivila: \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women, \"teyu\" = looked after, \"tauwau\" = two, \"nunumwaya\" = men → \"old women looked after two men\"\n\nSentence 7: \"That clever woman will see something.\" \nKilivila: \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"that clever woman\", \"minawena\" = something → \"will see something\"\n\nSentence 8: \"How many dogs arrived?\" \nKilivila: \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many, \"ka’ukwa\" = dogs → \"how many dogs?\"\n\nSentence 9: \"Which canoe did the chiefs see?\" \nKilivila: \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which, \"waga\" = chiefs, \"gweguyau\" = canoe → \"which canoe did the chiefs see?\"\n\nSentence 10: \"That beautiful child saw this stone.\" \nKilivila: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that, \"dakuna\" = beautiful, \"gwadi\" = child → \"that beautiful child\", \"gudimanabweta\" = stone → \"saw this stone\"\n\nSentence 11: \"How many things did those white men eat?\" \nKilivila: \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many, \"lekamkwamsi\" = white men, \"mtosiwena\" = things → \"how many things did those white men eat?\"\n\nSentence 12: \"The clever chief killed one wild pig.\" \nKilivila: \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = the clever chief, \"natala\" = one, \"bunukwa\" = wild pig → \"the clever chief killed one wild pig\"\n\nSentence 13: \"How many women will look after this man?\" \nKilivila: \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many, \"vivila\" = women, \"biyamatasi\" = will look after, \"tau\" = this, \"mtona\" = man → \"how many women will look after this man?\"\n\nNow analyze the translation patterns:\n\n- Quantifiers:\n - \"navasi\" = one\n - \"navila\" = how many\n - \"amtona\" = which\n - \"amakena\" = which\n - \"tau\" = two (as in “two men”)\n - \"teyu\" = look after\n - \"yena\" = these\n - \"waga\" = old, white, etc. (adjective)\n - \"bunukwa\" = wild pig\n - \"guyau\" = clever\n - \"gwadi\" = child\n - \"minasina\" = fish\n - \"makesiwena\" = woman\n - \"namwaya\" = canoes\n - \"mtona\" = man\n - \"vivila\" = woman\n - \"waga\" = can also be used with \"legisi\" → this old woman\n\n- English order: Subject + verb + object or modifier\n- Kilivila order: Often theme → modifier → verb\n- \"How many X did Y do?\" → \"Kwevila [X] [Y] did [Z]?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" = how many things did those white men eat?\n\nPattern: \n\"How many X did Y do?\" → \"kwevila [X] [Y] did [Z]?\" \n→ But in sentence 8: \"navila ka’ukwa lekotasi?\" → how many dogs arrived? → \"navila\" = how many, \"ka’ukwa\" = dogs → so \"how many [X]?\" = \"navila X?\" \n→ So \"navila\" = how many (for count nouns)\n\nSimilarly: \n\"amtona\" = which (for yes/no questions with choice)\n\nSo for all questions:\n- \"navila\" = how many\n- \"amtona\" = which\n- \"tau\" = two\n- \"teyu\" = look after\n- \"bunukwa\" = wild pig\n- \"guyau\" = clever\n- \"gwadi\" = child\n\nNow translate each of the given sentences:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many \n→ \"vivila\" = women \n→ \"biyamata\" → likely \"will look after\" (from \"biyamatasi\" in 13: \"biyamatasi\" = will look after) \n→ \"tomwaya\" → likely \"this man\" (from \"tau mtona\" in 13: \"this man\") \n→ So: \"how many women will look after this man?\"\n\nThis matches sentence 13, just reordered. So translation: \"How many women will look after this man?\"\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" → \"bikamkwamsi\" appears in 11: \"lekamkwamsi\" = white men → \"bikamkwamsi\" = likely \"those white men\" (bikota = that, but \"bika\" might be a variant) \n→ \"kweyu\" = look after (from \"teyu\") \n→ \"vivila\" = woman → so \"those white men look after a woman\" \n→ But \"minasina\" = fish? In 1: \"minasina\" = fish \nBut \"vivila minasina\" = woman fish? Unlikely \nCould \"minasina\" = fish? But \"vivila\" = woman → so would be \"woman fish\"? \nWait — is \"minasina\" = fish, and could it be used as object? \nIn sentence 1: \"catch these four fish\" → \"minasina\" → so likely object \nBut here, \"vivila minasina\" = ??? \nAlternative: \"minasina\" = something → but no \nWait — sentence 7: \"minawena\" = something \nSo perhaps \"minasina\" = fish → so \"those white men look after a fish\"? \nBut that is odd — men look after fish? \nAlternatively, \"vivila\" = woman, \"minasina\" = fish → not plausible \nBut in sentence 10: \"gwadi magudiwena\" = child, \"gudimanabweta\" = stone \nSo objects are always specific: fish, canoes, stone, pigs \nSo \"vivila minasina\" = woman fish? Unlikely \nPossibility: \"vivila\" is not \"woman\" here — could it be something else? \nIn 13: \"vivila biyamatasi\" = women who look after \nIn 15: \"bikamkwamsi kweyu vivila minasina\" → perhaps \"bikamkwamsi\" = those white men \n\"kweyu\" = look after \n\"vivila\" = woman? \n\"minasina\" = fish? \nBut men look after a fish? Unnatural \nAlternatively, misreading: \"vivila\" = a woman? Still odd \nWait — sentence 1: \"one man will catch these four fish\" — fish is object \nSentence 3: \"that child\" — subject \nSo in sentence 15, \"vivila minasina\" — could \"vivila\" be a noun meaning \"fish\"? No — \"minasina\" = fish \n\"vivila\" = woman \nSo structure: \"those white men look after (a) woman (fish)?\" — no \nAnother possibility: word order \nIn sentence 13: \"navila vivila biyamatasi tau mtona\" → how many women will look after this man? \n\"biyamatasi\" = look after \nSo \"kweyu\" = look after \nSo \"bikamkwamsi kweyu vivila minasina\" = those white men look after a woman fish? \nStill odd \nCould \"minasina\" be \"some fish\"? \nBut \"vivila\" cannot be \"some fish\" \nAlternative: typo or borrowing — but likely accurate \nWait — is there a pair with similar form?\n\nLook at sentence 4: \"Legisi waga makesiwena namwaya minana.\" → this old woman saw those canoes \n\"makesiwena\" = woman, \"namwaya\" = canoes → so woman saw canoes\n\nSentence 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → that beautiful child saw this stone\n\nSo it seems the pattern is: [modifier] + [noun] + verb\n\nSo sentence 15: \"bikamkwamsi\" = those white men \n\"kweyu\" = look after \n\"vivila\" = woman \n\"minasina\" = fish (or perhaps \"something\") \n\nBut \"look after a woman\" is plausible, \"look after a fish\" is odd \nBut \"vivila\" = woman, so \"a woman\" → \"minasina\" must be object → is \"minasina\" = fish?\n\nBut fish is object, not subject. \nCould \"minasina\" be a typo for \"mtona\"? No — \"mtona\" = man \n\nWait — in sentence 14: \"tomwaya mtona\" = this man \n\"tomwaya\" = this \n\"mtona\" = man \nSo \"tomwaya\" = this → used in 14 \n\nIn 15: \"vivila minasina\" — if \"minasina\" = fish, then \"those white men look after a fish\"? Unlikely \nBut sentence 5: \"amtona tau lekalimati nayu bunukwa?\" → which man killed two pigs? \nSo \"bunukwa\" = pig\n\nSimilarly, sentence 12: \"lekalimati natala bunukwa\" — the clever chief killed one wild pig\n\nSo \"bunukwa\" = pig (wild)\n\nThen \"minasina\" = fish → consistent\n\nSo \"those white men look after a fish\" → possible, though rare\n\nBut more likely — could \"vivila\" be a headword for something else?\n\nNo — only places where \"vivila\" appears are as woman or in compound nouns.\n\nThus, most plausible: \"those white men look after a woman\" → but \"vivila\" = woman → so \"a woman\" → \"vivila minasina\" = woman fish? \nNo.\n\nPossibility: \"minasina\" is a typo of \"minawena\"? \"minawena\" = something — in sentence 7\n\n\"minasina\" in 1 may be \"fish\", in others could be something else?\n\nSentence 6: \"teyu tauwau nunumwaya\" → looked after two men\n\nSo \"nunumwaya\" = men\n\nSentence 13: \"navila vivila biyamatasi tau mtona\" → how many women look after this man\n\nSo \"biyamatasi\" = look after\n\nThus, in 15: \"kweyu\" = look after\n\nSo \"bikamkwamsi kweyu vivila minasina\" → those white men look after a woman fish? \nNo\n\nBut \"vivila\" might be \"something\", not \"woman\"? But no evidence\n\nWait — sentence 7: \"vivila minawena\" → woman sees something\n\nSo \"vivila\" = woman\n\nIn 15: \"vivila minasina\" → woman fish → not possible\n\nUnless \"minasina\" = \"things\" or \"something\"\n\nBut word for something is \"minawena\"\n\nSo likely error or misalignment\n\nAlternative: \"vivila\" = a woman, and \"minasina\" = fish → so \"look after fish\"? Weak\n\nBut perhaps we accept: \"those white men look after a fish\" — possible in a metaphorical sense? Unlikely.\n\nWait — perhaps \"vivila\" is not the object — could it be the subject?\n\n\"those white men look after woman (fish)\" — same\n\nNo pattern.\n\nBut look at sentence 13: \"vivila biyamatasi tau mtona\" → women look after this man\n\nSo \"biyamatasi\" = look after\n\nLikewise, in 15: \"kweyu\" = look after\n\nSo verb is \"look after\"\n\nNoun phrase: \"vivila minasina\"\n\nOnly possibility: females are referred to by \"vivila\", so \"a woman\" but what is the object?\n\n\"minasina\" = fish — so \"look after fish\"?\n\nBut men look after fish? Possible in rural context?\n\nUnlikely, but possible.\n\nBut better: is there syntactic alternation?\n\nLook at sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" → old women looked after two men → so object is men\n\nIn 15: \"kweyu\" + \"vivila\" + \"minasina\" → so object is fish?\n\nYes — so \"those white men look after fish\" — possibly.\n\nBut \"minasina\" = fish → yes\n\nSo translation: \"Those white men look after fish.\"\n\nBut that sounds odd — but grammatically possible.\n\nNow 16: Amagudina gwadi lekota?\n\n\"amagudina\" → likely \"how many\" → \"navila\" = how many, \"amagudina\" = similar? \n\"am\" = how? \"gudina\" → not found \n\"amgudina\" → possibly \"amagudina\" = how many?\n\nBut in sentence 8: \"navila\" = how many \nIn sentence 5: \"amtona\" = which\n\nNo \"amagudina\"\n\nBut in sentence 9: \"amakena\" = which\n\nSo \"amagudina\" = might be misreading?\n\n\"amagudina\" → could be \"amagudina\" = how many?\n\nAlternative: \"amagudina\" = how many?\n\nCompare to sentence 8: \"navila ka’ukwa lekotasi?\" → how many dogs?\n\nSo \"amagudina\" → perhaps \"how many\"?\n\n\"gwadi\" = child \n\"lekota\" = this man\n\nSo \"how many children did this man?\" → \"how many children\" = \"amagudina gwadi\"?\n\n\"amagudina\" = how many? \n\"gwadi\" = child\n\nSo \"how many children?\"\n\nBut \"lekota\" = this man — so \"how many children did this man have?\"?\n\nAh — yes — in English: \"How many children does this man have?\"\n\nSo likely: \"How many children does this man have?\"\n\n17. Tevila tauwau bigisesi gugwadi gudigasisi?\n\n\"tevila\" = how many \n\"tauwau\" = two \n\"bigisesi\" = that chief (from \"bigisi\" = that chief) \n\"gugwadi\" = that → \"gudigasisi\" = that wild pig (from \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = that wild pig)\n\nSo \"how many two that chief saw that wild pig?\"\n\nGrammatically incorrect — two that chief saw that wild pig?\n\nBut \"how many two\" = how many two? \"how many two\" is ungrammatical.\n\nIn sentence 13: \"navila vivila biyamatasi tau mtona\" → how many women will look after this man?\n\n\"navila\" = how many\n\nIn sentence 8: \"navila ka’ukwa lekotasi?\" → how many dogs?\n\nSo \"tevila\" = how many → same as \"navila\"\n\nSo \"tevila tauwau\" = how many two → how many two? → but \"two\" is a number — \"how many two\" = how many two items?\n\nUngrammatical.\n\nCould \"tauwau\" = two — so \"how many two\" = how many two things?\n\nNot standard.\n\nIn sentence 5: \"amtona tau lekalimati nayu bunukwa?\" → which man killed two pigs?\n\n\"tau\" = two — number\n\nSo \"how many\" is \"navila\" or \"tev", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12048.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Analyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.", + "planner_output": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "anchor_output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 2, + "output": "Step 1: Identify core linguistic patterns from the given examples.\n\nLook at demonstratives:\n- Sentence 2: \"lekota dimdim mtona\" → \"this white man\". \"lekota\" = this.\n- Sentence 3: \"bikota gwadi magudiwena\" → \"that child\". \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. So \"gwadi\" is a demonstrative modifying \"magudiwena\".\n- Sentence 4: \"legisi waga makesiwena namwaya minana\" → \"this old woman saw those canoes\". \"legisi\" = this, \"namwaya\" = those → demonstratives independently modify nouns.\n\nThus, demonstratives are independent and can modify nouns directly: \"gwadi\" = that, \"lekota\" = this, \"bikota\" = that.\n\nStep 2: Identify number agreement and quantifiers.\n\n- Sentence 1: \"minasina tetala tau\" → \"four fish\". \"minasina\" = four, \"tetala\" = fish.\n- Sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → \"nayu\" = two, \"bunukwa\" = pigs.\n- Sentence 6: \"teyu tauwau nunumwaya\" → \"looked after two men\" → \"tauwau\" = two.\n- Sentence 8: \"Navila ka’ukwa lekotasi?\" → \"how many dogs arrived?\" → \"navila\" = how many.\n- Sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" → \"kwevila\" = how many.\n\nSo \"tauwau\", \"nayu\", \"minasina\", \"navila\", \"kwevila\" are number indicators: \"two\", \"four\", \"how many\".\n\nStep 3: Analyze structure of target sentences.\n\n14. \"Navila vivila biyamata tomwaya mtona?\"\n- \"navila\" = how many\n- \"vivila\" = women\n- \"biyamata\" = ? → similar to \"biyamatasi\" in sentence 13 → \"biyamatasi\" = women → so likely \"biyamata\" = women\n- \"tomwaya\" = ? → \"mtona\" = man → \"tomwaya\" likely = man\n- So: \"how many women will look after this man?\" → matches sentence 13: \"vivila biyamatasi tau mtona\" → \"women will look after this man\"\n\n→ Translation: \"How many women will look after this man?\"\n\n15. \"Bikamkwamsi kweyu vivila minasina.\"\n- \"bikamkwamsi\" = that (like \"bikota\")\n- \"kweyu\" = two\n- \"vivila\" = women\n- \"minasina\" = fish (from sentence 1)\n\nBut \"two women fish\"? no.\n\nIs \"minasina\" used for \"fish\" and paired with number? Only in sentence 1.\n\nAlternative: could \"vivila minasina\" mean \"two women\" if \"minasina\" is a number?\n\nBut \"minasina\" is \"four fish\", and \"kweyu\" is \"two\".\n\nSo \"kweyu\" = two → \"vivila\" = women → \"vivila minasina\" → seems to be \"two women\" + \"fish\"?\n\nThis is not grammatical.\n\nPossibility: \"minasina\" is a general noun meaning \"something\" — but not supported.\n\nBut in sentence 15: \"bikamkwamsi kweyu vivila minasina\" → could be \"that two women have something\"?\n\nUnlikely.\n\nAlternative: is \"minasina\" used as a noun in compound form? Possibly not.\n\nWait: could \"kweyu\" and \"vivila minasina\" be separate?\n\nBut no.\n\nAnother idea: in sentence 5, \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" modifies \"bunukwa\" → number + noun.\n\nSimilarly, in sentence 15: \"kweyu vivila minasina\" → \"two women fish\"? → invalid.\n\nBut sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man.\n\nSo in 15, perhaps \"vivila minasina\" = \"women\" and \"minasina\" is a noun, not number.\n\nBut \"kweyu\" is \"two\" — where does it go?\n\nOnly logical position is with a noun: \"two women\" → so \"kweyu vivila\" = two women\n\nThen \"minasina\" remains → unless \"minasina\" is a noun meaning \"something\", or perhaps it's a typo.\n\nBut in sentence 1, \"minasina tetala tau\" → \"four fish\" → so \"minasina\" is a number + noun.\n\nThus, \"kweyu vivila minasina\" must be \"two women\" and something else.\n\nNo other noun.\n\nBut what if \"minasina\" is a verb or transitive? Unlikely.\n\nOnly possible: the phrase is \"that two women\" and \"minasina\" is a noun, but without a following noun, it fails.\n\nThus, likely \"kweyu\" modifies \"vivila\" → \"two women\" → and the sentence is \"that two women [do something]\" — but what?\n\nBut no verb.\n\nCould \"bikamkwamsi kweyu vivila minasina\" mean \"which two women\" with \"minasina\" as object?\n\nBut no object.\n\nAlternatively, is \"minasina\" a typo for \"mtona\"? \"mtona\" = man.\n\nPossibility: \"vivila minasina\" → \"women and fish\"? No.\n\nAnother path: look at sentence 16.\n\n16. \"Amagudina gwadi lekota?\"\n\n- \"amagudina\" = which child\n- \"gwadi\" = that\n- \"lekota\" = this\n\nSo \"which child is that this?\"\n\nThis is redundant.\n\nBut demonstratives can be used for two possibilities: \"that child\" or \"this child\".\n\nSo \"amagudina gwadi lekota\" → \"which child is that?\" or \"which child is this?\"\n\nThat is, the demonstrative can point to one of the two — \"that\" or \"this\" — and the sentence asks \"which one?\"\n\nThis is a known pattern in some languages: demonstratives in questions can be semantically ambiguous due to dual demonstratives.\n\nCompare to sentence 2: \"lekota dimdim mtona\" → \"this white man\" → no ambiguity.\n\nSentence 3: \"bikota gwadi magudiwena\" → \"that child\" — \"gwadi\" modifies \"magudiwena\", not co-occurring with \"bikota\".\n\nBut in 16, \"amagudina gwadi lekota\" → \"which child\" with demonstratives.\n\nCould \"gwadi\" and \"lekota\" be competing for reference? For example, \"which child is that?\" or \"which child is this?\"\n\nYes — likely.\n\nSimilarly, in sentence 10: \"legisi dakuna makwena gwadi magudiwena\" → \"that beautiful child\" → \"gwadi\" modifies \"magudiwena\" — one demonstrative.\n\nBut in 16, there are two: \"gwadi\" and \"lekota\" — both demonstratives with \"amagudina\" — which means \"which child\".\n\nThus, the ambiguity is: does \"gwadi lekota\" mean \"that child\" or \"this child\"?\n\nSo \"which that child?\" or \"which this child?\"\n\nThus, two possible translations:\n- Which that child?\n- Which this child?\n\nBut \"which that child\" is ungrammatical — so only \"which this child\" makes sense?\n\nBut the problem says one sentence has two possible translations.\n\nThus, only plausible is that \"gwadi lekota\" can be interpreted as \"that child\" or \"this child\", and the sentence is asking which one.\n\nTherefore, translation ambiguity in 16.\n\nNow check others.\n\n17. \"Tevila tauwau bigisesi gugwadi gudigasisi?\"\n\n- \"tevila\" = how many\n- \"tauwau\" = two\n- \"bigisesi\" = that chief\n- \"gugwadi\" = that? (likely)\n- \"gudigasisi\" = wild pig? (from \"guyau\" = wild pig)\n\nSo \"how many two that chief saw that wild pig?\"\n\nUnnatural.\n\n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? — redundant.\n\nNo syntactic split.\n\nNo ambiguity.\n\n18. \"Legisesi ketala waga vivila minasiwena.\"\n\n- \"legisesi\" = that (like \"legisi\" = this)\n- \"ketala\" = clever\n- \"waga\" = saw\n- \"vivila\" = women\n- \"minasiwena\" = similar to \"minasina\" → fish?\n\nSo \"that clever woman saw those women\" — but \"minasiwena\" = women? → same as \"vivila\"?\n\n\"vivila\" = women → so \"women saw women\" — possible.\n\n\"minasiwena\" → if equivalent to \"minasina\", then \"fish\" or \"something\"?\n\nBut in context, could be a noun.\n\nThus, \"that clever woman saw those women\".\n\nNo ambiguity.\n\nNow back to 15.\n\n\"Bikamkwamsi kweyu vivila minasina.\"\n\n- \"bikamkwamsi\" = that\n- \"kweyu\" = two\n- \"vivila\" = women\n- \"minasina\" = fish\n\nNo clear meaning.\n\nBut if \"minasina\" is a noun, and \"vivila\" is \"women\", it's \"that two women fish\"? No.\n\nCould \"kweyu\" modify \"vivila\", meaning \"two women\", and \"minasina\" be a separate noun?\n\nNo.\n\nBut in sentence 1, \"minasina\" is number+fish → so \"minasina\" = four fish.\n\nCould \"minasina\" be used with \"kweyu\" to mean \"two\" or \"four\"?\n\nNo.\n\nNo evidence of syntactic ambiguity in 15.\n\nThus, only sentence with possible ambiguity is 16: \"Amagudina gwadi lekota?\"\n\nIt has two demonstratives: \"gwadi\" (that) and \"lekota\" (this), both modifying \"child\" (implied by \"amagudina\").\n\nSo the ambiguity is whether it means:\n- which that child?\n- which this child?\n\nAlthough \"which that child\" is awkward, in some languages, demonstratives are used in questions to pick between two possibilities.\n\nMoreover, in example sentence 3, \"bikota gwadi magudiwena\" → \"that child\" — shows \"gwadi\" can be a demonstrative used with a noun.\n\nIn 16, \"amagudina\" = which child, with demonstratives \"gwadi lekota\" — the phrase is semantically ambiguous.\n\nThus, two possible translations:\n1. Which that child?\n2. Which this child?\n\nNow, is this supported by other examples?\n\nSentence 2: \"lekota dimdim mtona\" → \"this white man\" — no ambiguity.\n\nSentence 4: \"legisi waga makesiwena namwaya minana\" → \"this old woman saw those canoes\" — clear demonstratives.\n\nNo sentence has two demonstratives modifying the same noun in a question.\n\nBut sentence 16 has \"amagudina\" + \"gwadi\" + \"lekota\" — only in this context.\n\nThus, it is the only sentence with structural ambiguity.\n\nFinal answer:\n\n14. How many women will look after this man?\n15. That two women have fish? → ungrammatical → likely misreading — but no ambiguity\n16. Which that child? / Which this child?\n17. How many two that chief saw that wild pig? → ungrammatical → no ambiguity\n18. That clever woman saw those women? → possible, but no ambiguity\n\nThus, only 16 has ambiguity.\n\nFinal translations:\n\na.1: How many women will look after this man?\na.2: That two women have fish? → not supported — likely not\n\nWait — 15: could it be \"bikamkwamsi kweyu vivila minasina\" → \"that two women fish\"?\n\nNo.\n\nAlternative: could \"minasina\" be \"something\" and \"kweyu\" modify \"vivila\" → \"two women\" → and \"minasina\" is object?\n\nNo verb.\n\nOnly plausible is that 16 has ambiguity.\n\nThus, only sentence with two translations is 16.\n\nSo:\n\na.1: How many women will look after this man?\na.2: That two women have fish? — no\n\nWait — earlier in sentence 1, \"minasina tetala tau\" → \"four fish\"\n\nSo \"minasina\" = fish.\n\nBut \"kweyu vivila\" = two women.\n\nSo \"two women fish\"? not possible.\n\nUnless \"vivila minasina\" = \"women\" and \"minasina\" = fish — but no verb.\n\nNo.\n\nBut perhaps \"bikamkwamsi kweyu vivila minasina\" = \"that two women fish\" — as in \"that two women eat fish\" or something?\n\nBut no verb.\n\nThus, no.\n\nSo only 16 has ambiguity.\n\nTherefore:\n\n14: How many women will look after this man?\n15: Cannot be formed — likely error in parsing.\n\nWait — sentence 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\nCompare to sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\"\n\n\"nayu\" = two → modifies \"bunukwa\"\n\nSimilarly, \"kweyu\" = two → should modify a noun.\n\nSo \"kweyu vivila\" = two women\n\nThen \"minasina\" remains.\n\nBut in sentence 1, \"minasina\" is \"four fish\".\n\nNo way to attach.\n\nUnless \"vivila minasina\" = \"women\" and \"minasina\" is a number form, like \"four\" — but \"kweyu\" is \"two\".\n\nNo.\n\nSo likely, the phrase is \"that two women\" and \"minasina\" is a mistake — but no.\n\nPerhaps \"minasina\" is not a noun but a verb — unsupported.\n\nThus, 15 has no clear translation.\n\nOnly 16 has ambiguity.\n\nThus, the sentence with two translations is 16.\n\nFinal answers:\n\na.1: How many women will look after this man?\na.2: Which that child?\na.3: Which this child?\na.4: That two women have fish? — invalid\na.5: ?\n\nWait — the question says: \"One of these sentences has two possible translations. Give them both.\"\n\nSo only one sentence has two translations — that is 16.\n\nSo for 14, 15, 17, 18: single translation.\n\nOnly 16 has two.\n\nSo:\n\na.1: Translation of 14 → \"How many women will look after this man?\"\na.2: Translation of 15 → ? — must be correct\n\n15: \"Bikamkwamsi kweyu vivila minasina\"\n\nBest interpretation: \"that two women\" and \"minasina\" = something → but no.\n\nPerhaps \"vivila minasina\" = \"women\" and \"minasina\" is a noun of \"fish\", and \"kweyu\" modifies the noun.\n\nBut no noun for \"fish\" before \"vivila\".\n\nUnless \"vivila minasina\" = \"two women fish\" — not possible.\n\nBut in sentence 1: \"minasina tetala tau\" — \"four fish\", so \"minasina\" = fish, \"tetala\" = something.\n\nSo \"vivila minasina\" = women fish? no.\n\nPerhaps it's a typo — \"vivila\" is \"man\", but no.\n\nAnother possibility: \"vivila\" = women, \"minasina\" = fish → \"women fish\" → ungrammatical.\n\nConclusion: likely, \"kweyu\" and \"vivila\" go together → \"two women\", and \"minasina\" is a noun not attached to a verb.\n\nNo.\n\nPerhaps the sentence is \"that two women have fish\" — but no verb \"have\".\n\nNo.\n\nThus, not possible.\n\nTherefore, likely, the only ambiguous sentence is 16.\n\nThus, a.1 to a.4 are translations of 14,15,17,18.\n\nFor 15: perhaps \"that two women\" — and \"minasina\" is a mistake.\n\nBut not.\n\nWait — in sentence 12: \"Lekalimati natala bunukwa nagasisi guyau tokabitam\" → \"the clever chief killed one wild pig\" — so \"bunukwa\" = pig.\n\nSo \"minasina\" = fish.\n\nSo no.\n\nFinal decision:\n\n- 14: \"How many women will look after this man?\"\n- 15: \"That two women fish\" → invalid\n- But perhaps \"That two women have fish\" → not supported\n\nNo.\n\nAlternative: in sentence 1, \"minasina\" is number + fish — so if \"kweyu\" is two, and \"minasina\" is fish, then \"that two fish\"?\n\nBut \"vivila\" is women — so not.\n\nOnly possible is that the phrase is \"that two women\" and the sentence is missing a verb.\n\nBut in the context, perhaps it's \"that two women\" as in \"that two women were seen\" — but no verb.\n\nThus, likely, 15 is not ambiguous, and its translation is \"that two women\" with a missing verb — not possible.\n\nTherefore, the only sentence with two translations is 16.\n\nSo a.1 to a.4 are standard translations, and for a.5, only 16 has two.\n\nBut a.5 is for sentence 18.\n\n18: \"Legisesi ketala waga vivila minasiwena.\"\n\n\"legisesi\" =", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12958.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\n\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "planner_output": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "anchor_output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_1x4", + "sample_index": 3, + "output": "We analyze the given English-Kilivila examples to identify linguistic patterns, focusing on syntax, morphology, and semantic roles such as subject, object, demonstratives, numerals, and questions.\n\nFirst, build a consistent alignment table using the provided sentences.\n\nExample 1: \n\"One man will catch these four fish.\" \n→ \"Bibani navasi yena minasina tetala tau.\" \n- \"Bibani\" = one \n- \"navasi\" = man \n- \"yena\" = these \n- \"minasina\" = fish \n- \"tetala\" = will catch \n- \"tau\" = four \n\nObservation: \"tetala\" is the verb \"to catch\", \"tau\" is \"four\", and \"yena\" is \"these\". \"Bibani\" and \"navasi\" are numeral and subject. \"minasina\" is object.\n\nExample 2: \n\"This white man arrived.\" \n→ \"Lekota dimdim mtona.\" \n- \"Lekota\" = this \n- \"dimdim\" = white \n- \"mtona\" = man \n- (arrived is implied by context? verb missing) — wait, no verb: must be a missing component.\n\nWait — in example 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\" \nBut \"arrived\" is not present. So maybe \"mtona\" includes both subject and verb? Unlikely.\n\nActually, in example 1, verb is \"tetala\". In example 2, there’s no clear verb. But example 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"Leyamatasi\" = old women \n→ \"teyu\" = looked after \n→ \"tauwau\" = two \n→ \"nunumwaya\" = men \n\nSo \"teyu\" = looked after (a verb), and \"tauwau\" = two, \"nunumwaya\" = men.\n\nBack to example 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\" \nNo verb. But in example 7: \"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"Bigisi\" = that \n\"kwetala\" = will see \n\"vivila\" = something \n\"minawena\" = woman \n\"nakabitam\" = clever \n\nSo \"kwetala\" is the verb \"to see\".\n\nTherefore, in example 2, \"Lekota dimdim mtona\" must be \"This white man came\" → the verb is “arrived” but not explicitly marked. So perhaps “mtona” includes “arrived” as a function word? Unlikely. Alternative: maybe the verb is missing from the translation — but all verbs are present in others.\n\nWait — in example 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which \n→ \"tau\" = two \n→ \"lekalimati\" = man \n→ \"nayu\" = killed \n→ \"bunukwa\" = pigs \n\nSo \"nayu\" = killed — verb. So in example 2: \"Lekota dimdim mtona.\" — likely \"Lekota dimdim mtona\" means \"This white man [arrived]\", with verb implied or missing.\n\nBut again, in example 3: \"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"Bikota\" = that \n→ \"gwadi\" = child \n→ \"magudiwena\" = will arrive (verb) \n\nAh — yes: \"magudiwena\" = will arrive.\n\nSo example 2 likely has “Lekota dimdim mtona” meaning “This white man arrived” — so “mtona” is the verb “arrived” — so “mtona” = man who arrived? No. “mtona” appears in other contexts as “man”.\n\nExample 1: \"navasi\" = man \nExample 2: \"mtona\" = man \nExample 6: \"nunumwaya\" = men \nExample 12: \"guyau\" = pig \nExample 5: \"bunukwa\" = pigs \n\nSo people: \n- navasi → man \n- mtona → man \n- gwadi → child \n- biyamatasi → women (example 6) \n- bigisi → woman (example 7) \n\nAlso, examples with numbers:\n\n1: \"tau\" = four \n5: \"tau\" = two \n6: \"tauwau\" = two \n12: \"guyau\" = pig, \"tokabitam\" = clever \n\n\"tau\" and \"tauwau\" appear together with numerals: \"tauwau\" = two, \"tetala tau\" = catch four fish → \"tau\" = four. So \"tau\" is a numeral.\n\n\"nayu\" = killed \n\"tetala\" = catch \n\"kwetala\" = will see \n\"teyu\" = looked after \n\"magudiwena\" = will arrive \n\"makwena\" = stone \n\"vivila\" = something \n\"gwe\" = see? \n\nExample 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"Legisi\" = that \n→ \"dakuna\" = beautiful \n→ \"makwena\" = stone \n→ \"gwadi\" = child \n→ \"magudiwena\" = saw? — wait, \"magudiwena\" = will arrive — conflict.\n\nWait — in example 3: \"That child will arrive\" → \"Bikota gwadi magudiwena\" — so \"magudiwena\" = will arrive.\n\nBut in example 10, it says \"saw this stone\" — so must be a different verb.\n\nIn example 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"Legisi\" = that \n\"dakuna\" = beautiful \n\"makwena\" = stone \n\"gwadi\" = child \n\"magudiwena\" = saw? — but \"magudiwena\" = will arrive.\n\nContradiction. So must be misalignment.\n\nLook again: example 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\"\n\nBut “magudiwena” occurs with \"gwadi\" — so can it be \"saw\"?\n\nAlternatively, perhaps “gudimanabweta” = saw?\n\nExample 7: \"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"kwetala\" = will see\n\nSo \"kwetala\" = see.\n\nIn example 10: \"gudimanabweta\" — compare to \"gudimanabweta\".\n\nCould \"gudimanabweta\" be \"saw\"?\n\nPossibly. Maybe \"gudiman\" = saw?\n\nIn example 4: \"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\"\n\n→ \"Legisi\" = this \n\"waga\" = those \n\"makesiwena\" = saw \n\"namwaya\" = canoes \n\"minana\" = old? — or \"minana\" = old women? \n\n\"makesiwena\" = saw — so verb is \"makesiwena\"\n\nSimilarly, example 10: \"gudimanabweta\" — likely derived from \"gudimanabweta\" = saw.\n\nSo “gudimanabweta” → saw (stone)\n\nThus, “makesiwena” = saw\n\nSo \"sees\" is part of \"makesiwena\" or \"gudimanabweta\"?\n\nLikely, \"gudimanabweta\" = saw (stone)\n\nBut in example 10, order: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" — that has \"magudiwena\" before \"gudimanabweta\" — but \"magudiwena\" = will arrive — so unlikely.\n\nMaybe typo in reference?\n\nWait: original says: \n10. That beautiful child saw this stone. \n→ Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n\nBut \"gwadi\" = child, so “gwadi magudiwena” = child who will arrive? But it says saw.\n\nSo likely a misplacement.\n\nAlternative: \"magudiwena\" is not the verb — perhaps \"magudiwena\" is a noun?\n\nBut in example 3: \"Bikota gwadi magudiwena\" → that child will arrive.\n\nSo \"magudiwena\" = will arrive.\n\nTherefore, in example 10, it can’t be.\n\nSo likely, the translation is miswritten — or we misread.\n\nWait — the original says:\n10. That beautiful child saw this stone.\nLegisi dakuna makwena gwadi magudiwena gudimanabweta.\n\nBut perhaps \"magudiwena\" is a typo and should be \"makesiwena\"?\n\nIn example 4: “makesiwena” = saw.\n\nSo perhaps in 10, it should be “makesiwena” instead.\n\nBut it's written as “magudiwena”.\n\nUnless “magudiwena” is a noun — like “stone”?\n\nNo — “makwena” = stone.\n\nSo best hypothesis: the verb is \"gudimanabweta\" = saw.\n\nAnd “magudiwena” is likely a typo — or from another sentence.\n\nBut in 7: \"Bigisi kwetala vivila minawena nakabitam\" → “kwetala” = will see.\n\nSo \"kwetala\" = see.\n\nThus, in 4: \"makesiwena\" = saw.\n\nSo in 10: must be \"makesiwena\" or similar.\n\nThus, \"gudimanabweta\" = saw.\n\nSo likely the verb for “saw” is “makesiwena” or “gudimanabweta”.\n\nNow, in 12: \"The clever chief killed one wild pig.\" \n→ \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n\"lekalimati\" = chief \n\"natala\" = killed \n\"bunukwa\" = pig \n\"gagasisi\" = wild? \n\"tokabitam\" = clever \n\nSo \"natala\" = killed \n\"bunukwa\" = pig \n\"gagasisi\" = wild \n\nSo \"bunukwa\" = pig → confirmed.\n\nSo verb: \n- tetala = catch \n- nayu = kill \n- teyu = looked after \n- magudiwena = will arrive \n- kwetala = will see \n- makesiwena = saw \n- natala = killed \n\nNow, question forms:\n\nExample 5: \"Which man killed two pigs?\" \n→ \"Amtona tau lekalimati nayu bunukwa?\" \n\"Amtona\" = which \n\"tau\" = two \n\"lekalimati\" = man \n\"nayu\" = killed \n\"bunukwa\" = pigs \n\nSo question with \"which\" and \"how many\" uses \"Amtona\" (which), so \"which\" = Amtona.\n\nExample 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n\"Navila\" = how many \n\"ka’ukwa\" = dogs \n\"lekotasi\" = arrived \n\nSo \"Navila\" = how many — question word for count.\n\nExample 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = which \n\"waga\" = which canoe (demonstrative) \n\"legisesi\" = chiefs \n\"gweguyau\" = saw \n\nSo \"gweguyau\" = saw — verb. \n\nSo “gweguyau” = saw.\n\nSo verbs: \n- tetala = catch \n- nayu = kill \n- teyu = looked after \n- magudiwena = will arrive \n- kwetala = will see \n- makesiwena = saw \n- natala = killed \n\nSo \"gweguyau\" = saw (same as makesiwena?) — possibly a variant.\n\nNow, numerals:\n\n1: \"tau\" = four \n5: \"tau\" = two \n6: \"tauwau\" = two \n12: \"bunukwa\" = one pig — \"one\" not present.\n\nBut 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"Navila\" = how many \n\"vivila\" = will look after \n\"biyamatasi\" = women \n\"tau\" = this \n\"mtona\" = man \n\nSo \"vivila\" = will look after — verb.\n\nSo \"vivila\" = will look after.\n\nNow, look at question 14: \n\"Navila vivila biyamata tomwaya mtona?\" \n\nCompare to 13: \n13. \"Navila vivila biyamatasi tau mtona?\" \n→ how many women will look after this man?\n\n“biyamatasi” = women \n“tau” = this \n“mtona” = man \n“vivila” = will look after\n\n14: \"Navila vivila biyamata tomwaya mtona?\"\n\n“biyamata” — not “biyamatasi” — different. \n“tomwaya” — not “tau”\n\nSo “biyamata” = women? Possible variant \n“tomwaya” = this? “tau” is this — so “tomwaya” = this? \n\nIn 13: \"tau\" = this, so likely “tomwaya” = this\n\nBut “biyamata” — looks like plural of “biyama” — women?\n\n“biyamatasi” = women — plural \n“biyamata” = women? Possibly same root\n\nCould be a substitution: “biyamata” instead of “biyamatasi”\n\nSo 14: \"how many women will look after this man?\"\n\nSame as 13 — but in 13, “biyamatasi” is used, here “biyamata” — likely same meaning.\n\nBut why different?\n\nWait — in 13: “biyamatasi” — direct. \n14: “biyamata” — possibly a grammatical form.\n\nBut “tomwaya” = this, vs “tau” = this.\n\nSo likely “tomwaya” = this (same as “tau”)\n\nSo 14: “how many women will look after this man?” — same as 13.\n\nBut the problem says one has two possible translations.\n\nSo 14 may be ambiguous.\n\nNow 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\n“Bikamkwamsi” — compare to “Bikota” = that \n“kweyu” — see example 6: “teyu” = looked after \nBut “kweyu” — could be “kweyu” = looked after? \n\nExample 6: \"Leyamatasi teyu tauwau nunumwaya\" → old women looked after two men.\n\nSo “teyu” = looked after.\n\nSo “kweyu” = looked after? Possibly.\n\nSo “Bikamkwamsi kweyu vivila minasina”\n\n“Bikamkwamsi” — like “Bikota” → “that” \n“kweyu” = looked after \n“vivila” = will look after? “vivila” = will look after (from 13) \n“minasina” = fish\n\nSo “that [something] will look after fish” — but “that fish”?\n\n\"minasina\" = fish → object\n\nSo if “kweyu” = looked after → subject is missing?\n\nStructure: “Bikamkwamsi kweyu vivila minasina” → “that [X] looked after fish”?\n\nBut “vivila” = will look after — verb, future.\n\nSo “Bikamkwamsi” = that man? But “kweyu” = looked after → past?\n\nConflict: “kweyu” is past, “vivila” is future.\n\nSo possibly “kweyu” is not “looked after”.\n\nAlternatively: in 15: \"Bikamkwamsi kweyu vivila minasina.\"\n\nCompare to example 1: “Bibani navasi yena minasina tetala tau.” → one man will catch four fish.\n\nSo “tetala” = catch — verb\n\nSo here, “vivila” = will look after — verb\n\nSo “kweyu” must be a different verb.\n\nIn example 12: “natala” = killed\n\nIn example 7: “kwetala” = will see\n\nPerhaps “kweyu” = see?\n\nBut in example 4: “makesiwena” = saw\n\nNo “kweyu”.\n\nUnless “kweyu” = saw.\n\nIn example 10: “gudimanabweta” = saw\n\nSo perhaps “kweyu” = saw.\n\nThen: “Bikamkwamsi kweyu vivila minasina” → “that man saw fish”?\n\nBut “vivila” = will look after — so doesn’t fit.\n\nIf “vivila” is the object, but no.\n\nStructure: likely \"Bikamkwamsi\" = subject — \"that\" \n\"kweyu\" = verb \n\"vivila\" = object — \"will look after\" — but that's not a noun.\n\nSo must be \"kweyu vivila\" = that [man] will look after fish?\n\nBut “kweyu” is not “will look after”.\n\nContradiction.\n\nAlternative: “kweyu” = “will look after” → so “vivila” is object — fish.\n\nSo “that man will look after fish”?\n\nBut in example 6, “teyu” = will look after.\n\nSo “kweyu” may be “will look after”.\n\nSo “Bikamkwamsi kweyu vivila minasina” → “that man will look after fish”\n\nYes", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ], + "unit_results": [ + { + "unit_id": "a.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "a.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 11779.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 518.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPrivate solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "planner_output": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "anchor_output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 0, + "output": "Analyze the given English-Kilivila pairs to infer morphological and syntactic patterns.\n\nFirst, observe verb patterns in the data:\n\n- \"see\" → makesiwena (e.g., 4: \"saw those canoes\" → \"makesiwena namwaya minana\")\n- \"arrive\" → lekotasi (e.g., 2: \"arrived\" → \"lekota mtona\")\n- \"look after\" → teyu (e.g., 6: \"looked after\" → \"leyamatasi teyu tauwau nunumwaya\")\n- \"kill\" → guyau (e.g., 12: \"killed\" → \"guyau tokabitam\")\n- \"will\" → vivila (e.g., 1: \"will catch\" → \"navasi yena minasina tetala tau\"; 7: \"will see\" → \"bigisi kwetala vivila minawena nakabitam\")\n\nNote: \"will\" is consistently expressed by \"vivila\" in future tense, attached to the verbal root.\n\nNow examine question 19: \"How many canoes did those old women see?\"\n\n- \"see\" → makesiwena\n- \"how many\" → navila (e.g., 8: \"How many dogs arrived?\" → \"navila ka’ukwa lekotasi?\")\n- \"those old women\" → legisi (e.g., 4: \"that old woman\" → \"legisi waga makesiwena\")\n - \"legisi\" = old woman; \"waga\" = those; so \"legisi waga\" = those old women\n- \"canoes\" → namwaya (e.g., 4: \"those canoes\" → \"namwaya minana\")\n\nSo: \"How many canoes did those old women see?\" → \"Navila namwaya legisi waga makesiwena?\"\n\nBut check if \"navila\" is used for \"how many\" with past tense. In 8: \"How many dogs arrived?\" → \"navila ka’ukwa lekotasi?\" → \"how many dogs\" = navila ka’ukwa → navila applies to count nouns.\n\nIn 4: \"That old woman saw those canoes\" → \"legisi waga makesiwena namwaya minana\" — opens with \"makesiwena\" for see, and \"namwaya\" for canoes.\n\nThus, for 19: \"How many canoes did those old women see?\" \n→ \"Navila namwaya legisi waga makesiwena?\"\n\nBut \"legisi waga\" is \"those old women\" — matches.\n\nSo 19: navila namwaya legisi waga makesiwena\n\nNow 20: \"These four white men will look after this clever child.\"\n\n- \"will\" → vivila (from previous use: e.g., 1: \"will catch\" → \"tetala tau\")\n- \"look after\" → teyu (sentence 6: \"looked after\" → \"teyu\")\n- \"these four\" → minasina (e.g., 1: \"one man\" → \"navasi\", \"four fish\" → \"tetala tau\" → \"tetala\" = four; \"tau\" = fish)\n- \"white men\" → dimdim mtosi (sentence 2: \"this white man\" → \"dimdim mtona\"; \"white\" → dimdim)\n- \"this clever child\" → gwadi magudiwena (sentence 3: \"that child\" → \"gwadi\"; 10: \"that beautiful child\" → \"dakuna makwena gwadi magudiwena\"; \"clever\" → \"kwetala\", \"magudiwena\" = child)\n\nSo: \"these four white men\" → \"minasina dimdim mtona\" \nthen \"will look after\" → \"vivila teyu\" \n\"this clever child\" → \"gwadi kwetala magudiwena\"\n\nThus: minasina dimdim mtona vivila teyu gwadi kwetala magudiwena\n\nCheck structure: symmetry with 6: \"leyamatasi teyu tauwau nunumwaya\" → \"look after\" is \"teyu\", and it is used with a subject and object. No \"will\" in that sentence, but in 1: \"will catch\" → \"tetala tau\" → the verb is \"minasina\" (one) + \"yena\" (will), but the base verb is \"minasina\" — actually, \"yena\" may be a form of \"will\".\n\nWait — in sentence 1: \"One man will catch these four fish\" → \"Bibani navasi yena minasina tetala tau\"\n\n\"navasi yena\" → \"one man will\" → so \"yena\" = will? But \"yena\" is attached to \"navasi\", not the verb.\n\n\"minasina\" = catch? In 1, \"minasina\" → catch? But in 12: \"lekalimati natala bunukwa\" → kill → \"lekalimati\" = kill, \"natala\" = one, \"bunukwa\" = wild pig.\n\nSo possible: \"yena\" is a future auxiliary → not a root verb.\n\nIn 1: \"One man will catch\" → \"navasi yena minasina\"\n\nSo \"yena\" = will → future marker\n\nIn 7: \"That clever woman will see something\" → \"bigisi kwetala vivila minawena nakabitam\" → \"vivila\" = will\n\nSo in sentence 7, \"vivila\" = will (future)\n\nIn sentence 1, \"will\" appears as \"yena\" → contradiction?\n\nSentences 1 and 7 use different forms for \"will\"?\n\n1: \"navasi yena minasina\" — \"yena\" = will \n7: \"bigisi kwetala vivila minawena\" — \"vivila\" = will\n\nSo \"will\" is expressed in two ways? Or is one a mistake?\n\nBut 1: \"navasi\" = one man; \"yena\" = will; \"minasina\" = catch\n\n7: \"bigisi\" = that clever woman; \"kwetala\" = clever; \"vivila\" = will; \"minawena\" = something\n\nSo \"vivila\" is used in 7 for \"will\", but \"yena\" in 1.\n\nIs \"yena\" a future tense marker? Is it part of a different construction?\n\nBut sentence 5: \"Which man killed two pigs?\" → \"amtona tau lekalimati nayu bunukwa?\" — no \"will\", present.\n\nSentence 13: \"How many women will look after this man?\" → \"navila vivila biyamatasi tau mtona?\"\n\n→ \"navila vivila biyamatasi tau mtona\" → \"how many women will look after this man?\"\n\nSo \"vivila\" is used for \"will\" here.\n\nThus, \"vivila\" is the consistent form for \"will\" in future tense.\n\nIn sentence 1, \"navasi yena minasina\" — \"yena\" is used for \"will\" — but possibly \"yena\" is not \"will\", but a different form?\n\nCould \"yena\" be related to \"one\", like \"navasi\" = one, \"yena\" = becomes?\n\nNo — sentence 1: \"One man will catch\" — not paraphrased.\n\nBut in 13: \"will look after\" is \"vivila biyamatasi\"\n\nAnd in 7: \"will see\" → \"vivila\"\n\nSo the future is marked by \"vivila\"\n\nTherefore, in 1: \"will\" is likely \"yena\", but that contradicts 13 and 7.\n\nAlternatively, \"yena\" may be a misalignment or marked by a different morpheme.\n\nBut in 13: \"navila vivila biyamatasi tau mtona\" — clearly \"vivila\" = will\n\nIn 7: \"vivila\" = will\n\nIn 1: if \"yena\" = will, then it is inconsistent.\n\nBut perhaps the words are not directly translatable and \"yena\" is a different marker.\n\nAlternatively, \"yena\" is for \"to\" or other.\n\nBut sentence 1: \"One man will catch\" → \"navasi yena minasina\"\n\nCompare 10: \"That beautiful child saw this stone\" → \"legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\nNo \"will\"\n\nSentence 13: \"will look after\" → \"vivila biyamatasi\"\n\nSo only in present and future forms.\n\nConclusion: \"vivila\" is used consistently for \"will\" in future contexts.\n\nThus, in 20: \"These four white men will look after this clever child\" \n→ \"minasina dimdim mtona vivila teyu gwadi kwetala magudiwena\"\n\nNow 21: \"How many children will eat these pigs?\"\n\n\"how many\" → navila \n\"children\" → gwadi magudiwena (sentence 3: \"that child\" → gwadi magudiwena) \n\"will\" → vivila \n\"eat\" → not directly given.\n\nBut \"eat\" is not present in any verb in data.\n\nSentence 11: \"How many things did those white men eat?\" → \"kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" — what is this?\n\n\"kwevila\" — similar to \"navila\", \"vivila\", \"lekotasi\"\n\n\"lekamkwamsi\" — perhaps related to \"eat\"?\n\nIn 11: \"How many things did those white men eat?\" → translation: \"kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"kwevila\" = how many? — same as navila?\n\n\"lekamkwamsi\" — likely verb for \"eat\"\n\nBut \"eat\" is missing from direct verb forms.\n\nSo likely, \"eat\" = lekamkwamsi\n\nIn 11: \"how many things\" → kwevila \n\"did\" → past tense marker? But no verb present \n\"eat\" → lekamkwamsi \n\"those white men\" → dimdim mtosiwena\n\nSo \"lekamkwamsi\" = eat\n\nThus, \"eat\" is represented by \"lekamkwamsi\"\n\nTherefore, in 21: \"How many children will eat these pigs?\"\n\n→ \"navila gwadi magudiwena vivila lekamkwamsi tetala tau\"\n\n\"children\" → gwadi magudiwena \n\"will\" → vivila \n\"eat\" → lekamkwamsi \n\"these pigs\" → tetala tau (from sentence 1: \"these four fish\" → \"tetala tau\" — \"tetala\" = four, \"tau\" = fish; \"pigs\" likely = tetala, origin unclear but \"tau\" used for fish)\n\nBut sentence 12: \"The clever chief killed one wild pig\" → \"lekalimati natala bunukwa\"\n\n\"bunukwa\" = wild pig\n\nSo \"pig\" = bunukwa\n\nThus, \"these pigs\" → tetala bunukwa?\n\nIn 1: \"these four fish\" → \"tetala tau\" → so \"tetala\" = four, \"tau\" = fish\n\nBut \"pigs\" is not in that form.\n\nIs there a form for \"pigs\"?\n\nIn 12: \"one wild pig\" → \"natala bunukwa\"\n\n\"in 11: things\" → \"mtosiwena\" — not specified.\n\nBut \"pigs\" = bunukwa\n\nSo \"these pigs\" → tetala bunukwa? But \"tetala\" only appears with fish.\n\nPossibility: \"these\" may be \"minasina\" or \"minana\"?\n\nSentence 1: \"these four fish\" → \"tetala tau\" — \"tetala\" = four, not \"these\"\n\n\"these\" is not directly marked in data.\n\nIn 4: \"those canoes\" → \"namwaya minana\"\n\n\"those\" = minana\n\nIn 2: \"this white man\" → \"dimdim mtona\"\n\n\"this\" = mtona\n\n\"those\" = minana\n\nSo \"these\" might be minasina (from sentence 1: \"one man\" → \"navasi\", \"four fish\" → \"tetala tau\", not these)\n\nIn 9: \"Which canoe did the chiefs see?\" → \"amakena waga legisesi gweguyau?\" — \"waga\" = those\n\n\"those\" = waga\n\nIn sentence 10: \"that beautiful child\" → \"dakuna makwena gwadi magudiwena\"\n\n\"that\" = dakuna\n\nThus, \"these\" is not directly marked. But in 20, \"these four white men\" → \"minasina dimdim mtona\" — minasina = four\n\nSo \"these\" = minasina\n\nSimilarly, in 21: \"these pigs\" → minasina bunukwa?\n\nBut in 1: \"these four fish\" → \"tetala tau\" — \"tetala\" = four\n\nThus, \"these\" is marked by \"minasina\" or \"tetala\" for quantity?\n\nTetala = four\n\nSo \"these\" likely = minasina (in context of number)\n\nBut in 20: \"these four white men\" → \"minasina dimdim mtona\" — minasina = four\n\nSo \"these\" = minasina\n\nThus, in 21: \"these pigs\" → minasina bunukwa\n\n\"children\" → gwadi magudiwena\n\n\"will\" → vivila\n\n\"eat\" → lekamkwamsi\n\nSo full: \"navila gwadi magudiwena vivila lekamkwamsi minasina bunukwa\"\n\nNow 22: \"Which woman caught those beautiful fish?\"\n\n\"which\" → am (in 5: \"which man killed\" → \"amtona tau lekalimati nayu bunukwa?\" — amtona = which)\n\n\"woman\" → legisi (old woman) — could be legisi or biyamatasi\n\n\"caught\" → minasina (from sentence 1: \"will catch\" → \"minasina\")\n\nBut \"caught\" in 1: \"catch\" → minasina\n\nSo \"caught\" = minasina\n\n\"those beautiful fish\" → waga dakuna tau\n\n\"those\" → waga (e.g., 4: \"those canoes\" → \"namwaya minana\", \"waga\" = those in 9: \"waga legisesi gweguyau\")\n\n\"beautiful\" → dakuna (sentence 10: \"that beautiful child\" → \"dakuna makwena\")\n\n\"fish\" → tau\n\nSo \"those beautiful fish\" → waga dakuna tau\n\n\"which woman\" → amtona legisi\n\nThus: amtona legisi minasina waga dakuna tau\n\nNow 23: \"Two wild dogs saw that old man.\"\n\n\"two\" → tetala (e.g., 1: \"four fish\" → \"tetala tau\")\n\n\"wild dogs\" → waga nayu (e.g., 12: \"one wild pig\" → \"bunukwa\", so \"wild\" = nayu?)\n\n\"dog\" → not in data\n\nBut dogs: possibly waga + nayu\n\n\"two wild dogs\" → tetala nayu waga\n\n\"saw\" → makesiwena (sentence 4)\n\n\"that old man\" → \"legisi\" (that old woman) — for man, likely \"mtona\" (sentence 2: \"this white man\" → \"dimdim mtona\")\n\n\"that\" → in 10: \"that beautiful child\" → \"dakuna\"\n\nSo \"that\" = dakuna\n\n\"old man\" → \"mtona\"?\n\nBut in 2: \"this white man\" → \"dimdim mtona\" — \"mtona\" = man\n\nSo \"that old man\" → dakuna mtona\n\nThus: tetala nayu waga makesiwena dakuna mtona\n\nFinal translations:\n\n19. How many canoes did those old women see? \n→ navila namwaya legisi waga makesiwena\n\n20. These four white men will look after this clever child. \n→ minasina dimdim mtona vivila teyu gwadi kwetala magudiwena\n\n21. How many children will eat these pigs? \n→ navila gwadi magudiwena vivila lekamkwamsi minasina bunukwa\n\n22. Which woman caught those beautiful fish? \n→ amtona legisi minasina waga dakuna tau\n\n23. Two wild dogs saw that old man. \n→ tetala nayu waga makesiwena dakuna mtona\n\nAll based on verb roots, articles, demonstratives, and morphological consistency from examples.\n\n\\boxed{b.1: navila namwaya legisi waga makesiwena; b.2: minasina dimdim mtona vivila teyu gwadi kwetala magudiwena; b.3: navila gwadi magudiwena vivila lekamkwamsi minasina bunukwa; b.4: amtona legisi minasina waga dakuna tau; b.5: tetala nayu waga makesiwena dakuna mtona}", + "generated_tokens": 3896, + "finish_reason": "stop", + "truncated": false, + "boxed_valid": true, + "boxed_error": "", + "boxed_text": "b.1: navila namwaya legisi waga makesiwena; b.2: minasina dimdim mtona vivila teyu gwadi kwetala magudiwena; b.3: navila gwadi magudiwena vivila lekamkwamsi minasina bunukwa; b.4: amtona legisi minasina waga dakuna tau; b.5: tetala nayu waga makesiwena dakuna mtona", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 1.0, + "ioling_format_valid": 1.0, + "ioling_format_error": 0.0, + "ioling_response_chars": 11074.0, + "ioling_final_answer_chars": 265.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Focus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.", + "planner_output": "\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\n\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\n\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\n\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n", + "anchor_output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nBut sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\nSo \"te" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 1, + "output": "Step 1: Identify key linguistic patterns from the provided examples.\n\nLook at tense markers:\n- Sentence 1: \"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\"\n - \"yena\" = future tense for \"will catch\" \n - So \"will\" is marked as \"yena\" in the catch verb (\"minasina\").\n- Sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\"\n - \"lekalimati\" = killed (past)\n- Sentence 2: \"This white man arrived.\" → \"Lekota dimdim mtona.\"\n - \"mtona\" = arrived (past)\n- Sentence 3: \"That child will arrive.\" → \"Bikota gwadi magudiwena.\"\n - \"magudiwena\" = will arrive → future, but no \"yena\" or \"vivila\" here.\n - \"magudiwena\" uses \"magudi\" + \"wena\", similar to \"mtona\" → suggests \"wena\" is the future or marking for arrive.\n- Sentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\"\n - \"tauwau\" = looked after → verb for \"look after\"\n- Sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n - \"vivila\" = will look after → future marker for \"look after\"\n - So \"vivila\" is used as future for \"look after\" (tauwau)\n\nCross-check: \n- In sentence 1, \"will catch\" uses \"yena\", not \"vivila\"\n- In sentence 3, \"will arrive\" = \"magudiwena\" — so \"wena\" is a future suffix\n- In sentence 13, \"will look after\" = \"vivila\" — \"vivila\" is future for that verb\n\nSo future tense is not monolithic: different verbs have different future markers:\n- \"catch\" → yena + catch\n- \"look after\" → vivila + look after\n- \"arrive\" → wena (in future) — not \"yena\" or \"vivila\"\n\nBut \"will\" is encoded in verb-specific way. Thus, future is not marked by a single morpheme — it depends on the verb.\n\nNow, agent-verb-object structure:\n- \"This white man arrived\" → \"Lekota dimdim mtona\"\n - \"Lekota\" = this man, agent\n - \"dimdim\" = white\n - \"mtona\" = arrived (no object)\n- \"That child will arrive\" → \"Bikota gwadi magudiwena\"\n - \"Bikota\" = that child (agent)\n - \"gwadi\" = beautiful? → but in 10: \"beautiful child\" → \"dakuna\" → so \"dakuna\" = beautiful\n - \"magudiwena\" = will arrive — agent + future verb\n- \"Saw\" → verb: makesiwena (sentence 4)\n - \"legisi\" = that woman → agent\n - \"waga\" = those canoes → object\n - \"makesiwena\" = saw\n- \"Killed\" → \"lekalimati nayu bunukwa\" → \"lekalimati\" = killed, \"nayu\" = two pigs, \"bunukwa\" = wild pigs\n\nSo verb structure: agent + descriptor (if any) + verb + object\n\nNow consider question 19: \"How many canoes did those old women see?\"\n\n- \"see\" → in sentence 4: \"legisi waga makesiwena namwaya minana\"\n - \"legisi\" = that woman\n - \"waga\" = those canoes\n - \"makesiwena\" = saw\n - \"namwaya minana\" = these four → object (number + noun)\n\nSo to form \"how many X did Y see?\" → subject = \"those old women\", object = \"canoes\", verb = \"saw\"\n\nPattern:\n- \"How many canoes did those old women see?\" → structured as: \"Navila [number] waga [agent] makesiwena?\"\n\nBut in sentence 11: \"How many things did those white men eat?\"\n- \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n- \"Kwevila\" = \"how many\"\n- \"lekamkwamsi\" = those white men\n- \"dimdim\" = white\n- \"mtosiwena\" = ate?\n\nBut there is no \"eat\" verb in the data. The verb \"eat\" is not present. In fact, the verb for \"eat\" does not appear in any provided sentence.\n\nTherefore, we may infer that \"eat\" is not in the basic lexicon or is not directly available.\n\nBut in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nSo \"mtosiwena\" must be \"eat\" → therefore, \"mtosiwena\" = eat.\n\nThus, in Kilivila, \"eat\" is \"mtosiwena\".\n\nSimilarly, \"saw\" = \"makesiwena\"\n\nSo we can generalize:\n- \"see\" = makesiwena\n- \"eat\" = mtosiwena\n- \"arrive\" = mtona / magudiwena (future)\n- \"look after\" = tauwau / vivila (future form of look after)\n\nNow, back to question 20: \"These four white men will look after this clever child.\"\n\nStructure:\n- Agent: \"these four white men\"\n- Verb: \"will look after\" → future, so use \"vivila\" + look after → \"vivila biyamatasi\"\n- Object: \"this clever child\"\n\nFrom sentence 13: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nSo \"vivila\" = will look after\n\nSo \"vivila biyamatasi\" = will look after\n\nNow, agent: \"these four white men\"\n- \"these four\" → in sentence 1: \"these four fish\" → \"tetala tau\" → \"tetala\" = four, \"tau\" = fish → so \"tetala\" = four\n- \"white men\" → in sentence 2: \"this white man\" → \"dimdim mtona\"\n- So \"these four white men\" → \"tetala dimdim mtona\" (but “mtona” is “man”)? \n - Sentence 2: \"Lekota dimdim mtona\" → \"this white man\"\n - So \"dimdim\" = white, \"mtona\" = man\n - So “white men” = \"dimdim mtona\" → plural of man is not marked? But \"mtona\" is masculine noun, and \"men\" could be plural.\n - But in \"these four\", \"tetala\" = four → \"tetala dimdim mtona\" → agent\n\nObject: \"this clever child\" → \"this\" = \"gwadi\"? → sentence 3: \"that child\" → \"gwadi\" → \"gwadi\" = child?\n- Sentence 10: \"that beautiful child\" → \"legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n - \"gwadi\" = child → so \"gwadi\" = child\n - \"dakuna\" = beautiful\n- So \"this\" → \"this\" in English may be \"mtona\" or \"bikota\"? \"bikota\" = that → \"this\" is not clearly distinct\n- But in sentence 13: \"this man\" → \"mtona\" → so \"this\" → \"mtona\"\n\nSo \"this clever child\" → \"mtona\" + \"clever\" → what is \"clever\"?\n- Sentence 7: \"That clever woman\" → \"Bigisi kwetala vivila minawena nakabitam\"\n - \"kwetala\" = clever\n- So \"clever\" = \"kwetala\"\n\nSo \"this clever child\" → \"mtona kwetala gwadi\"\n\nSo full: \"tetala dimdim mtona vivila biyamatasi mtona kwetala gwadi\"\n\nBut is \"mtona\" used for both agent and object? Yes — in sentence 13: \"women will look after this man\" → \"Navila vivila biyamatasi tau mtona\" → \"this man\" = \"mtona\"\n\nSo agent: \"these four white men\" = \"tetala dimdim mtona\"\nObject: \"this clever child\" = \"mtona kwetala gwadi\"\n\nVerb: \"will look after\" = \"vivila biyamatasi\"\n\nSo full: tetala dimdim mtona vivila biyamatasi mtona kwetala gwadi\n\nNow, 21: \"How many children will eat these pigs?\"\n\nStructure: \"how many\" → from sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nSo \"kwevila\" = how many\n\nVerb: \"will eat\" → \"will\" is marked with \"vivila\"? But earlier, \"will catch\" = yena, \"will arrive\" = magudiwena, \"will look after\" = vivila\n\nNo direct \"will eat\" → but in sentence 11, \"did eat\" → \"mtosiwena\" → past, no \"will\"\n\nIs there a future for \"eat\"?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" → no future\n\nBut is there a \"will\" marker in that sentence?\n\nThe verb is \"mtosiwena\" — which has \"wena\" ending. Could that be future?\n\nIn sentence 1: \"will catch\" = yena + minasina → yena = will\nIn sentence 3: \"will arrive\" = \"magudiwena\" → wena = future\nIn sentence 13: \"will look after\" = vivila + biyamatasi → vivila = future\n\nSo \"eat\" may have future marker \"wena\" or \"vivila\"?\n\nBut no instance of \"will eat\" in data.\n\nHowever, in sentence 11: \"did eat\" — past tense → \"mtosiwena\" → possibly without \"will\"\n\nBut the question is \"will eat\" → future\n\nSo which future marker applies?\n\nNo clear pattern. But all verbs have their own future.\n\nWe have no example of \"will eat\" → so we cannot derive a future form for \"eat\"\n\nBut in the data, \"eat\" is used in past: \"mtosiwena\"\n\nSo is it possible that the future form of \"eat\" is \"vivila\"? Or \"yena\"?\n\nGiven that \"look after\" uses \"vivila\" for future, and \"arrive\" uses \"wena\", and \"catch\" uses \"yena\", then each verb has its own future form.\n\nBut we are not given any verb with \"eat\" in future.\n\nTherefore, it is unsafe to assume a form.\n\nBut sentence 11 is the only occurrence of \"eat\" — it is in past.\n\nThus, cannot determine \"will eat\" form.\n\nTherefore, either the question is flawed or we are missing a pattern.\n\nBut the problem asks to translate — so we must assume a pattern.\n\nAlternative: maybe \"will\" is marked by a verb-specific marker, and \"eat\" has a future form not provided.\n\nBut nothing in data. So failure to derive.\n\nThus, we cannot give a correct translation for 21.\n\nBut the problem says to use the examples — and all data are given.\n\nWait — sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nIs \"mtosiwena\" a past tense? Yes — \"did eat\"\n\nBut is there any future for \"eat\"?\n\nNo. So \"will eat\" cannot be formed.\n\nUnless the future marker is shared.\n\nBut other verbs use different markers.\n\nThus, it is not possible to derive \"will eat\" from data.\n\nTherefore, the answer for 21 is not derivable — but the question requires it.\n\nAlternative: perhaps \"vivila\" is used for transitive verbs? But \"killed\" had no future, \"saw\" had \"makesiwena\", which is not \"vivila\".\n\nSo no.\n\nAnother idea: in sentence 1: \"will catch\" = \"yena\" → so \"yena\" is future for catch\nIn sentence 13: \"will look after\" = \"vivila\"\n\nSo different verbs have different markers.\n\nTherefore, no single future form.\n\nSo for \"will eat\", we must infer that the future marker for \"eat\" is not known.\n\nBut since it's asked, and only data given, we must assume one.\n\nIs there any other verb with future form that resembles?\n\n\"arrive\" → \"magudiwena\" — \"wena\" = future?\n\n\"look after\" → \"vivila\"\n\n\"see\" → not in future\n\nSo perhaps \"eat\" uses \"wena\" or \"vivila\"?\n\nBut no evidence.\n\nAlternatively, is \"mtosiwena\" the future form? But in sentence 11, it is past.\n\n\"did eat\" — past.\n\nSo future of \"eat\" must be inferred.\n\nBut no data.\n\nThus, we cannot translate 21.\n\nBut the problem gives it — so perhaps a pattern exists.\n\nWait — in sentence 4: \"saw\" → \"makesiwena\" → present or past?\n\nIn sentence 10: \"saw this stone\" → \"legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n- \"magudiwena\" → \"that old man\" → so past?\n\n\"comes after\" — \"saw\" = makesiwena\n\nSo \"makesiwena\" = saw (past)\n\nSimilarly, \"arrived\" = \"mtona\" — past\n\n\"looked after\" = \"tauwau\" — past\n\n\"will arrive\" = \"magudiwena\" — future\n\nSo \"wena\" may be future suffix.\n\nSo \"will eat\" = \"mtosiwena\" with \"wena\"? But that would be redundant.\n\nNo — \"mtosiwena\" may be the base verb.\n\nThen future form could be \"mtosiwena\" with future marker.\n\nBut no marker.\n\nBut in sentence 2: \"arrived\" = \"mtona\" — past\n\n\"will arrive\" = \"magudiwena\" — future\n\nSo \"wena\" = future for \"arrive\"\n\nSimilarly, \"saw\" = \"makesiwena\" — past\n\nNo future saw.\n\n\"will see\" not in data.\n\nSo \"see\" may not have a future form.\n\nBut for \"eat\", no future form in data.\n\nTherefore, we must conclude: future marker for \"eat\" is not established.\n\nThus, no translation for 21.\n\nBut the problem requires a translation.\n\nAlternative: perhaps \"vivila\" is used for all transitive verbs? But \"catch\" uses \"yena\", so no.\n\n\"catch\" = \"yena minasina\"\n\n\"look after\" = \"vivila\"\n\nSo different.\n\nFinal possibility: \"will\" is encoded by the verb itself.\n\nSo for \"will eat\", we don't have it — so cannot answer.\n\nBut we are forced.\n\nTherefore, only derived patterns from data:\n\n19. \"How many canoes did those old women see?\"\n- \"how many\" = \"navila\"\n- \"canoes\" = \"namwaya\"\n- \"did see\" = \"makesiwena\"\n- agent: \"those old women\"\n- \"old\" = in sentence 4: \"that old woman\" → \"legisi\" — no \"old\" descriptor\n- In sentence 4: \"that old woman\" → \"legisi\" — no descriptor\n- But in sentence 4: \"legisi\" = that woman — no adjective\n- In sentence 5: \"which man killed\" — no \"old\"\n\nIs \"old\" in any text?\nSentence 4: \"that old woman\" → absent in translation?\nSentence 4: \"Legisi waga makesiwena namwaya minana.\"\n- \"legisi\" = that woman\n- \"minana\" = old? Yes → \"minana\" = old\n\nYes — \"minana\" = old → in sentence 4, \"those canoes\" → \"namwaya minana\" → \"these four old canoes\"\n\n\"namwaya minana\" = these four old canoes\n\nSo \"old\" = minana\n\nSo \"those old women\" = \"legisi\" + \"minana\"? But \"legisi\" is that woman.\n\n\"those old women\" → \"those\" = \"tetala\"?\n- In sentence 1: \"these four fish\" → \"tetala tau\" → \"tetala\" = four\n- \"those\" → not directly.\n\n\"these\" = tetala\n\"those\" = ? \n\nIn sentence 2: \"this white man\" → \"leko\" + \"dimdim\" → \"this\"\nSentence 3: \"that child\" → \"bikota\"\n\nSo \"this\" = \"lekota\"\n\"that\" = \"bikota\"\n\n\"those\" = not used.\n\nIn sentence 9: \"which canoe did the chiefs see?\" → \"amakena waga legisesi gweguyau?\"\n\n\"amakena\" = which\n\"legisesi\" = chiefs\n\nSo no \"those\"\n\nIn sentence 13: \"how many women will look after this man?\" → \"navila vivila biyamatasi tau mtona?\"\n\n\"navila\" = how many\n\nSo \"those\" not explicitly marked.\n\nBut in sentence 6: \"the old women\" → \"leyamatasi\"\n- \"leyamatasi\" = the old women\n\nSo \"the\" = \"leyamatasi\"\n\"old\" = \"matasi\"? \"matasi\" → no, in \"leyamatasi\", \"matasi\" = women?\n\nNo — \"leyamatasi\" = old women → \"leya\" = old? \"matasi\" = women?\n\nNot clear.\n\nIn sentence 4: \"that old woman\" → \"legisi\" = woman, \"min", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12527.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Assume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.", + "planner_output": "\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\n\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\n\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\n\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n", + "anchor_output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nBut sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\nSo \"te" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 2, + "output": "Start by analyzing the given English-Kilivila pairs to extract consistent patterns.\n\nFirst, identify how questions are structured. Sentences 5, 8, 11, 13 are questions starting with “How many...” or “Which...”, suggesting a pattern for questions.\n\nLook at sentence 1: “One man will catch these four fish” → “Bibani navasi yena minasina tetala tau.” \n→ “will catch” = “yena minasina” \n→ “catch” verb = minasina, with “yena” as future marker \n“these four fish” = “tetala tau” → “tetala” = fish, “tau” = four\n\nSentence 2: “This white man arrived” → “Lekota dimdim mtona.” \n→ “arrived” = mtona? But “mtona” appears in “mtona” = man in sentence 2. Not a verb. So must be a different interpretation.\n\nWait: in sentence 8: “How many dogs arrived?” → “Navila ka’ukwa lekotasi?” \n→ “Navila” = how many? “ka’ukwa” = dogs? “lekotasi” = arrived? \n→ “lekotasi” = arrived, so “arrive” verb = lekotasi\n\nSentence 11: “How many things did those white men eat?” → “Kwevila lekamkwamsi dimdim mtosiwena?” \n→ “Kwevila” = how many? (how many + object) \n→ “lekamkwamsi” = ate? \n→ “dimdim” = white men \n→ “mtosiwena” = things \n→ So “eat” = lekamkwamsi? But “lekamkwamsi” appears to be the verb “eat” here.\n\nSentence 13: “How many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n→ “vivila” = will? \n→ “biyamatasi” = look after? \n→ “tau” = this? \n→ “mtona” = man\n\nSo \"look after\" = biyamatasi, future = vivila\n\nNow sentence 20: “These four white men will look after this clever child.” \n→ Objects: “four white men” = “tetala dimdim”? No — “tetala” = fish, “dimdim” = white \n→ “four” = tau (from tetala tau) \n→ “white men” = dimdim mtona? \n→ “will” = vivila \n→ “look after” = biyamatasi \n→ “this clever child” = “gwadi” = that, “kwetala” = clever, “minawena” = child \n→ So: “tetala dimdim mtona vivila biyamatasi gwadi kwetala minawena?”\n\nBut this matches the pattern. So overall, verb roots can be derived:\n\n- catch = minasina (transitive, present/future with yena)\n- arrived = lekotasi (see sentence 8)\n- eat = lekamkwamsi (sentence 11)\n- look after = biyamatasi (sentence 13)\n- saw = makesiwena (sentence 4: “This old woman saw those canoes” → “waga makesiwena namwaya minana”)\n\nNow, for the questions:\n\n19. How many canoes did those old women see? \n→ “how many” = navila (sentence 8: “Navila ka’ukwa lekotasi?”) \n→ “canoes” = namwaya (sentence 4: “those canoes” = namwaya minana) \n→ “old women” = legisi (sentence 4: “This old woman” → “legisi”) \n→ “see” = makesiwena (sentence 4) \n→ So: “Navila namwaya legisi makesiwena?”\n\nBut check: “those” → “minana” in sentence 4 → “namwaya minana” → “those canoes” \nSo “old women” = legisi \n→ “see” = makesiwena \n→ So “how many canoes did old women see?” = “Navila namwaya legisi makesiwena?”\n\nBut does it use “minana” for “those”? In sentence 4, “those canoes” is “namwaya minana” — so “minana” = those \nBut here, “did those old women see” — “these” or “those”? Only “those” appears in the source, so “minana” may be used for “those” in the translation. But in 19, it's not specified — it's “did those old women see” → “those” would be “minana” \nSo the object “canoes” is “namwaya” → “legisi” = old women → “makesiwena” = see \nSo: “Navila namwaya legisi makesiwena minana?”\n\nWait — does “see” take “those” as a particle? In sentence 4: “waga makesiwena namwaya minana” → “waga” = old woman, “makesiwena” = saw, “namwaya minana” = those canoes \nSo “makesiwena” takes a noun phrase with optional article or demonstrative \n→ So “legisi makesiwena namwaya minana” = old women saw those canoes \nSo for 19: “how many canoes did those old women see?” → “Navila namwaya legisi makesiwena minana?” \nBut “those” is already in “legisi” → “legisi” is the subject (old women), not “those” \nSo need to specify “those” as in “those canoes” → “namwaya minana” \nSo: “Navila namwaya legisi makesiwena minana?” — seems plausible\n\nBut “how many” = navila (sentence 8: “how many dogs arrived?” → “Navila ka’ukwa lekotasi?”)\n\nSo b.1 → 19 → Navila namwaya legisi makesiwena minana?\n\nBut is “makesiwena” reflexive? Sentence 4: “waga makesiwena” — “saw” \nSuggests “makesiwena” = saw \nSo yes.\n\nNow b.2: 20. These four white men will look after this clever child. \n→ “these four” = tetala tau? \n→ “white men” = dimdim mtona? \n→ “will” = vivila (from sentence 13: “will” = vivila) \n→ “look after” = biyamatasi \n→ “this clever child” = “gwadi kwetala minawena” \nSo: “tetala tau dimdim mtona vivila biyamatasi gwadi kwetala minawena”\n\nCheck sentence 5: “which man killed two pigs?” → “amtona tau lekalimati nayu bunukwa?” — “amtona” = which man, “tau” = two, “bunukwa” = pigs \nSo “two” = tau \n“white men” = dimdim — yes \n“four” = tau — so “tetala tau” → tetala = fish? No — “tetala” is fish in sentence 1 \nWhat is “tetala”? Sentence 1: “these four fish” → “tetala tau” \nSo “tetala” = fish? But here used for “four white men” — makes no sense.\n\nProblem: “tetala” is fish, “dimdim” = white, “mtona” = man \nIs there a “four” for men? Sentence 1: “one man” → “bibani” \nSentence 13: “how many women” → “navila” \nSentence 8: “how many dogs” → “navila” \nSo “four” is expressed by “tau” when used with a noun.\n\nIn sentence 1: “four fish” → “tetala tau” \nSo “tau” = four \nWhen used with a noun, “tau” counts it \nSo “these four white men” → “tetala dimdim mtona” — “tetala” = these four, “dimdim mtona” = white men \nYes — “tetala” marks quantity and demonstrative — “these four”\n\nSimilarly, “this” = gwadi (sentence 10: “this stone” → “gudimanabweta” — but “gwadi” appears in “gwadi magudiwena” → “that child”)\n\nIn sentence 10: “that beautiful child saw this stone” → “legisi dakuna makwena gwadi magudiwena gudimanabweta” \n→ “gwadi” = that, “magudiwena” = child, “gudimanabweta” = stone \nSo “gwadi” = that → “this” is missing?\n\nWait — is there “this”? In sentence 4: “those canoes” → “namwaya minana” → “minana” = those \nSentence 2: “this white man” → “leka dom dimdim mtona” — not in list \nSentence 13: “this man” → “tau mtona” → “tau” = this? \nSentence 13: “how many women will look after this man?” → “Navila vivila biyamatasi tau mtona?” \n→ “tau mtona” → “this man” \nSo “tau” = this \nSimilarly, “that” in sentence 3: “that child” → “bikota gwadi magudiwena” → “gwadi” = that \nSo “gwadi” = that, “tau” = this\n\nThus: \n- “this” = tau \n- “that” = gwadi\n\nSo b.2: “These four white men will look after this clever child” \n→ “These four” = tetala tau (since tetala = these, tau = four) — but tetala already implies “fish” \nSo “tetala” is not used for men.\n\nIs there a demonstrative for “men”?\n\nOnly “gwadi” and “tau” available.\n\nIn sentence 2: “this white man” — not given \nSentence 10: “this stone” → “gwadi” + “gudimanabweta” \nSo “this” = tau or gwadi? \nIn 13, “this man” = “tau mtona” \nIn 3, “that child” = “bikota gwadi magudiwena” → “gwadi” = that \nSo likely: \n- “this” = tau \n- “that” = gwadi\n\nAnd “these” might be “tetala” — as in sentence 1: “these four fish” = “tetala tau”\n\n→ So “these four white men” = “tetala tau dimdim mtona”\n\n→ “will” = vivila \n→ “look after” = biyamatasi \n→ “this clever child” = “tau gwetala minawena”\n\nSo: “tetala tau dimdim mtona vivila biyamatasi tau gwetala minawena”\n\nBut “this” appears twice — “these four” = tetala tau (these four), “this clever child” = tau\n\nIs “tau” repetitive? Possibly.\n\nAre there other ways? No evidence.\n\nSo b.2: tetala tau dimdim mtona vivila biyamatasi tau gwetala minawena\n\nBut check sentence 10: “this stone” → “gwadi magudiwena gudimanabweta” — so “gwadi” for “this”? But “gwadi” is used for “that”.\n\nIn 10: “that beautiful child” → “dakuna makwena gwadi magudiwena” → “gwadi” = that \n“this stone” → “gudimanabweta” — no “gwadi” — so “this” = no demonstrative? But “gudimanabweta” is just stone.\n\nContradiction?\n\nWait: in sentence 10: “that beautiful child saw this stone” → “Legisi dakuna makwena gwadi magudiwena gudimanabweta” \nSo “gwadi” → that child, “gudimanabweta” → this stone \nSo “this” = gudimanabweta — no demonstrative particle ? \n\nBut in sentence 13: “this man” → “tau mtona” — “tau” = this \nIn sentence 10: “this stone” → no particle with “gudimanabweta” \nBut in sentence 4: “those canoes” → “namwaya minana” — “minana” = those \n\nThus, likely: \n- “this” = tau \n- “that” = gwadi \n- “those” = minana\n\nAnd in 13: “this man” = “tau mtona” \nIn 10: “this stone” = “gudimanabweta” — the noun itself — but no particle? Why?\n\nPerhaps “this” is embedded in the noun. But “this” is not a particle.\n\nAlternatively, in sentence 10: “this stone” might not have a demonstrative due to syntactic position?\n\nBut in 13, “this man” has “tau” — so “tau” = this.\n\nSimilarly, “that” = gwadi — in sentence 3: “that child” → “bikota gwadi magudiwena” — so “gwadi” = that.\n\nSo for b.2: “this clever child” = “tau gwetala minawena”\n\nBack to 19: “how many canoes did those old women see?” \n→ “how many” = navila \n→ “canoes” = namwaya \n→ “those old women” = legisi (old women) — “those” = minana \n→ “see” = makesiwena \n\nSo: “Navila namwaya legisi makesiwena minana?”\n\nBut in sentence 4: “legisi waga makesiwena namwaya minana” — “waga” = old woman, so “legisi” = old women, “makesiwena” = saw, “namwaya minana” = those canoes\n\nSo structure: [how many] [object] [subject] [verb] [demonstrative]\n\nBut in that example, the demonstrative is on object — in 4: “namwaya minana” — so object has “minana” = those\n\nIn 19, the object is “canoes” — should have “minana” → so “namwaya minana”\n\nSubject is “old women” → “legisi” — does “legisi” include “those”? No — it's just “old women”\n\nSo “did those old women see” → “legisi makesiwena” — “those” is not in subject — so only on object.\n\nBut in sentence 4, “waga makesiwena namwaya minana” → subject is “waga”, object “namwaya minana”\n\nSo the demonstrative is on object.\n\nThus, for 19: “Navila namwaya minana legisi makesiwena?”\n\nBut that would be “how many canoes (those) did old women see?” — but the question is “how many canoes did those old women see?” — “those” modifies subject.\n\nIn English, “those” modifies “old women”, not “canoes”.\n\nSo must be in subject.\n\nBut in Kilivila, the demonstrative may be attached to subject or object.\n\nIn sentence 4: “waga” = old woman (singular), “legisi” = old women (plural)\n\nSo “old women” = legisi\n\nDid “those” go to subject?\n\nNo — sentence 4: “legisi waga makesiwena namwaya minana” — “waga” is subject, “legisi” is not used.\n\nOnly “waga” is the subject.\n\n“legisi” appears in sentence 4 as subject? No — sentence 4: “Legisi waga makesiwena namwaya minana” — so “Legisi” is subject, “waga” is noun?\n\n“Legisi” = old woman, “waga” = saw? No — “waga” = noun?\n\nCheck sentence 4: “Legisi waga makesiwena namwaya minana” \n→ “Legisi” → old women? \n→ “waga” → saw? But “makesiwena” is saw — so “waga” must be a noun.\n\nWait — likely typo in translation? Or word order.\n\nIn sentence 4: “This old woman saw those canoes” → “Legisi waga makesiwena namwaya minana”\n\nPossibility: “waga” = saw? But “makesiwena” is the verb.\n\nSo probably: “legisi” = old women, “waga” = saw? But no verb for “saw” in the root?\n\nOnly “makesiwena” = saw — so the verb is “makesiwena”, so “legisi makesiwena waga namwaya minana”?\n\nBut translation says “Legisi waga makesiwena namwaya minana” — so likely word order is subject-verb-object or subject-object-verb.\n\nBut “waga” is between subject and verb.\n\nPerhaps “waga” is a noun meaning “woman” — so “old women saw canoes” — “waga” = “that woman”?\n\nBut sentence 2: “This white man arrived” → “Lekota dimdim mtona” — no “waga”\n\nOnly in sentence 4: “Legisi waga makesiwena namwaya minana”\n\nIf “waga” is part of the object — “waga” = canoes? Unlikely.\n\nPerhaps typo: likely “legisi” = subject, “waga” = object, “makesiwena” = verb → “old women saw canoes” — but “waga” is not “canoes”\n\nIn sentence 1: “Bibani navasi yena minasina tetala tau” — “navasi” = will catch? “minasina” = catch\n\n“Bibani” = one man\n\nLikely “waga” is the object in sentence 4.\n\nBut canoes are “namwaya” — so “namwaya” is object.\n\nSo “legisi waga makesiwena namwaya minana” — awkward.\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12013.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Propose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.", + "planner_output": "\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\n\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\n\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\n\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n", + "anchor_output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nBut sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\nSo \"te" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_1x4", + "sample_index": 3, + "output": "Start by analyzing the structure and verb alignment in the given English-Kilivila pairs.\n\nLook at sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n\"minasina\" = catch (past or present), \"tetala\" = these four fish → \"tetala tau\" = \"these four fish\" \n\"will catch\" → \"minasina\" is used, not a future marker; future is implied by context or modal. \n\"will\" is not marked in Kilivila, suggesting that future is implicit or context-based.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n\"mtona\" = arrived → verb for \"arrive\" \nSo \"arrive\" = mtona.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n\"gwadi\" = that, \"magudiwena\" = will arrive? But \"magudiwena\" seems like a future or modalized form. \nWait: \"Bikota\" = that (subject), \"gwadi\" = that (demonstrative), \"magudiwena\" = will arrive? \nBut \"magudiwena\" is not \"mtona\" → shows morphological variation: the future is marked in \"magudiwena\" not in \"mtona\".\n\nCompare:\n- \"This white man arrived\" → \"Lekota dimdim mtona\"\n- \"That child will arrive\" → \"Bikota gwadi magudiwena\"\n\n\"mtona\" vs. \"magudiwena\" → both involve arrival, but one is present, one is future.\n\nSo likely \"mtona\" is base, \"magudiwena\" = \"will arrive\" (future).\n\nSimilarly, sentence 4: \n\"That old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n\"makesiwena\" = saw \n\"namwaya\" = those canoes \nSo \"saw\" = makesiwena\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n\"lekalimati\" = which man \n\"bunukwa\" = killed → so \"killed\" = bunukwa\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n\"teyu\" = looked after \n\"nunumwaya\" = two men \nSo \"look after\" = teyu\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n\"kwetala\" = clever \n\"vivila\" = something \n\"minawena\" = will see? But \"minawena\" = see? \n\"minasina\" = catch (sentence 1) \n\"makesiwena\" = saw (sentence 4) \n\"minawena\" = see? Possibly → \"minawena\" = to see (future) \n\"nakabitam\" = something → \"minawena\" = see \nSo \"see\" = minawena (future) or makesiwena (past)? \nIn sentence 4, \"makesiwena\" = saw (past) \nIn sentence 7: \"minawena\" = will see → future \nSo likely: \"see\" = minawena (future), \"makesiwena\" (past)\n\nBut sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\" \nPast → makesiwena\n\nSentence 7: \"Bigisi kwetala vivila minawena nakabitam\" → \"that clever woman will see something\" → future → minawena\n\nSo \"see\" = makesiwena (past), minawena (future)\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n\"ka’ukwa\" = dogs \n\"lekotasi\" = arrived \nSo \"arrive\" = lekotasi\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"legisesi\" = which canoe \n\"gweguyau\" = saw? \nBut no \"saw\" verb in this context — \"gweguyau\" = saw \nSo \"saw\" = gweguyau?\n\nWait — confusion: \nSentence 4: \"makesiwena\" = saw \nSentence 9: \"gweguyau\" = saw? \nBut \"gweguyau\" is used as past tense form of \"see\" → so \"see\" = gweguyau?\n\nConflict with earlier. \nSentence 4: \"makesiwena\" → saw \nSentence 9: \"gweguyau\" → saw \nTwo forms?\n\nPossibility: \"makesiwena\" and \"gweguyau\" are different forms of \"see\"? \nPossibly a morphological difference.\n\nBut sentence 7: \"minawena\" = will see \nSentence 9: \"gweguyau\" = saw \n\nSo \"see\" appears in multiple forms:\n- makesiwena → saw (past, in sentence 4)\n- gweguyau → saw (past, in sentence 9)\n- minawena → will see (future, in sentence 7)\n\nAll are past or future verbs for \"see\"? \nWait — sentence 7: \"will see something\" → minawena \nOthers: \"saw\" → makesiwena or gweguyau\n\nSo maybe \"see\" is not a single verb — but the pattern in structure matters.\n\nObserve the structure of question 19: \n\"How many canoes did those old women see?\" \n→ Based on sentence 4: \"that old woman saw those canoes\" → \"Legisi waga makesiwena namwaya minana\" \n\"Legisi\" = that old woman \n\"waga\" = those canoes → object \n\"makesiwena\" = saw \n\nSo the pattern for \"X saw Y\" → [subject] [object] makesiwena? \nBut in sentence 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = which canoe? \n\"legisesi\" = which canoe? \n\"Amakena waga legisesi\" → which canoe? \n\"gweguyau\" = saw? \nSo \"did [agent] see [object]\" → [which canoe] [gweguyau]? \nBut verb is gweguyau — past tense \"saw\"\n\nIn sentence 4: subject = Legisi (that old woman), object = waga (those canoes), verb = makesiwena → \"saw\"\n\nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → [which canoe] [saw] [object]? \nNo — \"Amakena waga legisesi\" → which canoe? — seems like \"which canoe\" is the subject? \n\"Amakena\" = that, \"waga\" = those canoes? \nWait — \"Amakena waga legisesi\" → \"which canoe did the chiefs see?\"? \n\"Amakena\" = which? \n\"waga\" = those? \n\"legisesi\" = canoe? \nNo — \"legisesi\" is \"which canoe\" — so \"Amakena waga legisesi\" = which canoe? \nThen \"gweguyau\" = saw → so \"which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \nSo \"did (agent) see (object)\" → \"Amakena waga legisesi gweguyau?\" \nBut \"gweguyau\" is the verb.\n\nIn sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\" \nSo agent: Legisi \nobject: namwaya minana → \"those canoes\" \nverb: makesiwena\n\nSo pattern: [agent] [object] [verb] → past tense verb for \"see\"\n\nTherefore, in sentence 19: \"How many canoes did those old women see?\" \n→ Similar to sentence 4: \"how many X did Y see?\" \nBut here, \"how many canoes did those old women see?\" → so agent = those old women, object = canoes\n\nSo structure: [how many] [object] did [agent] see?\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → agent → Legisi, object → namwaya minana, verb → makesiwena\n\nSo in 19: agent = \"those old women\", object = \"canoes\"\n\nWhat form of \"see\" is used? \nIn sentence 4: \"makesiwena\" = saw \nIn sentence 9: \"gweguyau\" = saw \nBut in both cases, it's past tense. \nSentence 7: \"minawena\" = will see — future\n\nSo \"see\" has different forms:\n- past: makesiwena or gweguyau\n- future: minawena\n\nBut in the question, \"did see\" = past → so past tense verb\n\nWhich form to use? \nSentence 4 uses \"makesiwena\" with agent → \"Legisi\" \nSentence 9 uses \"gweguyau\" with \"did the chiefs see\" → \"Amakena waga legisesi gweguyau?\" \nSo \"Amakena waga legisesi\" = which canoe? \nSo agent is implied — \"the chiefs\" is missing?\n\nWait — sentence 9: \"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n\"Amakena\" = which canoe? \n\"legisesi\" = which canoe? \n\"Amakena waga legisesi\" → which canoe? \n\"Amakena\" is used as \"which\" — could be error.\n\nPossibility: \"Amakena\" = the, \"waga\" = those, \"legisesi\" = which? — unclear.\n\nBut verb is \"gweguyau\", past tense of \"see\"\n\nSentence 4: \"makesiwena\" — past tense of \"see\"\n\nSo both are forms of \"saw\"\n\nWhich one to use for translation?\n\nPerhaps \"saw\" = makesiwena in most cases.\n\nSentence 10: \"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n\"Legisi\" = that child \n\"dakuna\" = beautiful \n\"gwadi\" = this \n\"magudiwena\" = will arrive? \nWait — \"magudiwena\" → from sentence 3: \"that child will arrive\" = \"Bikota gwadi magudiwena\" → so \"magudiwena\" = will arrive\n\nBut here \"saw this stone\"? — \"gudimanabweta\" = stone? \nStructure: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" \nPossibly \"magudiwena\" = arrived? But the child saw the stone. \nSo \"saw\" must be encoded earlier.\n\nBut no \"saw\" verb in sentence 10 — the verb is missing.\n\nWait — sentence 10: \"That beautiful child saw this stone.\" → translation given: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\nBut \"magudiwena\" is future \"arrive\", not \"saw\".\n\nSo contradiction.\n\nUnless the translation is wrong.\n\nWait — re-read sentence 10: \n\"The beautiful child saw this stone.\" → translation: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\"\n\n\"magudiwena\" = will arrive? But the child saw the stone — not arrived.\n\nThis suggests that \"gudimanabweta\" = stone, and \"magudiwena\" is not related.\n\nBut verb missing.\n\nNo verb for \"saw\" appears in the list.\n\nIn sentence 4: \"makesiwena\" → saw \nIn sentence 7: \"minawena\" → will see \nIn sentence 9: \"gweguyau\" → saw\n\nSo \"saw\" has multiple forms: makesiwena, gweguyau, minawena\n\nBut minawena = will see, future \ngweguyau = past saw \nmakesiwena = past saw\n\nSo all are past or future for \"see\"\n\nIn sentence 10: \"that beautiful child saw this stone\" → should have \"saw\" verb.\n\nBut translation has \"magudiwena\" — which is will arrive — so error.\n\nWait — sentence 10 translation: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n\"Legisi\" → that child \n\"dakuna\" → beautiful \n\"makwena\" → this? \n\"gwadi\" → this? \n\"gudimanabweta\" → stone \nSo it's \"that beautiful child, this [something] will arrive stone?\" — nonsensical.\n\nConclusion: typo in translation.\n\nLikely, \"saw\" is encoded in \"makesiwena\" or \"gweguyau\".\n\nTherefore, in 19: \"How many canoes did those old women see?\" \n→ Based on sentence 4: agent = \"those old women\" → \"lelegisi\" or \"leyamatasi\"? \nSentence 3: \"Bikota gwadi magudiwena\" → \"that child will arrive\" \nSentence 6: \"Leyamatasi teyu tauwau nunumwaya\" → \"old women looked after two men\" → \"leyamatasi\" = old women \nSo \"old women\" = leyamatasi\n\n\"those\" = yena? \nSentence 1: \"yena minasina\" → \"these four\" — \"yena\" = these four\n\nSo \"those\" = yena?\n\nSentence 2: \"Lekota dimdim mtona\" → \"this white man\"\n\nSentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\" \n\"namwaya minana\" = those canoes\n\nSo \"those canoes\" = namwaya minana\n\n\"how many canoes\" = navila? \nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" → navila = how many\n\nSo \"how many\" = navila\n\nSo 19: \"How many canoes did those old women see?\" \n→ navila namwaya leyamatasi makesiwena?\n\nBut agent: \"those old women\" → leyamatasi (old women), \"those\" → yena?\n\n\"yena\" = these/that — \"those\" might be yena\n\nIn sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"that old woman saw those canoes\"\n\n\"namwaya minana\" = those canoes\n\nSo \"those\" = namwaya minana → yes\n\nSo \"those old women\" = leyamatasi yena?\n\nBut \"yena\" is used for \"these four\" in sentence 1.\n\nIn sentence 19: \"those\" → similar to \"those canoes\" in sentence 4 → \"namwaya minana\" = those canoes\n\nSo \"those old women\" → \"leyamatasi yena\"\n\n\"see\" = makesiwena (past)\n\nSo full: \"navila namwaya leyamatasi yena makesiwena?\"\n\nBut order — likely subject first.\n\nIn sentence 4: \"Legisi waga makesiwena namwaya minana\" → agent, object, verb\n\nSo here: agent: leyamatasi yena, object: namwaya, verb: makesiwena\n\nBut \"how many\" = navila → at beginning\n\nSo: navila namwaya leyamatasi yena makesiwena?\n\nBut is \"namwaya\" used for \"canoes\"? Yes, in sentence 4.\n\nSo translation: navila namwaya leyamatasi yena makesiwena?\n\nBut sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" — \"ka’ukwa\" = dogs\n\nSo \"how many X\" = navila X\n\nSo 19: navila namwaya leyamatasi yena makesiwena?\n\nWait — agent is \"those old women\" — \"leyamatasi yena\" \nObject: \"canoes\" — \"namwaya\"\n\nVerb: \"saw\" = makesiwena\n\nYes.\n\nNow 20: \"These four white men will look after this clever child.\" \n\"will look after\" = teyu (sentence 6)\n\n\"these four\" — sentence 1: \"yena minasina\" → \"these four\" → yena\n\n\"white men\" — sentence 2: \"dimdim\" = white → \"dimdim\" = white man\n\n\"will\" → future → \"minawena\" in sentence 7 → \"will see\"\n\nBut in sentence 6: \"look after\" = teyu — no future marker\n\nIn sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"tau mtona\" = this man → so future? \n\"will look after\" = teyu? But \"tau mtona\" appears — so future?\n\nPossibly, \"teyu\" is used with future or present.\n\nBut in sentence 6: \"The old women looked after two men\" → \"leyamatasi teyu tauwau nunumwaya\" → past\n\nNo future form.\n\nBut sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = how many? \n\"biyamatasi\" = women \n\"tau mtona\" = this man\n\nSo \"will\" is not marked — \"vivila biyamatasi tau mtona\" — but \"vivila\" = how many?\n\nNo verb.\n\n\"look after\" = teyu — likely present or future.\n\nPossibly \"teyu\" is an aspectual or modal verb.\n\nIn sentence 20: \"these four white men will look after this clever child\"\n\nAgent: \"these four white men\" → \"yena dimdim\" (these four white men)\n\n\"will\" → future → may require future form\n\n", + "generated_tokens": 4096, + "finish_reason": "length", + "truncated": true, + "boxed_valid": false, + "boxed_error": "missing_boxed_answer", + "boxed_text": "", + "score_fraction": 0.0, + "exact": 0.0, + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ], + "unit_results": [ + { + "unit_id": "b.1", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.2", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.3", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.4", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + }, + { + "unit_id": "b.5", + "points": 1.0, + "matched": false, + "match_type": "none", + "final_similarity": 0.0, + "full_output_similarity": 0.0 + } + ], + "reward_logs": { + "ioling_unit_accuracy": 0.0, + "ioling_exact_accuracy": 0.0, + "ioling_matched_units": 0.0, + "ioling_total_units": 5.0, + "ioling_keyed_exact_reward": 0.0, + "ioling_strict_substring_reward": 0.0, + "ioling_has_boxed_answer": 0.0, + "ioling_format_valid": 0.0, + "ioling_format_error": 1.0, + "ioling_response_chars": 12378.0, + "ioling_final_answer_chars": 0.0, + "ioling_final_answer_too_long": 0.0, + "ioling_final_answer_char_limit": 600.0 + }, + "prompt": "Solve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nAdditional private guidance for this attempt:\nFollow this private strategy memo as a hypothesis, but verify it from the examples and fix any flaw you find. Present the solution as ordinary reasoning from the problem statement alone; do not mention the memo.\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n\nUse the guidance only to improve the derivation. The final line must still be exactly one boxed keyed answer using only the required unit ids.", + "hint": "Re-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.", + "planner_output": "\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\n\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\n\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\n\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n", + "anchor_output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\"\n\nBut sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\"\n\nSo \"te" + } + ], + "planner_records": [ + { + "split": "train", + "record_id": "iol-2012-individual-p5-sub-d", + "planner_index": 0, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- d.1 / word: answer for this requested item\n- d.2 / to exhaust: answer for this requested item\n\nFinal answer shape: \\boxed{d.1: ; d.2: }\n\nProblem #5 (20 points). Here are some words and word combinations in Rotuman as well as their English translations:\n\n‘el‘ele — shallow\n‘ele — to be near\n‘olo — to cut\na‘öf fau — year’s end\nfäeag ‘u‘u — to use sign language\nfau — year\nha.fha.fu — rocky\nhuag ‘el‘ele — impatient\nhuag to‘a — courageous\nhül ha.fu — to blow (of a hurricane)\nhün kia — base of the neck\nhuli — to turn over\nhuni — lower end\nis ‘ā — sharp-pointed\nis susu — nipple\nlala — deep\nmaf tiro — spectacles\nmamasa — solid\nma.titi — coldness\nma.tit mamasa — ice\nmoafmofa — littered with rubbish\nniu — copra\nnu‘suar tiro — window\nnu‘sura — door\npala — pierce\npiri — to curl\npoagpoga = palpala — covered with holes\npogi — night\npuhra.ki — to boil, to bubble up\npulu — glue\nka.lu — bracelet; to encircle\nriamrima — shiny\nrū huga — stomach-ache\nto‘a — hero\n\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nRotuman belongs to the Austronesian family. It is spoken by approximately 9000 people in Fiji. ‘ is a consonant (the so-called glottal stop); a. is an open o; ä is approximately the a in crack; ö is like French eu or German ö; ü is like French u or German ü. The mark ¯ denotes vowel length. Copra is the dried kernel of a coconut.\n\nTarget: solve (d) only.\n\nTarget question:\n(d) Using the material given above you cannot translate ‘word’ and ‘to exhaust’ into Rotuman with certainty. What would the theoretically possible translations of these words into Rotuman be?\n\nSAMPLED ATTEMPT:\nWe are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\n\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.\n\n\n\nConsider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.\n\n\n\nUse absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.\n\n\n\nAnalyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension.\n", + "approaches": [ + "Focus on root reuse and semantic extension. Identify existing verbs with meanings related to consumption or depletion. \"To use\" (fäeag) is directly given. \"To boil\" (puhra.ki) involves a process of consumption or reduction. \"To blow\" (hül ha.fu) may imply forceful removal. Among these, \"to boil\" most directly parallels \"to exhaust\" in process-based depletion. Verification: in many languages, \"to boil down\" is a metaphor for reducing to nothing — a core meaning of \"exhaust\". This aligns with the semantic field of \"to exhaust\" being a form of consumption. Thus, puhra.ki is a plausible theoretical translation based on metaphorical extension.", + "Consider compound formation patterns. The data shows that affixes or stems modify meaning (e.g., huag ‘el‘ele → impatient). \"To use\" is given as fäeag. \"To exhaust\" could be fäeag + a suffix meaning \"completely\" or \"to the end\". No such suffix is directly present, but \"kia\" (base of the neck) and \"to‘a\" (hero) appear in compounds. \"kia\" may represent a locative or endpoint. Thus, fäeag kia could mean \"to use the end\" or \"to use completely\". Verification: in Austronesian languages, compound verbs with endpoint markers often denote completion. Though \"kia\" is not a clear completion marker, its use in a physical endpoint supports its potential as a completion suffix in derived verbs.", + "Use absence of direct match to infer structural constraints. No word in the list translates to \"word\" or \"to exhaust\", so theoretical forms must follow known morphological patterns. \"Word\" likely derives from a verb of \"saying\" or \"making a sound\". Verbs like \"pala\" (to pierce) or \"puri\" (not present) are not relevant. \"To be near\" (‘ele) suggests something accessible — possibly a candidate for \"word\" as \"something near\" or \"something known\". Thus, ‘ele could be a plausible root. Verification: \"word\" as \"something known\" or \"something near\" fits the semantic field of knowledge-based entities. Though weak, it is the only plausible stem without direct contradiction.", + "Analyze affixation and root stacking. Many compounds use a stem + stem structure (e.g., huag ‘el‘ele, hün kia). The root \"to use\" (fäeag) appears standalone. To form \"to exhaust\", a suffix indicating completion or endpoint is needed. \"to‘a\" (hero) or \"kia\" (base) are not clearly intensive. However, \"ma.tit mamasa\" = ice, combining coldness and solidity — showing that compound nouns with adjectives are common. Similarly, a verb like \"fäeag\" + \"mamasa\" (solid) could imply \"to use solidly\", but that is not \"exhaust\". Instead, \"to exhaust\" likely requires a process root. The only process root with a depletion connotation is \"puhra.ki\" (to boil). Verification: boiling implies reduction and energy loss — a direct semantic match to \"to exhaust\" in physical or abstract contexts. This makes puhra.ki a stronger candidate than any compound extension." + ], + "anchor_output": "We are given a list of Rotuman words and their English equivalents, and asked to infer the theoretically possible translations of \"word\" and \"to exhaust\" into Rotuman, even though we cannot translate them with certainty from the data.\n\nWe must analyze the given examples to find patterns that could help us determine plausible roots or affixes for \"word\" and \"to exhaust\".\n\nStep 1: Look for patterns in the data.\n\nAll entries are compound or base words with morphological structure. Many are compound words formed using base stems and affixes.\n\nFor example:\n- ‘ele — to be near\n- ‘olo — to cut\n- a‘öf fau — year’s end → fau = year, a‘öf? Could be a particle or modifier\n- fau — year\n- huag ‘el‘ele — impatient → huag is a prefix, ‘el‘ele = shallow, so “impatient” = “to be near shallow”?\n- huag to‘a — courageous → huag + to‘a (hero)\n- hül ha.fu — to blow (of a hurricane) → hül + ha.fu (rocky?) → \"to blow of rocky\"\n- hün kia — base of the neck → hün + kia\n- huli — to turn over\n- huni — lower end\n- is ‘ā — sharp-pointed\n- is susu — nipple → is + susu\n- lala — deep\n- maf tiro — spectacles → maf + tiro (lenses?)\n- mamasa — solid\n- ma.titi — coldness\n- ma.tit mamasa — ice → coldness + solid\n- moafmofa — littered with rubbish\n- niu — copra\n- nu‘suar tiro — window → nu‘suar + tiro\n- nu‘sura — door\n- pala — pierce\n- piri — to curl\n- poagpoga = palpala — covered with holes → poagpoga = palpala; repeated form\n- pogi — night\n- puhra.ki — to boil, to bubble up\n- pulu — glue\n- ka.lu — bracelet; to encircle\n- riamrima — shiny\n- rū huga — stomach-ache\n- to‘a — hero\n\nWe see multiple affixes and combinations:\n- Some stem + stem (e.g., huag ‘el‘ele)\n- Some stem + root with morpheme (e.g., hün kia)\n- Some compound with a shared root (e.g., ma.tit mamasa → ice)\n\nObservation: Many verbs are formed with a root and a modifier or affix, often indicating location, quality, or action.\n\nNow, the verbs:\n- ‘olo — to cut\n- huli — to turn over\n- pala — pierce\n- piri — to curl\n- puhra.ki — to boil\n- hül ha.fu — to blow (of a hurricane)\n\nAlso, nouns:\n- fau — year\n- lala — deep\n- niu — copra\n- to‘a — hero\n\nNo word in the list is clearly “word” or “to exhaust”.\n\nBut we are asked: What are the **theoretically possible** translations?\n\nThat means: what forms could exist based on known patterns, even if not directly given?\n\nStep 2: Consider what \"word\" might be.\n\nIn many Austronesian languages, words related to \"word\" are often derived from roots meaning \"to say\", \"to speak\", or \"to express\".\n\nWe do not have a word for “to speak” or “to say”.\n\nBut we do have a base form: “to be near” = ‘ele.\n\nWe have \"to cut\" = ‘olo.\n\nWe have “to boil” = puhra.ki.\n\nWe have “to encircle” = ka.lu.\n\nWe have “to pierce” = pala.\n\nIs there a likely root for \"to speak\"?\n\nNo direct match. But perhaps a verb meaning \"to be near\" or \"to touch\" could be extended.\n\nIn some languages, \"word\" is derived from \"to utter\", \"to speak\", or \"to make a sound\".\n\nIn Rotuman, a root for \"to say\" may be missing, but there might be a compound involving a root like “pala” (to pierce) or “puri” (to speak) — but “puri” is not present.\n\nHowever, we see a pattern: many verbs are formed from a root with a bound morpheme or affix.\n\nAnother possibility: in Austronesian languages, there may be a root related to “to make” or “to form”.\n\nCould “word” be derived from a verb meaning “to make”?\n\nWe have no “to make”, but “to turn over” (huli), “to cut” (olo), “to boil” (puhra.ki), “to pierce” (pala).\n\nStill no clear candidate.\n\nWe might suspect that “word” would be a noun formed from a verbal root.\n\nBut we can infer: in such languages, a common way to form \"word\" is from a verb meaning “to speak” or “to say”.\n\nBut “to say” is not present.\n\nHowever, “to be near” = ‘ele. Could “word” be related to “to be accessed” or “to be near” — meaning “something that is near”?\n\n“word” can mean “something known” or “something said”.\n\nAlternatively, “word” could be formed with a root like “ta” (to go) or “pi” (to do), but these aren’t given.\n\nBut look at “poki” — not in list.\n\nNo strong basis for word.\n\nSo the theoretically possible forms could be derived from common patterns in Austronesian languages.\n\nWe see:\n- Compound formation: e.g., a‘öf fau → year’s end\n- Affixation: e.g., huag ‘el‘ele → impatient\n\nAlso, note: “to exhaust” is a verb.\n\nPossible meanings:\n- To deplete\n- To use up\n- To burn out\n\nWe have “to cut” (‘olo) — cutting could mean to reduce, to cut off.\n\n“to boil” (puhra.ki) — to bubble up, to heat, to overcome?\n\n“to blow” (hül ha.fu) — to blow off?\n\n“to pierce” (pala) — could mean to go through?\n\n“to turn over” (huli) — could mean to reverse?\n\n“to cut” (olo) — could be used to mean to deplete?\n\nIn some languages, “to exhaust” is formed from a root meaning “to use up”, “to consume”.\n\nWe have “to use sign language” = fäeag ‘u‘u — so “to use” is present.\n\n“to use” = fäeag?\n\nSo “to use” is fäeag.\n\nTherefore, “to exhaust” could be related to “to use up” → “to use completely”.\n\nSo “to exhaust” might be formed as “to use completely”.\n\nPossible root: “fäeag” (to use), with a suffix meaning “completely” or “up”.\n\nIs there a suffix in the data?\n\n“to boil” = puhra.ki — perhaps “ki” at the end is a critical suffix.\n\n“to blow” = hül ha.fu — no suffix.\n\n“to pierce” = pala — simple.\n\nBut look: “ma.tit mamasa” = ice — compound of coldness + solid.\n\n“pala” = pierce.\n\n“pogi” = night.\n\n“nu‘suar tiro” = window → nu‘suar = door? nu‘sura = door → perhaps tiro = window?\n\nSo “tiro” appears as part of a noun.\n\nIn “maf tiro” = spectacles — so “tiro” again used as part of a noun.\n\nSo tiro may be a root meaning “lens” or “glass”.\n\nIs there a word meaning “to use up”?\n\nWe have “fäeag” = to use — so “to exhaust” could be “fäeag” with a suffix meaning “fully” or “to the end”?\n\nCould “to exhaust” be “fäeag” with a suffix like “kia” or “to‘a”?\n\nWe have “hün kia” = base of the neck — “kia” is used.\n\nBut \"kia\" appears in a noun phrase.\n\nWe also have “huli” — to turn over.\n\n“to turn over” could imply “to use all of it” or “to exhaust”?\n\n“to turn over” might imply a process involving reversal, e.g., of a supply — could be extended to “to use up”.\n\nBut no direct link.\n\nAlternatively, “to boil” might be related — “to boil” could mean to consume energy, to deplete?\n\nIn some languages, “to boil down” means to reduce to a minimum — like to exhaust.\n\nCould “to exhaust” be related to “to boil”?\n\n“puhra.ki” = to boil, to bubble up — could involve a process of depletion?\n\nPossibly.\n\nBut is there a root that combines “use” + “to the end”?\n\nWe have “fäeag” = to use.\n\nCould it be “fäeag kia” or “fäeag to‘a”?\n\nBut “kia” is part of “hün kia” — not clearly used.\n\nAnother idea: the root “moafmofa” = littered with rubbish — implies fullness.\n\n“covered with holes” = poagpoga = palpala — implies presence of holes, so something is worn out?\n\n“to wear out” is not directly there.\n\n“to exhaust” → could be similar to “to wear out”.\n\nIn some languages, “to exhaust” is formed with a reduplicative structure or an agentive suffix.\n\nBut no such form is given.\n\nPossibly, without a direct root, the only way to form a plausible word for “to exhaust” is to derive it from “to use” + an agentive or intensive suffix.\n\nGiven that, the most plausible root is “fäeag” (to use), and adding a suffix meaning “up” or “completely”.\n\nIn Rotuman, “-titi” means coldness, but not “up”.\n\nIs there a particle meaning “to the end”?\n\nWe don’t have one.\n\nBut note: “to use” exists: fäeag.\n\nTherefore, “to exhaust” could be derived as fäeag + suffix.\n\nCommon forms in Austronesian: often a root + intensifier or agent.\n\nThe only clear stem we have that could mean “to use” is fäeag.\n\nSo theoretically, “to exhaust” could be fäeag + a suffix like “–kia”, “–to‘a”, or “–pala” — but no such form appears.\n\nAlternatively, could “to exhaust” be “pala” meaning “to pierce” — to pierce through is to consume?\n\nUnlikely.\n\nAnother possibility: the root “pi” or “ta” not given.\n\nBut perhaps a compound like “puri” — not given.\n\nSo we are forced to infer that since “to use” exists, and “to exhaust” is a kind of “to use completely”, the only plausible form based on known roots is **fäeag kia** or **fäeag to‘a**.\n\nWe have “huag to‘a” = courageous — that’s a compound.\n\n“huag ‘el‘ele” = impatient — so affixes can modify meaning.\n\nSo “fäeag kia” could be a compound meaning “to use the base of the neck”? Unlikely.\n\nAlternatively, “to exhaust” could be “puhra.ki” — to boil — as in boiling down, to reduce to a point.\n\nThat is plausible.\n\nIn some languages, “to boil down” means to reduce, to exhaust.\n\nSo “to boil” could be a metaphorical use for “to exhaust”.\n\nSimilarly, “to blow” — “hül ha.fu” — might mean to remove strongly.\n\nBut “to boil” is the strongest candidate.\n\nThus, theoretically possible translation of “to exhaust” is **puhra.ki** — because boiling implies consumption and depletion.\n\nis that valid?\n\nIn dictionary terms, “to boil” is not directly “to exhaust”.\n\nBut in semantic space, boiling down a liquid to a small amount implies exhausting it.\n\nSo in metaphorical or derived use, it could be a plausible translation.\n\nAlternatively, since “to use” is present, and “to exhaust” is a result of using up, then “to exhaust” could be a derivative of “to use up”, which might be formed from “fäeag” + a suffix like “-kia” or “-pala”.\n\nBut again, no clear suffix.\n\nWe have no root meaning “to consume” or “to deplete”.\n\nTherefore, the only theoretically possible translations are based on existing roots and compound formation.\n\nThus, for “word”:\n\nNo root is clear.\n\nBut perhaps a verb meaning “to say” or “to utter” is not in the list.\n\nBut in Austronesian languages, words for “word” are often derived from roots like “pala” (to pierce) or “ka” (to go), or “ta” (to go).\n\nWe have “ka.lu” = to encircle — not helpful.\n\nWe have “pali” not present.\n\nBut “pala” = to pierce — “word” might be analogous to “a sound that pierces”?\n\nOr “a thing that is said”?\n\nNo strong root.\n\nAnother possibility: “word” could be formed from a root like “to be near” — “‘ele” — as “a thing near” — meaning “a close thing” — could be a “word”?\n\nIn some languages, “word” is “near thing”.\n\nPossibly.\n\nSo “‘ele” = to be near — could “word” be “‘ele” in a noun sense?\n\nBut “‘ele” is a verb.\n\nIs there a noun form?\n\nNo.\n\nThus, the most plausible base is missing.\n\nTherefore, in absence of a direct root, the theoretically possible form of “word” must be a compound or inflected form using a root that could mean “to say” or “to speak”.\n\nWe find no such root.\n\nBut in Austronesian languages, a root like “puri” or “po” could be used.\n\nBut not in data.\n\nSo the only possibility is a derived form using a known root.\n\nAnother candidate: “nu‘suar” = door, “nu‘sura” = door — both have “nu‘” and “sura”.\n\n“tiro” = lens → perhaps “word” is a lens-like thing?\n\nNo.\n\nWe have “pogi” = night.\n\nNo.\n\nSo perhaps “word” has no direct equivalent, and the only theoretically possible form is based on existing patterns.\n\nBut for “to exhaust”, we have:\n\n- “to boil” (puhra.ki) — process of heating, going to end (to boil down)\n- “to use” (fäeag) — could be used to form “to exhaust”\n\nAnd “to cut” (‘olo) — to cut means to reduce — could “to cut” mean “to exhaust”?\n\nFor example, “to cut off” — to exhaust a supply?\n\nYes, in some contexts.\n\nSo “to cut” could be used to mean “to exhaust” — as in “to cut a supply” or “to cut out”.\n\nThus, “‘olo” is a strong candidate.\n\n“to cut” can be extended to mean “to exhaust” (as in cut off a resource).\n\nSimilarly, in English, “to cut” can mean “to reduce to zero”.\n\nSo theoretically, “to exhaust” could be translated as “‘olo”.\n\nAlternatively, “to boil” is also plausible.\n\nSo between “puhra.ki” and “‘olo”, which is more logical?\n\n“to cut” is more directly a root for reduction.\n\n“to boil” is more about heat.\n\nIn the context of “exhaust”, both are possible.\n\nBut in the absence of evidence, we must choose a plausible one.\n\nGiven that “to cut” is already a root, and “to exhaust” means to reduce to nothing, “to cut” is more semantically aligned.\n\nFor “word”, the only plausible candidate might be a form derived from “to say” or “to convey”.\n\nNo such root.\n\nBut perhaps “to be near” = ‘ele — “a thing near” could mean “a word”?\n\nLike “a spoken thing near me”?\n\nPossibly.\n\nSo “‘ele” might be used as a metaphor.\n\nTherefore, “word” could be “‘ele”.\n\nBut “‘ele” is a verb.\n\nWe have no noun form.\n\nBut in some languages, verbs can be used for nouns.\n\nHowever, we have no example of a verb being used as a noun.\n\nAll nouns are listed as standalone.\n\nFor example, “fau” = year, “lala” = deep — both are nouns.\n\n“pala” = pierce — verb.\n\n“pala” is listed as a verb.\n\nThus, “‘ele” is a verb.\n\nSo cannot be used as “word”.\n\nThus, no direct possibility.\n\nBut the question says: “theoretically possible translations” — not necessarily from direct examples.\n\nSo in the absence of a direct root, we infer that:\n\n- “word” could be formed from a root like “to say” or “to speak” — which may not exist — but could be constructed from a verb like “to express” or “to utter”.\n\nWe don’t have that.\n\nBut in Austronesian languages, a word for “word” might be derived from “to say”.\n\nSince we have “to use” (fäeag), and “to speak” is not present, we must conclude that the only possible form is a compound such as **fäeag ‘u‘u** — meaning “to use sign language” — and “word” might be related.\n\nBut no.\n\nAlternatively, “word” could be “ka.lu” — to encircle — as in a word surrounds a concept?\n\nUnlikely.\n\nThus, after full analysis:\n\n- “word” has no clear root, but in absence of data, the only likely form could be a compound with a verb stem, but nothing exists.\n\n- For “to exhaust”, we have “puhra.ki” (to boil) and “‘olo” (to cut) as plausible.\n\nBetween them, “to cut” implies reduction, which matches “to exhaust”.\n\nTherefore, “to exhaust” could be “‘olo”.\n\n“to boil” is less directly linked.\n\nThus, theoretically possible translation for “to exhaust” is **‘olo**.\n\nFor “word”, the most plausible root is missing, but in Austronesian, “word” might be derived from a root like “pah” or “hala” — not present.\n\nBut we have “lala” = deep — “deep word”?\n\nNo.\n\n“huni” = lower end — “word at lower end”?\n\nUnlikely.\n\nGiven that" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-a", + "planner_index": 1, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 1.: answer for this requested item\n- a.2 / 2.: answer for this requested item\n- a.3 / 3.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 1. utnhantxi\n\n 2. yapp”psa\n\n 3. yapup”psa\n\nSAMPLED ATTEMPT:\nWe are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap”\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.\n\n\n\nRe-examine all noun bases and question forms.\n\nList all words with “txi”:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll are of form: [base] + “txi” → is it in [base]?\n\nSo “txi” = is it in?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” → is it in my house?\n\nThis is consistent.\n\n2. yapp”psa” → no “txi” → not a question → must be a statement.\n\nWhat is the base?\n\n“yap” = field → from yaputxi.\n\n“psa” = too → from examples.\n\nSo “yapp”psa” = field too?\n\nBut “field too” — is that grammatically valid?\n\nWe have “p”ak”unhpsa” = my pot too → possessive + too.\n\nNo “field too” with possessive.\n\nBut might be a general “too”?\n\nSo yapp”psa” → the field too?\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” is not a known morpheme.\n\nBut “up” could be a typo for “un”?\n\n“un” appears in “unhpsa” → “unhpsa” = my pot too → “unh” = my\n\nSo “un” = my?\n\n“unh", + "approaches": [ + "Focus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.", + "Assume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:\n1. utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?\n\n2. yapp”psa” → “yap” = field → “psa” = too → so “field too”?\n\nBut is there a possessive?\n\nCompare to p”ak”unhpsa → “unh” = my → “my pot too”\n\nSimilarly, is there a “my” prefix for field?\n\nWe have no “my field” or “your field” examples.\n\nBut “markstxi” → is it our1+2 town? → “our” = group\n\nSo “our” in “our1+2”\n\nPossession:\n- chushp”a → his corner\n- ishinhna → in my bed → “ish” = my?\n- ishma → your bed → “ish” = my, “ism” = your?\n\n“ish” → my \n“ism” → your \n“chush” → his \n“mark” → our\n\nSo “ish” = my\n\nNow, does “yapp”psa” have “ish” or “ism”?\n\nNo.\n\n“yap” → field\n\n“yapp”psa” → no possessive → so “the field too”?\n\nBut “the field” is not in glosses — only “is it the field?”\n\nSo “field” is a noun.\n\nThus, yapp”psa” → the field too.\n\n3. yapup”psa” → “yap” + “up” + “psa”\n\n“up” not in any word.\n\nPossibility: “up” = “in”?\n\nBut “in” is marked by “na” — in aq”na, ishinhna.\n\n“yapup”psa” has no “na”.\n\n“yapup”psa” → could be “in the field too”?\n\nBut no “na”.\n\nThus, only if “up” = “na” — but no phonetic or morphological link.\n\nNo example of “up” or “in” as “up”.\n\nThus, failure: no support for “up” = “in”.\n\nTherefore, this approach is invalid.", + "\nFocus on the question marker “txi” as a consistent morpheme indicating “is it” in the structure “Xtxi” → “is it in X?”.\n\nEvidence:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll follow the pattern: [noun] + “txi” → is it in [that noun]?\n\nThus, for utnhantxi:\n- “utnha” = my house\n- “antxi” = is it? → in the structure, “utnha” + “antxi” → is it in my house?\n\nSo utnhantxi → is it in my house?\n\nFor yapp”psa:\n- “yap” appears in yaputxi → the field → so “yap” = field\n- “psa” appears in yapsanpsa → in our1+2 field too → “psa” = too\n- “na” appears in aq”na → in the cave, ishinhna → in my bed → “na” = in\n\nThus, “na” + “psa” → in + too\n\nBut yapp”psa” has “pp” not “na” — no “na” suffix.\n\nSo perhaps “yapp”psa” is not “in” + field + too.\n\nAlternative: “psa” = too → “yap” + “psa” = field too?\n\nBut “yap” alone is “field” → “yap” + “psa” → field too?\n\nBut no example of “field too” without “in”.\n\nBut compare to p”ak”unhpsa → my pot too → “unh” = my, “psa” = too\n\nSo “psa” = too\n\nSimilarly, yapsanpsa → in our1+2 field too → “na” + “psa” → in + too\n\nSo “yap” + “psa” → field too?\n\nBut no “in” — so perhaps field too, not in field too.\n\nThus, yapp”psa” → my field too? But no “my” marker.\n\nUnless “p” is a possessive.\n\nBut no example of “p” as possessive.\n\nNo instance of “p” with possession.\n\nThus, “yapp”psa” may be “field too” — lacking specificity.\n\nBut “yap” is not preceded by “my” or “our”.\n\nSo perhaps a default “the field too”?\n\nBut in Jaqaru, “the” is not in English glosses — instead, nouns are unambiguously referenced.\n\nBut still, “yapp”psa” has no possessive.\n\nThus, safest: “the field too”?\n\nBut “yapsanpsa” has “in our1+2 field too” — clearly “in” is marked.\n\nSo “yapp”psa” lacks “in” — so not “in field too”.\n\nVerdict: yapp”psa” = the field too.\n\nFor yapup”psa”:\n- “yap” = field\n- “up” → not a known morpheme\n- “psa” = too\n\nCould “up” be a misreading of “un”? Or “in”?\n\nBut “in” is “na”.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nCompare to yapsanpsa → “yap” + “s” + “an” + “psa” → “in our1+2 field too”\n\nNo “up”.\n\nBut “up” may be a typo or variant of “un”?\n\nUn seen.\n\nAlternatively, “yapup”psa” → in the field too?\n\nBut no “na”.\n\nUnless “up” = “na” — but no evidence.\n\nConclusion: yapup”psa” likely = in the field too — but no morpheme support.\n\nBut if “yapup”psa” has “up” and “psa”, and no “na”, and no “in” marker, then not in.\n\nThus, only plausible is “field too”.\n\nBut both yapp”psa” and yapup”psa” end in “psa” → both have “too”\n\nAnd “yap” = field → so both are “field too”?\n\nBut different forms.\n\nUnlikely.\n\nAlternative: “yap” + “p” → “in”?\n\nBut “p” not used.\n\nEvidence: no word contains “p” as a standalone possessive.\n\nThus, this route fails at consistency.\n\nFailure check: “yapup”psa” has no “na” → cannot be “in the field too” → must be something else.\n\nThus, this approach is invalid.\n\n\n\nAssume that “psa” is a copy of the “too” marker and appears in all “too” constructions.\n\nList all “too” constructions:\n- aq”ipsa → the cave too\n- p”ak”unhpsa → my pot too\n- qucxst”psa → from our1+2 lake too\n- yapsanpsa → in our1+2 field too\n\nAll end in “psa”.\n\nSo “psa” = too.\n\nAll other constructions lack “psa” → so not “too”.\n\nNow, “txi” in:\n- chushuntxi → is it in the corner?\n- markstxi → is it our1+2 town?\n- yaputxi → is it the field?\n\nAll have “txi” → so “txi” = is it?\n\nSo pattern for questions: [noun] + “txi” → is it in [that noun]?\n\nThus:", + "utnhantxi → “utnha” = my house → “antxi” = is it? → is it in my house?" + ], + "anchor_output": "We are given a set of Jaqaru words and their English translations. We are to translate three new words: utnhantxi, yapp”psa, and yapup”psa.\n\nStep 1: Look for patterns in the given data.\n\nGiven pairs:\n\n- aq”ipsa → the cave too \n- aq”na → in the cave \n- qucxap”a → through the lake \n- qucxst”psa → from our1+2 lake too \n- chushp”a → his corner \n- chushuntxi → is it in the corner? \n- marka → the town \n- markp”t”a → from his town \n- markstxi → is it our1+2 town? \n- ishinhna → in my bed \n- ishma → your bed \n- p”ak”u → the pot \n- p”ak”unhpsa → my pot too \n- utamt”a → from your house \n- utnha → my house \n- yaputxi → is it the field? \n- yapsanpsa → in our1+2 field too \n\nWe observe that:\n- “too” appears with particles that follow the form of “X” + “too” → e.g., aq”ipsa (\"the cave too\"), p”ak”unhpsa (\"my pot too\"), yapsanpsa (\"in our1+2 field too\")\n- “is it” questions appear with “Xt” → e.g., chushuntxi (\"is it in the corner?\"), markstxi (\"is it our1+2 town?\"), yaputxi (\"is it the field?\")\n- “from” appears with “Xp”a or “Xt” with a possessive prefix (e.g., qucxst”psa → from our1+2 lake too)\n- “in” appears with “X” + “na” (e.g., aq”na → in the cave, ishinhna → in my bed)\n\nNow consider the structure of the words to translate:\n\n1. utnhantxi \nCompare to: \n- utnha → my house \n- utamt”a → from your house \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nLook at “utnhantxi”: \nThis looks similar to “utnhantxi” — notice “t” and “x” at the end. \nCompare to “utnhantxi” vs “utnhantxi” — likely a morphological pattern.\n\nWe observe that:\n“utnhantxi” → likely a question with “is it” structure → endings like “txi” appear in questions.\n\ne.g., \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “txi” marks a question: “is it…” — similar to “untxi” in other cases.\n\nThus, “utnhantxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house” = is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\n2. yapp”psa \nCompare to: \n- yapsanpsa → in our1+2 field too \n- yaputxi → is it the field?\n\nWe see:\n- yapsanpsa → in our1+2 field too → has “na” and “psa”\n- yaputxi → is it the field?\n- yapp”psa → similar to yaputxi but with “p” instead of “u”?\n\nWait — “yaputxi” → is it the field → has “utxi” → likely “is it” \n“yapp”psa” → has “p” → maybe “in” or “from”?\n\nCompare with: \n- aq”ipsa → the cave too \n- aq”na → in the cave \n- p”ak”unhpsa → my pot too\n\n“yapp”psa” → “ya” + “pp” + “psa”\n\nNotice that “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → has “unhpsa”\n\nSimilarly, “utnha” → my house \n“utnha” + “t” → utnth”a”? No.\n\nAlternatively: \n“yapsanpsa” → in our1+2 field too → “in” + “field” + “too” \nThis has a “na” at the end? No — “npsa”\n\nActually: \n“yapsanpsa” ends in “npsa” — shares the “psa” ending.\n\n“yaputxi” → ends in “utxi” → question \n“yapp”psa” → ends in “p”psa” — possibly “in” + something?\n\nWait: \nLook at: \n- aq”na → in the cave \n- ishinhna → in my bed \n- markstxi → is it our town? \n→ “na” = in\n\nSo “in” = “na”?\n\nSo if “yapp”psa” has “na” at end → “in”?\n\n“yapp”psa” → “ya” + “pp” + “psa” → not clearly “na”\n\nBut “yapsanpsa” → \"in our1+2 field too\" → ends in “npsa”\n\n“yapsanpsa” → “in (our1+2) field too”\n\nSimilarly, “yapp”psa” → “in my field”? or “in your field”?\n\nAnother possibility: “psa” = “too”?\n\n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- qucxst”psa → from our1+2 lake too \n- yapsanpsa → in our1+2 field too \n\nYes — “psa” = “too”\n\nSo: \n- aq”ipsa → the cave too \n- p”ak”unhpsa → my pot too \n- yapsanpsa → in our1+2 field too \n\nSo “psa” = “too”\n\nThus, “yapp”psa” → if it ends with “psa”, it likely means “my field too”? or “in my field too”?\n\nBut “yapu” appears in “yaputxi” → “is it the field?”\n\nSo “yapu” → field?\n\nThen “yapp”psa” could be “in my field too”?\n\nOr “my field too”?\n\nBut the structure: “yap” → field?\n\nWe have:\n- yaputxi → is it the field? \n→ has “utxi” → question marker \n- yapsanpsa → in our1+2 field too → has “npsa” → “in” + “our1+2” + “field” + “too”\n\nSo “in” = “na”?\n\nBut \"yapsanpsa\" = “in our1+2 field too” — ends with “npsa” — seems “na” + “psa”?\n\nBut “psa” = “too” — so “na” + “psa” = “in + too”?\n\n“na” = in, “psa” = too → “in too”?\n\nBut “in our1+2 field too” would be “in + too” — not exactly.\n\nAlternatively: “na” is marker for “in”, “psa” for “too”\n\nSimilarly, “utnha” = my house \n“utnha” + “t” → “utnhat”? Not given.\n\nBack to “yapp”psa” → “ya” + “pp” + “psa”\n\nWhat is “yapp”? Compare with “yapu” → field?\n\n“yapu” → field? In “yaputxi” = is it the field?\n\nSo “yap” → field → “yapp” → maybe “my field”?\n\n“yapp”psa” → my field too?\n\nBut we also have “p”ak”u → the pot \n“p”ak”unhpsa → my pot too → “unh” = my\n\nSo “unh” = my?\n\n“utnha” = my house \n“utnha” → “unh” not present → but no obvious marker.\n\nBut “p”ak”unhpsa” → “unh” + “psa” → my pot too → “unh” = my\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“mark” + “p”t”a” → from his town\n\n“markstxi” → is it our1+2 town?\n\n“our1+2” → possession for group, not individual.\n\nPossession markers:\n- “his” → chushp”a \n- “my” → in ishinhna → in my bed → “ish” → my? \n- “your” → ishma → your bed \n- “our1+2” → markstxi, qucxst”psa → our1+2\n\nSo “ish” → my? \n“ism” → your? \n“chush” → his? \n“mark” → our\n\nNow go to “yapp”psa”\n\nWe do not see “yapp” directly.\n\nBut can we infer that “yap” = field?\n\nSo “my field” → something like “yap” + “unh”?\n\nBut “yapp”psa” → no “unh” — instead it has “pp”\n\nWait: is there a “pp” marker?\n\nNo clear examples.\n\nBut “yaputxi” → is it the field? \n→ has “utxi” → question marker\n\nSo “t” in “t”xi may mark question → “untxi” = is it in the corner?\n\n“chushuntxi” = is it in the corner?\n\n“markstxi” = is it our town?\n\n“yaputxi” = is it the field?\n\nSo “t”xi → is it?\n\nSo “utnhantxi” → ends with “antxi” → likely “is it in my house”?\n\nBecause:\n- “utnha” = my house\n- “in” = in → indicated by “na” in “aq”na, “ishinhna”\n- “antxi” → is it in the corner? (but “corner” is chushp”a)\n\nWait — “in my house” → is it in my house?\n\nSo “utnhantxi” → is it in my house?\n\nWhat about “yapp”psa”?\n\nCompare to “yaputxi” → is it the field?\n\nSo “yap” → field?\n\nThen “yapp”psa” → if “psa” = too, then perhaps “in my field too”? or “my field too”?\n\nBut no clear “in” or “my” marker.\n\nWait: “yapsanpsa” → in our1+2 field too → has “npsa” → “in” + “too”\n\n“n” may be “in” marker? Or “na”?\n\n“aq”na” → in the cave → “na”\n\n“ishinhna” → in my bed → “na”\n\nSo “na” = in\n\nSo “in” = “na”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “na” + “psa” → “in + too”\n\nSo “na” + “psa” = in + too\n\nSo “yap” + “na” + “psa” = in our1+2 field too?\n\nBut “yapsanpsa” = in our1+2 field too → contains “npsa” — likely “na” + “psa”\n\nSo “na” = in, “psa” = too\n\nThus, “yap” = field?\n\nSo “yap” is “field”\n\nTherefore: \n“yapp”psa” → “yap” + “p” → what is “p”?\n\nPerhaps a possessive?\n\nWe have no “p” trigger.\n\nBut in “p”ak”u” → the pot → “p”ak”u\n\nSimilarly, “utnha” → my house\n\nNo “p” possession.\n\nBut “p” appears in “yap” → field?\n\nMaybe “yap” = field, and “p” is just a phonetic form?\n\nBut consider “yapup”psa” → next item\n\n3. yapup”psa\n\n“yapup”psa” → “yapu” + “p” + “psa”?\n\nCompare to “yaputxi” → is it the field?\n\n“yapup”psa” → ends with “psa” so likely “too”\n\nSo perhaps “in the field too”?\n\nBut what is “yapu”?\n\n“yaputxi” → is it the field → “yapu” = field?\n\nSo “in the field too” → in + field + too?\n\nSo “na” + “yapu” + “psa”\n\nBut “yapup”psa” has “up” — “up” may be a typo?\n\nWait — the original says “yapup”psa”\n\nIs it “yapup”psa” → “yap” + “up” + “psa”?\n\nBut we don’t have “up” examples.\n\nCompare with:\n- yapsanpsa → in our1+2 field too → “na” + “psa” → “na” + “psa” = in + too\n\n“yapup”psa” — if it’s “in our1+2 field too”, then it should have “na”\n\nBut it doesn’t.\n\nWait — “yapup”psa” — perhaps “yap” + “up” → “in”?\n\nBut “up” not found.\n\nWait — go back to the first form: “utnhantxi”\n\nWe proposed: is it in my house?\n\n- “utnh” → my house? \n- “antxi” → is it?\n\nYes — pattern: [noun] + “txi” → is it in the [noun]?\n\nIn: \n- chushuntxi → is it in the corner? \n- markstxi → is it our1+2 town? \n- yaputxi → is it the field?\n\nSo “t”xi → is it?\n\nAnd “in” → built into the structure? Or implied?\n\nBut in chushuntxi → “in the corner” → “chush” = corner → “untxi” → “is it in the corner?”\n\nSo “chush” + “untxi” → is it in the corner?\n\nSimilarly, “markstxi” → is it our1+2 town? → “mark” + “stxi” → but “st”?\n\nWait — “markstxi” → not “mark” + “txi” → “stxi”\n\n“markp”t”a” → from his town → “p”t”a” = from his?\n\n“markstxi” → is it our1+2 town?\n\nPossibility: “stxi” is the question form.\n\nSimilarly, “chushuntxi” → “untxi” → is it?\n\nSo the form “X + txi” → is it in X?\n\nBut in chushuntxi → X = corner → “in corner” → the form is “Xuntxi”?\n\n“chushuntxi” → “chush” + “untxi” → yes.\n\n“markstxi” → “mark” + “stxi” → is it our+2 town?\n\n“yaputxi” → “yap” + “utxi” → is it the field?\n\nSo the pattern is “noun + txi” → is it in that noun?\n\nSo “utnhantxi” → “utnha” + “antxi” → is it in my house?\n\nBut “utnha” = my house → so “in my house”?\n\nYes.\n\nSimilarly, “yapp”psa” → what?\n\nNow, “yapp”psa” → “yap” + “p” + “psa”\n\nWe have no “p” + “psa” in the list.\n\nBut “p”ak”u” = the pot \n“p”ak”unhpsa” = my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nCould “p” = something else?\n\nPerhaps “p” is a possessive marker?\n\nFor example, “p” might mean “your”?\n\nBut “ism” = your bed, “utamt”a = from your house → “utam” + “t”a” → from your house\n\n“utamt”a” → “utam” = your? “t”a” = house?\n\nNo clear.\n\nAlternatively, is “yapp”psa” similar to “yapsanpsa”?\n\n“yapsanpsa” = in our1+2 field too → in + field + too\n\n“yapsanpsa” → “na” + “psa” → in + too\n\nSo “na” = in, “psa” = too\n\nSo “yap” + “na” + “psa” = in field too → but “yapsanpsa” is given.\n\n“yapup”psa” → “yap” + “up” + “psa”\n\nNo such form.\n\nWhat if “yapup”psa” is missing a marker?\n\nWait — perhaps the word is “yapantxi” or something?\n\nNo, it's written as “yapup”psa”\n\nAlternative: “yapp”psa” might be “in my field”\n\nBut we need a possessive.\n\n“yap” → field → so “my field” = “yap” + “unh”?\n\nBut “yapp”psa” has “p”, not “unh”\n\nUnless “p” = “unh”?\n\nUnlikely.\n\nBut in “p”ak”u” → the pot \n“p”ak”unhpsa” → my pot too → “unh” + “psa”\n\nSo “unh” = my\n\nBut “yapp”psa” has “p” — perhaps a typo or written incorrectly?\n\nNo — we must work with what’s given.\n\nAnother possibility: “psa” = “too”\n\nSo “yapp”psa” → the field too? or my field too?\n\nBut “the field too” — “the” not in system.\n\nWe have “the cave too”" + }, + { + "split": "train", + "record_id": "iol-2012-individual-p1-sub-b", + "planner_index": 2, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 17.: answer for this requested item\n- b.2 / 18.: answer for this requested item\n- b.3 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: }\n\nProblem #1 (20 points). Here are some sentences in the central dialect of Dyirbal as well\nas their English translations:\n 1. bayi yaóa NunéaymuNa baNgu gurugugu biNgunman.\n Booze is making the man that is always being blamed tired.\n 2. balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu.\n The strong man is blaming the mother that is always following death adders.\n 3. balan waymin bambun baNgu éugaNgu éamiman.\n Sugar is making the healthy mother-in-law fat.\n 4. bala yila wura baNgul bargandu biNgundu guniñu.\n The tired wallaby is searching for the little feather.\n 5. balan malayigara baNgu garandu biNgunman.\n The smoke is making the scorpion tired.\n 6. bala gurugu baNgul NumaNgu munduNgu dimbañu.\n The offended father is carrying the booze.\n 7. bayi midin baNgun bimaNgu malayigaraguninaymuNagu banéan.\n The death adder that is always searching for scorpions is following the possum.\n 8. bayi gubimbulu biNgun baNgu gurugugu éagunman.\n Booze is making the tired doctor fall asleep.\n 9. bala garan baNgul biñéiriñéu banéan.\n The lizard is following the smoke.\n 10. balan duNan baNgul yiriñéilagu guniñu.\n The dragonfly is searching for the stinging tree.\n 11. bala éuga baNgun yabuNgu NaéilmuNagu dimbañu.\n The mother that is always being ignored is carrying the sugar.\n 12. bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban.\n The fat doctor is pushing the big stone.\n 13. bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan.\n The mother-in-law that is always pushing stones is looking at the smoke.\n 14. balan baNgay waóu baNgun bundiñéu éagiñéu guniñu.\n The big grasshopper is searching for the bent spear.\n 15. bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan.\n The quiet boy is looking at the tired lizard.\n 16. bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman.\n The man that is always being followed is offending the strong father.\n\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into English:\n\n 17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\n 18. bala diban bilmbalmuNa baNgun biñéiriñéu guniñu.\n 19. bayi bargan baNgul yaóaNgu gubimbuluNunéanaymuNagu banéan.\n\nSAMPLED ATTEMPT:\nStep 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" \n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "approaches": [ + "Focus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.", + "Assume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.", + "\nFocus on verb semantics and case structure. Identify that \"baNgul\" consistently acts as a causative or directional verb. In example 9: \"bala garan baNgul biñéiriñéu banéan\" → \"lizard is following smoke\", and in 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"mother-in-law is looking at smoke\", \"baNgun\" is used for \"looking at\", while \"baNgul\" is for \"following\". Thus, \"baNgul\" specifically denotes \"following\" as a directional action, not \"carrying\" or \"searching\".\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n- \"balan ñalNga\" = the quiet one \n- \"baNgul\" = is following \n- \"NumaNgu\" = the one that is always being followed \n- \"guniymuNagu\" = the one that is searching \n- \"bambunman\" = the one who is healthy \n\nBut \"NumaNgu\" is a passive state — it is being followed. So the structure is: [X] is following [Y], where Y is a person with two properties: being always followed and searching for the healthy one.\n\nThis implies a compound object: \"the one who is always being followed and is searching for the healthy one\".\n\nTherefore, the translation is: \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nVerification: Check consistency with example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" → \"The man that is always being followed is following the strong father.\" \nHere, \"Numa\" = being followed (passive), \"guli\" = is following (active), so \"the one who is always being followed\" is the subject of \"is following\". But in 17, \"NumaNgu\" is the object of \"following\" — so it's not the subject. Hence, it is being followed, not following. This supports that \"NumaNgu\" is the object, not the subject.\n\nThus, the parsing is valid: the quiet one is following a person who is passively followed and actively searching for a healthy person.\n\n\n\nAssume that \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\" and that \"bambunman\" is a property of that person. \"bambun\" = healthy, so \"bambunman\" = healthy one.\n\n\"NumaNgu\" = the one who is always being followed → passive.\n\nSo \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed, who is searching for the healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nSo the sentence is: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nCheck against example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"The quiet boy is looking at the tired lizard.\" \nHere, \"biñéiriñ\" = quiet boy, \"baNgul\" = looking at → so \"baNgul\" can be \"looking at\", not only \"following\".\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following smoke — \"baNgul\" = following.\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → mother-in-law is looking at smoke — \"baNgun\" = looking at.\n\nSo \"baNgul\" is specifically \"following\", while \"baNgun\" is \"looking at\".\n\nTherefore, in 17, \"baNgul\" = following, not looking at.\n\nThus, the translation must be: The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nVerification: In example 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching for the little feather\" — \"baNgul\" is not used with \"for\", but with \"searching\" implied. In 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"searching for\", so \"baNgay\" = searching, \"guniñu\" = for.\n\nNo direct use of \"baNgul\" with \"for\", so \"guniymuNagu\" likely means \"is searching\" not \"searching for\".\n\nTherefore, \"guniymuNagu\" = the one who is searching (as a state), not \"searching for X\".\n\nThus, the object is a person with two attributes: passively followed and actively searching.\n\nThis confirms the parsing.\n\n\n\nInvestigate morphological patterns. All modifiers are encoded as suffixes or clitics attached to a noun. For example:\n\n- \"Numa\" = always being followed → passive property\n- \"guli\" = is following → active property\n- \"midin\" = always searching → active\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gurugugu\" = tired\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n\"Numa\" = always being followed (passive) \n\"guli\" = is following (active) \nSo the subject is the man who is always being followed and is following others.\n\nIn sentence 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman\" \n\"NumaNgu\" = the one who is always being followed (passive) \n\"guniymuNagu\" = the one who is searching (active) \n\"bambunman\" = the one who is healthy (active)\n\nSo the object of \"following\" has two properties: being passively followed and actively searching for a healthy one.\n\n\"baNgul\" = following.\n\n\"balan ñalNga\" = the quiet one.\n\nThus, \"The quiet one is following the one who is always being followed and is searching for the healthy one.\"\n\nCheck if \"bambunman\" can be \"the one who is healthy\" — yes, in example 3: \"bambun\" = healthy → so \"bambunman\" = the healthy one.\n\n\"guniymuNagu\" = is searching — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"searching for\", so \"guni\" = search, \"ymu\" = for.\n\n\"guniymu\" likely means \"searching for\", not \"is searching\".\n\nThis is a contradiction.\n\nIf \"guniymuNagu\" = searching for, then it would require a noun object.\n\nBut there is no noun after it — only \"bambunman\".\n\nSo it cannot be \"searching for the healthy one\" unless \"bambunman\" is the object.\n\nBut \"bambunman\" is a property, not a noun.\n\nTherefore, \"guniymuNagu\" must mean \"is searching\" as a state, not \"searching for\".\n\nThus, the object is a person who is searching (as a state), not actively searching for someone.\n\nSo the interpretation is: the quiet one is following the person who is always being followed and is searching (as a state).\n\nBut \"searching\" is a verb, not a state — and no such state is named.\n\nThis suggests that the phrase \"guniymuNagu\" is a noun phrase meaning \"the one who is searching\", and \"bambunman\" is an attribute of that person.\n\nThus, it's acceptable to say \"is searching for the healthy one\" only if \"bambunman\" is the object.\n\nBut in Dyirbal, when \"searching\" is used, it's often with \"for\".\n\nExample 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" — \"is searching for the bent spear\"\n\nSo \"baNgay\" = searching, \"guniñu\" = for.\n\n\"baNgul\" in 17 is not used with \"for\", so likely \"following\" without object.\n\nThus, \"guniymuNagu\" likely means \"is searching\" as a state, not \"searching for\".\n\nTherefore, the phrase \"NumaNgu guniymuNagu bambunman\" = the one who is always being followed and is searching (and is healthy).\n\nBut \"bambunman\" is not a state — it's a property.\n\nThus, it's likely that \"bambunman\" describes the person who is being searched by.\n\nThus, \"the one who is always being followed and is searching for the healthy one\" is the only semantically coherent interpretation.\n\nEven if \"guniymuNagu\" is not directly \"searching for\", the structure of the sentence suggests it is.\n\nThus,", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "Step 1: Identify the basic structure of the Dyirbal sentences.\n\nAll sentences follow a similar pattern:\n[Subject] [verb] [object] [modifier/attribute phrase].\n\nThe verb comes after the subject and is followed by a noun that describes the object or state. The modifiers (e.g., \"that is always being blamed\", \"that is always following\") are encoded in suffixes, often using a structure like [X] + [modifier suffix].\n\nStep 2: Extract core components from examples.\n\nExample 1: \n\"bayi yaóa NunéaymuNa baNgu gurugugu biNgunman\" \n→ \"Booze is making the man that is always being blamed tired.\" \n→ \"bayi\" = booze \n\"yaóa\" = is making \n\"NunéaymuNa\" = the man that is always being blamed \n\"baNgu\" = the one being made (or the object) \n\"gurugugu\" = tired \n\nSo: [A] is making [B] tired → [A] + [verb] + [B] + [tired]\n\nThe tense or state is marked by a noun or adjective (e.g. gurugugu = tired), which appears after the object.\n\nExample 5: \n\"balan malayigara baNgu garandu biNgunman\" \n→ The smoke is making the scorpion tired. \n\"malayigara\" = smoke \n\"garandu\" = scorpion \n\"biNgunman\" = tired\n\nSo: [X] is making [Y] tired → [X] + [verb] + [Y] + [tired]\n\nBut in example 8: \n\"bayi gurugu baNgul NumaNgu munduNgu dimbañu\" \n→ Booze is making the offended father carry the booze. \n\"baNgul\" = carry \n\"NumaNgu\" = offended father \n\"munduNgu\" = carrying (possibly a state or verb) \n\"dimbañu\" = the booze?\n\nActually, \"NumaNgu\" is \"the offended father\" → shows that a noun + modifier = person with a quality.\n\nKey pattern: \n[Noun] + [modifier] = a person or thing with a property. \n[Subject] + [verb] + [object with modifier] + [state] → [X] is making [Y] [state]\n\nAlways: verb is associated with the transformation.\n\nLook at sentence 10: \n\"balan duNan baNgul yiriñéilagu guniñu\" \n→ The dragonfly is searching for the stinging tree. \n\"duNan\" = dragonfly \n\"baNgul\" = searching \n\"yiriñéilagu\" = the stinging tree \n\"guniñu\" = for\n\nSo: [X] is searching [Y] → [X] + [verb] + [Y] + [for]\n\nStep 3: Identify the case marking and structure for modifiers.\n\nExample 3: \n\"balan waymin bambun baNgu éugaNgu éamiman\" \n→ Sugar is making the healthy mother-in-law fat. \n\"waymin\" = sugar \n\"bambun\" = healthy \n\"baNgu\" = mother-in-law \n\"éugaNgu\" = fat\n\nSo: [X] is making [Y] fat → [X] + [verb] + [Y] (with modifier) + [fat]\n\nPattern: \n[Substance/agent] + [verb] + [object] + [attribute] = \"X is making Y [state]\"\n\nAlso, adjective phrase like \"bambun\" = healthy, \"gurugugu\" = tired, \"éugaNgu\" = fat, \"biban\" = strong, \"guli\" = following.\n\nNow, at the word level:\n\n- \"baNgul\" = searching / carrying / following?\n- \"gurugu\" = tired\n- \"biban\" = strong\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"midin\" = always searching?\n- \"waymin\" = sugar\n- \"ñalNga\" = quiet\n- \"gubimbulu\" = offended\n- \"Numa\" = always being followed\n\nNotice that \"Numa\" appears in example 16: \n\"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" + \"guli\" = \"the man that is always being followed\" \n\"baNgul\" = is following (or offending?) — actually, \"baNgul\" is often \"following\" or \"is carrying\"\n\nIn 2: \"balan yabu bimabanéalNaymuNa baNgul yaóaNgu guliNgu Nunéañu\" \n→ \"The strong man is blaming the mother that is always following death adders.\"\n\n\"bimabanéal\" = strong \n\"baNgul\" = following \n\"yaóaNgu\" → makes?\n\nWait — \"yaóaNgu\" appears in several cases: is making.\n\nIn 1: \"yaóa\" \nIn 2: \"yaóaNgu\" \nIn 3: not used \nIn 6: \"munduNgu\" → carrying\n\nSo: \n\"yaóaNgu\" = is making → corresponds to causation.\n\n\"baNgul\" can mean \"is following\", or \"is carrying\".\n\n\"baNgul\" appears as verb when object has the property.\n\nLook at 9: \"bala garan baNgul biñéiriñéu banéan\" \n→ The lizard is following the smoke. \n\"garan\" = lizard \n\"baNgul\" = following \n\"biñéiriñéu\" = smoke\n\nSo: [X] is following [Y]\n\n\"bala\" = subject (lizard), \"baNgul\" = verb (following), object = smoke.\n\nSimilarly, 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" \n→ The mother-in-law that is always pushing stones is looking at the smoke. \n\"waymindu\" = always pushing? \n\"dibanbilmbalNaymuNagu\" = mother-in-law that always pushes stones \n\"buóan\" = smoke\n\n\"baNgun\" = looking at? Possibly regional variation.\n\nBut in 5: \"balan malayigara baNgu garandu biNgunman\" \n→ smoke is making scorpion tired → \"biNgunman\" = tired\n\nSo: causative: [X] is making [Y] [state]\n\nThus:\n\n- \"yaóaNgu\" or \"yaóa\" → causative verb (is making)\n- \"baNgul\" → following\n- \"baNgun\" → looking at / carrying / being with?\n- \"gurugugu\" = tired\n- \"bambun\" = healthy\n- \"diban\" = fat\n- \"gubimbulu\" = offended\n- \"numa\" = always being followed\n- \"midin\" = always searching?\n\nNow go to sentence 17: \n\"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nBreak it down:\n\n- \"balan\" = subject (something, likely a substance or agent)\n- \"ñalNga\" = quiet → from example 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" → \"the quiet boy is looking at the tired lizard\"\n→ so \"ñalNga\" = quiet\n\nSo \"balan ñalNga\" = the quiet thing → but \"balan\" is not a noun like \"bayi\", it's a substance.\n\nWait — \"balan\" appears in 2,3,5,7,8,9,10,11,12,13,14 — in all cases, it's a noun (e.g. \"strong man\", \"dragonfly\", \"mother-in-law\", etc.)\n\nBut in 4: \"bala yila wura baNgul\" → \"the tired wallaby is searching\" → \"bala\" = wallaby\n\nSo: \"bala\" and \"balan\" both are subjects.\n\n\"bala\" = animal / person → \"wallaby\", \"lizard\", etc. \n\"balan\" = something else — example 2: \"balan\" + \"yabu\" = strong man → so \"balan\" can be a noun for a person.\n\nIn fact, in 1: \"bayi\" = booze → agent \nIn 2: \"balan\" = strong man → person \nIn 3: \"balan\" = sugar → substance \nSo \"balan\" can be a substance or person.\n\nSo in 17: \"balan\" = substance or person? \nþ with \"ñalNga\" — quiet → so \"the quiet one\"\n\nBut then \"baNgul\" → verb: following?\n\n\"baNgul\" is following.\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching? — in example 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → \"big grasshopper is searching for the bent spear\"\n\n\"guniñu\" = for\n\n\"guniymuNagu\" — likely \"is searching\" or \"is searching for\"\n\nCheck: \"guniymu\" — \"guni\" = search, \"ymu\" = for?\n\nCompare with 14: \"guniñu\" = for \n\nSo: \"guniymuNagu\" = one that is searching for? or searching?\n\nPossibly: \"guniymuNagu\" = one who is searching.\n\n\"bambunman\" = fat?\n\n\"bambun\" = healthy → \"bambunman\" = fat?\n\nBut no — in 3: \"bambun\" = healthy → \"éamiman\" = fat → maybe it's a mismatch.\n\nIn 3: \"bambun\" = healthy → object has quality.\n\nIn 5: \"malayigara\" = smoke → makes scorpion tired → \"biNgunman\" = tired\n\nSo \"bambunman\" → likely not \"fat\"\n\nWait — \"éugam\" = fat → \"éamiman\" = fat?\n\nIn example 3: \"éugaNgu éamiman\" → \"fat\" \nSo \"éamiman\" = fat\n\nThen \"bambunman\" = healthy?\n\nNo — \"bambun\" = healthy, not fat.\n\nSo \"bambunman\" → the one who is healthy?\n\n\"NumaNgu\" → the one that is always being followed \n\"guniymuNagu\" → the one that is searching for? \n\"bambunman\" → the one who is healthy?\n\nBut in 17: \"balan ñalNga baNgul NumaNgu guniymuNagu bambunman.\"\n\nStructure: [X] + [modifier] + [verb] + [target object] + [state modifier]\n\nSo: [quiet one] is following [the one that is always being followed] [who is searching for the healthy one]?\n\nThat seems forced.\n\nReverse the dependency:\n\nIs \"baNgul\" the verb? Yes — following.\n\nSo: [balan ñalNga] is following [NumaNgu guniymuNagu bambunman]\n\nSo: the quiet one is following [the person who is always being followed and is searching for the healthy one]?\n\nBut that is illogical.\n\nAlternative: word order.\n\nIn example 16: \"bayi Numa guli baNgul yaóaNgu banéalmuNagu munduman\" \n→ \"The man that is always being followed is offending the strong father.\"\n\n\"Numa\" = always being followed \n\"guli\" = is following \n\"baNgul\" = is following? No — \"guli baNgul\" → \"is following\" → \"the man that is always being followed\" is following someone?\n\nNo — \"guli baNgul\" might be \"that is always following\"\n\nBut \"Numa\" is \"being followed\" → indicates passive.\n\nSo \"Numa\" = being followed → passive\n\n\"guli\" = following → active\n\nSo \"Numa guli\" = the one that is always following → the one that is always following others.\n\nIn 17: \"NumaNgu\" = always being followed → passive \n\"guniymuNagu\" → is searching → active \n\"bambunman\" → is healthy → active\n\nSo NumaNgu guniymuNagu bambunman → the one that is always being followed, is searching for, the healthy one?\n\nBut who is being followed? The one doing the following?\n\nSo: \"balan ñalNga\" is following \"the one who is always being followed and is searching for the healthy one\"?\n\nBut then why is \"the one who is always being followed\" being searched for?\n\nThat doesn’t make sense.\n\nAlternative parsing: maybe it's not \"following\" of a person with a property.\n\nIn 4: \"bala yila wura baNgul\" → tired wallaby is searching for the little feather \n\"baNgul\" = searching\n\nSo \"baNgul\" = searching for\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" \n→ big grasshopper is searching for the bent spear → \"baNgay\" = searching, \"guniñu\" = for\n\nBut in 17: \"baNgul\" → not with \"for\"\n\nUnless \"guniymuNagu\" is the for-part?\n\n\"guniymuNagu\" = searching for?\n\nSo \"NumaNgu guniymuNagu\" = the one that is always being followed and is searching for?\n\nThen \"bambunman\" → healthy?\n\nSo: the quiet one is following [the one that is always being followed and is searching for the healthy one]?\n\nStill odd.\n\nBut in 15: \"bayi biñéiriñ biNgun baNgul ñalNgaNgu mugurugu buóan\" \n→ \"The quiet boy is looking at the tired lizard.\"\n\n\"biñéiriñ\" = quiet boy \n\"biNgun\" = tired \n\"baNgul\" = looking at \n\"ñalNgaNgu\" = lizard \n\"mugurugu\" = tired → redundant?\n\n\"mugurugu\" = tired → so \"tired lizard\"\n\nSo \"baNgul\" = looking at\n\nSimilarly, 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke\n\nSo \"baNgul\" = following\n\nHence: \n\"baNgul\" = following (not searching)\n\nBut \"baNgul\" appears with \"for\" in other cases? No.\n\nOnly in 4 and 14: \"baNgay\" (searching) + \"guniñu\" (for)\n\nSo possibly two verbs:\n\n- \"baNgul\" = following / looking at \n- \"baNgay\" = searching for\n\nIn sentence 17: \"baNgul\" → following\n\nSo: \"balan ñalNga\" is following \"NumaNgu guniymuNagu bambunman\"\n\nSo: the quiet one is following the one who is always being followed and searching for the healthy one?\n\nThat is odd.\n\nPerhaps \"guniymuNagu\" is not a modifier of Numa, but of something else.\n\nBut only Numa and guniymuNagu are with Numa.\n\nAnother idea: the modifiers are combined to form a noun phrase:\n\n- NumaNguiyuNagu → the one who is always being followed and is searching for the healthy one\n\nBut \"bambunman\" = healthy?\n\nBut in example 3: \"bambun\" = healthy → \"bambunman\" = might be singular, but not \"fat\"\n\nLater: in 15, \"mugurugu\" = tired → so \"tired\" appears as a separate noun\n\nSo final parsing:\n\n17. balan ñalNga baNgul NumaNgu guniymuNagu bambunman \n→ The quiet one is following the one who is always being followed and is searching for the healthy one.\n\nBut this is awkward.\n\nAlternative: maybe \"bambunman\" = fat?\n\nNo — \"bambun\" = healthy, \"éamiman\" = fat\n\nSo no.\n\nBack to sentence 18:\n\n\"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n\"bala\" = subject \n\"diban\" = fat \n\"bilmbalmuNa\" = ?? \n\"baNgun\" = looking at \n\"biñéiriñéu\" = smoke \n\"guniñu\" = for\n\nSo: the fat one is looking at the smoke for [something]?\n\n\"guniñu\" = for → \"looking at the smoke for [X]\"\n\nBut what is X?\n\nIn 9: \"bala garan baNgul biñéiriñéu banéan\" → lizard is following the smoke → no \"for\"\n\nIn 14: \"balan baNgay waóu baNgun bundiñéu éagiñéu guniñu\" → grasshopper is searching for bent spear\n\nSo \"baNgun\" + \"guniñu\" = looking at for?\n\n\"baNgun\" = looking at / carrying? \nIn 15: \"baNgul\" = looking at → so \"baNgul\" = looking at\n\n\"baNgun\" — in 13: \"baNgun waymindu\" → \"looking at\" or \"carrying\"?\n\nIn 13: \"bala garan baNgun waymindu dibanbilmbalNaymuNagu buóan\" → \"the mother-in-law that is always pushing stones is looking at the smoke\" — so \"baNgun\" = looking at\n\nSo \"baNgun\" = looking at\n\nThen \"guniñu\" = for\n\nSo in 18: \"bala diban bilmbalmuNa baNgun biñéiriñéu guniñu\"\n\n→ the fat one is looking at the smoke for [something]\n\n\"bilmbalmuNa\" = ???\n\n\"bilmba\" = pushing? Or pushing stones?\n\nIn 12: \"bala diban éagiñ baNgul gubimbulugu éamiNgu bilmban\" → \"" + }, + { + "split": "train", + "record_id": "iol-2011-individual-p1-sub-b", + "planner_index": 3, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n- b.3 / bullet 3: answer for this requested item\n- b.4 / bullet 4: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: }\n\nProblem #1 (20 points). Given are verb forms of the Menominee language as well as their English\ntranslations:\n kewǣpeqtaq we1+2 begin\n kawāham he fells it by tool\n nepītohnæm I walk here (to this place)\n kēskenam he breaks it through by hand\n pahkǣsam he cuts it off\n kekǣtohnæq we1+2 walk out\n pītenam he passes it here\n kewǣpānæhkæq we1+2 begin to dig\n tawǣsam he cuts a hole in it\n nekǣtahan I pry it out by tool\n pāhkaham he opens it by tool (by raising a lid or opening a door)\n kekēskahtæq we1+2 bite it through\n wackōhnæw he walks roundabout, by a detour\n newāckesan I cut around it\n ketǣnam he takes it out by hand\n ketāwahtæq we1+2 bite, gnaw a hole in it\n wǣpohnæw he begins walking\n nekāweqtam I lie down\n pāhkeqtaw he opens up\n kepītahtæq we1+2 come eating it; we1+2 bring it in our mouths\n nekāwāhpem I fall over laughing\n\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n!△ The Menominee Indians live in Wisconsin, USA. They number 5 000–10 000 people, but the eponymous language of the Algonquian family is only spoken by a few dozen of the oldest among\nthem, although effort has been put lately into expanding its teaching and use.\n “we1+2” = ‘we and you’. æ ≈ a in crack, c = ch in church, q is a consonant (the so-called glottal stop). The mark “ ̄” denotes vowel length. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Menominee:\n • I begin to eat it\n • we1+2 lay it flat by hand\n • he digs a hole\n • he walks out\n\nSAMPLED ATTEMPT:\nStep 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.\n\n\n\nTarget: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.\n\n\n\nTarget: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.\n\n\n\nTarget: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern.\n", + "approaches": [ + "Focus on semantic alignment and person-marking patterns. Identify that first-person singular is marked by \"ne-\", second-person plural with \"ke-\", and third-person with \"kaw-\". For \"I begin to eat it\", note that \"kepītahtæq\" = \"we1+2 come eating it\", which semantically matches \"begin to eat it\". Since \"come\" may be a synonym for \"begin\" in this context, and \"eat\" is embedded in \"eating it\", the only form with \"begin to eat\" is kepītahtæq. However, this is for \"we1+2\". For first person, no direct form exists, but first-person forms are marked by \"ne-\". Therefore, \"I begin to eat it\" should be formed as \"ne\" + the root of \"begin\" + \"eating\". The root for \"begin\" appears in \"wǣpohnæw\" (he begins walking) and \"kewǣpeqtaq\" (we begin). The root is \"wǣp-\". The verb \"come eating\" in \"kepītahtæq\" suggests \"wǣp-\" is used with \"eating\" as a complement. Thus, \"ne wǣpītahtæq\" may be a plausible form. Verification: \"ne\" = I, \"wǣp\" = begin, \"ītaht\" = eating? But \"kepītahtæq\" is \"we come eating\", so \"pītaht\" may be the verb. In \"kepītahtæq\", \"ke\" + \"pītahtæq\" = we come eating. So \"pītaht\" is the verb root. But \"wǣp\" is for \"begin\", not \"come\". So inconsistency. Therefore, \"begin\" and \"come\" are distinct. Thus, no overlap. So \"I begin to eat it\" cannot be formed from existing data. Likely, the intended form is \"ne\" + \"pītaht\" + \"it\" — but no such form. So failure.", + "Target: \"we1+2 lay it flat by hand\". Look for verbs with \"lay\", \"put\", or \"place\". None are directly given. However, \"by hand\" appears in \"kēskenam\" (he breaks it through by hand), \"ketǣnam\" (he takes it out by hand), \"nekǣtahan\" (I pry it out by tool). \"By hand\" is used with various verbs. \"Lay\" may be related to \"put down\". No verb with \"lay\" exists. But \"pahkǣsam\" = he cuts it off — not related. \"pāhkeqtaw\" = he opens up — not \"lay\". All verbs involving \"pāh\" are for cutting or opening. No \"lay\". Thus, \"we1+2 lay it flat by hand\" must be formed from a root not in the list. But the only plausible root is \"pāh\" for \"open/place\"? But \"pāh\" verbs are for cutting or opening. \"Lay flat\" is not covered. Alternative: perhaps \"lay\" is equivalent to \"set down\", which may be similar to \"put\". But no such verb. Therefore, no valid form exists in the data. Conclusion: cannot derive from given forms. Failure.", + "Target: \"he digs a hole\". The closest form is \"tawǣsam\" = he cuts a hole in it. \"Cut a hole\" vs \"dig a hole\" — are these equivalent? In context, \"dig\" may imply excavation, while \"cut\" may imply a narrow opening. But in Menominee, verb roots may be shared. \"kewǣpānæhkæq\" = we begin to dig — so \"dig\" is a verb. \"He digs\" is not isolated, but \"he begins to dig\" is given. \"He digs a hole\" may be a simplification. Since \"tawǣsam\" means \"he cuts a hole in it\", and \"dig a hole\" is a common expression, the intended form might be a translation of tawǣsam. However, \"cut\" and \"dig\" are distinct. But in absence of a \"dig\" verb, and given that \"begin to dig\" is given, \"he digs a hole\" may be inferred as a derived form. But no standalone form. Thus, cannot assign a distinct form. Verification: if \"tawǣsam\" = cut a hole, then \"dig a hole\" is not equivalent. So failure to identify a clear match.", + "Target: \"he walks out\". We have \"kekǣtohnæq\" = we1+2 walk out. So \"walk out\" is explicitly given. \"he walks out\" should be the third-person singular form. The verb \"walk out\" is in the list for \"we1+2\". The root is likely \"kekǣtohn\" or similar. The form for \"he\" would be derived by replacing \"ke\" (we1+2) with \"kaw\" (he). So \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. But is this a valid pattern? In \"kawāham\" = he fells it → \"kaw\" + \"āham\" → he fells. In \"kēskenam\" = he breaks → \"kēsk\" + \"enam\". In \"wackōhnæw\" = he walks roundabout → \"wack\" + \"ōhnæw\". So the pattern is that third-person verbs use \"kaw-\" or \"kē-\" for he, and the verb stem follows. \"kekǣtohnæq\" = we1+2 walk out → \"ke\" + \"kǣtohnæq\". So for \"he walks out\", likely \"kaw\" + \"kǣtohnæq\" = kawkǣtohnæq. Verification: \"kaw\" is used for \"he\" in multiple verbs (kawāham, wackōhnæw). \"kaw\" appears in kawāham → he fells. \"wackōhnæw\" → he walks roundabout. So \"kaw\" is the he-marking. The verb \"walk out\" is in \"kekǣtohnæq\" with \"ke\". So replacing \"ke\" with \"kaw\" gives kawkǣtohnæq. This is consistent. So this form is valid and supported by pattern." + ], + "anchor_output": "Step 1: Identify the relevant verb forms in the given list that match the meaning of each target translation.\n\nTarget 1: \"I begin to eat it\" \nLook for a verb meaning \"begin\" or \"start\" used with \"eat\" or \"consume\". \nWe have:\n- kewǣpeqtaq: we1+2 begin → base form for \"begin\"\n- kewǣpānæhkæq: we1+2 begin to dig → \"begin to dig\"\n- kepītahtæq: we1+2 come eating it; we1+2 bring it in our mouths → \"come eating it\", i.e., eat/bring in mouth \nBut the target is \"I begin to eat it\" — subject is \"I\", not \"we1+2\", and the action is \"begin to eat\".\n\nWe need a form of \"begin\" with the object of eating.\n\nBut there’s no direct form for \"I begin to eat it\".\n\nHowever, notice that \"kepītahtæq\" means \"we1+2 come eating it\", which is similar in meaning to \"we begin to eat it\". So if \"come eating\" is equivalent to \"begin to eat\", and \"we1+2\" is used, then likely \"begin to eat\" is semantically close.\n\nBut the subject is \"I\", not \"we1+2\". So we need a form of \"begin\" with first-person singular.\n\nThere is no direct \"I begin to eat it\" form.\n\nBut in the list, \"kewǣpeqtaq\" = \"we1+2 begin\" — so \"begin\" is the root.\n\nWe need a personal form of \"begin\" with first-person singular. However, no such form is given.\n\nBut consider: \"kepītahtæq\" = \"we1+2 come eating it\"; the verb is \"come eating it\" — this might be equivalent to \"begin to eat it\" in meaning, though it's not exactly \"begin\" alone.\n\nNo direct \"I begin to eat\" is listed. But perhaps \"I begin to eat\" is derived from \"begin\" with object \"it\".\n\nWe have \"kewǣpeqtaq\" = we begin. So the verb \"begin\" is kewǣp-.\n\nIs there a form like \"kewǣp...\" used with first person singular?\n\nNo. The only similar form is \"kepītahtæq\" which describes eating, but with \"we1+2\".\n\nBut the structure \"come eating\" may be used as \"begin to eat\".\n\nSo if we interpret \"I begin to eat it\" as equivalent to \"we1+2 come eating it\" but with first person, but no form for first person.\n\nWait — is there a form for \"I begin to eat\"?\n\nAlternative: \"kepītahtæq\" is \"we1+2 come eating it\" — perhaps \"come eating\" means \"begin to eat\", and \"come\" = \"begin\". So if that's the only form, and no first-person personal form exists, perhaps we must use an equivalent.\n\nBut the only verb with \"begin to eat\" meaning is \"kepītahtæq\" — and it is for \"we1+2\".\n\nWe must infer the pattern.\n\nAnother thought: in Menominee, verbs may be patterned with person and object.\n\nWe have:\n- nepītohnæm → I walk here\n- nepītohnæm = I walk here\nSo \"I walk\" is nepītohnæm.\n\nSimilarly, \"nekāweqtam\" = I lie down\n\n\"nekāweqtam\" = I lie down\n\nSo likely, first-person forms of verbs are present.\n\nNow, \"kewǣpeqtaq\" = we1+2 begin → so \"begin\" is kewǣp- (with we1+2)\n\nBut for \"I\", we may expect a form like \"ke-...\" or \"nep-...\"?\n\nIs there a root for \"begin\" used in first person?\n\nWe have \"wǣpohnæw\" → he begins walking → \"he begins walking\"\n\nSo \"wǣpohnæw\" = he begins walking → \"he begins\" with \"walking\"\n\nCompare to \"kewǣpeqtaq\" = we begin\n\nSo the root for \"begin\" is likely *wǣp- or *kewǣp-?\n\n\"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw (walking)\n\n\"kepītahtæq\" = we come eating — but \"come\" may be different root.\n\nBut \"wǣpohnæw\" = he begins walking → so \"begin\" verb is derived from \"wǣp-\"\n\nSo \"begin\" root = wǣp-?\n\nThen \"I begin\" would be a first-person form.\n\nDo we have that?\n\nWe have no direct form. But perhaps first-person form is formed by adding *ke- or *ne-?\n\nIn \"nekatahan\" = I pry it out by tool → \"ne\" + kā + tahan → \"ne\" = first person?\n\n\"ne\" is in \"nekāweqtam\" = I lie down → \"ne\" = first person\n\nSimilarly, \"ne\" appears in \"nekāwāhpem\" = I fall over laughing → \"ne\" = first person\n\n\"ne\" = first person singular\n\nSimilarly, \"kawāham\" = he fells → \"kawa\" = he\n\n\"kēskenam\" = he breaks → \"kēsk\" = he\n\nSo the person-marking is likely:\n\n- \"ne-\" = I\n- \"ke-\" = we1+2\n- \"kaw-\" = he\n\nSo for \"begin\", if \"wǣpohnæw\" = he begins walking → root is \"wǣp-\", with \"wǣpohnæw\" = he begins walking\n\nSo \"begin\" is wǣp- with suffix for \"walking\"\n\nBut what is the base form?\n\nWe have \"kewǣpeqtaq\" = we1+2 begin → \"ke\" (we) + wǣp- + eqtaq (begin)\n\nSo \"wǣp-\" is the root for begin.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → \"wǣp- + on + hnæw\"\n\nSo \"begin\" root is wǣp-\n\nThen first person singular: \"I begin\" = ne + wǣp- + ?\n\nBut what suffix?\n\nIn \"nepītohnæm\" = I walk here → \"ne\" + pītohnæm\n\nSo \"ne\" marks first person.\n\nSimilarly, \"ne\" is used in \"ne\" + verb.\n\nSo likely, \"I begin\" = ne + wǣp- + ?\n\nBut in \"wǣpohnæw\" = he begins walking → so the verb part is wǣp- + something\n\nIn \"wǣpohnæw\", the verb is \"begin walking\", not just \"begin\".\n\nSo base form of \"begin\" may be \"wǣp-\"\n\nIn \"kewǣpeqtaq\" = we begin → \"kewǣp- + eqtaq\"\n\n\"eqtaq\" may be the marking for \"begin\"\n\n\"eqtaq\" is a suffix.\n\nSimilarly, \"wǣpohnæw\" = he begins walking → wǣp- + on + hnæw → so \"on\" is for \"walking\"\n\nSo different verbs have different suffixes.\n\nThus, \"I begin to eat\" — likely requires a form where \"begin\" is with the object \"to eat\".\n\nBut no direct form exists.\n\nBut we have \"kepītahtæq\" = we1+2 come eating it → \"come eating\"\n\n\"come\" may mean \"begin\" in this context.\n\n\"come eating it\" = start eating it.\n\nSo \"come eating\" = begin to eat.\n\nAnd we have a form: kepītahtæq = we1+2 come eating it\n\nBut is there a form for \"I come eating it\"?\n\nWe have no such form.\n\nBut perhaps the verb \"come eating\" is used in both persons.\n\nAlternatively, maybe \"begin to eat\" is formed with the root of \"begin\" + \"eat\".\n\nBut we don't have such a form.\n\nAnother possibility: perhaps \"begin to eat\" is expressed via \"come eating\" with first person.\n\nBut no such form is given.\n\nAlternatively, look at \"ketāwahtæq\" = we1+2 bite, gnaw a hole in it → \"bite\" or \"gnaw\"\n\n\"ketāwahtæq\" = we bite, gnaw\n\nSo \"bite\" = ketāw-?\n\nBut that’s for \"gnaw\"\n\nNo clear correspondence.\n\nIs there a parallel with \"lay it flat\"?\n\nTarget 2: \"we1+2 lay it flat by hand\"\n\nLook for a verb meaning \"lay down\", \"put flat\", \"place flat\".\n\nWe have:\n- nepītohnæm → I walk here\n- pītenam → he passes it here\n- pahkǣsam → he cuts it off\n- pāhkaham → he opens it by tool\n- ketǣnam → he takes it out by hand → \"take out\"\n- kepītahtæq → we come eating it\n- wackōhnæw → he walks roundabout\n- newāckesan → I cut around it\n- nekāwāhpem → I fall over laughing\n\nNo verb for \"lay flat\".\n\nBut \"kepītahtæq\" → \"we come eating it\" — does not match.\n\nWhat about \"pāhkeqtaw\" → he opens up → opens\n\n\"pāhkeqtaw\" = he opens up → \"opens\"\n\nNot \"lay\".\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\nBut perhaps \"lay\" is similar to \"put down\" or \"place\".\n\nWe have \"kewǣpānæhkæq\" = we begin to dig → dig\n\nNo.\n\nBut consider \"pahkǣsam\" = he cuts it off — cutting\n\n\"pāhkaham\" = he opens by tool\n\n\"nekǣtahan\" = I pry it out by tool\n\n\"ketǣnam\" = he takes it out by hand\n\n\"take it out\" → similar to \"lay it down\"?\n\n\"lay it flat\" → to put it flat on a surface.\n\nBut none of the verbs say that.\n\nWait — is there a form with \"place\" or \"put\"?\n\nNo.\n\nBut perhaps \"lay it flat\" is formed from root \"pāh\" or \"pah\"?\n\nWe have \"pahkǣsam\" = he cuts it off — \"cut off\"\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\nAll involve \"pāh\" but different meanings.\n\nNo clear \"lay flat\".\n\nBut \"we1+2 lay it flat by hand\" — hand implies \"by hand\", so no tool.\n\nSo \"by hand\" is important.\n\nWe have \"kēskenam\" = he breaks it through by hand → \"breaks by hand\"\n\n\"ketǣnam\" = he takes it out by hand → \"by hand\"\n\nSo \"by hand\" is possible in verb.\n\nBut still, no \"lay flat\".\n\nWait — perhaps there's a missing form.\n\nBut perhaps from pattern, the verb for \"lay flat by hand\" is formed from root \"pāh\"?\n\npāh is in:\n- pahkǣsam → cuts it off\n- pāhkaham → opens by tool\n- pāhkeqtaw → opens up\n\nAll have \"pāh\", but meanings differ.\n\nNo \"lay flat\".\n\nBut perhaps \"lay\" is not present — we must infer from structure.\n\nAlternative: go to target 3: \"he digs a hole\"\n\nLook for \"dig a hole\".\n\nWe have:\n- kewǣpānæhkæq → we1+2 begin to dig\n- tawǣsam → he cuts a hole in it\n\n\"tawǣsam\" = he cuts a hole in it\n\nSo \"cuts a hole in it\"\n\nBut \"dig a hole\" — \"dig\" is likely a verb of excavation.\n\nIs there a form for \"dig\"?\n\n\"kewǣpānæhkæq\" = we1+2 begin to dig\n\nSo \"begin to dig\" = kewǣpānæhkæq\n\n\"begin to dig\" → so the verb \"dig\" is likely in the base.\n\nSo \"he digs a hole\" = he + digs?\n\nBut is there a form for \"he digs\"?\n\nWe have no isolated \"he digs\", but perhaps \"he digs\" = he + dig\n\nBut no separate verb.\n\n\"tawǣsam\" = he cuts a hole in it → so \"cut a hole\"\n\nBut \"dig\" and \"cut a hole\" are different.\n\nHowever, in many languages, \"dig a hole\" and \"cut a hole\" are related.\n\nBut \"dig\" is more for earth, \"cut\" for material.\n\n\"tawǣsam\" = he cuts a hole in it → does not say \"in ground\"\n\nSo likely not the same.\n\nBut what about \"kewǣpānæhkæq\" = we begin to dig → so \"dig\" is the action.\n\nSo perhaps \"he digs\" = he + dig root.\n\nBut no standalone form.\n\nBut the only form with \"dig\" is in \"kewǣpānæhkæq\" = we begin to dig → so the verb \"dig\" is present.\n\nSo likely, for \"he digs a hole\", we can use a form derived from that.\n\nBut what root?\n\n\"begin to dig\" = kewǣpānæhkæq → \"ke\" + wǣp- + ān + æhkæq?\n\nOr is it \"kewǣpānæhkæq\" = we begin to dig → so the root is \"wǣpān\"?\n\nBut \"wǣpān\" isn't standalone.\n\nPerhaps the verb \"dig\" is built from root \"pān\" or \"pān\" with particle.\n\nBut no.\n\nWait — \"kewǣpānæhkæq\" = we begin to dig\n\nSo \"begin to dig\" is a compound form.\n\nBut \"dig\" is not isolated.\n\nSimilarly, \"tawǣsam\" = he cuts a hole in it\n\nSo \"cut a hole\" is formed.\n\nBut for \"dig a hole\", we may have to use \"dig\" as root.\n\nBut in absence of direct form, perhaps the only verb with excavation is \"begin to dig\".\n\nBut \"begin to dig\" is for \"we\", not \"he\".\n\nSo for \"he digs a hole\", likely \"he + dig\" = ?\n\nBut we don't have a standalone form.\n\nUnless \"begin to dig\" is used with he?\n\nBut no.\n\nPerhaps the verb \"dig\" is expressed by \"pān\" or another root.\n\nWe have no such form.\n\nBut perhaps in Menominee, \"dig a hole\" is expressed with the same form as \"begin to dig\", but with he.\n\nBut there is no such form given.\n\nWait — perhaps there is a form like \"kewǣpānæhkæq\" but for he?\n\nNot listed.\n\nSo conclusion: the only form for digging is in \"kewǣpānæhkæq\", which means \"we begin to dig\".\n\nSo for \"he digs a hole\", since no direct form, and no other verb, perhaps it is an exact parallel.\n\nBut the verb \"dig\" may be in the base.\n\nPerhaps for \"he digs a hole\", it is derived as \"he + dig\" = same as \"we begin to dig\" but with he.\n\nBut no such form.\n\nAlternatively, the form \"tawǣsam\" = he cuts a hole — so \"cut a hole\" is present.\n\nBut \"dig\" is different from \"cut\".\n\nSo not parallel.\n\nBut perhaps \"dig a hole\" is not directly expressible, but \"begin to dig\" is.\n\nBut the question says \"he digs a hole\" — not \"he begins to dig\".\n\nSo likely, we need a form for \"dig\".\n\nBut in the given forms, the only verb involving digging is \"begin to dig\".\n\nSo perhaps \"he digs a hole\" is translated as \"he begins to dig\" — but that is not accurate.\n\nUnless in Menominee, \"dig\" is only expressed with \"begin\".\n\nBut no.\n\nAnother possibility: perhaps \"kewǣpānæhkæq\" is the only form with \"dig\", so for he, it is the same root.\n\nBut with he.\n\nWe have no such form.\n\nBack to target 1: \"I begin to eat it\"\n\nWe have \"kepītahtæq\" = we1+2 come eating it → \"come eating it\"\n\n\"come\" may mean \"begin\"\n\nSo \"begin to eat it\" = come eating it\n\nSo for \"I come eating it\" — first person.\n\nBut is there a form for \"I come eating it\"?\n\nWe have \"ne\" for first person: \"nekāweqtam\" = I lie down\n\n\"ne\" is first person.\n\nIn \"nekāwāhpem\" = I fall over laughing\n\nSo first person is marked by \"ne-\"\n\nSo \"I come eating it\" = ne + pītaht + ? → but \"pītaht\" is not in the list.\n\n\"kepītahtæq\" = we come eating it → so the root is \"pītaht\"\n\nSo \"I come eating it\" = ne + pītaht + æq\n\nBut is that valid?\n\nWe have no such form, but the root \"pītaht\" may be for \"come eating\"\n\nSo for first person, \"ne\" + pītaht + æq = ne + pītahtæq?\n\nBut \"ne + pītahtæq\" = ?\n\nNot in list.\n\nBut perhaps it's acceptable.\n\nSimilarly, for \"we1+2 lay it flat by hand\"\n\nWe have no verb for \"lay flat\".\n\nBut consider \"pītenam\" = he passes it here → \"passes\"\n\n\"nepītohnæm\" = I walk here\n\nNo.\n\n\"pāhkeqtaw\" = he opens up\n\nNo.\n\nPerhaps \"lay\" is not present.\n\nBut \"lay it flat\" might be formed from \"pāh\" meaning \"open\" or \"place\".\n\nBut no.\n\nAnother idea: perhaps \"lay flat\" is equivalent to \"place on a surface\".\n\nWe have no such verb.\n\nBut perhaps it is formed from \"pāh\" with hand.\n\n\"pāhkaham\" = he opens by tool\n\n\"pāhkeqtaw\" = he opens up\n\n\"pāhkeqtaw\" = he opens up → so \"open\" by hand or tool?\n\nNo hand marking.\n\n\"ketǣnam\" = he takes it out by hand\n\nSo \"by hand\" is used.\n\nSo for \"lay it" + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-a", + "planner_index": 4, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 16.: answer for this requested item\n- a.2 / 17.: answer for this requested item\n- a.3 / 18.: answer for this requested item\n- a.4 / 19.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n spoken on Bvuŋkaden\n\n 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n 17. me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n.\n\n 18. wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn.\n\n 19. bèsèn nǔ bóy tɔ́ fɔ̀wǎy bvúzhı᷇ːde᷆n.\n\nSAMPLED ATTEMPT:\nWe are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "approaches": [ + "Focus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"", + "Re-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"", + "\nFocus on temporal reference patterns and day order. The days are ordered as: Bvutfu → Bvusɔw → Bvuzhi → Bvuŋka → Bvuŋkaden. This is confirmed by: \n- Sentence 1: \"Yesterday was Bvumbon\" → Bvumbon is before Bvutfu \n- Sentence 5: \"The day after tomorrow is Bvutfu\" → so Bvutfu is after two days \n- Sentence 8: \"Tomorrow is Bvuŋkaden\" → current day is Bvuŋka \n- Sentence 11: \"The day before yesterday was Bvuŋka\" → current day is Bvuŋkaden \n\nThus, Bvuŋkaden is the day after Bvuŋka. \n\nFor sentence 16: \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" \n- \"fɔ̀ shě ntfǔː\" = \"the day after tomorrow is Bvutfu\" \n- \"bvúsɔ̀w nǔ\" = \"on Bvusɔw, you\" \n→ So: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this is illogical. \nInstead, the structure may be: \"On Bvusɔw, you (will) be the day after tomorrow\" — but \"fɔ̀ shě\" is not \"be\". \nAlternative: perhaps \"fɔ̀ shě\" is a time marker modifying the action. \nBut in sentence 5, it's used as a time reference. \nThus, \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" is the only grammatical parse. \nBut it is not a natural English sentence. \nVerification: sentence 5 uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → \"the day after tomorrow is Bvutfu\" \nSo \"fɔ̀ shě X\" = \"the day after tomorrow is X\" \nThus, \"bvúsɔ̀w nǔ fɔ̀ shě ntfǔː\" = \"On Bvusɔw, you have the day after tomorrow be Bvutfu\" — likely a misapplication. \nBut if we interpret \"nǔ\" as agent, and \"fɔ̀ shě\" as time reference, then the meaning is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — still unnatural. \nConclusion: likely error in parsing — perhaps \"bvúsɔ̀w\" is the time, \"nǔ\" is subject, \"fɔ̀ shě ntfǔː\" is the event. \nBut no event involving \"the day after tomorrow\" as a state. \nThus, the only consistent translation is: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — but this fails semantic verification. \nHence, likely incorrect. \nFinal interpretation: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\" — despite oddity. \nVerification: presence of \"fɔ̀ shě X\" = \"the day after tomorrow is X\" in known sentence. \nSo pattern holds. \n→ 16: \"On Bvusɔw, you will have the day after tomorrow be Bvutfu\"\n\n\n\nRe-examine word classes and verb-noun roles. \nIn sentence 17: \"me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n\" \n- \"me nú\" = \"on that day, I\" \n- \"ŋgéː\" = \"will help\" \n- \"nyɛ́n\" = \"the woman\" \n- \"kèŋkfǔ\" = \"the yam\" \n- \"lé\" = \"saw\" \n- \"ɛ̀bɛ̀n\" = \"the woman\" \n\nPossible compound: \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" \nThen \"nyɛ́n\" = \"the woman\" — redundant. \nAlternative: \"nyɛ́n\" modifies \"kèŋkfǔ\" → \"the woman stole the yam\" → but \"lé\" is \"saw\", not \"stole\" \nSentence 2: \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\" = \"you will steal the yam on Bvusɔw\" → \"cɔ́ŋ\" = steal \nSo \"kèŋkfǔ\" is yam, not verb. \nThus, \"kèŋkfǔ lé\" = \"the yam saw\" → the yam saw the woman? Unnatural. \nAlternative: \"kèŋkfǔ\" is a verb? Unlikely. \nAnother possibility: \"nyɛ́n kèŋkfǔ\" = \"the woman who stole the yam\", and \"lé ɛ̀bɛ̀n\" = \"saw the woman\" \nBut that would be \"the woman who stole the yam saw the woman\" — redundant. \nBest possible: \"I will help the woman who saw the yam\" — but \"ɛ̀bɛ̀n\" is not \"the yam\" \nUnless \"ɛ̀bɛ̀n\" is a typo or misgloss. \nBut in sentence 13: \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" = \"the woman saw the market\" \nSo “yɛ᷅n wáy” = saw the market \nThus, “kèŋkfǔ lé” = “saw the yam” \nThen “lé ɛ̀bɛ̀n” = “saw the woman” \nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” \nSo the full sentence: “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is “the woman” \nSo perhaps “nyɛ́n” is the subject of the action, and “kèŋkfǔ lé ɛ̀bɛ̀n” is a clause about what she did. \nThus: \"On that day, I will help the woman who saw the yam\" — and “the woman” is the subject, not the object. \nBut “saw the yam” is attributed to her. \nSo: \"I will help the woman who saw the yam\" \nVerification: sentence 13 has \"saw the market\", so \"saw X\" structure is consistent. \nThus, \"kèŋkfǔ lé\" = \"saw the yam\", \"lé ɛ̀bɛ̀n\" = \"saw the woman\" — cannot both be. \nOnly one \"lé\" verb. \nSo likely \"kèŋkfǔ lé ɛ̀bɛ̀n\" = \"the yam saw the woman\" — not plausible. \nConclusion: likely \"I will help the woman (who saw the yam)\" — with \"ɛ̀bɛ̀n\" as error or misgloss. \nBut in context, “kèŋkfǔ” is “the yam”, so “the woman saw the yam” is the event. \nSo “I will help the woman who saw the yam” — and “ɛ̀bɛ̀n” is a red herring. \nBut “ɛ̀bɛ̀n” is used in other sentences (e.g., “killed the woman”) — so likely object. \nThus, “saw the woman” is the event. \nSo “kèŋkfǔ” is not involved. \nPossibility: typo in gloss — should be \"kèŋkfǔ\" as \"the yam\", and \"lé\" as \"saw\", and \"ɛ̀bɛ̀n\" as object → “the yam saw the woman” \nBut no one \"saw\" the yam. \nFinal: structure is \"I will help the woman who saw the yam\" — and \"ɛ̀bɛ̀n\" is a mistake. \nBut it's not. \nAlternate: “I will help the woman (who is seen by the yam)” — no. \nBest: \"On that day, I will help the woman who saw the yam\" — despite the \"ɛ̀bɛ̀n\" being out of place. \nVerification: in sentence 13, \"the woman saw the market\" — so \"saw X\" is standard. \nThus, “saw the yam” is plausible. \nSo 17: \"On that day, I will help the woman who saw the yam\"\n\n\n\nAnalyze sentence 18: \"wvù tɔ̀ nɔ̂ː yɛ᷅n bèsèn ě bvúmbòn\" \n- \"wvù\" = \"he\" \n- \"tɔ̀ nɔ̂ː\" = \"found\" \n- \"yɛ᷅n\" = \"saw\" \n- \"bèsèn\" = \"the future\" or \"will\" \n- \"ě\" = \"the\" \n- \"bvúmbòn\" = \"Bvumbon\" \n\nSo:", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "We are given sentences in Nooni spoken on different days of the Nooni week and their English translations. The task is to translate four sentences (16–19) spoken on **Bvuŋkaden**, based on patterns observed in earlier sentences.\n\n---\n\n### Step 1: Identify the day structure\n\nWe observe days like:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nFrom the data:\n- Sentence 1: “Yesterday was Bvumbon.” → Indicates Bvumbon is a day in the past relative to Bvutfu.\n- Sentence 5: “The day after tomorrow is Bvutfu.” → Day after tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → So Bvuŋkaden is the day after Bvuŋka.\n- Sentence 11: “The day before yesterday was Bvuŋka” → Bvuŋka is two days before current day.\n\nThus, the days follow a sequence:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo the week likely follows:\n1. Bvutfu\n2. Bvusɔw\n3. Bvuzhi\n4. Bvuŋka\n5. Bvuŋkaden\n\nThis is consistent with the progression:\n- On Bvutfu → next day Bvusɔw → next Bvuzhi → next Bvuŋka → next Bvuŋkaden\n\nFrom sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden.\n\nThus, days are ordered as:\n- Bvutfu\n- Bvusɔw\n- Bvuzhi\n- Bvuŋka\n- Bvuŋkaden\n\nSo Bvuŋkaden is the last day of the week, or a day after Bvuŋka.\n\n---\n\n### Step 2: Identify patterns in temporal expressions\n\nWe need to understand how time references are formed.\n\nLook at known translations:\n\n- Sentence 1: “Yesterday was Bvumbon” → Bvumbon is the day before Bvutfu\n- Sentence 5: “The day after tomorrow is Bvutfu” → tomorrow = Bvutfu\n- Sentence 8: “Tomorrow is Bvuŋkaden” → current day is Bvuŋka → tomorrow is Bvuŋkaden\n- Sentence 11: “The day before yesterday was Bvuŋka” → two days before current day = Bvuŋka → current day is Bvuŋkaden\n\nSo:\n- Bvumbon = day before Bvutfu\n- Bvutfu = day after day before Bvutfu\n- Bvuŋka = day before Bvuŋkaden\n\nThus, time expressions seem to be directly tied to reference days.\n\nNow, look at temporal markers:\n- “fɔ̀ shě ntfǔː” = “the day after tomorrow”\n- “ntfǔː nú” = “tomorrow is”\n- “cí nú” = “yesterday was”\n- “me nú” = “on that day, I (will)…”\n- “wvù tɔ̀ nɔ̂ː” = “he found”\n- “kwɔ᷆ːn” = “on that day”\n- “nǔ” = “you (sg)”, “the woman”, etc.\n- “bèsèn” = future tense (will)\n- “yɛ᷅n” = “saw”\n- “kèŋkfǔ” = “the yam”\n- “ɛ̀bɛ̀n” = “the woman”\n- “fí” = “help”\n- “mutù” = “the car”\n\n---\n\n### Step 3: Translate each sentence (spoken on Bvuŋkaden)\n\n#### 16. bvúsɔ̀w nǔ fɔ̀ shě ntfǔː.\n\n“bvúsɔ̀w” = Bvusɔw \n“nǔ” = you (sg) \n“fɔ̀ shě” = the day after tomorrow \n“ntfǔː” = Bvutfu\n\nSo: “On Bvusɔw, you (sg) will have the day after tomorrow be Bvutfu?” — no, that doesn’t make sense.\n\nWait — the structure is: “X nǔ fɔ̀ shě Y” → “On X, Y will be the day after tomorrow”?\n\nBut that doesn't fit.\n\nWait — from sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo: “fɔ̀ shě ntfǔː” = “the day after tomorrow is” followed by a day name\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu?” — still awkward.\n\nWait — perhaps it's: “On Bvusɔw, you will [have] the day after tomorrow be Bvutfu”?\n\nBut that’s not idiomatic.\n\nAlternative: maybe “fɔ̀ shě” is a time marker, not a verb.\n\nIn sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “The day after tomorrow is Bvutfu”\n\nSo the form is: [fɔ̀ shě X] = \"the day after tomorrow is X\"\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you (sg) have the day after tomorrow be Bvutfu” — no.\n\nWait — perhaps “nǔ” modifies the day?\n\nIs it “you (sg), on the day after tomorrow is Bvutfu”?\n\nNo — syntax must be parsed as: subject + time reference + event?\n\nLook at sentence 17 later: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nWait — “nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “the woman saw the yam the woman”? Makes no sense.\n\nWait — perhaps “lé” is not “saw”, but “in the market”?\n\nBut earlier sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = saw the market\n\nSo “lé” = “saw”\n\nBack to 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nOn that day, I will help the woman saw the yam (the woman)? — still awkward.\n\nWait — maybe “nyɛ́n kèŋkfǔ” means “the woman stole the yam”?\n\nBut “nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam”\n\n“lé” = “saw”\n\nNo.\n\nAnother possibility: “nyɛ́n kèŋkfǔ” is “the woman who stole the yam”, and “lé ɛ̀bɛ̀n” is “saw the woman”?\n\nBut “lé” is seen.\n\nAlternate: perhaps “nyɛ́n” = “it” or “her”?\n\nOr misreading: is it “me nú ŋgéː nyɛ́n” = “I will help the woman”, and “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman” — no.\n\nPerhaps “kèŋkfǔ” is a verb? But it's followed by “lé”\n\nBetter: look at sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “géː” = “will steal”\n\nSimilarly, sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\nSo “yɛ᷅n wáy” = “saw the market”\n\nSimilarly, sentence 6: “wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n” = “Today, he killed the woman”\n\nSo “bɛ̂ː” = “killed”\n\nBack to sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\nPossibly: “On that day, I will help the woman who saw the yam” — but “kèŋkfǔ lé” = “saw the yam”?\n\nYes — “kèŋkfǔ” = “yam”, “lé” = “saw” → “the woman saw the yam”\n\nBut “nyɛ́n” = “the woman” → would be “the woman saw the yam”\n\nSo “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n” → “On that day, I will help the woman who saw the yam” — but “nyɛ́n” is already “the woman”, so it’s redundant.\n\nAlternate: “I will help (the woman) (who saw the yam)”\n\nSo: “On that day, I will help the woman who saw the yam”\n\nBut “the woman” is repeated — no.\n\nIs there a missing link?\n\nWait, perhaps the structure is: “me nú ŋgéː [X] [event]” = “On that day, I will help X [in the event]”\n\nBut the event is “kèŋkfǔ lé ɛ̀bɛ̀n” → “the yam saw the woman” — makes no sense.\n\nBack to full pattern.\n\nFrom sentence 3: “On Bvuzhi, the woman will help me” → “kwɔ᷆ːn nǔ bóy fí me bvúzhí” → “the woman helps me”\n\nSo “nǔ bóy” = “the woman” \n“fí” = “helps” \n“me” = “me”\n\nSo “nǔ bóy fí me” = “the woman will help me”\n\nSimilarly, sentence 14: “bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n” = “Today, we will steal the car”\n\nSo “nǔ géː” = “we will steal”\n\nAnd sentence 15: “bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy” = “They saw me at the market just now”\n\nSo “yɛ᷅n me lé” = “saw me”, “fɔ̀wǎy” = “at the market”\n\nNow sentence 17: “me nú ŋgéː nyɛ́n kèŋkfǔ lé ɛ̀bɛ̀n”\n\n“me nú” = “on that day, I” \n“ŋgéː” = “will help” \n“nyɛ́n” = “the woman” \n“kèŋkfǔ” = “the yam” \n“lé” = “saw” \n“ɛ̀bɛ̀n” = “the woman”\n\nSo: “On that day, I will help the woman who saw the yam the woman”?\n\nNo.\n\nPossibility: “I will help the woman (who saw the yam)” → “kèŋkfǔ lé” = “saw the yam” \nBut “lé ɛ̀bɛ̀n” = “saw the woman”?\n\nSo “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”\n\nSo “I will help the woman who saw the yam” → but \"saw the yam\" is attributed to the woman?\n\nNot clear.\n\nAlternative: perhaps “kèŋkfǔ” is a noun, “lé” is verb, “ɛ̀bɛ̀n” is object — that is, “the yam saw the woman”\n\nBut “nyɛ́n” is separate — “the woman”\n\nSo “I will help the woman (who saw the yam)”\n\nMust be: “On that day, I will help the woman who saw the yam”\n\nBut why “ɛ̀bɛ̀n”?\n\nWait, perhaps the object is “the woman”, and “kèŋkfǔ” is not “the yam”.\n\nIs there a compound?\n\nCompare sentence 13: “kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅” = “On Bvutfu, the woman saw the market”\n\n“yɛ᷅n wáy” = “saw the market”\n\nIn 17: “kèŋkfǔ lé ɛ̀bɛ̀n” = “the yam saw the woman”?\n\nBut “the yam saw the woman” doesn’t sound right.\n\nUnless “kèŋkfǔ” means “(someone) who stole the yam”, and “lé” = “saw”, “ɛ̀bɛ̀n” = “the woman”\n\nNo.\n\nAlternatively, is “kèŋkfǔ” a verb? Unlikely.\n\nBack to 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nWe have: “fɔ̀ shě ntfǔː” = “the day after tomorrow is Bvutfu” — from sentence 5\n\nSo “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu”\n\nBut that’s not grammatical.\n\nWait — “nǔ” = “you (sg)”\n\nSo: “On Bvusɔw, you have the day after tomorrow be Bvutfu”?\n\nNo.\n\nPossibility: it's a misordering.\n\nAnother possibility: “fɔ̀ shě” is not “the day after tomorrow is”, but “in the day after tomorrow”\n\nBut \"fɔ̀ shě\" is found only in \"fɔ̀ shě ntfǔː nú bvútfu᷅\" → clearly “the day after tomorrow is Bvutfu”\n\nSo pattern: “fɔ̀ shě X” = “the day after tomorrow is X”\n\nThus, “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still odd.\n\nWait — perhaps “nǔ” is not “you”, but a time marker?\n\nNo — in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” → “On Bvusɔw, you will steal the yam”\n\nSo “wɔ̀ nǔ” = “you (sg), on Bvusɔw”\n\nSimilarly, sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you have [the day after tomorrow be Bvutfu]”\n\nStill odd.\n\nPerhaps it's \"On Bvusɔw, you (will) be the day after tomorrow\" — but that doesn't work.\n\nWait — perhaps “fɔ̀ shě” is not a time expression, but a verb.\n\nBut sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → clearly “the day after tomorrow is Bvutfu”\n\nSo it is a time expression.\n\nThen only possible interpretation is that “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː” = “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — maybe it's a mistake in the sentence.\n\nWait — perhaps it’s “On Bvusɔw, the day after tomorrow is Bvutfu” — with “nǔ” as a typo?\n\nBut “nǔ” is always used for “you (sg)”\n\nUnless in this case it's a different role.\n\nWait — sentence 11: “kefwé cí nú bvûŋka” → “The day before yesterday was Bvuŋka”\n\nSo “cí nú” = “yesterday was”\n\nSimilarly, sentence 5: “fɔ̀ shě ntfǔː nú bvútfu᷅” → “the day after tomorrow is Bvutfu”\n\nSo time expressions:\n- fɔ̀ shě X = “the day after tomorrow is X”\n- cí nú X = “yesterday was X”\n- ntfǔː nú X = “tomorrow is X”\n- bɛ̂ː = “killed”\n- yɛ᷅n = “saw”\n- géː = “will steal”\n- fí = “help”\n- bèsèn = “will”\n\nNow sentence 16: “bvúsɔ̀w nǔ fɔ̀ shě ntfǔː”\n\nPattern: “[day] nǔ [time expression] [day]”\n\nBut in sentence 2: “wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w” = “On Bvusɔw, you will steal the yam”\n\nSo “day nǔ verb object”\n\nSo here, “day nǔ fɔ̀ shě day” — doesn’t follow.\n\nUnless “fɔ̀ shě” is a verb meaning “to be” or “to have”\n\nBut it's used with a day to mean “the day after tomorrow is that day”\n\nSo likely, “fɔ̀ shě” is a time expression.\n\nThen, only way: “On Bvusɔw, you will have the day after tomorrow be Bvutfu” — still awkward.\n\nBut from the timeline:\n- Bvuŋkaden is the day after Bvuŋka\n- So day after tomorrow from Bvuŋkaden would be Bvutfu?\n- Bvuŋk" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-b", + "planner_index": 5, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Inuktitut:\n 19. The shaman hurt you.\n 20. The teacher saw the boy.\n 21. Your wolf fell.\n 22. You shot a dog.\n 23. Your dog hurt a teacher.\n\nNB: Inuktitut (Canadian Inuit) belongs to the Eskimo-Aleut family of languages. It is spoken by\napprox. 35 000 people in the northern part of Canada.\n The letter r denotes a ‘Parisian’ r (pronounced far back in the mouth), and q stands for a\nk-like sound made in the same place.\n A shaman is a priest, sorcerer and healer in some cultures. —Bozhidar Bozhanov\n\nSAMPLED ATTEMPT:\nStep 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3r\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "approaches": [ + "Focus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point.", + "\nFocus on subject marking and verb alignment. In Inuktitut, possessive markers are attached to nouns, and verbs take person/number markers. For \"you shot a dog\", identify the verb root for \"shot\" from sentence 2: \"qukiqtanga\" → \"qukiqt\" + \"anga\" = shoot. \"qukiq\" is likely the root. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" = shot. The suffix \"-suq\" appears in \"qukiqsijuq\" and is likely the 3rd person form. In contrast, sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared, with \"you\" as subject. \"Qingmiq\" may be \"you\" + \"dog\" or \"you\". But \"q\" is not used in \"v\" (possessive). Instead, \"you\" may be expressed without a noun, relying on the verb's person suffix. In \"Ukiakhaqtutit\" (\"you fell\"), the verb ends in \"-utit\", indicating first person. So \"you\" is marked by the verb's suffix. Thus, \"you shot\" = \"qukiq\" + \"it\" = \"qukiqit\"? But \"qukiqsijuq\" has \"-suq\", not \"-it\". However, \"qukiqsijuq\" may be \"qukiq\" + \"sijuq\" → object marker. The object is \"a polar bear\", not \"a dog\". So \"shot\" is not marked with person in object form. Instead, the subject is marked separately. In sentence 12, \"Angunahukti\" = the hunter → marked. So for \"you\", if no noun, it may be implied. But sentence 5 has \"Qingmiq\" — if \"Qingmi\" = dog, then \"Qingmiq\" = dog with q → \"you\" not present. Therefore, \"you shot\" must use a first-person subject marker. In the absence of such, the only consistent pattern is that first-person subject is marked by a verb suffix. In sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should be \"qukiq\" + \"utit\"? But \"qukiqsijuq\" has \"-suq\", not \"-utit\". Contradiction. Therefore, \"you shot\" must be \"qukiq\" + \"it\" or \"qukiqit\", but no such form appears. Alternative: \"qukiq\" is the root, and the person is marked by context. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → subject \"the boy\", object \"the doctor\". No first person. So \"you shot a dog\" → likely \"you\" is not marked by a separate word, and the verb is used with object. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" likely = you. So \"Qingmiq\" = you. Then \"qukiq\" = shot. So perhaps \"you\" is expressed as a noun form like \"Qingmiq\", but that is dog. Therefore, the root \"qukiq\" is used with a person marker. But no direct evidence. Verification: in sentence 10, \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → subject \"the dog\", verb \"hurt\", object \"your teacher\". No first-person subject. So for \"you shot a dog\", the subject \"you\" is likely marked by the verb suffix. But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → so \"you\" = first person. So \"you shot\" should have suffix \"-utit\" → \"qukiqutit\"? But no such form. Instead, \"qukiqsijuq\" has \"-suq\" → 3rd person. So \"you\" must be expressed differently. Conclusion: the verb root for \"shot\" is \"qukiq\", and for first person, use \"qukiqit\" or similar. But no such form. Therefore, the only consistent form is \"you shot a dog\" = \"uk\" + \"qukiq\" + \"a dog\", but no \"uk\". Thus, the pattern is that first-person subject is not marked in the verb but is implied. But in sentence 5, \"Qingmiq iputujait\" → \"you speared the dog\" → \"Qingmiq\" = you? Unlikely. So perhaps \"Qingmiq\" = the dog, and \"you\" is not present. This suggests a flaw in the pattern. Final decision: use \"qukiq\" + \"it\" → \"qukiqit\" for \"you shot\" → but not supported. Better: in sentence 5, \"Qingmiq\" = you → so \"you\" is a form of \"Qingmi\" with \"q\". But \"Qingmi\" = dog. So \"q\" must be a marker for first person. But not consistent. Therefore, \"you shot a dog\" = \"qukiq\" + \"a dog\" → with \"you\" implied. But in sentence 12, \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → so \"qukiqsijuq\" = shot → so for first person, no such form. So it is likely that \"you shot\" is not directly formed. Therefore, the only logical path is that \"you\" is expressed via the verb with a suffix. In \"Ukiakhaqtutit\", \"utit\" = you. So \"you shot\" = \"qukiqutit\"? But no such form. So error in pattern. Verification: in sentence 11, \"Ukiakhaqtutit\" = you fell → so first person is marked by \"-utit\" in verb. So for \"you shot\", must be \"qukiqutit\"? But \"qukiqsijuq\" is 3rd person. So contradiction. Therefore, the verb for \"shot\" is not marked by person, or the form is different. So \"you shot a dog\" = \"qukiq\" + \"a dog\" → with first person subject missing. But in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → so \"Qingmiq\" = you → so \"you\" is a noun form. So \"you\" = \"Qingmiq\" → implies that \"Qingmi\" is used for \"you\". But \"Qingmi\" is dog. So only if \"q\" marks \"you\". But in sentence 1: \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" is not possessive. So \"Qingmiq\" = dog with q → not \"you\". Therefore, \"you\" is not marked in that way. Final decision: \"you shot a dog\" = \"qukiq\" + \"it\" → \"qukiqit\" → not in data. So likely incorrect. Instead, use \"qukiqsijuq\" with first person? No. So the pattern is that \"you\" is not a noun but a subject marked by verb. So \"you shot\" = \"qukiqutit\" → but no such form. Therefore, the attempt fails at this point. \n\n\n\nRe-analyze verb person marking. In Inuktitut, verbs often carry person markers. From sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb ends in \"-utit\" → 1st person. In sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb \"qukiqtanga\" → likely \"qukiq\" + \"tanga\" = shoot (with object marker). No person suffix. In sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → \"qukiqsijuq\" → \"qukiq\" + \"sijuq\" → 3rd person. So \"you shot\" must be first person. But no form with \"it\". However, in sentence 5: \"Qingmiq iputujait\" → \"you speared the dog\" → \"iputujait\" = speared → verb with object. If \"Qingmiq\" = you, then \"you\" is a noun. But \"Qingmi\" = dog → so \"q\" = marker for \"you\"? But in \"Qingmivit\" = your dog → \"v\" = possessive. So \"q\" ≠ possessive. So \"Qingmiq\" = dog with \"q\" → not \"you\". Therefore, \"you\" is not a noun. So \"you shot\" must be verb with 1st person", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "Step 1: Identify the verb patterns in the given sentences.\n\nLook at sentence 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtut\" = hurt; \"-it\" = 1st person (you) in a causative or reflexive form \n→ So \"aanniqtut\" is \"hurt\", and \"-it\" marks the subject as \"you\" (first person)\n\nSentence 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaat\" = cured; \"-it\" = 3rd person (you) \n→ So \"aarqijaatit\" = \"cured you\"\n\nSentence 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (the dog) → verb with \"you\" as subject + object \"dog\"\n\nSentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aariqisijuq\" = cured → so \"aarqisijuq\" = cured (someone) \n→ \"iluaqhaijimik\" = a doctor (genitive) \n→ \"Angatkuq\" = the shaman → so \"Angatkuq\" + \"aarqisijuq\" → \"The shaman cured a doctor\"\n\nNow, note:\n- \"hurt\" appears as \"aanniqtut\"\n- \"cured\" appears as \"aarqijaat\", \"aarqisijuq\"\n- \"saw\" appears in sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\"\n→ \"takujait\" = saw → verb form\n\nSo:\n- \"saw\" = takujaat\n- \"hurt\" = aanniqtut\n- \"cured\" = aarqijaat / aarqisijuq\n- \"speared\" = iputujait\n\nNow, look at subject markers.\n\nSentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\" → possessive + noun \n→ \"it\" is a suffix marking the subject (first person?) but actually, \"Qingmivit\" = your dog → possessive \"your\" + \"dog\"\n\nIn Inuktitut, possessive markers are often attached to nouns.\n\nSentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor\" \n→ \"Inuuhuktuup\" = the boy → \"inuuhukt\" + \"up\" → \"up\" = definite marker \n→ \"qukiqtanga\" = doctor → \"qukiqt\" + \"anga\" → verb? Wait, no, \"qukiqtanga\" is likely noun + marker \nWait: “qukiqtanga” = doctor → so \"qukiq\" + \"tanga\" → 'doctor'\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you + dog? No → \"Qingmiq\" = you? Or \"dog\"?\n\nWait: sentence 1: \"Qingmivit takujaatit\" → \"Your dog saw you\" \n→ \"Qingmivit\" = your dog \n→ \"takujaatit\" = saw you → so verb + object?\n\nWait: pivotal structure: verbs take possessive forms and appear with object.\n\nBut now, look at sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" \n→ \"Qingmiup\" → \"dog\" + \"up\" → \"your\" added? No → \"up\" = definite \n→ \"ilinniaqtitsijiit\" → \"hurt\" → \"ilinniaqt\" + \"itsijiit\" → verb \n→ \"aanniqtanga\" = your teacher → \"aanniqt\" + \"anga\"\n\nSo verb forms:\n\n- \"aanniqtut\" = hurt (third person, \"you\" as subject) \n- \"aanniqtanga\" = your teacher\n\nSo we can infer:\n\n| English | Inuktitut |\n|--------|-----------|\n| hurt (you) | aanniqtutit |\n| hurt (you, reflexive) | aanniqtut |\n| cured (someone) | aarqijaatit |\n| saw | takujaat |\n| speared | iputujait |\n\nNow, for sentence 19: \"The shaman hurt you.\"\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n→ \"Angatkuq\" = shaman \n→ \"aarqisijuq\" = cured \n→ So \"cured\" = aarqisijuq (has a \"su\" suffix, likely form of \"aarqijaat\")\n\nSimilarly, \"hurt\" = aanniqtut → so \"the shaman hurt you\" → \"Angatkuq aanniqtutit\"\n\n→ \"aanniqtutit\" = hurt (you)\n\nSo 19: \"Angatkuq aanniqtutit\"\n\nSentence 20: \"The teacher saw the boy.\"\n\n\"Teacher\" → not directly given. Sentence 10 says \"your teacher\" = \"aanniqtanga\"\n\nSo \"teacher\" = aanniqtanga (as in \"your teacher\") → root: aanniqt\n\n\"the teacher\" → definite form → \"aanniqt\" + \"up\"?\n\nBut in sentence 10: \"ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → so \"aanniqtanga\" = your teacher → so \"aanniqt\" is base for teacher.\n\nIs \"the teacher\" = \"aanniqtup\"? Or \"aanniqtangup\"?\n\nWait, sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → \"Inuuhuktuup\" = the boy → so \"up\" = definite article.\n\nSo likely \"aanniqtup\" = the teacher\n\nNow, \"saw\" = takujaat (from sentence 1: \"takujaatit\" → \"saw you\")\n\nSo \"the teacher saw the boy\" → \"aanniqtup takujaat iluaqhaiji\"\n\n→ \"iluaqhaiji\" = the boy → \"iluaqhaij\" + \"i\" → genitive? No — in sentence 2, \"iluaqhaiji\" is object.\n\nSo object = \"iluaqhaiji\" → \"the boy\"\n\nSo verb: \"takujaat\" → saw (a person)\n\nSo 20: \"aanniqtup takujaat iluaqhaiji\"\n\nSentence 21: \"Your wolf fell.\"\n\n\"Your\" → from sentence 1: \"Qingmivit\" = your dog \n→ \"Qingmivit\" = your dog → \"Qingmi\" + \"v\" + \"it\"\n\n\"wolf\" → missing. But sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf\" \n→ \"amaruq\" = wolf → so \"amaruq\" = wolf\n\nSo \"your wolf\" → \"amaruq\" with possessive \"your\"\n\nIn sentence 1: \"Qingmivit\" → your dog → so \"v\" = your? \"v\" = possessive marker?\n\nIn sentence 1: \"Qingmivit\" = your dog \nIn sentence 7: \"Nanuq qaijuq\" → \"The polar bear came\" → \"Nanuq\" = polar bear → \"qaijuq\" = came\n\nSo \"your wolf\" → \"amaruq\" + \"v\"? → \"amaruqv\"? But sentence 1 has \"Qingmivit\" — so \"v\" + noun\n\nPossibility: possessive suffix \"v\" → \"your\"\n\nSo \"your wolf\" = \"amaruqv\"\n\n\"fell\" → not directly given. Sentence 11: \"Ukiakhaqtutit\" → \"You fell\" \n→ \"Ukiakhaqtutit\" = you fell → verb root: \"ukiakhaqt\" → fell, with \"-utit\" = you\n\nSo \"fell you\" = ukiakhaqtutit → subject \"you\"\n\nSo \"your wolf fell\" → (your wolf) + (fell) → so \"amaruqv ukiakhaqtutit\"\n\nSo 21: \"amaruqv ukiakhaqtutit\"\n\nSentence 22: \"You shot a dog.\"\n\n\"shot\" → in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb = \"qukiqtanga\" → \"qukiqt\" + \"anga\" → likely \"qukiq\" = shoot\n\nSo \"shot\" = qukiq?\n\nIn sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" → speared → \"iputuj\" = speared\n\nSo \"qukiq\" = shoot, \"iputuj\" = speared\n\nSo \"you shot a dog\" → \"you\" + \"shot\" + \"a dog\"\n\n\"you\" → from sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = first person\n\nSo \"you\" = ? → is there a marker?\n\nSentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → \"you\" = \"takujait\" → but the subject is \"you\"\n\nPossibility: \"you\" is marked by \"-it\" on the end of verb? But in sentence 11: \"Ukiakhaqtutit\" → \"you fell\", so verb ends in \"utit\"\n\nSo \"you\" = verb + \"it\" = subject?\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → so \"you\" is object → subject is dog → so object is marked.\n\nBut \"you shot\" → \"you\" is subject → so need \"you\" in subject position.\n\nIn Inuktitut, the subject may be marked with a possessive or a stand-alone marker.\n\nBut look at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? \n→ \"Qingmiq\" → possibly \"Qingmi\" + \"q\" — what is \"q\"?\n\nGiven: q = k-like sound — but \"Qingmi\" = dog? \nIn sentence 1: \"Qingmivit\" = your dog → so \"Qingmi\" = dog\n\nSo \"Qingmiq\" → dog + q? Or \"you\" + dog?\n\nMaybe form \"you\" is \"Qingmiq\"?\n\nUnlikely.\n\nIn sentence 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher\" → \"Qingmiup\" = the dog → so \"up\" = definite\n\nSo \"Qingmi\" = dog\n\nNow, \"you\" → in sentence 11: \"Ukiakhaqtutit\" → \"you fell\" → verb form \"utit\"\n\nSo \"you\" may be marked by the verb suffix.\n\nSo \"you shot\" → verb = \"qukiq\" → so \"qukiq\" + \"?\"\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → so \"qukiqtanga\" = shot doctor → verb with object\n\nSo \"qukiqt\" = shoot\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"a dog\"\n\nWhat is \"you\"? In this language, first person subject may be implicit or marked by context.\n\nBut sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" likely = you? Or dog?\n\nBut \"Qingmi\" is dog → so \"Qingmiq\" = a variant?\n\nPossibility: \"you\" = \"uk\" or \"a\" or no marker?\n\nLook at structure: in sentence 1: \"Qingmivit takujaatit\" — \"your dog saw you\" → \"you\" is object → presumably marked by \"-it\"\n\nIn sentence 11: \"Ukiakhaqtutit\" — \"you fell\" → verb ends in \"-utit\" → 1st person\n\nSo how is \"you\" expressed in a clause?\n\nPossibly without a subject marker, or with a prefix.\n\nBut in \"you shot a dog\", if no clear marker, perhaps \"you\" is not attached.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → \"Qingmiq\" = you? Or dog?\n\n\"iputujait\" = speared → so verb = \"iputujait\" → object: the dog → which is \"qingmi\"?\n\nSo \"Qingmiq\" = the dog? But that would be \"dog\" with \"q\" → \"q\" → k-like\n\nBut in sentences, \"q\" appears in different contexts.\n\nPossibility: the subject \"you\" is not marked — it may be default.\n\nLooking at sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"the shaman cured a doctor\" → subject is \"the shaman\" → marked\n\nSimilarly, sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear\" → \"qukiqsijuq\" = shot?\n\n\"qukiqsijuq\" — may be \"qukiq\" → shot\n\nSo \"you shot a dog\" → similar to \"the hunter shot a polar bear\" → but subject is \"you\"\n\nIn sentence 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" → is \"Angunahukti\" = the hunter → so subject is marked\n\nSo \"you\" may be marked as a full clause with subject.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → no explicit \"you\" in subject?\n\nWait — \"Qingmiq\" = you? Possibly.\n\nBut in sentence 1: \"Qingmivit\" = your dog — so \"v\" = possessive\n\nIn sentence 5: \"Qingmiq\" — \"q\" instead of \"v\"?\n\n\"q\" and \"v\" are different.\n\nPossibility: \"q\" = non-possessive (like 3rd person?) or \"you\" marker?\n\nAlternatively, \"you\" = \"uk\" or not explicit.\n\nBut in 22: \"You shot a dog\" → likely a standalone clause with \"you\" as subject.\n\nWe need to find a form of \"you\" as subject.\n\nSentence 11: \"Ukiakhaqtutit\" → you fell → \"utit\" = 1st person\n\nSo perhaps 1st person subject is marked by the verb suffix.\n\nSo \"you shot\" → verb \"qukiq\" with 1st person subject? But verb form is not given.\n\nIn sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" → verb form is \"qukiqtanga\" — likely \"qukiq\" + \"tanga\" = shot + object\n\nSimilarly, in sentence 9: \"Angunahuktiup amaruq iputujanga\" → \"the hunter speared the wolf\" → \"iputujanga\" = speared\n\nSo \"qukiqtanga\" = shot + object\n\nSo \"you shot a dog\" → likely \"u\" + \"qukiq\" + \"a dog\" → but \"you\"?\n\nPerhaps the subject \"you\" is expressed by a simple form — or the verb itself links.\n\nBut in sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → if \"Qingmiq\" = you, then \"you\" is fronted?\n\nMore likely: \"Qingmiq\" = you → because \"Qingmi\" is dog, \"q\" = you?\n\nBut this is speculative.\n\nAlternatively, the structure might be:\n\n- Object = \"a dog\" → \"qingmi\" → dog, so \"qingmi\" = dog\n\nSo \"you shot a dog\" → \"you\" + \"qukiqt\" + \"qingmi\"\n\nBut \"you\" → in absence, perhaps it's implied.\n\nIn Inuktitut, first person is often not marked explicitly, or marked via verb.\n\nBut sentence 11: \"Ukiakhaqtutit\" → \"you fell\" — verb \"ukiakhaqtutit\" → 1st person.\n\nSo in \"you shot a dog\", \"you\" = 1st person subject → so must be \"you\" + verb.\n\nLooking at sentence 5: \"Qingmiq iputujait\" → \"You speared the dog\" → the verb is \"iputujait\" — which is likely 1st person (you) + speared.\n\nSo the verb form with \"you\" is marked by the suffix.\n\nSimilarly, \"qukiqt\" for \"shot\" → how is \"you\" marked?\n\nIn sentence 2: \"inuuhuktuup\" = the boy → 3rd person → marked with \"up\"\n\nSo if \"you\" is 1st person, possibly no marker.\n\nBut in sentence 11: \"Ukiakhaqtutit\" → you fell → verb ends with \"utit\" → so \"utit\" = 1st person\n\nSo for \"you shot\", we may need \"qukiqtut\" or something with \"ut\"?\n\nBut sentence 2: \"qukiqtanga\" → 3rd person → \"anga\"\n\nSo 1st person: maybe \"qukiqtut\"? → like \"ut\" = you\n\nBut sentence 11: \"Ukiakhaqtutit\" → well," + }, + { + "split": "train", + "record_id": "iol-2019-individual-p5-sub-c", + "planner_index": 6, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 20.: answer for this requested item\n- c.2 / 21.: answer for this requested item\n- c.3 / 22.: answer for this requested item\n- c.4 / 23.: answer for this requested item\n- c.5 / 24.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: ; c.3: ; c.4: ; c.5: }\n\nProblem 5 (20 points). Here are some sentences in Nooni that were spoken on different\ndays of the Nooni “week” and their English translations:\n\n spoken on Bvutfu\n 1. fɔgò cǐ nú bvúmbòn. Yesterday was Bvumbon.\n me ncí nɔ̂ː ntɔ᷅ fɔ̀wǎy bvúmbòn. On Bvumbon, I came to the market.\n 2. wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w. On Bvusɔw, you(sg) will steal the yam.\n 3. kwɔ᷆ːn nǔ bóy fí me bvúzhí. On Bvuzhi, the woman will help me.\n\n spoken on Bvusɔw\n 4. wvù tɔ̀ nɔ̂ː bɔ᷅ŋ ŋwà bvûŋka᷆ː. On Bvuŋka, he found the book.\n 5. fɔ̀ shě ntfǔː nú bvútfu᷅. The day after tomorrow is Bvutfu.\n me nú mbóy ncáw mutù bvútfu᷅. On Bvutfu, I will choose the car.\n 6. wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n. Today, he killed the woman.\n 7. wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ. You(sg) heard the thief a long time ago.\n\n spoken on Bvukema\n 8. ntfǔː nú bvûŋka᷆ːde᷆n. Tomorrow is Bvuŋkaden.\n cɔ̌ŋ nú bóy bɔ́ŋ bèsèn bvûŋka᷆ːde᷆n. On Bvuŋkaden, the thief will find us.\n 9. me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n. Today, I chose the book.\n 10. dìɛ̀msɛ̌n nú yɛ́n wvù lě. The man is about to see him.\n 11. kefwé cí nú bvûŋka᷆ː. The day before yesterday was Bvuŋka.\n\n spoken on Bvuŋka\n 12. me nú nfí dìɛ̀msɛ̌n. I am about to help the man.\n 13. kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅. On Bvutfu, the woman saw the market.\n 14. bèsèn nǔ géː cɔ́ŋ mutù ɛ̀bɛ̀n. Today, we will steal the car.\n 15. bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy. They saw me at the market just now.\n\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\n!△ Nooni belongs to the Beboid group of the Atlantic-Congo family. It is spoken by approx.\n40,000 people in Cameroon.\n ɛ and ɔ are vowels. ŋ, sh, y and zh are consonants. The mark ː indicates that the vowel\nis long. The superscript marks denote tones: –́ high, –̂ falling (high ↘low), –᷆falling (middle\n↘low), –̀ low, –᷅rising (low ↗middle), –̌ rising (low ↗high); if none are present, the syllable\nhas middle tone.\n Yam is the edible tuber of the tropical plant of the same name. —Samuel Ahmed\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Translate into Nooni:\n\n spoken on Bvumbon\n\n 20. On Bvusɔw, I helped the man.\n\n 21. The thief stole the yam just now.\n\n 22. On Bvuŋkaden, I will hear the car.\n\n 23. Today, the woman will kill the man.\n\n 24. Today, the man saw you(sg).\n\nSAMPLED ATTEMPT:\nWe are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "approaches": [ + "\nFocus on the temporal reference system: identify how days are referred to in relation to the current day (Bvumbon), and verify if \"today\" is consistently marked by \"wɔ̀\" across contexts.\n\nVerification: In sentence 7 (\"You(sg) heard the thief a long time ago\"), \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — the \"wɔ̀\" is used with a past action, and \"a long time ago\" is contrasted with \"just now\". This suggests \"wɔ̀\" marks the present day, not a past or future one. In sentence 1 (\"Yesterday was Bvumbon\"), \"fɔgò\" is used for \"yesterday\", and \"wɔ̀\" appears only in present-tense or current-day references. In sentence 9 (\"Today, I chose the book\"), \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\" is used, but the sentence begins with \"me\", suggesting subject, not temporal marker. However, sentence 10: \"The man is about to see him\" lacks temporal marker. Thus, \"wɔ̀\" appears only in verb-initial constructions with present-tense events. In sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"bɔ́\" marks \"just now\", not \"today\". So \"wɔ̀\" is not the only present marker.\n\nTherefore, \"today\" may be implied by context, not a fixed morpheme. In sentence 23: \"Today, the woman will kill the man\" — must use a temporal marker. The only consistent present-day reference is in sentence 7 with \"wɔ̀\" as part of a clause. But since the sentence is about \"you(sg) heard\", and not an event, it's ambiguous.\n\nCounter-check: In sentence 8, \"Tomorrow is Bvuŋkaden\" uses \"ntfǔː nú\" → \"the day after tomorrow is Bvutfu\" (sentence 5) uses \"fɔ̀ shě ntfǔː nú bvútfu᷅\" — here, \"fɔ̀ shě\" = \"the day after tomorrow\", so \"shě\" = \"after tomorrow\", \"fɔ̀\" = \"after\". So temporal markers are built with prefixes.\n\nThus, \"today\" may not be marked by \"wɔ̀\" in all contexts. Instead, the day is named, and \"on\" is used. But in translation 23 and 24, \"today\" is required. Since no sentence explicitly uses \"today\" as a standalone word, it may be inferred from the context of the day being spoken on — Bvumbon.\n\nSo, if the speaker is on Bvumbon, and the event is today, then \"today\" is not marked by a specific morpheme but by the absence of temporal reference. However, in all earlier sentences, when a day is not named, it is implied to be current. For example, sentence 13: \"On Bvutfu, the woman saw the market\" — no \"today\", just \"on Bvutfu\".\n\nThus, in translation 23 and 24, \"today\" may be implied by the sentence structure, and \"wɔ̀\" is not required. But in sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" — \"wvù\" = \"he\", not \"today\". So the temporal marker is not \"wɔ̀\" here.\n\nTherefore, \"wɔ̀\" only appears in the first person in the past or present, not as a temporal marker.\n\nConclusion: \"wɔ̀\" is not a temporal marker; it is a subject marker. The only temporal marker is \"on X\" for specific days. So \"today\" should be expressed by omitting temporal reference or by using a day name that is current. But in the problem, the sentences are spoken on Bvumbon, and reference other days.\n\nSo in translation 23 and 24, \"today\" is not marked by a morpheme but by context. However, in sentence 5: \"The day after tomorrow is Bvutfu\" — uses \"fɔ̀ shě\" as a temporal prefix. So \"the day after tomorrow\" = \"fɔ̀ shě\", \"the day before yesterday\" = \"kefwé cí\".\n\nThus, \"today\" is not marked by a morpheme. Therefore, in 23 and 24, \"today\" is not needed — it is implied by being on Bvumbon. But the sentence says \"today\", so must be expressed.\n\nRe-examination: In sentence 9: \"Today, I chose the book\" — \"me mbɛ̂ː nca᷅w ŋwà ɛ̀bɛ̀n\" — no \"wɔ̀\", yet it is \"today\". So \"wɔ̀\" is not used for \"today\".\n\nThus, the temporal marker for \"today\" is missing in the data. Therefore, the only way to express \"today\" is by using the day name or by context. Since the day is Bvumbon, and the sentence is spoken on Bvumbon, \"today\" is already implied. But the sentence explicitly states \"today\", so must be marked.\n\nThis suggests that \"wɔ̀\" is not the temporal marker. The temporal marker is only \"on X\" or with prefixes like \"fɔ̀ shě\", \"ntfǔː\".\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme, and the sentence can be built without \"wɔ̀\".\n\nBut in 23: \"Today, the woman will kill the man\" — the only available temporal reference is \"on\" for a day. But the event is not on a named day. So \"today\" must be used.\n\nBut no example uses \"today\" with a verb. Therefore, the only consistent temporal marker is \"on X\", and \"today\" is not a morpheme.\n\nThus, the sampled attempt incorrectly assumes \"wɔ̀\" = \"today\".\n\nCorrection: \"today\" is not marked by a morpheme. It is either implied or expressed by context. In the absence of a marker, the sentence may not require one.\n\nBut sentence 9: \"Today, I chose the book\" is given — it is expressed without a temporal marker. So \"today\" is not a morpheme.\n\nTherefore, in translation 23 and 24, \"today\" may be omitted or implied. But the sentence says \"today\", so must be expressed.\n\nThis is a contradiction.\n\nFinal decision: despite lack of evidence, the only consistent use of \"today\" in data is in sentence 9, where it is not marked. So \"today\" is not a morpheme. Thus, in translation, it should not be marked.\n\nBut the problem says \"today\", so must be included in the sentence.\n\nThus, the sampled attempt is flawed in assuming \"wɔ̀\" = \"today\".\n\nThe correct approach is to use the day name or omit temporal marker. Since the day is Bvumbon, and the event is current, \"today\" is implicit.\n\nTherefore, in 23 and 24, \"today\" is not marked by a morpheme.\n\nSo 23: \"the woman will kill the man\" → \"nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n\" \n24: \"the man saw you(sg)\" → \"dìɛ̀msɛ̌n yɛ᷅n wɔ̀\"\n\nBut \"wɔ̀\" is used in 24 as object — which is inconsistent.\n\nIn sentence 7: \"you(sg) heard the thief\" — \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" — \"wɔ̀\" is subject, not object.\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only as subject.\n\nThus, object \"you(sg)\" is not marked with \"wɔ̀\".\n\nIn sentence 15: \"They saw me at the market just now\" — \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" — \"me\" is object, not \"wɔ̀\".\n\nSo \"you(sg)\" as object should be \"wɔ̀\" only when subject.\n\nTherefore, in 24, \"you(sg)\" as object should not be \"wɔ̀\".\n\nThus, the correct form is: \"dìɛ̀msɛ̌n yɛ᷅n nǔ\" — but \"nǔ\" is \"the woman\", not \"you(sg)\".\n\n\"you(sg)\" is not \"nǔ\" — in sentence 2: \"you(sg) will steal\" → \"wɔ̀ nǔ yúː cɔ́ŋ\" → \"wɔ̀\" is subject, \"nǔ\" is object? No — \"wɔ̀ nǔ\" = \"you(sg)\" — so \"wɔ̀\" is subject, \"nǔ\" is object?\n\nNo — in \"wɔ̀ nǔ yúː cɔ́ŋ\", \"wɔ̀\" = \"you(s", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples.", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "We are given a series of Nooni sentences across different days of the \"week\" (Bvutfu, Bvusɔw, Bvuzhi, Bvuŋka, Bvukema), and we are to translate five new sentences into Nooni, all spoken on **Bvumbon**.\n\nWe need to infer the grammatical patterns for:\n\n- Time references (e.g., \"yesterday\", \"today\", \"tomorrow\", \"the day before yesterday\", \"the day after tomorrow\")\n- Verb aspect (e.g., \"just now\", \"will\", \"heard\", \"helped\", \"killed\", \"saw\")\n- Subject-verb-object structure, with correct tense and aspect markers\n- Use of particles for temporal references (like \"on\", \"the day after tomorrow\", \"today\", etc.)\n\n---\n\n### Step 1: Analyze time expressions across days.\n\nWe see that:\n\n- **Bvumbon** is referenced in sentence 1: \"Yesterday was Bvumbon.\"\n- On **Bvusɔw**: sentence 5 says \"the day after tomorrow is Bvutfu\"\n- On **Bvukema**: \"Tomorrow is Bvuŋkaden\"\n- On **Bvukema**: \"The day before yesterday was Bvuŋka\"\n\nSo we can map time markers:\n\n| English | Nooni (Reference) |\n|--------|-------------------|\n| Today | wɔ̀ nǔ → \"you(sg) heard\" in 7 → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w...\" → \"You heard...\" → so \"today\" is expressed with \"wɔ̀\" (from sentence 7) |\n| Yesterday | fɔgò cǐ nú bvúmbòn → \"Yesterday was Bvumbon\" |\n| Tomorrow | ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is Bvuŋkaden\" |\n| The day before yesterday | kefwé cí nú bvûŋka → \"The day before yesterday was Bvuŋka\" |\n| The day after tomorrow | fɔ̀ shě ntfǔː nú bvútfu᷅ → \"The day after tomorrow is Bvutfu\" |\n\nNote: All time references are **fixed** to a specific day in the cycle. So:\n- \"On X\" = On day X\n- \"Tomorrow\" = next day after current day\n- \"Yesterday\" = previous day\n- \"The day before yesterday\" = two days before\n- \"The day after tomorrow\" = two days after\n\nWe must assign correct time markers to each of our translations.\n\n---\n\n### Step 2: Identify verb aspect markers\n\nLook at:\n- Sentence 3: \"On Bvuzhi, the woman will help me\" → \"kwɔ᷆ːn nǔ bóy fí me bvúzhí\" → \"kwɔ᷆ːn\" = \"on\", \"nǔ bóy\" = \"the woman\", \"fí\" = \"will help\"\n→ So \"will\" is expressed with **fí** (\"help\" but in future)\n\n- Sentence 13: \"On Bvutfu, the woman saw the market\" → \"kwɔ᷆ːn cǐ nɔ̂ː yɛ᷅n wáy é bvútfu᷅\" → \"cǐ\" = \"saw\"\n\n- Sentence 6: \"Today, he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\" → \"bɛ̂ː\" = killed\n\n- Sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"nɔ̂ː\" = \"heard\" (with long vowel), \"cɔ̌ŋ\" = \"the thief\"\n\nSo:\n- \"heard\" = nɔ̂ː (long vowel, middle/falling tone)\n- \"killed\" = bɛ̂ː (future or present with high tone)\n- \"saw\" = yɛ᷅n (with falling tone)\n- \"helped\" = fí (in future, specifically \"will help\")\n\nNow, note:\n- \"just now\" appears in:\n - Sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"bɔ́\" = \"just now\", \"nɔ̂ː\" = \"heard\", \"yɛ᷅n me lé\" = \"saw me\"\n - So \"just now\" = **bɔ́**\n\nSo we can infer that:\n- \"just now\" is marked by **bɔ́** (a rising tone syllable, found in verb prefix)\n\nThis matches on sentence 15: \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"Just now, they saw me at the market\"\n\nSo:\n- **just now = bɔ́** (preceding the verb)\n\nAlso:\n- \"the thief stole the yam\" → in sentence 2: \"On Bvusɔw, you(sg) will steal the yam\" → \"wɔ̀ nǔ yúː cɔ́ŋ kèŋkfǔ bvúsɔ̀w\"\n→ \"yúː\" = \"steal\" (steal with high tone), \"kèŋkfǔ\" = \"the yam\" → so \"the thief stole = cɔ́ŋ kèŋkfǔ\"\n\nSo:\n- \"steal\" = cɔ́ŋ\n- \"the yam\" = kèŋkfǔ\n\nThus:\n- \"The thief stole the yam just now\" → use \"bɔ́\" + \"cɔ́ŋ\" + \"kèŋkfǔ\"\n\n---\n\n### Step 3: Build each sentence\n\n**20. On Bvusɔw, I helped the man.**\n\n- On → kwɔ᷆ːn (used in 3, 13)\n- I = me (subject)\n- helped = fí (in future)\n- the man = dìɛ̀msɛ̌n (from sentence 10: \"The man is about to see him\" → \"dìɛ̀msɛ̌n\")\n\nSo: **kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw**\n\nNote: The day Bvusɔw is specified in the sentence — just like 3, 13, etc.\n\nSo: ✔️\n\n**21. The thief stole the yam just now.**\n\n- The thief = yo᷅kwɔ᷆ːn (used in 6: \"he killed the woman\" → \"wvù bɛ̂ː yo᷅kwɔ᷆ːn ɛ̀bɛ̀n\")\n- stole = cɔ́ŋ (from sentence 2)\n- the yam = kèŋkfǔ\n- just now = bɔ́\n\nSo: **bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ**\n\nNote: No \"on\" required — just the event in past with \"just now\"\n\n✔️\n\n**22. On Bvuŋkaden, I will hear the car.**\n\n- On Bvuŋkaden = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n (sentence 8: \"Tomorrow is Bvuŋkaden\" → ntfǔː nú bvûŋka᷆ːde᷆n → \"Tomorrow is\", so \"on Bvuŋkaden\" = kwɔ᷆ːn nú bvûŋka᷆ːde᷆n)\n- I = me\n- will hear = fí (will) + nɔ̂ː (hear)\n- the car = mutù (sentence 5: \"On Bvutfu, I will choose the car\" → \"me nú mbóy ncáw mutù bvútfu᷅\" → \"mutù\" = car)\n\nSo: **kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù**\n\n✔️\n\n**23. Today, the woman will kill the man.**\n\n- Today = wɔ̀ (in sentence 7: \"You(sg) heard the thief a long time ago\" → \"wɔ̀ tɔ̀ nɔ̂ː yo᷅w cɔ̌ŋ\" → \"wɔ̀\" = today)\n- the woman = nǔ bóy (sentence 3: \"the woman will help me\")\n- will kill = fí + bɛ̂ː (sentence 6: \"he killed the woman\" → \"bɛ̂ː\" = killed)\n- the man = dìɛ̀msɛ̌n\n\nSo: **wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n**\n\n✔️\n\n**24. Today, the man saw you(sg).**\n\n- Today = wɔ̀\n- the man = dìɛ̀msɛ̌n\n- saw = yɛ᷅n (sentence 15: \"They saw me at the market just now\" → \"bɔ́ nɔ̂ː yɛ᷅n me lé fɔ̀wǎy\" → \"yɛ᷅n\" = saw)\n- you(sg) = wɔ̀ (same as in \"you heard\")\n\nSo: **wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀**\n\nNote: \"you(sg)\" is the object — same pronoun. Consistent with sentence 7.\n\n✔️\n\n---\n\nFinal translations:\n\n20. On Bvusɔw, I helped the man. → kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw \n21. The thief stole the yam just now. → bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ \n22. On Bvuŋkaden, I will hear the car. → kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù \n23. Today, the woman will kill the man. → wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n \n24. Today, the man saw you(sg). → wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀ \n\nAll patterns match earlier examples.\n\n\\boxed{c.1: kwɔ᷆ːn me fí dìɛ̀msɛ̌n bvúsɔw; c.2: bɔ́ yo᷅kwɔ᷆ːn cɔ́ŋ kèŋkfǔ; c.3: kwɔ᷆ːn nú bvûŋka᷆ːde᷆n me fí nɔ̂ː mutù; c.4: wɔ̀ nǔ bóy fí bɛ̂ː dìɛ̀msɛ̌n; c.5: wɔ̀ dìɛ̀msɛ̌n yɛ᷅n wɔ̀}" + }, + { + "split": "train", + "record_id": "iol-2016-individual-p5-sub-b", + "planner_index": 7, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 4.: answer for this requested item\n- b.2 / 5.: answer for this requested item\n- b.3 / 6.: answer for this requested item\n- b.4 / 7.: answer for this requested item\n- b.5 / 8.: answer for this requested item\n- b.6 / 9.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: ; b.6: }\n\nProblem 5 (20 points). Here are some words in Jaqaru and their English translations:\n\n aq”ipsa the cave too qucxap”a through the lake\n aq”na in the cave qucxst”psa from our1+2 lake too\n chushp”a his corner marka the town\n chushuntxi is it in the corner? markp”t”a from his town\n ishinhna in my bed markstxi is it our1+2 town?\n ishma your bed utamt”a from your house\n p”ak”u the pot utnha my house\n p”ak”unhpsa my pot too yaputxi is it the field?\n qaqat”a from the cliff yapsanpsa in our1+2 field too\n\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\n!△ Jaqaru belongs to the Aymaran family. It is spoken by approx. 730 people in Peru.\n nh = ng in hang. ch, cx, q, sh, tx are consonants. The mark ” indicates aspiration.\n our1+2 = ‘mine and yours’. —Ivan Derzhanski\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Jaqaru:\n\n 4. our1+2 cliff\n 5. in your corner\n\n 6. in your corner too\n\n 7. from your corner too\n\n 8. is it from the cave?\n\n 9. is it the house?\n\nSAMPLED ATTEMPT:\nWe are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not", + "approaches": [ + "Focus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast”", + "Analyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a", + "Address the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes.", + "\nFocus on the pattern of possessive markers and locative prefixes. Identify that \"our1+2\" is consistently marked by the suffix -st in compounds with nouns: \n- qucxst”psa = from our1+2 lake → \"st\" attached to \"qucx\" (lake) \n- markstxi = is it our1+2 town? → \"st\" attached to \"mark\" (town) \n- yapsanpsa = in our1+2 field too → \"an\" appears, but \"sanpsa\" suggests \"st\" is not directly visible; however, \"an\" may derive from \"a\" + \"n\" for field, and \"st\" is implied in \"too\" context. \n\nBut crucially, \"our1+2\" is not a separate word; it is a possessive suffix attached to the noun root. \nFor \"our1+2 cliff\": cliff root is \"qaqat”a\" (from the cliff). \nThus, \"our1+2 cliff\" = qaqat”ast” → but the example of \"qucxst”psa\" shows \"st\" after the root. \nNo example of \"our1+2 cliff\" directly, but \"our1+2 field\" is in yapsanpsa, which is \"in our1+2 field too\" → so \"an\" may be part of \"field\", not a separate suffix. \n\nHowever, \"in our1+2 field\" likely has \"st\" as suffix on field root. \nField root = \"yap\" → \"yapsanpsa\" → \"yap\" + \"sanpsa\"? \n\"sanpsa\" = \"st\" + \"anpsa\"? Not clear. \n\nBut the pattern for \"our1+2\" is consistently marked by -st when in a possessive or locative phrase. \nTherefore, \"our1+2 cliff\" = qaqat”ast” → but no such form exists in the data. \n\nVerification: \"from our1+2 lake\" is qucxst”psa → \"st\" immediately follows \"qucx\" (lake root). \n\"our1+2 town\" = markstxi → \"st\" after \"mark\". \nSo \"our1+2 cliff\" should be qaqat”ast” → but the base form is qaqat”a, so adding -st → qaqat”ast”. \nNo contradiction. \nThus, 4. our1+2 cliff = qaqat”ast” \n\n\n\nAnalyze the locative prefix system. \n- \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"ish\" is locative prefix for \"in\" \n- \"your bed\" = ishma → \"ish\" + \"ma\" → same prefix \n- \"in your corner\" → should be \"ish\" + \"your corner\" \n\nNow, what is \"your corner\"? \nWe have \"his corner\" = chushp”a → \"chush\" + \"p”a\" → so \"p”a\" = corner \n\"your\" → no direct form, but \"ishma\" = your bed → suggests \"ish\" is used with \"your\" in bed \nBut \"your corner\" → must use \"ish\" + \"corner\" → what is corner form? \n\"p”a\" = corner → so \"your corner\" = \"ish\" + \"your\" + \"p”a\" → but what is \"your\" marker? \n\nPossibility: the possessive suffix for \"your\" is not a separate marker; instead, the locative \"in\" is shared. \nSo \"in your corner\" = ish + p”a + ? → no \"your\" marker. \n\nBut \"chushp”a\" = his corner → \"chush\" = his \n\"ishma\" = your bed → \"ish\" = locative, \"ma\" = bed \nNo separate \"your\" possessive. \n\nTherefore, \"your corner\" may be formed as \"ishp”a\" with a possessive prefix? Not supported. \n\nAlternative: \"your\" = \"ish\" in some contexts — but \"ish\" is used for \"my\" in \"ishinhna\" and for \"your\" in \"ishma\" — so \"ish\" is the locative prefix, and the noun varies. \n\nThus, \"in your corner\" = ish + p”a → ishp”a? \nBut no such form. \n\"ishp”a\" not in data. \n\"chushp”a\" exists → \"chush\" + p”a\" \n\"ish\" + p”a\" → would be \"in your corner\" — plausible. \n\nVerification: \"in my bed\" = ishinhna → \"ish\" + \"inhna\" → \"inhna\" = my bed \n\"your bed\" = ishma → \"ish\" + \"ma\" → \"ma\" = your bed \nSo \"corner\" root = p”a → thus \"in your corner\" = ish + p”a = ishp”a \nYes — consistent with pattern. \nSo 5. in your corner = ishp”a \n\n\n\nAddress the \"too\" suffix pattern. \nExamples with \"too\": \n- aq”ipsa = the cave too → \"ipsa\" = too \n- p”ak”unhpsa = my pot too → \"unhpsa\" = too \n- qucxst”psa = from our1+2 lake too → \"st”psa\" → may be \"st\" + \"psa\" = too \n- yapsanpsa = in our1+2 field too → \"anpsa\" = too \n\nSo \"too\" is marked by suffixes: -ipsa, -nhpsa, -stpsa, -anpsa \nAll involve a suffix ending in -psa or -hpsa \n\nPattern: the suffix -psa is used with \"too\" in various contexts. \n- \"my pot too\" = p”ak”unhpsa → -nhpsa \n- \"in our1+2 field too\" = yapsanpsa → -anpsa \n- \"the cave too\" = aq”ipsa → -ipsa \n\nSo \"too\" is not a single suffix; it is context-sensitive. \nBut for \"in your corner too\" → should be \"ishp”a\" + \"too\" → likely -anpsa or -nhpsa? \n\nBut \"in your corner\" = ishp”a → adding \"too\" → ishp”a + \"anpsa\" or \"nhpsa\"? \n\nCompare to \"in our1+2 field too\" = yapsanpsa → \"in\" + \"our1+2\" + field + \"too\" → the \"too\" is attached to the end of the field phrase. \n\nSimilarly, \"my pot too\" = p”ak”unhpsa → \"my pot\" + \"too\" → \"unhpsa\" \n\nSo likely, \"in your corner too\" = ishp”a + \"anpsa\" → ishp”a anpsa? \n\nBut ishp”a is not in data. \n\nAlternatively, \"in your corner too\" = ishp”a + \"nhpsa\"? Unlikely — no pattern. \n\nBut \"our1+2 field too\" = yapsanpsa → uses -anpsa \n\"our1+2 lake too\" = qucxst”psa\" → uses -stpsa → \"st”psa\" → so \"st\" + \"psa\" \n\nSo the \"too\" suffix appears as a separate morpheme, and its form depends on the noun. \n\nNo consistent suffix for \"in your corner too\". \n\nBut \"in my bed\" is not in list — \"in my bed\" is not given; \"in my bed\" is \"ishinhna\" — which may be \"in my bed\" → no \"too\". \n\nThus, \"in your corner too\" = likely ishp”a anpsa? \nBut \"anpsa\" is used in \"in our1+2 field too\" → so may be standard for locative + too. \n\nSo 6. in your corner too = ishp”a anpsa \nVerification: \"in our1+2 field too\" = yapsanpsa → uses -anpsa → so for locative phrase with \"too\", -anpsa is used. \nThus, \"in your corner too\" = ish + p”a + anpsa = ishp”a anpsa \nYes. \n\n\n\nFor \"from your corner too\" → \"from\" is a direction. \nWe have: \n- qaqat”a = from the cliff \n- markp”t”a = from his town \n- from his town = markp”t”a → \"p”t”a\" = his town → so \"from\" + \"his\" + \"town\" \n\nSo \"from your corner\" → \"from\" + \"your\" + \"corner\" \n\n\"corner\" = p”a (from chushp”a) \n\"your\" — what marker? \n\n\"his\" = chush- \n\"our1+2\" = st- \n\"my\" = ish- (in locative) \n\"your\" — not" + ], + "anchor_output": "We are given a set of Jaqaru words and their translations, and we are to translate specific phrases into Jaqaru.\n\nFirst, observe the known word forms and their patterns.\n\nFrom the given examples:\n\n- aq”ipsa = the cave too \n- aq”na = in the cave \n- qucxap”a = through the lake \n- qucxst”psa = from our1+2 lake too \n- chushp”a = his corner \n- marka = the town \n- chushuntxi = is it in the corner? \n- markp”t”a = from his town \n- markstxi = is it our1+2 town? \n- ishinhna = in my bed \n- ishma = your bed \n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too \n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too \n- qaqat”a = from the cliff \n- qaqat”a = from the cliff → so “from the cliff” is qaqat”a \n- qaqat”a is base form for “from the cliff”\n\nNow analyze the structure and build patterns.\n\nPattern 1: “our1+2” appears in compound expressions:\n- qucxst”psa = from our1+2 lake too → so from + our1+2 lake → derived from qcxap”a + our1+2 → modified by “too”\n- yapsanpsa = in our1+2 field too → in + our1+2 field → so “our1+2” is attached to a noun with a locative or possessive sense.\n\nPattern 2: Possessive markers:\n- “his corner” = chushp”a \n- “from his town” = markp”t”a \n- “is it our1+2 town?” = markstxi → “our1+2” + town → “markstxi” \n- “in my bed” = ishinhna → “in” + “my” → forms of locative \n- “your bed” = ishma → “your” \n- “my pot” = p”ak”u → “the pot” \n- “my pot too” = p”ak”unhpsa → “my pot” + too → “unhpsa” = too \n- “in your corner” → would be similar to “in my bed” → “ish”+“your corner”?\n\nBut “ish” is used in “ishinhna” = in my bed → “ish” + “inhna” → “inhna” = my bed \nSimilarly, “ishma” = your bed → so “ish” is a locative prefix.\n\nSo:\n- ish + [something] = in + [something]\n- mark + [something] = the town / from + something\n- chush + [something] = his corner\n- qaqat”a = from the cliff\n- qaqat”a = base for “from the cliff”\n\nThus:\n\n4. our1+2 cliff \n→ “our1+2” + cliff → cliff is “qaqat”a → so with “our1+2” → need a form like qucxst”psa (from our1+2 + lake) \nBut “from” is a direction, “in” is locative.\n\nCliff is “qaqat”a → so “from” + cliff = qaqat”a \nThen “our1+2 cliff” → likely just “our1+2” + “cliff” → like “our1+2 lake” in “qucxst”psa” → which is from our1+2 lake\n\nBut “our1+2 lake” is not directly translated; “qucxst”psa” = from our1+2 lake too → so “our1+2 lake” is part of it.\n\nLook: qucxst”psa = from our1+2 lake too \n→ so “our1+2 lake” = thing being modified → no standalone.\n\nBut in yapsanpsa = in our1+2 field too → “in” + our1+2 field → so “in” + [our1+2] + field\n\nSimilarly, “in your corner” → “ish” + “your corner”\n\nWe need to find the form for “your corner”.\n\nWe have:\n- chushp”a = his corner \n→ “chush” = his → so “chush” + “p”a = his corner → “p”a may be a root for “corner”\n\nTherefore, “your corner” → likely “ishma” + “corner”? But “ishma” = your bed → not corner.\n\nAlternatively, is there a form for “your”?\n\nWe have:\n- ishinhna = in my bed → “ish” + “inhna” \n- ishma = your bed → “ism” + “ha”? Wait — “ism” is not in list.\n\nBut “chushp”a” = his corner → “chush” = his → so possessive root is “chush” for “his”\n\nSimilarly, “marka” = the town → “mark” for town → “markp”t”a” = from his town → “mark” + his → “p”t”a = his town?\n\nBut “markstxi” = is it our1+2 town → “mark” + our1+2 → “stxi”\n\nSo:\n\n- Possessive markers:\n - his = chush-\n - our1+2 = st-\n - my = ish- → in my bed = ishinhna\n - your = ? — in your bed = ishma → so “ish” is used for “my”, “your” seems to be “ism” or “isha”?\n\nBut in “ishma” = your bed → ish + ma → \"ish\" appears in \"in my bed\" and \"your bed\"\n\nWait: “ishinhna” = in my bed → “ish” + “inhna” \n“ishma” = your bed → “ish” + “ma” → “ma” vs “inhna”?\n\nSo “ish” seems to be the locative prefix, and the noun varies.\n\nBut then “in your corner” would be “ish” + [corner] → what is corner?\n\nWe have:\n- chushp”a = his corner → “chush” + “p”a → so “p”a = corner?\n\nThus corner root = “p”a\n\nSo “in your corner” → “ish” + “your” + “p”a?\n\nBut “your corner” → no direct form.\n\nBut perhaps “your” is marked by a possessive root.\n\n“his” = chush- → chush + p”a → his corner\n\nSo “your” = ? → from “ishma” = your bed → “ish” + “ma” → so possibly “ish” is used for “your” in some forms?\n\nNo — “ish” is used in “my” and “your” in bed.\n\nBut “your” must be a separate marker.\n\nPossibility: “your” = “ish” (but in a different context) — but that seems inconsistent.\n\nAlternatively, “your corner” = “ish” + “corner” — but what is the form?\n\nWe have no direct “your corner”.\n\nBut look at “in your corner too” → 6.\n\nWe have “in your corner too” → “ish” + “your” + corner → “too” = -nhpsa?\n\nFrom examples:\n- p”ak”u = the pot \n- p”ak”unhpsa = my pot too → adds “too” → suffix “nhpsa”\n\nSimilarly:\n- yaputxi = is it the field? \n- yapsanpsa = in our1+2 field too → adds “too” → “sanpsa” → not “nhpsa”\n\n“p”ak”unhpsa” = my pot too → “unhpsa” = too → so “-nhpsa” = too\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st” + lake → “too” appeared in suffix “st”p”sa? No.\n\n“qucxst”psa” = from our1+2 lake too → “too” → the suffix may be “-t”psa or “-psa”?\n\n“yapsanpsa” = in our1+2 field too → “sanpsa” → so “-anpsa” = too?\n\nBut “p”ak”unhpsa” → “unhpsa” → “-nhpsa”\n\nSo different suffixes?\n\nWait: “p”ak”u” = pot \n“p”ak”unhpsa” = my pot too → adds “-nhpsa”\n\n“yapsanpsa” = in our1+2 field too → adds “-anpsa” → not the same.\n\nBut “anhpsa” vs “anpsa”\n\n“inhna” = my bed \n“ishma” = your bed \n“chushp”a = his corner \n“marka” = the town \n“markp”t”a” = from his town → “p”t”a” → his town \n“markstxi” = is it our1+2 town? → “stxi” = our1+2 town\n\nSo, forms with “too”:\n- aq”ipsa = the cave too → “ipsa” → “ipsa” = cave too\n→ “aqui” (cave) + “ipsa”? Or perhaps “-ipsa” = too?\n\n“aq”ipsa” = the cave too — base is “aq” (cave) + “ipsa” → “ipsa” = too?\n\nSimilarly:\n- qucxst”psa = from our1+2 lake too → “st”psa” = lake too?\n- yapsanpsa = in our1+2 field too → “anpsa” = field too?\n\nSo “-nsa” = too in some cases?\n\nBut in “p”ak”unhpsa” → “unhpsa” — “unh” → not “an”?\n\nSo different suffixes.\n\nBut perhaps the “too” marker is context-dependent.\n\nFor now, focus on the translation.\n\n4. our1+2 cliff \n→ “our1+2” + cliff \n→ we have qaqat”a = from the cliff → so “cliff” = qaqat”a \nThen “our1+2 cliff” → should be like “our1+2 lake” in “qucxst”psa”? But that is “from our1+2 lake”.\n\nWe have no “our1+2 cliff” directly.\n\nBut look at “in our1+2 field” → “yapsanpsa” = in our1+2 field too → so “in” + “our1+2” + field\n\nSimilarly, “our1+2” appears with locative or prepositional phrases.\n\nSo “our1+2 cliff” — is “the cliff” with “our1+2”?\n\nIn Jaqaru, possession can be expressed by adding “our1+2” to a noun.\n\nWe have:\n- “the cave too” = aq”ipsa → “a”cave” + “ipsa” → “too”\nNot clear.\n\nBut “our1+2 lake” → in “qucxst”psa” = from our1+2 lake too → so the form “our1+2 lake” is embedded.\n\nSimilarly, “our1+2 field” → “yapsanpsa” = in our1+2 field too\n\nSo likely, “our1+2 cliff” = “our1+2” + “cliff”\n\nBut what is the form of “cliff”? qaqat”a = from the cliff\n\nSo “cliff” = qaqat”a → root is qaqat”\n\nSo “our1+2 cliff” = st + qaqat” → but with which suffix?\n\nin “qucxst”psa” = from our1+2 lake → “q”+“cx”+“st”+“psa” → so “st” for our1+2 → attached to lake?\n\nWait: lake is “qucxap”a → so “qucxap”a” = through the lake\n\n“qucxst”psa” = from our1+2 lake too → “st” → our1+2 → attached to lake?\n\nSo “st” + “qucxap”a” → “qucxst”psa”\n\nSimilarly, “yapsanpsa” = in our1+2 field too → “an” → prefix for field?\n\n“yap” = field → “yap” + “utxi” = is it the field? → “yapsanpsa” — “s” and “an” → “sanpsa”\n\nMaybe the “our1+2” is attached via a marker.\n\nIn “qucxst”psa” → “st” → our1+2 → attached to “qucxap”a”\n\nIn “markstxi” → “st” + “mark” → “stxi” → “our1+2 town”\n\nSo “our1+2” is attached as a suffix to the noun root.\n\nSo:\n- “our1+2 lake” = “qucxap”a + “st” → “qucxst”psa” → but written as “qucxst”psa”\n\nSo root + “st” → for locative or definite?\n\nBut “from our1+2 lake” → implies “from” + “our1+2 lake”\n\nSimilarly, “our1+2 cliff” → likely root of cliff + “st” → qaqat”a → qaqat”ast”?\n\nBut not in list.\n\nWe have “qaqat”a” = from the cliff → so cliff is qaqat”a\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nLook at “from our1+2 lake” → “qucxst”psa”\n\nSo it uses “st” for “our1+2”\n\nSimilarly, “is it our1+2 town?” = markstxi → “mark” + “stxi”\n\nSo “st” + “xi” → “stxi” → so “our1+2” attached as a suffix to noun root.\n\nThus, for “our1+2 cliff” → cliff root is “qaqat” → so qaqat”ast”?\n\nBut no such form in examples.\n\nIs the “st” attached to the noun?\n\nIn “qucxap”a” = through the lake → “qucx” is “lake”?\n\nWait: “qucxap”a” = through the lake → “qucx” = lake? \nBut “qucxst”psa” = from our1+2 lake too → so “qucx” is lake.\n\nSo “lake” root = qucx → then “our1+2 lake” = qucxst”psa” → “st” = our1+2\n\nSimilarly:\n- “field” = “yap” → “yaputxi” = is it the field? → “yapsanpsa” = in our1+2 field too → “sanpsa” — perhaps “an” is prefix\n\nBut “yapsanpsa” = in our1+2 field too → “in” + “our1+2” + “field”\n\nBut in “qucxst”psa”, “from our1+2 lake” — “from” is an adverbial.\n\nSo for “our1+2 cliff” — just “our1+2 cliff” → likely similar to “our1+2 field” in “yapsanpsa”\n\n“yapsanpsa” = in our1+2 field too — so “in” + our1+2 + field\n\nBut it has “too”, so only the suffixed form.\n\nSo “our1+2 cliff” — would be just “cliff” with “our1+2” → so qaqat”ast”?\n\nBut in the word “qaqat”a” = from the cliff → so “cliff” is “qaqat”a”\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut no such form.\n\nIs “cliff” a root that takes “st”?\n\nFrom “qucxst”psa” → lake takes “st” → so “st” is added to noun.\n\nSimilarly, “markstxi” → “mark” + “st” + “xi” → “stxi” — so “st” attached to noun root.\n\nSo same pattern.\n\nSo “our1+2 cliff” = qaqat”ast”\n\nBut we have no phonetic examples.\n\nBut “qaqat”a” = from the cliff → so the root is qaqat” → “a” at end?\n\nSo “our1+2 cliff” = qaqat”ast”?\n\nBut “st” is the marker for “our1+2” → yes.\n\nTherefore, 4. our1+2 cliff → qaqat”ast”\n\nNow 5. in your corner\n\nWe have:\n- chushp”a = his corner\n- ishinhna = in my bed\n- ishma = your bed\n\nSo “in” + your corner?\n\n“in” prefix is “ish” → used in “ishinhna” = in my bed → “ish” + “inhna”\n\nSimilarly, “in your corner” → “ish” + “your” + “corner”\n\nWhat is “your”?\n\nIn chushp”a” = his corner → “chush” = his\n\nSo “your” = ? — perhaps “ish” for “your”? But “ish” is used in “your bed” → “ishma”\n\nSo “ish” may be a locative prefix for “in” with “your bed”\n\nBut “your” as a possessive? Unlikely.\n\nAlternatively, “your corner” → “isha” + “p”a?\n\nBut no such form.\n\nLook at “in your corner too” → item 6.\n\nWe have no “your corner” directly.\n\nBut in “is it in the corner?” = chushuntxi → “chush” + “untxi” → “untxi” = in the corner?\n\nSo “in the corner” = chushuntxi\n\nSimilarly, “in my bed” = ishinhna\n\nSo “in your corner” → should be “ish” + “your” + “corner”?\n\nBut “chush” is for “his”, so “your” might be “ish”?\n\nBut" + }, + { + "split": "train", + "record_id": "iol-2008-individual-p5-sub-a", + "planner_index": 8, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 13.: answer for this requested item\n- a.2 / 14.: answer for this requested item\n- a.3 / 15.: answer for this requested item\n- a.4 / 16.: answer for this requested item\n- a.5 / 17.: answer for this requested item\n- a.6 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: ; a.6: }\n\nProblem #5 (20 points). The following are sentences in Inuktitut and their English transla-\ntions:\n 1. Qingmivit takujaatit. Your dog saw you.\n 2. Inuuhuktuup iluaqhaiji qukiqtanga. The boy shot the doctor.\n 3. Aanniqtutit. You hurt yourself.\n 4. Iluaqhaijiup aarqijaatit. The doctor cured you.\n 5. Qingmiq iputujait. You speared the dog.\n 6. Angatkuq iluaqhaijimik aarqisijuq. The shaman cured a doctor.\n 7. Nanuq qaijuq. The polar bear came.\n 8. Iluaqhaijivit inuuhuktuit aarqijanga. Your doctor cured your boy.\n 9. Angunahuktiup amaruq iputujanga. The hunter speared the wolf.\n 10. Qingmiup ilinniaqtitsijiit aanniqtanga. The dog hurt your teacher.\n 11. Ukiakhaqtutit. You fell.\n 12. Angunahukti nanurmik qukiqsijuq. The hunter shot a polar bear.\n\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n 13. Amaruup angatkuit takujanga.\n 14. Nanuit inuuhukturmik aanniqsijuq.\n 15. Angunahuktiit aarqijuq.\n 16. Ilinniaqtitsiji qukiqtait.\n 17. Qaijutit.\n 18. Angunahuktimik aarqisijutit.\n\nSAMPLED ATTEMPT:\nStep 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context. \n\n\n\nAnalyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative. \n\n\n\nInvestigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied. \n\n\n\nCheck for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied. \n", + "approaches": [ + "Focus on verb stem + tense suffix + object marking. Identify consistent suffixes for past tense and object attachment. \n- In \"Qingmivit takujaatit\", \"takujaatit\" = saw you → \"takuj\" + \"aate\" (object \"you\") + past suffix. \n- In \"qukiqtanga\", \"qukiq\" + \"tanga\" → shot → \"tanga\" is past tense. \n- In \"aarqijaatit\", \"aarqij\" + \"aate\" → cured you → \"aate\" marks object. \n- In \"iputujait\", \"iputuj\" + \"ait\" → speared → \"ait\" is past tense. \n- In \"aanniqtutit\", \"aanniqt\" + \"utit\" → hurt yourself → reflexive. \n\nPattern: \n- Past tense suffixes: -tanga, -ait, -janga, -utit \n- Object marking: -aate (or -aati, -aatiq), attached after verb stem \n- Possessive: \"nanuit\" = your, \"inuuhukturmik\" = your boy \n\nTarget 13: Amaruup angatkuit takujanga \n- \"Amaruup\" = the hunter \n- \"angatkuit\" = came (past of \"angatkuq\") \n- \"takujanga\" = saw (takuj + anga) — \"anga\" is past tense, no object → implies \"saw\" (something) \n→ Translation: \"The hunter came and saw.\" \nVerification: In sentence 1, \"Qingmivit takujaatit\" → \"your dog saw you\" → saw + object. Here, no object → general \"saw\" is acceptable in context.", + "Analyze grammatical roles and object presence. If object is missing, it may be implied or absent due to context. \n- All verbs in provided examples are transitive (require object) except reflexives like \"you hurt yourself\". \n- In 13: \"Amaruup angatkuit takujanga\" → agent (hunter), action (came), action (saw) — two verbs → likely \"came and saw\" \n- \"angatkuit\" = came (past) → consistent with \"nanuq qaijuq\" (polar bear came) \n- \"takujanga\" = saw → \"takuj\" (to see) + past suffix \"anga\" \n→ \"The hunter came and saw\" \nVerification: In sentence 8, \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → agent, object, verb. Here, no object after \"saw\", so must be unmarked — plausible in narrative.", + "Investigate possessive markers and object derivation. \n- \"Nanuit\" = your \n- \"inuuhukturmik\" = your boy (in 8: \"inuuhuktuit\" = your boy) \n- \"aanniqsijuq\" = hurt → past tense of \"aanniqt\" \n- \"aanniqsijuq\" appears in 3: \"Aanniqtutit\" = you hurt yourself, and 10: \"aanniqtanga\" = hurt your teacher → object required \n- Thus, \"aanniqsijuq\" requires object → in 14: \"Nanuit inuuhukturmik aanniqsijuq\" → your boy hurt [someone] \n→ Object is \"a doctor\" (implied by context of similar verbs) \n→ \"Your boy hurt a doctor\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object after verb. Similarly, here object is missing but must be implied.", + "Check for tense and agent-object structure in all sentences. \n- Sentence 15: \"Angunahuktiit aarqijuq\" \n- \"Angunahuktiit\" = the hunter (past tense) \n- \"aarqijuq\" = cured (past tense) \n- No object → cannot be literal \"cured\" without object \n- But in 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object after verb \n- In 8: \"your doctor cured your boy\" → object after verb \n- So \"cured\" requires object \n- Thus, \"Angunahuktiit aarqijuq\" is incomplete or missing object → likely error in structure \n- But given the pattern, it may mean \"the hunter cured [someone]\" — object implied \n- In context, similar to \"the hunter cured the doctor\" or \"the hunter cured a patient\" \n- But without object, only possible if it's a reflexive or self-cure — not supported \n- Alternative: \"it\" in \"Angunahuktiit\" is possessive? Unlikely — \"it\" is past tense marker \n→ Best interpretation: \"The hunter cured\" — with implied object \n→ \"The hunter cured someone\" \nVerification: In sentence 6, \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object present. Without object, it's incomplete — but in absence of other data, must assume object is implied." + ], + "anchor_output": "Step 1: Analyze the given Inuktitut sentences and their English translations to identify common patterns in verb structure and meaning.\n\nExample 1: \"Qingmivit takujaatit\" → \"Your dog saw you.\" \n- \"Qingmivit\" = your dog (subject) \n- \"takujaatit\" = saw you (verb with object \"you\") \n→ The verb stem is \"takuj\" with a suffix indicating action and object.\n\nExample 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"The boy shot the doctor.\" \n- \"Inuuhuktuup\" = the boy \n- \"iluaqhaiji\" = the doctor (object) \n- \"qukiqtanga\" = shot (past tense verb) \n→ \"qukiqtanga\" = \"qukiq\" + \"tanga\" = (to shoot) + past tense or object\n\nExample 3: \"Aanniqtutit\" → \"You hurt yourself.\" \n→ \"aanniqtutit\" = you hurt yourself (reflexive)\n\nExample 4: \"Iluaqhaijiup aarqijaatit\" → \"The doctor cured you.\" \n→ \"aarqijaatit\" = cured you (verb: aarqij + past tense + object)\n\nExample 5: \"Qingmiq iputujait\" → \"You speared the dog.\" \n→ \"iputujait\" = speared (verb stem \"iputuj\" + past tense)\n\nExample 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor.\" \n→ \"aarqisijuq\" = cured (past tense), \"a\" + \"arqisijuq\" → cured someone\n\nExample 7: \"Nanuq qaijuq\" → \"The polar bear came.\" \n→ \"qaijuq\" = came (simple past)\n\nExample 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"Your doctor cured your boy.\" \n→ \"aarqijanga\" = cured (past tense), \"your\" is marked in both subject and object\n\nExample 9: \"Angunahuktiup amaruq iputujanga\" → \"The hunter speared the wolf.\" \n→ \"iputujanga\" = speared (past tense)\n\nExample 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"The dog hurt your teacher.\" \n→ \"aanniqtanga\" = hurt (verb), \"your teacher\" is object\n\nExample 11: \"Ukiakhaqtutit\" → \"You fell.\" \n→ \"ukiakhaqtutit\" = you fell (past tense)\n\nExample 12: \"Angunahukti nanurmik qukiqsijuq\" → \"The hunter shot a polar bear.\" \n→ \"qukiqsijuq\" = shot (past tense), object \"a polar bear\"\n\nNow, observe the verb stems and how they combine with cases or possessives.\n\nKey patterns:\n- Verbs are in past tense with specific derivational suffixes.\n- Possessive markers (like \"your\", \"your\" boy) appear in the subject or object depending on context.\n- Reflexive forms (e.g. \"you hurt yourself\") use a suffix like -utit or -tutit.\n- Agent and patient roles are clearly marked by form and order.\n\nNow, analyze the target sentences:\n\n13. Amaruup angatkuit takujanga. \n- \"Amaruup\" → \"the hunter\" (agent) \n- \"angatkuit\" → \"came\"? But \"angatkuit\" = \"angatuq\" + \"uit\" → pattern of \"angatuq\" = come, \"uit\" = past/final form \nWait: \"Nanuq qaijuq\" → \"the polar bear came\" → \"qaijuq\" = came \nBut \"angatkuit\" → likely derived from \"angatkuq\" (came) → \"angatkuit\" = past tense \n\"takujanga\" → \"takuj\" + \"anga\"? → \"takuj\" = see, \"anga\" = past tense? \nBut \"takujaatit\" = saw you → so \"takuj\" + object + past \n\"takujanga\" → \"takuj\" + \"anga\" → see/observe? But no object? \nBut in 13, \"angatkuit takujanga\" — agent (hunter) + verb (came) + verb? \nWait — perhaps \"angatkuit\" is \"came\", and \"takujanga\" is \"saw\"?\n\nBut in example 1: \"Qingmivit takujaatit\" → \"your dog saw you\" \n\"takuj\" + \"aate\" (you) → \"takujaatit\" \nSo \"takujanga\" → \"takuj\" + \"anga\"? \n\"anga\" may be a past tense suffix — similar to \"tanga\" in \"qukiqtanga\"\n\nCompare: \n- takujaatit → took + object (you) + past \n- takujanga → takuj + anga → \"saw\" (without object?) — but that doesn’t make sense.\n\nWait, in sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" \n\"aarqijanga\" = cured\n\nFrom 12: \"Angunahukti nanurmik qukiqsijuq\" → \"the hunter shot a polar bear\" \n\"qukiqsijuq\" = shot → so \"qukiq\" + past suffix\n\nSo verbs: \n- takuj → to see \n- qukiq → to shoot \n- aarqij → to cure \n- iputuj → to spear \n- aanniqt → to hurt\n\nPast tense markers: \n- -tutit → \"hurt yourself\" \n- -tanga → \"shot\" (in 2, 12) \n- -janga → \"cured\" (in 4, 8) \n- -ait → \"saw\" in 1, 5 \n- -qaijuq → \"came\" in 7\n\nNote: \"takuj\" in 1 → takujaatit → \"saw you\" → object attached \n\"takujanga\" → if \"anga\" = past, and no object, perhaps \"saw\" (something) — but object missing?\n\nBut in 13: \"Amaruup angatkuit takujanga\" \n\"Amaruup\" = the hunter \n\"angatkuit\" = came (past form) \n\"takujanga\" = saw? (with no object)\n\nBut \"saw\" must take an object — unless it's \"saw\" in general.\n\nBut in the context, hunter came and saw? → \"the hunter came and saw\" — possible.\n\nBut better: assemble pattern.\n\nFrom sentence 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"The shaman cured a doctor\" \n\"angatkuq\" = the shaman (subject) \n\"iluaqhaijimik\" = a doctor (object) \n\"aarqisijuq\" = cured\n\nSo \"aarqisijuq\" = cured + object\n\nSimilarly, \"qukiqsijuq\" = shot + object\n\n\"iputujanga\" = speared (object)\n\n\"takujanga\" = saw (object?) — but no object given.\n\nBut in sentence 1: \"Qingmivit takujaatit\" → \"your dog saw you\" → object is \"you\"\n\nIn 13: no object → so \"the hunter came and saw\" (saw something)? \nBut it's not complete.\n\nPerhaps \"takujanga\" = \"saw\" and object is implied.\n\nBut in sentence 2: \"Inuuhuktuup iluaqhaiji qukiqtanga\" → \"the boy shot the doctor\" — object after agent and verb\n\nSo the verb-stem + past + object\n\nIn 13: \"Amaruup angatkuit takujanga\" → \"the hunter came and saw\" → possibly \"came and saw\" — implies saw something not specified.\n\nSo translation: \"The hunter came and saw.\"\n\nBut in context: similar to English idioms.\n\nNow 14: Nanuit inuuhukturmik aanniqsijuq \n\"Amaruup\" → \"the hunter\" \n\"nanuit\" → \"your\" (possessive) — \"nanuit\" = \"your\" \n\"inuuhukturmik\" → \"your boy\"? \"inuuhuktuit\" = your boy (in 8) → \"inuuhukturmik\" = your boy (possessive) \n\"aanniqsijuq\" → \"hurt\" — \"aanniqt\" = hurt, + suffix → \"aanniqsijuq\" = hurt (past) \nSo: \"Your boy hurt a doctor?\" → \"Your boy hurt the doctor\"\n\n\"aanniqsijuq\" = hurt → so \"inuuhukturmik\" = your boy, \"aanniqsijuq\" = hurt? But no object?\n\nWait: in 3: \"Aanniqtutit\" = you hurt yourself — so \"aanniqtutit\" → you hurt yourself (reflexive)\n\nIn 10: \"Qingmiup ilinniaqtitsijiit aanniqtanga\" → \"the dog hurt your teacher\" → so \"aanniqtanga\" = hurt (object)\n\nBut here: \"aanniqsijuq\" → likely \"hurt\" with object missing — or object implied?\n\n\"inuuhukturmik\" = your boy (subject), \"aanniqsijuq\" = hurt — missing object.\n\nBut only one object? In context of translation, likely \"your boy hurt a doctor\".\n\nSince \"aanniqsijuq\" = hurt → past tense of \"aanniqt\", so likely \"hurt\" something.\n\nSo: \"Your boy hurt a doctor.\"\n\nBut in example 4: \"iluaqhaijiup aarqijaatit\" = the doctor cured you — so object → subject\n\nHere, subject is \"your boy\", verb is \"hurt\", object \"a doctor\" — yes.\n\nSo 14: \"Your boy hurt a doctor.\"\n\n15: Angunahuktiit aarqijuq \n\"Angunahuktiit\" → \"the hunter\" (with \"it\" = past tense) → \"angunahukti\" = the hunter, \"it\" = past \n\"aarqijuq\" → \"cured\" (past) — likely \"cured someone\"\n\nBut no object? → verb without object → so \"the hunter cured\" → what?\n\nBut verb takes object → unless implied?\n\nLook at sentence 8: \"Iluaqhaijivit inuuhuktuit aarqijanga\" → \"your doctor cured your boy\" → object included.\n\nHere, no object → possible subject action with implied object.\n\nBut \"aarqijuq\" = cured → likely \"cured someone\" — but who?\n\nCould be \"the hunter cured\" — but no one.\n\nCompare 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → \"shaman cured a doctor\" → object needed.\n\nBut here: no object — so perhaps it's missing or object is implied.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw — object not present.\n\nSimilarly, \"Angunahuktiit aarqijuq\" = \"the hunter cured\" → but something?\n\nBut if no object, perhaps it is incomplete.\n\nWait — perhaps \"aarqijuq\" = cured, and object is missing, but from structure, no object → so it may be a simple act.\n\nBut in other examples, verbs require an object.\n\nAlternative: \"aarqijuq\" can mean \"cured\" with object omitted or implied.\n\nBut in context of others, like 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object = you\n\nSo \"cure\" verb takes object.\n\nSo if no object, cannot be literal.\n\nPossibility: \"it\" is possessive? \"Angunahuktiit\" = the hunter (past) — \"it\" = past tense marker\n\n\"aarqijuq\" = cured\n\nSo subject and verb → \"the hunter cured\" — but who?\n\nBut all sentences seem to have two clear elements: agent, action, object.\n\nUnless in 15, object is missing — perhaps error?\n\nBut look at 16: Ilinniaqtitsiji qukiqtait \n\"ilinniaqtitsiji\" = \"your teacher\" (in 10: \"ilinniaqtitsijiit aanniqtanga\" → dog hurt your teacher) \n\"qukiqtait\" = shot? From 2: \"qukiqtanga\" → shot — \"ait\" = past tense \nSo \"qukiqtait\" = shot \nSo: \"your teacher shot\"\n\nBut \"qukiqtait\" — a similar form to \"qukiqtanga\"\n\nSo \"ilinniaqtitsiji qukiqtait\" → \"your teacher shot\"\n\nBut shot what? Missing object.\n\nAgain — verb without object.\n\nBut in 17: Qaijutit → \"you fell\" → \"qaijutit\" → from 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" = fallen? \n\"qaijutit\" → seems like \"qaijuq\" (came) → but \"qaijutit\" — similar to \"qaijaqtutit\" → \"fell\"\n\nSo \"qaijutit\" = you fell.\n\nAfter 11: \"Ukiakhaqtutit\" = you fell → \"qaijutit\" may be similar.\n\n\"qaijutit\" → likely \"you fell\"\n\nYes — pattern of \"qaijutit\" = you fell (past tense)\n\n18: Angunahuktimik aarqisijutit \n\"Angunahuktimik\" → \"the hunter\" (with \"mik\" = past) — similar to \"inuuhuktuit\" \n\"aarqisijutit\" → \"cured\" + past tense — \"aarqij\" + \"utit\" — like \"aarqijaatit\" = cured you\n\n\"aarqisijutit\" → cured (past) + object?\n\nBut no object — again, verb without object?\n\nBut earlier verbs take object — so perhaps structure is agent + verb + object, and here no object → so not full.\n\nBut in 13: \"Amaruup angatkuit takujanga\" — two verbs: came and saw → distinct actions\n\nSimilarly, 14: \"your boy hurt a doctor\" — object present\n\nSo in 15: \"Angunahuktiit aarqijuq\" — no object → so perhaps \"the hunter cured\" → missing object → not grammatical\n\nBut all sentences are grammatical — so perhaps \"aarqijuq\" = cured + implied object\n\nWait — perhaps \"it\" is not past tense — but possessive?\n\nNo — \"inuuhuktuit\" = your boy (in 8) — possessive marker \"uit\"\n\nSo \"angunahuktiit\" = the hunter (agent) + \"it\" → past tense\n\nSimilarly, \"aarqijuq\" = cured (with object implied)\n\nBut no object present.\n\nBut look at 5: \"Qingmiq iputujait\" → you speared the dog — verb has object\n\nOnly when subject is not present or object is implied.\n\nBut in 15, no object → so likely it's a simple statement: \"The hunter cured\" — but incomplete.\n\nHowever, in real Inuktitut, such sentences can exist with implied object.\n\nBut more likely, the verb has a dependent object.\n\nBut in the list, all verbs have an object unless it's reflexive.\n\nOnly 3: \"Aanniqtutit\" = you hurt yourself → reflexive\n\nOthers have object.\n\nSo 15 must have an object — perhaps missing in translation?\n\nBut in the sentence: \"Angunahuktiit aarqijuq\" → agent + verb → object not present.\n\nUnless \"aarqijuq\" has an implied object.\n\nCompare 4: \"iluaqhaijiup aarqijaatit\" → doctor cured you → object \"you\"\n\nBut here: no object → so not like.\n\nSimilarly, 6: \"Angatkuq iluaqhaijimik aarqisijuq\" → shaman cured a doctor → object given\n\nSo in 15, no object — so perhaps it's \"the hunter cured\" → but of what?\n\nBut perhaps from context, it's just \"the hunter cured\".\n\nAlternatively, is \"aarqijuq\" different?\n\n\"aarqisijuq\" = cured someone \n\"aarqijuq\" = cured (same stem)?\n\nIn 4: \"aarqijaatit\" = cured you \nIn 6: \"aarqisijuq\" = cured a doctor\n\nSo both use different suffixes for object.\n\nSimilarly, \"aanniqsijuq\" = hurt a doctor (14)\n\nSo \"aarqijuq\" → might be short form, not with object.\n\nBut likely, \"aarqijuq\" means \"he cured\" — with object implied or missing.\n\nBut in the context, the only consistent inference is:\n\n13. Amaruup angatkuit takujanga → the hunter came and saw \n14. Nanuit inuuhukturmik aanniqsijuq → your boy hurt a doctor \n15. Angunahuktiit aarqijuq → the hunter cured \n16. Ilinniaqtitsiji qukiqtait → your teacher shot \n17. Qaijutit → you fell \n18. Angunahuktimik aarqisijutit → the hunter cured (with object?)\n\nBut 18 has \"aarqisijutit\" — like \"aarqijaatit\" → cured you\n\nSo perhaps object is implied.\n\nBut look at the structure:\n\nIn 18: \"Angunahuktimik aarqisijutit\" \n\"mik\" = past tense marker? \n\"aarqisijutit\" = cured (with object?) — but not marked.\n\nBut" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-b", + "planner_index": 9, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / bullet 1: answer for this requested item\n- b.2 / bullet 2: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(b) Write out in Nahuatl: 42; 494.\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Write out in Nahuatl: 42; 494.\n\nSAMPLED ATTEMPT:\nWe are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "approaches": [ + "Focus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.", + "Assume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.", + "\nFocus on identifying the base number system from known equivalences. From equation (4): mäcuïlli + öme = chicöme. Assume mäcuïlli = 20, öme = 1 → chicöme = 21. From equation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli. Try ëyi = 5 → caxtölli = 100. This suggests a base-20 system where units are multiples of 20. From equation (2): cem-pöhualli × öme = öm-pöhualli. If cem = 20, öme = 1, then left = 20. Right = öm-pöhualli. If öm = 1, then 1-pöhualli = 1 → contradiction. If öm = 20, then 20-pöhualli = 20 → matches. Thus, pöhualli = 1, cem = 20, öm = 20. But cem and öm both 20? Unlikely. Alternatively, pöhualli = 20, so cem-pöhualli = 20, and öm-pöhualli = 20 → then 20 × 1 = 20 → works. Thus, öme = 1, pöhualli = 20. So consistent: pöhualli = 20, öme = 1.\n\nThus, multiplication with units: a × b → (a) times (b). Addition: a + b → (a) and (b) combined.\n\nNow, 42 = 2 × 20 + 2 → need to express 2. \nFrom equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \ntzontli = 180 = 9 × 20 → likely tzontli = 180 \npöhualli = 20 \ncaxtölli = 100 \ncë = 1 \nyë = 1 \nSo: 1-tzontli-on-20-on-100-on-1 → if \"on\" means multiplication: 1 × 180 × 20 × 100 × 1 = 360,000 → too big. \nIf \"on\" means addition: 1 + 180 + 20 + 100 + 1 = 302 → not 42.\n\nBut 42 = 2×20 + 2 → so we need a way to express 2.\n\nFrom (4): 20 + 1 = 21 → 21 is a known sum. Is there a way to write 2?\n\nNo direct expression for 2. But perhaps yë = 1, and other units are built. Perhaps 2 = yë-tzontli? No — tzontli = 180.\n\nAlternative: in equation (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë \nSuppose: (1×20) + (20×nähui) = 20 + cë \nLeft: 20 + 20×nähui \nRight: 20 + cë \nThus: 20 + 20×nähui = 20 + cë → 20×nähui = cë \nIf nähui = 1 → cë = 20 → not 1.\n\nIf nähui = 0.1 → not integer.\n\nSo no. \nBut if nähui = 1, cë = 20 → then cë = 20 → so cë = pöhualli.\n\nThus, cë = 20.\n\nThen equation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \n= 1-tzontli-on-20-on-100-on-20 \nIf \"on\" = ×: 1×180×20×100×20 = 72,000,000 → no \nIf \"on\" = +: 1+180+20+100+20 = 321 → not 42.\n\nSo not matching.\n\nConclusion: the expression for 42 is likely 2×pöhualli + 2 → which may be written as \"yë-tzontli\" or \"mahtlactli\" in some form.\n\nBut no clear 2.\n\nThus, the path fails: no consistent derivation of number 2 or 42 in the language based on given equations.\n\n\n\nAssume that the language uses a base-20 positional system where numbers are composed via additive and multiplicative expressions. Use equation (13) and (14) to extract values.\n\nEquation (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno \nEquation (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nFrom historical Nahuatl, tzontli = 180 = 9 × 20 → so tzontli = 180 \npöhualli = 20 \nThus, tzontli = 9 × pöhualli\n\nIn (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë \nIf yë = 1, then 1-tzontli = 1 × 180 \n“on” = “plus” → so total = 180 + 20 + 100 + 1 = 301 → if caxtölli = 100 (from mäcuïlli × ëyi = caxtölli, mäcuïlli = 20, ëyi = 5) and cë = 1\n\nThen 301 = ndamno\n\nNow, 42 = 2×20 + 2 → need to express 2.\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nSet cem = 20, pöhualli = 20 → 20×öme = öm-pöhualli \nSuppose öme = 1 → 20 = öm-pöhualli → so öm = 1 → 1-pöhualli = 1 → not 20.\n\nSuppose öme = 1, and öm = 20 → 20×1 = 20 → 20-pöhualli = 20 → works.\n\nSo öm = 20 → consistent with pöhualli.\n\nSo multiplication: cem-pöhualli = 20 × 20 = 400 → not used.\n\nBut equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21\n\nStill no 2.\n\nPerhaps 2 is represented as \"yë-tzontli\" or \"mahtlactli\" — but values too large.\n\nThus, no way to derive 2 → cannot write 42.\n\nThis path fails due to inability to generate the numeral for 2.\n\n\n\nUse the Arammba system to infer number values, then transfer to Nahuatl via structure.\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo \nLet ngámbi = 1 → 1+1 = 1 × yànparo → yànparo = 2\n\n(8): ngámbi + asàr = tambaroy → 1 + asàr = tambaroy → asàr = 1 → tambaroy = 2\n\n(11): nimbo × fete = tarumba \n(12): nimbo + yànparo tàxwo = yenówe tàxwo \n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → implies fete = yenówe\n\nSo from (12): nimbo + 2 = yenówe → fete = nimbo + 2\n\nThen (11): nimbo × (nimbo + 2) = tarumba\n\n(15): cen-tzontli = tarumba + tambaroy + fete + asàr\n\nSuppose values: \nTry nimbo = 2 → fete = 4 → tarumba = 2×4 = 8 \ntambaroy = 2, asàr = 1 → sum: 8 + 2 + 4 + 1 = 15 → cen-tzontli = 15 → contradicts tzontli = 1", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "We are given a set of equations in Nahuatl and Arammba, which appear to represent arithmetic operations with symbolic expressions. The task is to determine how numbers like 42 and 494 are expressed in Nahuatl.\n\nLet’s first analyze the structure and patterns in the equations.\n\n---\n\n**Step 1: Look at the arithmetic in the Nahuatl equations.**\n\nEquation (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \nThis appears to be multiplication. Let's try to interpret the components.\n\nNotably, “mahtlactli” appears often. Also, “pöhualli” is likely a key term for \"days\" or \"cycle\", and is often used in calendars.\n\nEquation (2): \n`cem-pöhualli × öme = öm-pöhualli` \nThis suggests that multiplying cem-pöhualli by öme yields öm-pöhualli. Possibly, cem-pöhualli = 20, öme = 1, since 20 × 1 = 20. But the result is öm-pöhualli, which may be 1. That suggests a reduction.\n\nBut better: perhaps “pöhualli” is the base unit, and “cem” = 20, “öme” = 1.\n\nBut equation (2) says: cem-pöhualli × öme = öm-pöhualli \nThis might mean 20 × 1 = 1, which is not arithmetic.\n\nWait: maybe it's inversion or fraction?\n\nAlternatively, consider equation (6): \n`mäcuïlli × ëyi = caxtölli` \nEquation (4): `mäcuïlli + öme = chicöme`\n\nAlso, equation (5): `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui`\n\nNow, equation (3): \n`yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nThese suggest compositions involving addition and multiplication.\n\nLet me try to decode units.\n\nWe can look for number values.\n\nTry to assign values to base units.\n\nFrom (2): \n`cem-pöhualli × öme = öm-pöhualli`\n\nAssume:\n- cem = 20\n- pöhualli = 1\n- öme = 1\n\nThen left side: (20 × 1) × 1 = 20 \nRight side: öm-pöhualli → which might be 1 (if it's öm = 1)\n\nImplies 20 × 1 = 1 → impossible.\n\nAlternatively: maybe \"pöhualli\" is a unit, and the operation is not multiplication in the familiar sense.\n\nAlternatively, note that in many such olympiad problems, the language expressions represent a base-20 number system with additive composition.\n\nBack to (1): \n`mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli`\n\nLet’s suppose:\n- “mahtlactli” = 20\n- “on” = “times” or “multiplied by”\n\nThen: (20 × k) × 20 = mäcuïl-pöhualli-om-mahtlactli\n\nBut what is mäcuïl-pöhualli?\n\nCompare with equation (4): mäcuïlli + öme = chicöme\n\nIf mäcuïlli = 20, and öme = 1, then 20 + 1 = 21? But chicöme may be 21.\n\nNote: equation (6): mäcuïlli × ëyi = caxtölli\n\nSo if mäcuïlli = 20, then 20 × ëyi = caxtölli → could be 100?\n\nThat suggests ëyi = 5.\n\nThen caxtölli = 100.\n\nAlso, equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21 → chicöme = 21.\n\nNow equation (5): mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nCompute: (mahtlactli-om-ëyi) × ëyi\n\nmahtlactli = 20 (assume), ëyi = 5 → mahtlactli-om-ëyi = 20 - 5? Or 20 × 5? Or 20 + 5?\n\n\"om\" might mean \"and\" or \"plus\"?\n\n“mahtlactli-om-ëyi” could be “mahtlactli and ëyi” → 20 + 5 = 25\n\nThen 25 × 5 = 125\n\nRight-hand side: cem-pöhualli-on-caxtölli-on-nähui\n\nWe have cem = 20, pöhualli = 1, caxtölli = 100 → 20 + 1 + 100 = 121? Or cem-pöhualli-on-caxtölli → 20 × 1 × 100 = 2000?\n\nUnlikely.\n\nWait — “on” might mean “times”.\n\nSo: cem-pöhualli-on-caxtölli-on-nähui = (cem-pöhualli) × (caxtölli) × (nähui)\n\nBut we don't have nähui.\n\nAlternatively, “on” might be an infix meaning “structured with”, not multiplication.\n\nBut consider equation (3): \nyë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nIf we suppose:\n- yë = 1 (e.g., yë-pöhualli = 1 day)\n- pöhualli = 1\n- chicöme = 21 (from earlier)\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli-on-cë → total?\n\nAddition: (1 × 1) + (20 × 1) = 21? → 1 + 20 = 21 → 21 = 21?\n\nBut output is näuh-pöhualli-on-cë → if cë = 1, then 21?\n\nThen that could work.\n\nBut still not giving a clear number.\n\nNow look at equation (13) and (14), which are the key linking equations.\n\nEquation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nEquation (14): \n`cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\nEquation (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nEquation (16): \n`cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\nWe need to relate these to numerals.\n\nWe suspect a base-20 system is involved.\n\nAlso, in many Mayan/Nahuatl systems, numbers are built on 20:\n\n- Units: 1\n- 20s: 20, 400, etc.\n\nNow, we are to write 42 and 494 in Nahuatl.\n\n42 = 2 × 20 + 2 → 2 × 20 + 2 \n494: 494 ÷ 20 = 24.7 → 24 × 20 = 480, 494 - 480 = 14 → 24 × 20 + 14\n\nSo we need expressions involving 20, 2, 14.\n\nBut how are numbers composed?\n\nNow look at equation (4): mäcuïlli + öme = chicöme \n→ mäcuïlli = 20, öme = 1 → 20 + 1 = 21 → chicöme = 21\n\nEquation (6): mäcuïlli × ëyi = caxtölli → 20 × ëyi = caxtölli\n\nLet’s say ëyi = 5 → 100 → caxtölli = 100\n\nEquation (2): cem-pöhualli × öme = öm-pöhualli → cem = 20 → (20 × öme) = öm-pöhualli\n\nSuppose öme = 1 → left = 20 → right = 1 → unbalanced.\n\nBut if öme = 1, and öm-pöhualli = 20, then it works.\n\nMaybe öm = 20, so öm-pöhualli = 20, then 20 × 1 = 20 → it works.\n\nSo perhaps öm = 20, cem = 20 → implies two different markers for 20?\n\nUnlikely.\n\nAlternative: perhaps the operation is not multiplication of numbers, but addition.\n\nBut equation (6) has ×.\n\nNow equation (5): (mahtlactli-om-ëyi) × ëyi = cem-pöhualli-on-caxtölli-on-nähui\n\nWe have from above: \nmahtlactli = 20, ëyi = 5 → mahtlactli-om-ëyi = 20 + 5 = 25 \nThen 25 × 5 = 125\n\nRHS: cem-pöhualli-on-caxtölli-on-nähui \nIf “on” = × → (cem × pöhualli) × caxtölli × nähui\n\ncem = 20, pöhualli = ? → maybe 1, so 20 × 1 = 20 \ncaxtölli = 100 \nnähui = 1?\n\nThen 20 × 100 × 1 = 2000 → too big.\n\nIf cem-pöhualli = 20, caxtölli = 100, nähui = 1 → 20 × 100 = 2000 → 125? No.\n\nNot matching.\n\nAlternative: suppose “on” means “plus”?\n\nThen cem-pöhualli + caxtölli + nähui → 20 + 100 + 1 = 121 → close to 125?\n\nStill off.\n\nWait — 125 = 20 × 6 + 5 → not clear.\n\nAlternatively, perhaps the numbers relate to calendar units.\n\nIn Nahuatl, “pöhualli” is 20 days, “tznontli” is 180 days.\n\nWait — historically:\n\n- A day = 1\n- A cycle = 20 days = one pöhualli\n- 180 days = tzontli = 180 = 9 × 20 → so 20 × 9 = 180\n\nAh! That's promising.\n\nSo:\n- 1 day = 1\n- 20 = pöhualli = 20\n- 180 = tzontli = 9 × 20 → so tzontli = 180\n\nNow see equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nThis is a compound expression.\n\n“yë” = 1? “tzontli” = 180 → yë-tzontli → 1 × 180 = 180?\n\n“on” is a joining operator.\n\n“näuh-pöhualli” = 1 × 20? or 20?\n\n“caxtölli” = ? (from earlier, may be 100)\n\n“cë” = ?\n\nBut result is “ndamno” — a single number?\n\nWe may need to assign values from known equations.\n\nEquation (14): \ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\nIf cen-tzontli = 20 × 9 = 180 \ncem-pöhualli = 20 \nmahtlactli = 20 \nöme = 1\n\n\"on\" may mean × or +?\n\n“cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme” → 180 × 20 × 20 × 1? = 72,000 → too high.\n\nIf “on” is +, then 180 + 20 + 20 + 1 = 221 → result is \"yànparo tarumba\"\n\nBut from equation (15): cen-tzontli = tarumba tambaroy fete asàr\n\nSo cen-tzontli = 180 = tarumba tambaroy fete asàr\n\nSo likely 180 = tarumba + tambaroy + fete + asàr\n\nFrom equation (12): nimbo + yànparo tàxwo = yenówe tàxwo\n\n(11): nimbo × fete = tarumba\n\n(10): yenówe × yenówe tàxwo = fete yenówe tàxwo → (a × a) = a × a → identity → perhaps both sides are equal, so a² = a × a → tautology.\n\nBut suggests that yenówe = 1?\n\nOr that \"on\" is associative.\n\nFrom (8): ngámbi + asàr = tambaroy → in Arammba\n\nFrom (7): ngámbi + ngámbi = ngámbi × yànparo\n\nLet’s suppose ngámbi = 1 → left: 1+1=2 → right: 1 × yànparo → so yànparo = 2\n\nThen (8): 1 + asàr = tambaroy → tambaroy = 1 + asàr\n\n(11): nimbo × fete = tarumba\n\n(12): nimbo + yànparo tàxwo = yenówe tàxwo\n\nWe have yànparo = 2, so nimbo + 2 = yenówe\n\nThen (10): yenówe × yenówe tàxwo = fete yenówe tàxwo → left: a × a → right: fete × a\n\nSo a² = fete × a → if a ≠ 0, then a = fete\n\nSo fete = a = yenówe\n\nBut from above: yenówe = nimbo + 2 → so fete = nimbo + 2\n\nFrom (11): nimbo × fete = tarumba\n\nSo nimbo × (nimbo + 2) = tarumba\n\nNow from (15): cen-tzontli = tarumba tambaroy fete asàr → 180 = tarumba + tambaroy + fete + asàr\n\nWe don’t have values.\n\nBut perhaps the values are small.\n\nBack to Nahuatl.\n\nWe suspect:\n- 20 = pöhualli\n- 1 = unit\n- 180 = tzontli = 9 × 20\n\nNow check equation (13): \nyë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno\n\nIf:\n- yë = 1\n- tzontli = 180\n- näuh-pöhualli = 20\n- caxtölli = 100\n- cë = 1\n\nThen “on” may mean “times” → 1 × 180 × 20 × 100 × 1 = 360,000 → too big.\n\nIf “on” means “plus”: 1 + 180 + 20 + 100 + 1 = 302 → not recognizable.\n\nBut 42 = 2 × 20 + 2\n\n494 = 24 × 20 + 14\n\nSo expression for 42 might be: 2 × pöhualli + 2\n\nBut how is 2 written?\n\nFrom equation (4): mäcuïlli + öme = chicöme → 20 + 1 = 21\n\nPerhaps 2 = yë or something.\n\nFrom (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë\n\nSuppose:\n- yë = 1\n- pöhualli = 20\n- chicöme = 21\n- mahtlactli = 20\n- nähui = 1\n- näuh-pöhualli = 20\n- cë = 1\n\nThen left: (1 × 20) + (20 × 1) = 20 + 20 = 40 \nRight: 20 + 1 = 21 → 40 ≠ 21 → no.\n\nAlternatively, if “on” is × → (1 × 20) × (21) = 420 → right side 21 → no.\n\nBut wait! The left-hand side: yë-pöhualli-on-chicöme + mahtlactli-on-nähui\n\nIf “on” means multiplication, then “yë-pöhualli-on-chicöme” = 1 × 20 × 21 = 420? \nThen plus “mahtlactli-on-nähui” = 20 × 1 = 20 → total 440 → not" + }, + { + "split": "val", + "record_id": "iol-2015-individual-p1-sub-c", + "planner_index": 10, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- c.1 / 43.: answer for this requested item\n- c.2 / 569.: answer for this requested item\n\nFinal answer shape: \\boxed{c.1: ; c.2: }\n\nProblem 1 (20 points). Nahuatl:\n\n mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli (1)\n cem-pöhualli × öme = öm-pöhualli (2)\n yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë (3)\n mäcuïlli + öme = chicöme (4)\n mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui (5)\n mäcuïlli × ëyi = caxtölli (6)\n\n Arammba:\n\n ngámbi + ngámbi = ngámbi × yànparo (7)\n ngámbi + asàr = tambaroy (8)\n yànparo tàxwo + fete asàr tàxwo = yànparo fete (9)\n yenówe × yenówe tàxwo = fete yenówe tàxwo (10)\n nimbo × fete = tarumba (11)\n nimbo + yànparo tàxwo = yenówe tàxwo (12)\n\n Nahuatl: Arammba:\n yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno (13)\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba (14)\n cen-tzontli = tarumba tambaroy fete asàr (15)\n cen-xiquipilli = weremeke tarumba nimbo yànparo (16)\n\n(c) Write out in Arammba: 43; 569.\n !△ Classical Nahuatl, of the Uto–Aztecan family, was the language of the Aztec Empire in\n Mexico.\n The Arammba language (also called Serki, Serkisetavi, or Upper Morehead) belongs to\n the South-Central Papuan family. It is spoken by approx. 970 people in Papua New Guinea.\n —Milena Veneva\n\nTarget: solve (c) only.\n\nTarget question:\n(c) Write out in Arammba: 43; 569.\n\nSAMPLED ATTEMPT:\nWe are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a", + "approaches": [ + "Focus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.", + "Assume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.", + "The core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.", + "\nFocus on arithmetic structure in Arammba equations to derive numerical values. From (7): ngámbi + ngámbi = ngámbi × yànparo → 2ngámbi = ngámbi × yànparo → yànparo = 2. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → yenówe = fete. Thus, fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = tarumba. From (15): cen-tzontli = tarumba + tambaroy + fete + asàr. Assume cen-tzontli = 100. Then 100 = tarumba + tambaroy + fete + asàr. From (8): tambaroy = ngámbi + asàr. Substitute into equation: 100 = tarumba + (ngámbi + asàr) + fete + asàr = tarumba + ngámbi + fete + 2asàr. Use (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies fete + asàr = fete → asàr = 0, contradiction. Therefore, \"fete asàr\" must be a compound term, not additive. Re-evaluate: likely \"fete asàr\" is a single unit. But (9) suggests addition: left side is sum of two terms. So (2 + (fete + asàr)) = (2 + fete) → implies asàr = 0. Contradiction. Thus, the only consistent interpretation is that \"fete asàr\" is not additive. Instead, \"fete asàr\" is a single unit with value fete × asàr or fete + asàr. But no multiplication rule given. Hence, the equation (9) must be interpreted as: (yànparo + fete) + asàr = yànparo + fete → implies asàr = 0. Contradiction. So the system is inconsistent under standard interpretation. Therefore, the known values (yànparo=2, fete=9, nimbo=7) may be invalid. Alternative: yànparo = 1. From (7): 2ngámbi = ngámbi × 1 → only if ngámbi = 0. Invalid. Thus, only valid solution is yànparo = 2. Then (9) implies asàr = 0. But asàr appears in (8) and (15). Hence, contradiction. Conclusion: the system is inconsistent, and the assumption that the equations represent standard arithmetic is flawed. Thus, the representation of 43 and 569 in Arammba cannot be derived from the given equations due to internal inconsistency.\n\n\n\nAssume that the compound forms in Arammba represent addition or multiplication based on known Nahuatl equivalents. From (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. In Nahuatl, \"tzontli\" = 1, \"pöhualli\" = 20-day cycle, so \"tzontli-on\" likely means \"1 +\". \"caxtölli\" = 13? \"cë\" = 20? But no. In (4): mäcuïlli + öme = chicöme → 13 + 5 = 18. So \"cë\" may be 20. From (3): yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë → 20 + 18 + 1 = 39 → 20 + 20 = 40? Not clear. From (14): cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba. cen-tzontli = 100, cem = 20, mahtlactli = 1, öme = 5 → 100 + 20 + 1 + 5 = 126. yànparo tarumba = 2 × tarumba → 2 × tarumba = 126 → tarumba = 63. Then from (15): cen-tzontli = tarumba + tambaroy + fete + asàr → 100 = 63 + tambaroy + fete + asàr → sum = 37. From (8): tambaroy = ngámbi + asàr. So ngámbi + asàr + fete = 37. From (12): nimbo + yànparo = yenówe → nimbo + 2 = yenówe. From (10): yenówe × yenówe = fete × yenówe → fete = yenówe → fete = nimbo + 2. From (11): nimbo × fete = tarumba → nimbo × (nimbo + 2) = 63 → nimbo = 7 → fete = 9. Then from above: ngámbi + asàr + 9 = 37 → ngámbi + asàr = 28. From (8): ngámbi + asàr = tambaroy → tambaroy = 28. So ngámbi and asàr sum to 28. No unique values. Now, to write 43 in Arammba: 43 = 100 - 57 → but no 57. 43 = 63 - 20 → 63 is tarumba, 20 is cem. So if \"tarumba - cem\" exists, then 43 = tarumba - cem. But no subtraction rule. 43 = 2 × 21 + 1 → no 21. 43 = 7×6 + 1 → 6 not present. So no direct representation. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction. Conclusion: numbers like 43 and 569 cannot be directly derived in Arammba from given equations without defined operations.\n\n\n\nThe core of the problem is to find a consistent mapping from Nahuatl to Arammba numerical expressions. From (14) and (15), we derive values: cen-tzontli = 100, tarumba = 63, fete = 9, nimbo = 7, yànparo = 2. From (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete → (2 + fete + asàr) = 2 + fete → implies asàr = 0. Contradiction. Therefore, the only consistent interpretation is that \"fete asàr\" is a single unit, and the equation means: (2 + fete asàr) = (2 + fete), so fete asàr = fete → asàr = 1. Then from (8): tambaroy = ngámbi + 1. From (15): 100 = 63 + tambaroy + 9 + 1 = 73 + tambaroy → tambaroy = 27 → ngámbi = 26. Now, from (13): yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno. \"tzontli\" = 1, \"pöhualli\" = 20, \"caxtölli\" = 13, \"cë\" = 20 → so 1 + 20 + 13 + 20 = 54 → ndamno = 54. So 54 is represented as ndamno. Then 43 = 54 - 11 → no. 43 = 2×21 + 1 → no. 43 = 7×6 + 1 → no. 569 = 100×5 + 69 → 5×100 = 500, 69 = 63 + 6 → no. Thus, no known construction for 43 or 569. The system lacks a defined number system for arbitrary integers beyond known values. Therefore, the requested numbers cannot be expressed in Arammba using the provided equations.\n\n\n\nUse the derived values to build a" + ], + "anchor_output": "We are given a series of equations in Nahuatl and Arammba, and we are to determine how to write the numbers 43 and 569 in Arammba.\n\nWe must find a linguistic pattern (likely based on arithmetic operations, composition, or derivation rules) that maps Nahuatl numerical expressions to Arammba ones. Then use that pattern to derive 43 and 569 in Arammba.\n\n---\n\n### Step 1: Look for patterns in the given equations\n\n**Nahuatl equations:**\n\n(1) `mahtlactli-on-cë × mahtlactli = mäcuïl-pöhualli-om-mahtlactli` \n(2) `cem-pöhualli × öme = öm-pöhualli` \n(3) `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë` \n(4) `mäcuïlli + öme = chicöme` \n(5) `mahtlactli-om-ëyi × ëyi = cem-pöhualli-on-caxtölli-on-nähui` \n(6) `mäcuïlli × ëyi = caxtölli`\n\n**Arammba equations:**\n\n(7) `ngámbi + ngámbi = ngámbi × yànparo` \n(8) `ngámbi + asàr = tambaroy` \n(9) `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n(10) `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n(11) `nimbo × fete = tarumba` \n(12) `nimbo + yànparo tàxwo = yenówe tàxwo`\n\n(13) `yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno` \n(14) `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n(15) `cen-tzontli = tarumba tambaroy fete asàr` \n(16) `cen-xiquipilli = weremeke tarumba nimbo yànparo`\n\n---\n\nLet’s examine the structured forms.\n\nNote: \"cen-tzontli\" appears in (15) and (14), and in (16) \"cen-xiquipilli\" appears.\n\nWe observe that:\n\n- In (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba` \n But (15) says `cen-tzontli = tarumba tambaroy fete asàr`\n\nSo if `cen-tzontli` represents a number, and it equals `tarumba tambaroy fete asàr`, which are compound forms, then likely \"cen-tzontli\" is 1?\n\nBut (14) has `cen-tzontli-on-... = yànparo tarumba`, which suggests that `cen-tzontli` may be a \"unit\" or a base.\n\nWait — what is “cen”? In Nahuatl, “cen” often means “100” or “hundred”. That’s a known fact. Similarly, “mahtlactli” is “1” in some contexts.\n\nLet’s infer values.\n\n---\n\n### Step 2: Use known Nahuatl number structure\n\nIn Classical Nahuatl:\n\n- “mahtlactli” = 1\n- “cem” = 20\n- “mäcuïl” = 13\n- “öme” = 5\n- “ëyi” = 15? Or 10?\n- “pöhualli” = 20-day cycle\n- “tzontli” = 1? Or “cen-tzontli” = 100?\n\nLikely: “cen” = 100.\n\nSo “cen-tzontli” = 100.\n\nFrom (15): \n`cen-tzontli = tarumba tambaroy fete asàr`\n\nSo 100 = tarumba + tambaroy + fete + asàr?\n\nBut in (11): `nimbo × fete = tarumba` \n(8): `ngámbi + asàr = tambaroy` \n(7): `ngámbi + ngámbi = ngámbi × yànparo`\n\nLet’s find a base unit.\n\nFrom (7): `ngámbi + ngámbi = ngámbi × yànparo` \n→ 2ngámbi = ngámbi × yànparo \n→ if ngámbi ≠ 0, divide both sides: 2 = yànparo\n\n→ So yànparo = 2\n\nFrom (8): ngámbi + asàr = tambaroy \n→ tambaroy = ngámbi + asàr\n\nFrom (10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ Let x = yenówe \nThen x × x tàxwo = fete x tàxwo \nThis seems like multiplication with a suffix.\n\nLikely: \"tàxwo\" is a \"operator\", meaning \"additive to\", or \"added to\", like in a compound.\n\nIn many Papuan languages, \"tàxwo\" means \"plus\".\n\nSo (9): `yànparo tàxwo + fete asàr tàxwo = yànparo fete` \n→ (yànparo + fete asàr) = yànparo fete \n→ So (2 + fete asàr) = 2 fete?\n\nBut this doesn't quite work.\n\n(10): `yenówe × yenówe tàxwo = fete yenówe tàxwo` \n→ If we suppose \"×\" means \"multiplied\", and \"tàxwo\" means \"plus\", then:\n\nLet x = yenówe \nx × (x + ...) = fete × (x + ...) \n\nBut left side is x × (x + something), right side is fete × (x + something)\n\nSo if both have same multiplier, then x = fete\n\n→ So yenówe = fete\n\nSimilarly, from (11): nimbo × fete = tarumba \nSo nimbo × yenówe = tarumba\n\nFrom (12): nimbo + yànparo tàxwo = yenówe tàxwo \n→ nimbo + 2 = yenówe \nBut yenówe = fete\n\nSo fete = nimbo + 2\n\nNow from (11): nimbo × fete = tarumba\n\nFrom (15): cen-tzontli = tarumba tambaroy fete asàr\n\nWe assume cen-tzontli = 100\n\nSo 100 = tarumba + tambaroy + fete + asàr \nBut we don’t have individual units, only sum.\n\nWe need to determine what numbers are represented by each word.\n\nLet’s now try to determine the values:\n\nLet:\n- yànparo = 2 (from (7))\n- fete = yenówe\n- from (12): nimbo + 2 = fete → fete = nimbo + 2\n- from (11): nimbo × fete = tarumba\n\nSo tarumba = nimbo × (nimbo + 2)\n\nNow from (15): 100 = tarumba + tambaroy + fete + asàr\n\nAlso (8): tambaroy = ngámbi + asàr\n\nWe don’t have ngámbi yet.\n\nBut from (7): 2ngámbi = ngámbi × 2 → always true.\n\nWe need another equation.\n\nNow (14): `cen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba`\n\ncen-tzontli = 100\n\nSo: 100 + cem-pöhualli + mahtlactli + öme = yànparo tarumba\n\nWe need values of those.\n\nAssume:\n- mahtlactli = 1\n- öme = 5\n- cem-pöhualli = 20? (since “cem” = 20)\n- yànparo = 2\n\nSo left side: 100 + 20 + 1 + 5 = 126\n\nRight side: yànparo tarumba = 2 × tarumba\n\nSo 2 × tarumba = 126 → tarumba = 63\n\nNow from earlier:\ntarumba = nimbo × fete\nfete = nimbo + 2\n\nSo: nimbo × (nimbo + 2) = 63\n\nTry small integers:\n\nn = 7 → 7×9 = 63 → yes!\n\nSo nimbo = 7 \nfete = 9 \ntarumba = 63\n\nCheck (15): 100 = tarumba + tambaroy + fete + asàr \n→ 100 = 63 + tambaroy + 9 + asàr \n→ tambaroy + asàr = 28\n\nNow (8): tambaroy = ngámbi + asàr \nSo ngámbi + asàr + asàr = 28 → ngámbi + 2 asàr = 28\n\nWe have: \ntambaroy = ngámbi + asàr \n→ so (ngámbi + asàr) + asàr = 28 → ngámbi + 2asàr = 28\n\nSo two equations:\n1. ngámbi + asàr = tambaroy\n2. ngámbi + 2asàr = 28\n\nSubtract: (ngámbi + 2asàr) - (ngámbi + asàr) = 28 - tambaroy \n→ asàr = 28 - tambaroy\n\nPlug into (1): ngámbi + (28 - tambaroy) = tambaroy → ngámbi = 2 tambaroy - 28\n\nNo unique solution? But we need to assign values.\n\nPossible values: try asàr = 4 → then ngámbi = 28 - 8 = 20? Wait:\n\nFrom asàr = 28 - tambaroy → tambaroy = 28 - asàr\n\nThen ngámbi = tambaroy - asàr = (28 - asàr) - asàr = 28 - 2asàr\n\nSo ngámbi = 28 - 2asàr\n\nAll values must be positive integers.\n\nTry asàr = 4 → ngámbi = 20 → tambaroy = 24 \nasàr = 6 → ngámbi = 16 → tambaroy = 22 \nasàr = 7 → ngámbi = 14 → tambaroy = 21 \nasàr = 14 → ngámbi = 0 → invalid\n\nIs there a unique assignment?\n\nPossibly not — but in the equations, we may not need exact values. Perhaps we just need to know that:\n\n- 1 = mahtlactli \n- 2 = yànparo \n- 5 = öme \n- 20 = cem \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow look at equation (13): \n`yë-tzontli-on-näuh-pöhualli-on-caxtölli-on-cë = ndamno`\n\nWe seek a number in Arammba.\n\nBut we are to write 43 and 569 in Arammba.\n\nCan we find how to represent numbers?\n\nWe have:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 63 = tarumba \n- 100 = cen-tzontli\n\nNow, 43?\n\n43 = 63 - 20 → which is tarumba - cem\n\nBut how to express?\n\nNote: from (3): `yë-pöhualli-on-chicöme + mahtlactli-on-nähui = näuh-pöhualli-on-cë`\n\nFrom (4): `mäcuïlli + öme = chicöme`\n\nWe have `öme = 5`, so if mäcuïlli is 13 (standard), then 13 + 5 = 18 → chicöme = 18\n\nThen (3): yë-pöhualli-on-chicöme → yë-pöhualli-on-18\n\nAdd mahtlactli-on-nähui = 1-on-nähui\n\nSum = näuh-pöhualli-on-cë\n\nThis suggests that some numbers are composed.\n\nBut more importantly, from (14) we have:\n\ncen-tzontli-on-cem-pöhualli-om-mahtlactli-om-öme = yànparo tarumba\n\n→ 100 + 20 + 1 + 5 = 126 \n→ 2 × 63 = 126 → matches.\n\nBut 43?\n\nWe know that 43 = 40 + 3 → if we can express 40 and 3.\n\nDo we have a base?\n\nWe have yànparo = 2, nimbo = 7, fete = 9, tarumba = 63.\n\nSo 43 = 63 - 20 → but we lack \"20\".\n\nIs \"cem\" = 20 available?\n\nIn Nahuatl, cem = 20.\n\nIs this preserved?\n\nFrom (2): cem-pöhualli × öme = öm-pöhualli \nIf öme = 5 → 20×5 = 100 → öm-pöhualli\n\nSo 100 → so öm-pöhualli = 100?\n\nBut öm is 100? Or 5?\n\nActually, in (2): cem-pöhualli × öme = öm-pöhualli\n\nIf cem = 20, öme = 5 → 100 → so öm-pöhualli = 100 → implies öm = 100?\n\nBut earlier we have cen-tzontli = 100.\n\nSo possibly öm = cen = 100?\n\nWait — inconsistency?\n\nNo, likely \"cem\" = 20, \"öme\" = 5.\n\nThen 20×5 = 100.\n\nSo 100 is the product.\n\nBut in the addition (14): no product.\n\nNow back — to find 43.\n\nWe can try to see if 43 can be built from known units.\n\nNote: 43 = 2 × 21 + 1 → but no 21.\n\n43 = 7×6 + 1 → 7×6 = 42\n\nBut we don’t have 6.\n\nWe have yànparo = 2, nimbo = 7, fete = 9.\n\nSo 7×6 = 42 → perhaps 6 is expressible?\n\nWe don’t have 6.\n\nAlternatively, from (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nThat is: (2 + fete asàr) = 2 fete → 2 + fete asàr = 2 fete\n\nSo fete asàr = 2 fete - 2 → fete asàr = 2(fete - 1)\n\nBut fete = 9 → fete asàr = 16 → asàr = 16 / 9 → not integer.\n\nInconsistent?\n\nWait — “fete asàr” may be a compound meaning “fete + asàr”\n\nIn (9): yànparo tàxwo + fete asàr tàxwo = yànparo fete\n\nSo: (2 + (fete + asàr)) = (2 + fete) → no.\n\n\"tàxwo\" might mean \"and\" or \"plus\" — so:\n\nLeft: 2 + (fete asàr) \nRight: 2 fete\n\nSo 2 + (fete + asàr) = 2 fete → fete + asàr = 2 fete - 2 → asàr = fete - 2\n\nWith fete = 9 → asàr = 7\n\nEarlier from (15), tambaroy + asàr = 28\n\nSo tambaroy = 28 - 7 = 21\n\nAnd from (8): tambaroy = ngámbi + asàr → ngámbi + 7 = 21 → ngámbi = 14\n\nSo now:\n\n- ngámbi = 14 \n- asàr = 7 \n- tambaroy = 21 \n- fete = 9 \n- nimbo = 7 \n- yànparo = 2 \n- tarumba = 63 \n- cen-tzontli = 100\n\nPattern: \n- ngámbi = 14 \n- asàr = 7 \n- fete = 9 \n- nimbo = 7 \n→ seems asàr and nimbo both = 7\n\nNow, what is the value of each?\n\nWe know:\n- 2 = yànparo \n- 7 = nimbo \n- 9 = fete \n- 14 = ngámbi \n- 21 = tambaroy \n- 63 = tarumba \n- 100 = cen-tzontli\n\nObserve: \n- 2 = 2 \n- 7" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "planner_index": 11, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 11.: answer for this requested item\n- a.2 / 12.: answer for this requested item\n- a.3 / 13.: answer for this requested item\n- a.4 / 14.: answer for this requested item\n- a.5 / 15.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 11. magasi argi ajomirra.\n\n 12. ay kanarriːg baːbki alletirsi.\n\n 13. hanu tirtiːg elirsu.\n\n 14. tirti argi kamgi deːccirsa.\n\n 15. ay darbadki bijaːndi.\n\nSAMPLED ATTEMPT:\nStep 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tir\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey", + "approaches": [ + "Focus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.", + "Re-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.", + "Re-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.", + "\nFocus on verb morphology and syntactic pattern alignment. Identify that verbs in Kunuz Nubian are often followed by a noun object and then a recipient marked by a suffix. The verb \"argi\" appears in sentences 11 and 14. In sentence 14, \"tirti argi kamgi deːccirsa\", \"tirti\" is a repair verb, which does not logically take \"argi\" (to give) as a separate verb. This inconsistency suggests that \"argi\" is not a standalone verb in these contexts. Instead, \"argi\" likely serves as a prepositional or directional marker, possibly meaning \"to give\" or \"to deliver\", but only when paired with an object. In sentence 11, if \"ajomirra\" means \"to the donkey\", then \"magasi argi ajomirra\" must have an object. Since no object is listed, the only plausible interpretation is that \"ajomirra\" is the object (the donkey), and \"argi\" is a verb meaning \"give\". Thus, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — but this is odd semantically. However, if \"argi\" is a verb, and \"ajomirra\" is the object, then the recipient is missing. This structural gap suggests a misreading of word order or morpheme boundaries. Verification: in example 3, \"darbadki biticcirra\" = \"give the chicken\" — verb + object. In sentence 11, if \"argi\" is verb and \"ajomirra\" is object, then \"magasi\" (subject) + \"argi\" (verb) + \"ajomirra\" (object) = \"The thief gives the donkey\" — acceptable only if \"gives the donkey\" is a valid action. But in example 9, \"hanuːg bijomri\" = \"strike the donkey\" — so \"bijomri\" is object. Thus, \"ajomirra\" likely means \"the donkey\", not \"to the donkey\". Therefore, \"magasi argi ajomirra\" = \"The thief gives the donkey\" — implies giving something to it, but no donor is specified. This is grammatically incomplete. However, if \"argi\" is not a verb but a preposition, the sentence is malformed. Thus, this path leads to inconsistency in verb structure. Reject.\n\n\n\nRe-evaluate the core syntactic pattern by isolating verb-object-recipient constructions. From examples, the pattern is consistently [subject] [verb] [object] [recipient], with recipient marked by suffixes like -ki (to) or -su (for). In example 3: \"jahali waliːg darbadki biticcirra\" → \"give the chicken to the dogs\" → verb + object + recipient. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + recipient. In example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient. Thus, the structure is verb + object + recipient. Now analyze sentence 11: \"magasi argi ajomirra\". If \"argi\" is the verb (give), then \"ajomirra\" must be the recipient. But \"ajomirra\" resembles \"bijomri\" (donkey) — the noun. Thus, \"ajomirra\" = \"to the donkey\" (recipient). But there is no object. This violates the pattern. Similarly, in sentence 14: \"tirti argi kamgi deːccirsa\" — \"tirti\" is repair, not give. So \"argi\" cannot be a verb here. Thus, \"argi\" cannot be a verb in both contexts. Therefore, \"argi\" must be a prepositional phrase, and the verb must be elsewhere. But no verb is present. Alternative: \"argi\" is a verb root, and \"kamgi\" is object, \"deːccirsa\" is recipient. Then \"tirti\" is not a verb — it is a noun or adjective? In example 2, \"tirt\" = repaired. So \"tirti\" = repaired. So \"tirti argi kamgi deːccirsa\" is not a verb-object-recipient structure. Therefore, the pattern is not uniformly applied. This suggests the verb is not always directly expressed. Instead, the verb may be embedded or morphologically fused. In sentence 14, if \"argi\" is the verb, then \"tirti\" is a noun (e.g., \"the repair\") and \"kamgi\" is object, \"deːccirsa\" is recipient. \"Tirti\" may be a noun meaning \"repair\", and \"argi\" is \"give\". Then \"give the repair to the thief\"? Unlikely. So this path fails to maintain consistency. Reject.\n\n\n\nRe-analyze word correspondences using known noun forms. In example 9: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = the donkey. In example 13: \"hanu tirtiːg elirsu\" → \"hanu\" = strike, \"tirtiːg\" = future of repair? \"tirti\" = repair, \"tirtiːg\" = will repair. \"elirsu\" = for me? \"eldeːnsu\" = for me → so \"elirsu\" likely = for me. Thus, \"hanu tirtiːg elirsu\" = \"I will strike the repair for me\"? Nonsensical. Alternatively, \"hanu\" = strike, \"tirtiːg\" = the repair (noun)? Then \"I will strike the repair for me\"? Still odd. But if \"tirtiːg\" is an object, and \"elirsu\" is recipient, then \"I will strike the repair to me\"? That makes sense — \"to me\" as recipient. But \"strike the repair\" is not idiomatic. However, \"hanu\" as verb, \"tirtiːg\" as object (the repair), \"elirsu\" as recipient (to me) → \"I will strike the repair to me\" — acceptable as a literal translation. Therefore, the pattern is: [subject] [verb] [object] [recipient]. Now apply to 11: \"magasi argi ajomirra\". \"magasi\" = thief (subject), \"argi\" = verb (give), \"ajomirra\" = object (the donkey)? But \"ajomirra\" = to the donkey. If \"ajomirra\" is the object, then \"to the donkey\" is redundant. But in example 9, \"bijomri\" = the donkey. So \"ajomirra\" = the donkey. Then \"magasi argi ajomirra\" = \"The thief gives the donkey\" — which means \"gives the donkey to someone\", but recipient missing. Unless \"argi\" is not \"give\". But in example 3, \"darbadki\" = give. So \"argi\" is likely \"give\". Thus, the sentence is grammatically incomplete. However, if \"argi\" is a preposition meaning \"to\", and \"ajomirra\" is the object, then \"magasi argi ajomirra\" = \"The thief to the donkey\" — nonsensical. Therefore, the only viable interpretation is that \"argi\" is the verb \"give\", and \"ajomirra\" is the object (the donkey), and the recipient is missing. This violates the pattern seen in other examples. Hence, this path is inconsistent and fails verification. Reject.\n\n\n\nEstablish a consistent verb-recipient pattern using suffix analysis. Identify that recipient markers are always suffixes: -ki (to), -su (for), -g, -si. In example 2: \"tirt kadeːg allesu\" → \"repaired the dress\" — no recipient? But \"allesu\" = repair, not a recipient. In example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → \"eldeːnsu\" = for me. In example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"stole the dresses for the young man\" → \"maːgtirsu\" = for the young man. In example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → \"magaski\" = to the thief. So recipient suffixes are: -ki (to), -su (for). Now examine sentence 11: \"magasi argi ajomirra\". \"magasi\" = subject (thief). \"argi\" = verb? \"ajomirra\" = noun or recipient? Compare with \"bijomri\" = donkey → \"ajomirra\" = to the donkey → recipient. So \"ajomirra\" = to the donkey" + ], + "anchor_output": "Step 1: Identify core verb structures and their meanings from the examples.\n\nExample 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"kanarriːcciːg\" = bought (past tense of \"buy\") \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours \n→ Structure: [subject] [verb] [object] [purpose/preposition phrase]\n\nExample 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = repaired (verb) \n- \"kadeːg\" = the dress \n- \"allesu\" = (to) repair \n→ Simple: [subject] [verb] [object]\n\nExample 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"waliːg\" = young men (subject) \n- \"darbadki\" = give (verb) \n- \"biticcirra\" = the chicken (object) \n- \"to the dogs\" = added to meaning \n→ \"give X to Y\" = [subject] [verb] [object] [recipient]\n\nExample 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole (past of steal) \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man \n→ \"stole X for Y\"\n\nExample 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present progressive) \n- \"ajaːnirri\" = the necklaces \n→ \"I am buying X\"\n\nExample 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n- \"wal\" = dog \n- \"aygi\" = found \n- \"baːbiːg\" = the doors \n- \"eldeːnsu\" = for me \n→ \"found X for Y\"\n\nExample 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs.\" \n- \"magas\" = thief \n- \"ikki\" = you (pl.) \n- \"ticcirsu\" = gave \n→ \"gave X to Y\"\n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n- \"iːdi\" = the men \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \n- \"tirsa\" = gave \n→ \"gave X to Y\"\n\nExample 9: \"ay hanuːg bijomri\" → \"I will strike the donkey.\" \n- \"ay\" = I \n- \"hanuːg\" = will strike (future) \n- \"bijomri\" = the donkey \n→ \"will strike X\"\n\nExample 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present progressive) \n- \"beyyeːcciːg\" = the necklaces \n- \"adeːnda\" = to me \n→ \"are giving X to Y\"\n\nPattern: \n- The verb can be in various tenses: present, past, future \n- The object is expressed directly \n- A recipient/recipient-like phrase (e.g., \"for the neighbour\", \"to me\") is marked by a reflexive or prepositional construction, often with a specific suffix or word. \n- \"for\" and \"to\" constructions use suffixes such as -su, -g, or -si, often attached to the verb or adjunct.\n\nLook for verb + object + recipient pattern.\n\nNow analyze each sentence:\n\n11. magasi argi ajomirra \n- \"magasi\" = likely thief (like \"magas\" in example 7) \n- \"argi\" = similar to \"darbadki\" or \"kanarriːg\"; possibly \"give\" \n- \"ajomirra\" = likely \"to the donkey\" or \"to the dog\"? \n\"ajomirra\" → compare with \"bijomri\" (donkey) → \"ajomirra\" = \"to the donkey\"? \nBut note: \"hanuːg bijomri\" = \"I will strike the donkey\" → \"bijomri\" = donkey \nSo \"ajomirra\" likely = \"to the donkey\" (with -irra = to the + noun)\n\nThus: \"magasi argi ajomirra\" → \"The thief gives to the donkey\" \nBut \"gives to\" who? The recipient is \"the donkey\"? \nBut \"give to the donkey\" implies giving something to a donkey. \nIn example 3: \"give the chicken to the dogs\" → so yes, \"give X to Y\" \nHere, no object? \"argi\" = give, \"ajomirra\" = to the donkey \nBut \"what is given?\" → missing object?\n\nWait: perhaps \"argi\" is \"to give\", and object is implied? Or is there a missing element?\n\nCompare to example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" \n- \"magaski\" = to the thief \n- \"kamiːg\" = the camels \nVerb: \"tirsa\" = gave \n\nIn sentence 11: \"magasi argi ajomirra\" \n\"magasi\" = thief? \n\"argi\" = give? \n\"ajomirra\" = to the donkey? \nBut no object of giving? That is problematic.\n\nBut in example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"bijomri\" = the donkey \nSo \"bijomri\" = the donkey \nIn example 3: \"biticcirra\" = the chicken → object \nSo \"ajomirra\" = the donkey? \nThus, \"magasi argi ajomirra\" → could be \"The thief gives the donkey\"?\n\nBut \"gives the donkey\" → of what? Not clear.\n\nAlternatively, can \"argi\" be a verb meaning \"to give\" and \"ajomirra\" be the object?\n\nBut \"ajomirra\" = \"the donkey\" → so \"gives the donkey\"?\n\nIn example 8: \"gave the camels to the thief\" → object is the camels, recipient is thief.\n\nSo structure: [subject] [verb] [object] [recipient] \nBut here, only \"to the donkey\", no object.\n\nUnless \"the donkey\" is the object.\n\nTry: \"The thief gives the donkey\" — but what is \"gave\" to? That would be odd. Giving the donkey implies giving something to it.\n\nSimilarly, \"he stole the dresses for the young man\" → object: dresses, recipient: young man.\n\nSo in 11: \"magasi argi ajomirra\" — \"argi\" = give? → \"gives (something) to the donkey\"\n\nBut what is the something? Missing.\n\nWait — look at example 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces\" → verb + object\n\nSo object comes after verb.\n\nIn example 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"are giving me the necklaces\" → verb + object + recipient\n\nSo verb + object + recipient → common pattern.\n\nIn 11: \"magasi argi ajomirra\" \n\"magasi\" = subject (the thief) \n\"argi\" = verb (give) \n\"ajomirra\" = \"to the donkey\" → likely recipient\n\nBut object missing.\n\nAnother possibility: \"argi\" = \"to give to\", combined with a noun?\n\nCompare to example 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\" → verb + object + for recipient\n\n\"argi\" may be a verb, like \"give\", and \"ajomirra\" = to the donkey?\n\nMissing object.\n\nLook at example 3: \"jahali waliːg darbadki biticcirra\" → \"will give the chicken to the dogs\" → subject + verb + object + recipient\n\nIn 11: \"magasi argi ajomirra\" — still missing object.\n\nWait: could \"argi\" mean \"to give\" and the object be the donkey? So \"gives the donkey\" → gives the donkey to whom? \n\nNo — unusual.\n\nAlternatively, could \"ajomirra\" be \"the donkey\" as object, and \"argi\" be \"to give\"?\n\nNo — \"argi\" is not clearly a preposition.\n\nAnother idea: look at suffixes.\n\nIn example 3: \"darbadki biticcirra\" → \"give the chicken\" → \"darbadki\" = give, \"biticcirra\" = object\n\nIn example 9: \"hanuːg bijomri\" → \"strike the donkey\" → \"hanuːg\" = strike, \"bijomri\" = object\n\nSo the object comes after the verb.\n\nIn example 6: \"wal aygi baːbiːg eldeːnsu\" → \"found the doors for me\" → verb + object + for + recipient\n\n\"eldeːnsu\" = for me\n\nIn example 8: \"iːdi magaski kamiːg tirsa\" → \"gave the camels to the thief\" → verb + object + to recipient\n\nSo the recipient is marked by a suffix like -ki, -su, etc.\n\nLook at:\n\n- \"maːgtirsu\" → for the young man → \"su\" at end → for \n- \"eldeːnsu\" → for me → \"su\"\n- \"tirsa\" → gave → verb root\n- \"magaski\" → to the thief → \"ki\"\n\nSo suffix patterns:\n- -su: for/for me\n- -ki: to (someone)\n\nThus:\n- \"argi ajomirra\" → \"argi\" is verb, \"ajomirra\" is probably the recipient: \"to the donkey\" → \"ajomirra\" → \"ajomir\" + \"ra\"? → compare to \"bijomri\" = to the donkey?\n\nIn example 9: \"hanuːg bijomri\" = I will strike the donkey → \"bijomri\" = the donkey\n\nSo \"ajomirra\" = to the donkey → likely \"to the donkey\"\n\nBut again, no object.\n\nUnless \"argi\" is \"to give\", and \"ajomirra\" is the recipient.\n\nBut object is missing.\n\nLook at sentence 14: \"tirti argi kamgi deːccirsa\" \n\"tirti\" = repaired (like \"tirt\") → verb \n\"argi\" = give? \n\"kamgi\" = the camels (object) \n\"deːccirsa\" = to the thief? → \"deːccirsa\" → compare to \"kamiːg\" = the camels, \"deːccirsu\" = to the thief? \n\nExample 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\" = \"magaski\"\n\nSo \"deːccirsa\" → likely \"to the thief\" → with suffix -sa\n\nSimilarly, \"deːccirsu\" = for the thief? → not clearly.\n\nBut in 14: \"tirti argi kamgi deːccirsa\" → \"repaired the camels to the thief\"? No — \"repaired\" doesn't take to recipient.\n\n\"tirti\" = repaired — verb, \"kamgi\" = object? → \"repaired the camels\" → object.\n\nThen \"deːccirsa\" = to the thief → recipient.\n\nBut why is \"argi\" present? That would be \"give\", not \"repair\".\n\nContradiction.\n\nSo likely \"argi\" is not \"give\" in this context.\n\nWait — in sentence 11: \"magasi argi ajomirra\"\n\n\"magasi\" = thief \n\"argi\" = verb? \n\"ajomirra\" = to the donkey?\n\nBut what if \"argi\" = \"to give\", and \"ajomirra\" = the donkey as object?\n\nBut \"ajomirra\" contains \"bijomri\" = donkey → so likely \"the donkey\"\n\nSo perhaps \"magasi argi ajomirra\" = \"The thief gives the donkey\" → but gives what?\n\nUnless it's \"gives the donkey to someone\" — but no one.\n\nWait — sentence 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike (like \"hanuːg\") \n\"tirtiːg\" = repaired? \"tirti\" = repaired → \"tirtiːg\" = repaired \n\"elirsu\" = to me? \"elirsu\" = for me? \"eldeːnsu\" = for me\n\n\"elirsu\" → possibly \"for me\"\n\nSo \"hanu tirtiːg elirsu\" → \"I will strike the repaired\" → no.\n\n\"hanu\" = strike \n\"tirtiːg\" = future tense of repair? \n\"tirti\" = repair → \"tirtiːg\" = will repair?\n\nIn example 9: \"ay hanuːg bijomri\" → \"I will strike the donkey\" → \"hanuːg\" = will strike\n\nSo \"hanu tirtiːg\" → \"hanu\" = strike, \"tirtiːg\" = will repair? → that’s two verbs?\n\nNo — likely \"hanu\" is the verb, \"tirtiːg\" is a form?\n\nCompare with example 13: \"hanu tirtiːg elirsu\"\n\n\"hanu\" = strike verb \n\"tirtiːg\" → could be a verb form — perhaps \"will strike\" or \"repair\"?\n\nBut \"tirt\" = repair → \"tirtiːg\" = will repair?\n\nBut \"hanu\" is not repair.\n\nUnless it's a compound?\n\nNote: \"hanu\" and \"tirt\" are both verbs.\n\nIn example 9: \"ay hanuːg bijomri\" — \"I will strike the donkey\"\n\nSo \"hanuːg\" = future of strike\n\nIn 13: \"hanu tirtiːg elirsu\" → if \"tirtiːg\" = future of repair, and \"hanu\" = strike, no.\n\nBut \"hanu\" may be the verb, and \"tirtiːg\" = object? \"tirti\" = repair → \"repair\" not \"donkey\"\n\n\"elirsu\" = to me\n\nSo \"hanu tirtiːg elirsu\" → \"strike the repair to me\"? no.\n\nAlternative: \"hanu\" = strike, \"tirtiːg\" = \"the door\" or \"the repaired thing\" — but no.\n\nBack to 11.\n\nWhat if \"argi\" is not the verb? Could it be a modifier?\n\nLook at sentence 15: \"ay darbadki bijaːndi\" \n\"ay\" = I \n\"darbadki\" = give \n\"bijaːndi\" = the chicken? → \"bijaːndi\" → compare to \"biticcirra\" = chicken\n\nIn example 3: \"darbadki biticcirra\" = give the chicken\n\nSo in 15: \"ay darbadki bijaːndi\" = \"I will give the chicken\"\n\n\"bijaːndi\" = the chicken\n\nSo \"darbadki\" = give, \"bijaːndi\" = object\n\nSimilarly, in sentence 11: \"magasi argi ajomirra\"\n\n\"argi\" = give? \n\"ajomirra\" = ? → if \"ajomirra\" = the donkey, then \"gives the donkey\"\n\nBut in 15, \"bijaːndi\" = the chicken → object\n\nSo \"argi\" = give, \"ajomirra\" = the donkey → \"the thief gives the donkey\"\n\nBut to whom? Not specified.\n\nUnless \"ajomirra\" is a recipient.\n\nIn example 9: \"hanuːg bijomri\" = strike the donkey → \"bijomri\" = the donkey\n\nIn example 3: \"darbadki biticcirra\" = give the chicken → \"biticcirra\" = the chicken\n\nIn example 4: \"kadeːcciːg maːgtirsu\" = the dresses for the young man → object + for recipient\n\nSo in 11, if \"ajomirra\" is \"to the donkey\", then it's a recipient.\n\nBut no object.\n\nUnless \"argi\" includes object? Unlikely.\n\nPerhaps \"magasi\" is not subject.\n\nWhat if \"magasi\" = a noun, and \"argi\" is verb?\n\nCompare to example 7: \"magas ikki waliːg ticcirsu\" → \"the thief gave you the dogs\" \nSo \"magas\" = thief, \"ikki\" = you, \"ticcirsu\" = gave\n\nSo \"magasi\" = thief (likely same as \"magas\")\n\n\"argi\" = give (as in \"darbadki\")\n\n\"ajomirra\" = to the donkey?\n\nBut give what? No object.\n\nUnless the object is missing or implied.\n\nBut in all other cases, there is a clear object after the verb.\n\nLook at sentence 12: \"ay kanarriːg baːbki alletirsi\"\n\n\"ay\" = I \n\"kanarriːg\" = bought (from example 1" + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "planner_index": 12, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 16.: answer for this requested item\n- b.2 / 17.: answer for this requested item\n- b.3 / 18.: answer for this requested item\n- b.4 / 19.: answer for this requested item\n- b.5 / 20.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in Kunuz Nubian and their English\ntranslations:\n\n 1. ar kanarriːcciːg kamiːg jaːnticcirsu.\n We bought the camels for the neighbours.\n 2. tirt kadeːg allesu.\n The owner repaired the dress.\n 3. jahali waliːg darbadki biticcirra.\n The young men will give the chicken to the dogs.\n 4. man jahalgi kadeːcciːg maːgtirsu.\n He stole the dresses for the young man.\n 5. ay beyyeːcciːg ajaːnirri.\n I am buying the necklaces.\n 6. wal aygi baːbiːg eldeːnsu.\n The dog found the doors for me.\n 7. magas ikki waliːg ticcirsu.\n The thief gave you (pl.) the dogs.\n 8. iːdi magaski kamiːg tirsa.\n The men gave the camels to the thief.\n 9. ay hanuːg bijomri.\n I will strike the donkey.\n 10. sarkaːyi aygi beyyeːcciːg adeːnda.\n The cowards are giving me the necklaces.\n\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\n!△ Kunuz Nubian belongs to the Eastern Sudanic family. It is spoken by approx. 50,000\npeople in Egypt.\n y = y in yum. The mark ː indicates that the preceding vowel is long.\n —Aleksejs Peguševs\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kunuz Nubian:\n\n 16. The neighbours are giving the necklace to the owner.\n\n 17. The young man bought the dog for us.\n\n 18. We will steal him.\n\n 19. The owners struck the thieves.\n\n 20. The dogs found the chickens for the coward.\n\nSAMPLED ATTEMPT:\nStep 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\"\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express", + "approaches": [ + "Focus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".", + "Assume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.", + "Shift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.", + "\nFocus on verb morphology and object alignment. Identify that \"give\" and \"buy\" share a root verb form (e.g., beyyeːcciːg, darbadki, magaski) with consistent object and prepositional structure. In sentence 10, \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"the cowards are giving me the necklaces\", the verb \"beyyeːcciːg\" is used with a direct object (\"necklaces\") and a prepositional phrase (\"adeːnda\" = for me). Similarly, in sentence 1, \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\", the prepositional phrase \"jaːnticcirsu\" = for the neighbours. This indicates that the prepositional form is attached to the end, and the noun (e.g., \"neighbours\", \"owner\") is either the subject or implied in the preposition. For translation 16: \"The neighbours are giving the necklace to the owner\" → subject = neighbours (unknown noun), verb = present tense \"are giving\" → \"aygi\" (from sentence 10), object = \"necklace\" → \"ajaːnirri\", preposition \"to the owner\" → \"eldeːnsu\" (from sentence 6: \"for me\" = eldeːnsu). But \"eldeːnsu\" is \"for me\", not \"to the owner\". However, in sentence 8: \"iːdi magaski kamiːg tirsa\" → \"to the thief\", so \"tirsa\" = to. Therefore, \"to the owner\" → \"tirsa\" with \"tirt\" = owner. But \"tirsa\" is used for \"to the thief\", so it might be general. Verify: in sentence 6, \"baːbiːg eldeːnsu\" → \"doors for me\", so \"eldeːnsu\" = for me. \"tirsa\" = to the thief. So \"to\" and \"for\" are distinct. Thus, \"to the owner\" requires a form like \"tirsa\", with \"tirt\" as the owner. But \"tirsa\" is used with \"the thief\", not \"the owner\". Is there a form for \"to the owner\"? Not given. However, in sentence 1, \"jaːnticcirsu\" = for the neighbours. So \"to\" might be a different structure. But sentence 3: \"biticcirra\" = to the dogs. So \"biticcirra\" = to the dogs → likely \"to\" is marked by \"biticcirra\" or \"tirsa\". \"tirsa\" = to the thief → so \"tirsa\" = to. So \"to the owner\" → \"tirsa\" with \"tirt\". But \"tirt\" is the owner, so \"tirsa\" must be used. But in sentence 1, \"jaːnticcirsu\" is used for \"for neighbours\", not \"to\". So \"to\" is marked by \"tirsa\" or \"biticcirra\". In 3: \"to the dogs\" → biticcirra; in 8: \"to the thief\" → tirsa. So \"to\" is marked by different forms depending on the recipient. Therefore, \"to the owner\" → use \"tirsa\" (to the thief) → likely generalized. So structure: [subject] [verb] [object] [to X]. Subject: \"the neighbours\" → not directly given. But in sentence 1, \"jaːnticcirsu\" = for the neighbours → so perhaps the noun form is missing. However, no noun for \"neighbours\" appears. The only candidate is \"jaːnticcirsu\" as a noun? But it's a preposition. So conclusion: there is no standalone noun for \"neighbours\"; thus, the structure may use a prepositional phrase to indicate the group. But that would not work for subject. So likely, the subject is \"jaːnticcirsu\" as in \"the neighbours\" — but it's used in \"for\" context. Thus, this route fails due to lack of subject noun. \nVerification: In no sentence is \"the neighbours\" used as a subject noun. All use of \"neighbours\" is in the prepositional phrase \"for the neighbours\". So no direct noun form. Therefore, translation 16 cannot be formed without assuming a missing noun. \n→ Failure mode: missing subject noun for \"neighbours\".\n\n\n\nAssume that all prepositional phrases are formed with a consistent suffix and that the verb \"give\" is marked by \"magaski\" or \"aygi\" with tense and direct object. The tense for present is \"aygi\" (as in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\"). So \"are giving\" → \"aygi\". The direct object is \"necklace\" → from sentence 5: \"ajaːnirri\" = necklaces. So \"the necklace\" → \"ajaːnirri\". The recipient is \"the owner\" → \"tirt\" = the owner. The preposition \"to\" is marked by \"tirsa\" (sentence 8: \"to the thief\"), so \"to the owner\" → \"tirsa\". But does \"tirsa\" require \"tirt\" to be specified? In sentence 8, \"tirsa\" is directly after \"magaski\" → \"gave to the thief\". So \"to the owner\" → \"tirsa\" with \"tirt\" as the object. But in sentence 1, \"jaːnticcirsu\" is used for \"for the neighbours\", not \"to\". So \"to\" is distinct. Therefore, \"to the owner\" = \"tirsa\". Subject: \"the neighbours\" → not directly present. But from sentence 1: \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So is \"jaːnticcirsu\" the noun? It appears to be a prepositional phrase. But in sentence 1, it is the final part. So \"the neighbours\" is not a standalone noun. Therefore, subject must be formed differently. No other noun matches. Thus, the subject is missing. \nVerification: In all given sentences, \"neighbours\" only appears in \"for the neighbours\" → \"jaːnticcirsu\". No standalone noun. So cannot form \"the neighbours\" as subject. \n→ Failure mode: no lexical form for \"neighbours\" as subject.\n\n\n\nShift focus to verb agreement and syntactic symmetry. In sentence 3: \"jahali waliːg darbadki biticcirra\" → \"the young men will give the chicken to the dogs\" → verb \"darbadki\" = give, future tense \"waliːg\", object \"chicken\", prepositional phrase \"biticcirra\" = to the dogs. In sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → present tense \"aygi\", object \"necklaces\", \"adeːnda\" = for me. In sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"the dog found the doors for me\" → \"eldeːnsu\" = for me. So \"for\" = eldeːnsu, \"to\" = biticcirra or tirsa. For 16: \"The neighbours are giving the necklace to the owner\" → subject = \"neighbours\" → unknown, verb = \"are giving\" → \"aygi\" (present), object = \"necklace\" → \"ajaːnirri\", recipient = \"the owner\" → \"tirt\", and \"to\" → \"tirsa\". So full structure: [neighbours] [aygi] [ajaːnirri] [tirsa] with \"tirt\" as object. But where is \"neighbours\" as subject? No noun form. However, in sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"we bought the camels for the neighbours\" → \"jaːnticcirsu\" = for the neighbours. So perhaps \"jaːnticcirsu\" is a noun form. But it is used as a preposition. If we assume that \"jaːnticcirsu\" can function as a noun meaning \"the neighbours\", then subject = \"jaːnticcirsu\". But in context, it's used with \"for\", not as subject. In sentence 8: \"iːdi magaski kamiːg tirsa\" → \"the men gave the camels to the thief\" → \"tirsa\" = to. So \"to\" is distinct. So \"to the owner\" → \"tirsa\" with \"tirt\". But no subject noun. So this is invalid. \nVerification: No sentence has \"the neighbours\" as subject. The phrase only appears in prepositional form. Thus, cannot use \"jaːnticcirsu\" as subject. \n→ Failure mode: prepositional use of \"jaːnticcirsu\" prevents subject formation.\n\n\n\nRe-express" + ], + "anchor_output": "Step 1: Analyze the given sentences to detect patterns in Kunuz Nubian syntax and verb structure.\n\nLook at the verb constructions:\n\nSentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → \"We bought the camels for the neighbours.\" \n- \"ar\" = we (subject) \n- \"kanarriːcciːg\" = bought (past tense) \n- \"kamiːg\" = the camels \n- \"jaːnticcirsu\" = for the neighbours (goal/for-object)\n\nSentence 5: \"ay beyyeːcciːg ajaːnirri\" → \"I am buying the necklaces.\" \n- \"ay\" = I \n- \"beyyeːcciːg\" = buying (present tense) \n- \"ajaːnirri\" = the necklaces\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces.\" \n- \"sarkaːyi\" = the cowards \n- \"aygi\" = are giving (present passive?) \n- \"beyyeːcciːg\" = buying/giving (verb) \n- \"adeːnda\" = to me \n\nWait: the verb \"beyyeːcciːg\" appears in both \"buying\" and \"giving\", and the object is \"the necklaces\", with a \"for\" or indirect object.\n\nSentence 2: \"tirt kadeːg allesu\" → \"The owner repaired the dress.\" \n- \"tirt\" = the owner \n- \"kadeːg\" = repaired \n- \"allesu\" = the dress\n\nSentence 3: \"jahali waliːg darbadki biticcirra\" → \"The young men will give the chicken to the dogs.\" \n- \"jahali\" = young men \n- \"waliːg\" = will \n- \"darbadki\" = give \n- \"biticcirra\" = to the dogs (goal)\n\nSentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man.\" \n- \"man\" = he \n- \"jahalgi\" = stole \n- \"kadeːcciːg\" = the dresses \n- \"maːgtirsu\" = for the young man\n\nSo \"for X\" is marked by a phrase like \"maːgtirsu\" (for the young man) or \"jaːnticcirsu\" (for the neighbours).\n\nVerb patterns:\n\n- \"kanarriːcciːg\" → bought \n- \"kadeːg\" → repaired \n- \"darbadki\" → give \n- \"kadeːcciːg\" → stole (stolen) \n- \"beyyeːcciːg\" → buying/giving\n\nVerbs often end in -cciːg or -cirsu, with different markers for tense and direction.\n\nNote that \"giving\" and \"buying\" use the same root in form, differing in tense and subject.\n\nNow, look at the objects and direction:\n\n- Some verbs are transitive: take an object, then a for-object (direct/indirect object).\n- The structure often follows: [subject] [verb] [object] [for X].\n\nIn sentence 1: \"We bought the camels for the neighbours\" → ar kanarriːcciːg kamiːg jaːnticcirsu \n→ subject + verb + direct object + for-object\n\nSimilarly, sentence 10: \"The cowards are giving me the necklaces\" → sarkaːyi aygi beyyeːcciːg adeːnda \n→ subject + verb + object + for me\n\nSo \"for\" is attached to the end, directly after the object.\n\nThus, the structure is: \n[subject] [verb] [direct object] [for indirect object]\n\nNow examine the tense markers:\n\n- Past: \"ar kanarriːcciːg\", \"tirt kadeːg\" (past tense verb)\n- Present: \"ay beyyeːcciːg\" (present), \"sarkaːyi aygi beyyeːcciːg\" (present)\n- Future: \"jahali waliːg darbadki\" → \"will give\"\n\nSo “waliːg” = future, or “will”\n\nSimilarly, “man” = he, “tirt” = owner, “ay” = I\n\nSo for future tense, use \"waliːg\" (will)\n\nNow, real-translation:\n\n16. \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for neighbours → so \"jaːnticcirsu\" = neighbours \nIn sentence 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → we bought the camels for the neighbours \nSo the phrase \"jaːnticcirsu\" means \"for the neighbours\", not \"the neighbours\".\n\nSo how do we say \"the neighbours\"?\n\nWe need a noun for \"the neighbours\".\n\nFrom sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = for neighbours → the noun is implied?\n\nSentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief.\" \n→ iːdi = the men \n→ magaski = gave \n→ kamiːg = the camels \n→ tirsa = to the thief\n\nSo \"tirsa\" → to the thief (indirect object)\n\nIn 3: \"biticcirra\" → to the dogs\n\nSo \"biticcirra\" = to the dogs → \"tirsa\" = to the thief\n\nSo structure: \n[subject] [verb] [direct object] [to X]\n\nBut in 1: \"ar kanarriːcciːg kamiːg jaːnticcirsu\" → for neighbours → \"jaːnticcirsu\"\n\nIn 8: \"iːdi magaski kamiːg tirsa\" → to the thief → \"tirsa\"\n\nSo \"jaːnticcirsu\" = for the neighbours \n\"tirsa\" = to the thief \n\"biticcirra\" = to the dogs\n\nSo \"to\" vs \"for\" — different prepositions?\n\nBut in sentence 1: \"for\" → jaːnticcirsu \nIn sentence 8: \"to\" → tirsa\n\nSo the verb \"gave\" is \"magaski\" → giving\n\nThen to give, it's: [subject] [verb] [object] [for or to X]\n\nIn 1: \"for the neighbours\" → jaːnticcirsu \nIn 8: \"to the thief\" → tirsa \nIn 3: \"to the dogs\" → biticcirra\n\nSo “for” and “to” are distinct?\n\nBut look at sentence 4: \"man jahalgi kadeːcciːg maːgtirsu\" → \"He stole the dresses for the young man\"\n\n“maːgtirsu” = for the young man\n\nSo \"for\" = maːgtirsu\n\nIn 1: \"jaːnticcirsu\" = for the neighbours\n\nThus, \"for X\" = [X-object] with a specific suffix.\n\nSimilarly, \"to\" = ? \"tirsa\" → to the thief\n\nSo for verb \"give\", we have:\n\n- “magaski” = give \n- \"biticcirra\" = to the dogs \n- \"tirsa\" = to the thief \n- \"jaːnticcirsu\" = for the neighbours\n\nBut in 1: \"we bought the camels for the neighbours\" → for = jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\", which is a prepositional phrase.\n\nAlso, \"the necklace\" → from sentence 5: \"beyyeːcciːg ajaːnirri\" = buying the necklaces → \"ajaːnirri\" = necklaces\n\nSo \"necklace\" → \"beyyeːcciːg\" is the verb, \"ajaːnirri\" = necklaces\n\nSo objects:\n\n- camels → kamiːg \n- dresses → kadeːcciːg \n- chickens → ? \n- dogs → ? \n- donkey → ? \n- owner → ?\n\nIn sentence 2: \"kadeːg\" = repaired the dress → \"allesu\" = dress\n\nIn sentence 3: \"biticcirra\" = to the dogs → so \"dogs\" = biticcirra\n\nIn sentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me.\" \n\"wal\" = the dog \n\"aygi\" = found (present, active) \n\"baːbiːg\" = doors \n\"eldeːnsu\" = for me\n\nSo \"baːbiːg\" = doors → noun \n\"eldeːnsu\" = for me\n\nSo structure: [subject] [verb] [object] [for X]\n\nSimilarly, sentence 5: \"ay beyyeːcciːg ajaːnirri\" → I am buying the necklaces → ajaːnirri = necklaces\n\nSo \"necklace\" = ajaːnirri\n\nNow back to 16: \"The neighbours are giving the necklace to the owner.\"\n\n- Subject: \"the neighbours\" → from sentence 1: \"jaːnticcirsu\" = for the neighbours → so \"jaːnticcirsu\" = to the neighbours?\n\nBut in sentence 1: \"we bought the camels for the neighbours\" → for → jaːnticcirsu \nSo \"jaːnticcirsu\" means \"for the neighbours\"\n\nSo to say \"the neighbours\", we can reconstruct from the object.\n\nIn sentence 8: \"The men gave the camels to the thief\" → \"tirsa\" = to the thief\n\nSo \"tirsa\" → to the thief\n\nSimilarly, \"biticcirra\" → to the dogs\n\nSo for \"to the owner\" → use \"eldeːnsu\"? In sentence 6: \"eldeːnsu\" = for me\n\nBut in sentence 6: \"for me\" → eldeːnsu\n\nAlso, in sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nSo \"tirt\" = the owner\n\nSo for \"the neighbours\" → in sentence 1, it's \"jaːnticcirsu\" → for the neighbours → so perhaps \"jaːnticcirsu\" is the object, but likely the adjective or noun?\n\nThe only noun form for \"neighbours\" is not given directly, but in 1, \"jaːnticcirsu\" appears as \"for the neighbours\" → so perhaps \"jaːnticcirsu\" is a phrase meaning \"for the neighbours\" → the noun is missing.\n\nBut we must form \"the neighbours\" from known patterns.\n\nIn 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → the cowards are giving me the necklaces → subject \"sarkaːyi\" = the cowards\n\nSo \"sarkaːyi\" = the cowards → so a noun phrase with \"sarkaːyi\" = the cowards\n\nSimilarly, in 3: \"jahali\" = the young men → so \"jahali\" = the young men\n\nIn 4: \"man\" = he\n\nSo possible nouns:\n\n- young men → jahali \n- neighbours → ? \n- owner → tirt \n- dog → wal \n- cowards → sarkaːyi \n- thief → magas (sentence 7: \"magas\" = thief)\n\nSo \"the thief\" = magas\n\nSimilarly, \"the owner\" = tirt\n\n\"the dogs\" = biticcirra? In 3: \"to the dogs\" → biticcirra → so \"biticcirra\" = to the dogs → not the dogs.\n\nSo perhaps the noun is \"tirsu\" or something?\n\nIn sentence 8: \"iːdi magaski kamiːg tirsa\" → \"The men gave the camels to the thief\" \n→ \"tirsa\" = to the thief\n\nBut is there a noun \"the thief\"? \"magas\" — in sentence 7: \"magas ikki waliːg ticcirsu\" → \"The thief gave you (pl.) the dogs\" → \"magas\" = thief\n\nSo \"magas\" = thief → the thief\n\nSimilarly, \"tirt\" = owner\n\n\"wal\" = dog\n\n\"jahali\" = young men\n\n\"sarkaːyi\" = cowards\n\nSo for \"the neighbours\", is there a known form?\n\nIn sentence 1: \"for the neighbours\" → \"jaːnticcirsu\"\n\nSo \"jaːnticcirsu\" = for the neighbours → so the noun is implied.\n\nTherefore, \"jaːnticcirsu\" is used as a prepositional phrase meaning \"for the neighbours\".\n\nThus, to say \"the neighbours\", we need to derive a noun form.\n\nBut no direct noun form is given.\n\nPossibly, \"jaːnticcirsu\" is an object form, not a subject noun.\n\nSo likely, the noun must be reconstructed from context.\n\nBut in the verb \"give\", the object is direct, then for/to.\n\nIn 16: \"The neighbours are giving the necklace to the owner.\"\n\nSubject: \"the neighbours\" → unknown noun → the only one with \"for\" is \"jaːnticcirsu\" → perhaps \"jaːnticcirsu\" is the group?\n\nBut it functions as \"for the neighbours\" — so it's a preposition.\n\nSimilarly, \"for the owner\" → what would that be?\n\nIn sentence 2: \"the owner repaired\" → \"tirt\" = the owner\n\nIn sentence 6: \"the dog found the doors for me\" → \"eldeːnsu\" = for me\n\nSo \"eldeːnsu\" = for me → for person\n\nSo for \"the owner\" → likely \"eldeːnsu\" is used for \"for me\", not for \"the owner\".\n\nSo for \"the owner\", perhaps \"tirsa\" — but \"tirsa\" = to the thief.\n\nWe have no phrase \"for the owner\".\n\nBut in sentence 1: \"for the neighbours\" → jaːnticcirsu \nSo \"jaːnticcirsu\" likely means \"for the neighbours\", and since \"jaːnticcirsu\" appears in that sentence, and \"the neighbours\" is subject, it's likely that \"jaːnticcirsu\" is the preposition phrase.\n\nSo for \"to the owner\", we need a phrase.\n\nIn sentence 2: \"the owner\" → \"tirt\"\n\nIn sentence 6: \"for me\" → \"eldeːnsu\"\n\nSo perhaps \"for the owner\" = \"tirsa\" but no.\n\nWait — in sentence 8: \"to the thief\" = \"tirsa\"\n\nSo \"tirsa\" = to the thief\n\n\"biticcirra\" = to the dogs\n\nSo \"to the owner\" = [to + owner] → not directly known.\n\nBut in sentence 2: \"tirt kadeːg allesu\" → the owner repaired the dress → \"tirt\" = owner\n\nSo perhaps \"eldeːnsu\" is used for \"for me\", but not for \"for the owner\".\n\nBut maybe \"eldeːnsu\" can be generalized?\n\nAlternatively, the preposition \"to\" is used for animate beings.\n\nBut in 1: \"for the neighbours\" → jaːnticcirsu\n\nSo \"for\" is used with \"jaːnticcirsu\"\n\nIn 8: \"to the thief\" → \"tirsa\"\n\nSo \"to\" is used with \"tirsa\"\n\nSo two prepositions:\n\n- \"for\" → jaːnticcirsu \n- \"to\" → tirsa\n\nSo \"to the owner\" = \"tirsa\" → but not with \"owner\", but with \"thief\".\n\nSo likely, the noun must be given.\n\nBut \"the owner\" is \"tirt\"\n\nSo \"to the owner\" = \"tirt\" + preposition?\n\nBut no such phrase.\n\nWait — in sentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me? In sentence 6: \"for me\" → eldeːnsu\n\nIn 10: \"adeːnda\" = to me\n\nSo \"adeːnda\" = to me\n\n\"eldeːnsu\" = for me\n\nSo preposition \"to\" → adeːnda\n\n\"for\" → eldeːnsu\n\nWait — contradiction?\n\nSentence 6: \"wal aygi baːbiːg eldeːnsu\" → \"The dog found the doors for me\" → eldeːnsu = for me\n\nSentence 10: \"sarkaːyi aygi beyyeːcciːg adeːnda\" → \"The cowards are giving me the necklaces\" → adeːnda = to me\n\nSo different prepositions:\n\n- for me → eldeːnsu \n- to me → adeːnda\n\nSo \"to\" = adeːnda \n\"for\" = eldeːnsu\n\nIn sentence 1: \"for the neighbours\" → jaːnticcirsu → \"jaːnticcirsu\" = for the neighbours\n\nSo \"for\" applies to jaːnticcirsu, which is for a group.\n\nSimilarly, \"to\" applies to adeːnda (to me)\n\nSo \"to the owner\" = ? \n\n\"tirsa\" = to the thief — what is the owner?\n\nNo verb with \"to the owner\".\n\nBut in sentence 8: \"iːdi magaski kamiːg tirsa\" → the men gave the camels to the thief → \"tirsa\" = to the thief\n\nSo \"tirsa\" = to X, where X = thief\n\nSo to say \"to the owner\", we need a phrase like \"tirsa\" with owner?\n\nBut \"tirt\" = owner\n\nSo perhaps \"tirsa\" is used with the noun?\n\nBut no example.\n\nBut \"tirsa\" = to the thief → thief is \"magas\"\n\nSo \"tirsa\" = to the thief → for \"thief\", it's \"tirsa\"\n\nSo for \"owner" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "planner_index": 13, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- a.1 / 14.: answer for this requested item\n- a.2 / 15.: answer for this requested item\n- a.3 / 16.: answer for this requested item\n- a.4 / 17.: answer for this requested item\n- a.5 / 18.: answer for this requested item\n\nFinal answer shape: \\boxed{a.1: ; a.2: ; a.3: ; a.4: ; a.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nTarget: solve (a) only.\n\nTarget question:\n(a) Translate into English:\n\n 14. Navila vivila biyamata tomwaya mtona?\n 15. Bikamkwamsi kweyu vivila minasina.\n 16. Amagudina gwadi lekota?\n 17. Tevila tauwau bigisesi gugwadi gudigasisi?\n 18. Legisesi ketala waga vivila minasiwena.\n\n One of these sentences has two possible translations. Give them both.\n\nSAMPLED ATTEMPT:\nStep 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” \n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "approaches": [ + "Focus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.", + "Analyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.", + "\nFocus on demonstratives and number agreement to identify ambiguity. In sentence 10, \"legisi dakuna makwena gwadi magudiwena\" is interpreted as \"that beautiful child saw this stone\" — here, \"gwadi magudiwena\" = that child. This suggests that \"gwadi\" is a demonstrative modifying \"magudiwena\" (child). Similarly, in sentence 16: \"Amagudina gwadi lekota?\" — if \"amagudina\" means \"which child\", then \"gwadi lekota\" could be interpreted as \"that this\" or \"this that\", but both are demonstrative. However, \"gwadi\" and \"lekota\" are not co-occurring in other examples. In sentence 2, \"lekota dimdim mtona\" = \"this white man\" — \"lekota\" = this. In sentence 3, \"bikota gwadi magudiwena\" = \"that child\" — \"bikota\" = that, \"gwadi\" = that, \"magudiwena\" = child. This shows \"gwadi\" can be a demonstrative independent of \"bikota\". But in 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, then \"gwadi lekota\" might be a noun phrase meaning \"that this\" — which is ungrammatical. Alternatively, if \"gwadi\" is a demonstrative and \"lekota\" is a determiner, perhaps \"gwadi lekota\" = \"that this\" → \"that this child\"? But no such phrase exists. The only plausible reading is \"which child\" (amagudina) and \"that this\" (gwadi lekota) — which is redundant. Thus, the phrase likely means \"which child\" with a demonstrative ambiguity: either \"which that child\" or \"which this child\". But \"gwadi\" and \"lekota\" are distinct. Verification: In sentence 4, \"legisi waga makesiwena namwaya minana\" — \"this old woman saw those canoes\" → \"legisi\" = this, \"namwaya\" = those. So demonstratives are used independently. In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = that this → no clear match. But if \"gwadi\" = that and \"lekota\" = this, and they are both modifying \"child\", it could be a binary demonstrative for \"which child\" — one that is \"that\" and one that is \"this\". But this is not supported. The only grammatical possibility is that \"amagudina\" = which child, and \"gwadi lekota\" is a misreading. But the problem says one sentence has two translations. So if 16 is ambiguous, it must be due to demonstrative overlap. Hypothesis: \"amagudina\" = which child, and \"gwadi\" = that, \"lekota\" = this → so the sentence is \"which that this child?\" → ungrammatical. Alternatively, \"gwadi\" = that, \"lekota\" = this → so \"that this child\" → i.e., \"which child is that this\"? No. Final check: in sentence 10, \"legisi dakuna makwena gwadi magudiwena\" — \"makwena\" = child, \"gwadi magudiwena\" = that child → so \"gwadi\" modifies \"magudiwena\". In 16, \"amagudina gwadi lekota\" — if \"amagudina\" = which child, and \"gwadi lekota\" = a noun phrase, it might mean \"which child is that this\" — still flawed. Alternatively, \"amagudina\" = which, and \"gwadi lekota\" = that this (a demonstrative compound). But no such phrase. Therefore, 16 is likely not ambiguous. So move to others.\n\n\n\nAnalyze the structure of sentence 17: \"Tevila tauwau bigisesi gugwadi gudigasisi?\" \n\"tevila\" = how many? → sentence 8: \"navila\" = how many → so \"tevila\" may be same → \"how many\" \n\"tauwau\" = two → sentence 6: \"teyu tauwau\" = looked after two men → \"tauwau\" = two \n\"bigisesi\" = that chief? → sentence 7: \"bigisi\" = that, \"kwetala\" = clever, \"vivila\" = woman → \"bigisi\" = that \n\"bigisesi\" = likely \"that chief\" → \"gugwadi\" = that? → \"gudigasisi\" = wild pig? → \"guyau\" = clever, \"bunukwa\" = wild pig → \"gudigasisi\" = perhaps \"that wild pig\" \n\"gugwadi\" = that → \"gugwadi gudigasisi\" = that that wild pig? → redundant \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that pig? → ungrammatical \nPossibility: \"gugwadi\" = which → but no \"amtona\" → \"gugwadi\" appears only here \n\"bigisesi\" = that chief → so \"that chief saw that wild pig\"? \nBut \"gugwadi gudigasisi\" → \"gugwadi\" = that, \"gudigasisi\" = wild pig → so \"that wild pig\" \nSo \"how many two that chief saw that wild pig?\" → grammatically broken \nAlternative: \"tauwau\" = two → \"bigisesi\" = that chief → \"gugwadi\" = which → but no \"amtona\" \nCould \"gugwadi\" = which? → not supported \nIn sentence 9: \"Amakena waga legisesi gweguyau?\" → \"which canoe did the chiefs see?\" → \"amakena\" = which \nSo \"amtona\" or \"amakena\" = which \nIn 17: no \"amtona\" → so not \"which\" \nThus, \"tevila tauwau bigisesi gugwadi gudigasisi?\" → \"how many two that chief saw that wild pig?\" → nonsense \nBut \"gugwadi\" might be a typo or misreading of \"gweguyau\" → gweguyau = canoe → so \"gugwadi\" = not in original \n\"bigisesi\" = that chief → \"gugwadi gudigasisi\" = that that wild pig? \nSo likely error. But if \"gugwadi\" = which, then \"which wild pig\" → so \"how many two that chief saw which wild pig?\" — still odd \nThus, no clear ambiguity here. The phrase is ungrammatical. So not likely the ambiguous sentence.\n\n\n\nReexamine sentence 15: \"Bikamkwamsi kweyu vivila minasina\" \n\"bikamkwamsi\" → similar to \"bikota\" = that → so \"that\" \n\"kweyu\" = two → as in \"nayu\" = two pigs in sentence 5 \n\"vivila\" = women \n\"minasina\" = in sentence 1: \"minasina tetala tau\" → \"four fish\" → so \"number + noun\" \nSo \"vivila minasina\" = women + fish? But no such noun \nUnless \"minasina\" is a general term for \"something\" → but no \nBut in sentence 13: \"vivila biyamatasi tau mtona\" → women will look after this man → \"vivila\" = women \nNo number with \"minasina\" — only in sentence 1 \nSo \"minasina\" is bound to \"four fish\" \nThus \"kweyu vivila minasina\" → \"two women\" with \"fish\"? → no \nAlternative: perhaps \"minasina\" is a noun meaning \"something\" — but not supported \nAnother idea: \"kweyu\" = two → \"vivila\" = women → \"minasina\" = fish → so \"two women fish\"? → no \nBut in sentence 5: \"Amtona tau lekalimati nayu bunukwa?\" → \"which man killed two pigs?\" → so \"nayu\" = two, \"bunukwa\" = pigs \nSo \"kweyu\" = two → so \"kweyu vivila\" = two women \nThen \"minasina\" is a mistake? But not. \nCould \"vivila minasina\" = \"two women\" if \"minasina\" is a number form? But \"minasina\" = four fish → not two. \nBut what if \"minasina\" is used as a general count? No evidence. \nThus, likely \"kweyu vivila\" = two women → \"bikamkwamsi\" = that → \"that two women\"? \nBut \"that two women\" is not standard. \nHowever, in sentence 10: \"leg", + "Private solving checklist. Build an explicit alignment table before answering. For each example, identify reusable words, morphemes, affixes, word order, and any number-system operations. Use minimal pairs where possible. For translations, track subject, object, plurality, tense/aspect, demonstratives, adjectives, and question words separately. For numerals, write the arithmetic decomposition first, then map each part into the language. Finally, verify every requested unit by substituting its pieces back into the examples." + ], + "anchor_output": "Step 1: Identify core linguistic patterns in the given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n→ \"navasi\" = man; \"tetala\" = will catch; \"minasina\" = four fish → \"yena\" = these. \n\"yena\" = demonstrative (these), \"minasina\" = number + noun → scale with number.\n\nSentence 2: \n\"This white man arrived.\" → \"Lekota dimdim mtona.\" \n→ \"lekota\" = this; \"dimdim\" = white; \"mtona\" = arrived.\n\nSentence 3: \n\"That child will arrive.\" → \"Bikota gwadi magudiwena.\" \n→ \"bikota\" = that; \"gwadi\" = child; \"magudiwena\" = will arrive.\n\nSentence 4: \n\"This old woman saw those canoes.\" → \"Legisi waga makesiwena namwaya minana.\" \n→ \"legisi\" = this; \"waga\" = old; \"makesiwena\" = saw; \"namwaya\" = those; \"minana\" = canoes.\n\nSentence 5: \n\"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n→ \"Amtona\" = which; \"tau\" = man; \"lekalimati\" = killed; \"nayu\" = two; \"bunukwa\" = pigs.\n\nSentence 6: \n\"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya.\" \n→ \"leyamatasi\" = old women; \"teyu\" = looked after; \"tauwau\" = two; \"nunumwaya\" = men.\n\nSentence 7: \n\"That clever woman will see something.\" → \"Bigisi kwetala vivila minawena nakabitam.\" \n→ \"bigisi\" = that; \"kwetala\" = clever; \"vivila\" = woman; \"minawena\" = will see; \"nakabitam\" = something.\n\nSentence 8: \n\"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n→ \"navila\" = how many; \"ka’ukwa\" = dogs; \"lekotasi\" = arrived.\n\nSentence 9: \n\"Which canoe did the chiefs see?\" → \"Amakena waga legisesi gweguyau?\" \n→ \"amakena\" = which; \"waga\" = chiefs; \"legisesi\" = saw; \"gweguyau\" = canoe.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = child? But \"magudiwena\" = will arrive? Inconsistency?\n\nWait — “magudiwena” appears in 3, 4, 10 → in 3: “will arrive” → in 10: “saw this stone” → so \"magudiwena\" may not mean \"will arrive\" in all contexts.\n\nPossibility: “magudiwena” = child → \"gwadi magudiwena\" = that child → \"gwadi\" = that; \"magudiwena\" = child.\n\nSimilarly, in sentence 4: \"gwadi magudiwena\" → “that child” → so likely \"gwadi\" = that, \"magudiwena\" = child.\n\nThus, in sentence 10: \"legisi dakuna makwena gwadi magudiwena gudimanabweta\" \n→ \"legisi\" = that; \"dakuna\" = beautiful; \"makwena\" = child; \"gwadi\" = that; \"magudiwena\" = child → double use of child?\n\nBut \"makwena\" = child; \"gwadi magudiwena\" = that child → so \"makwena gwadi magudiwena\" = that child → so “makwena” may be a form of “child” and \"gwadi\" is the demonstrative.\n\nThus, likely \"makwena\" = child; \"gwadi\" = that → “that child”.\n\nSo sentence 10: \"That beautiful child saw this stone.\"\n\nSimilarly, sentence 11: \n\"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n→ \"kwevila\" = how many; \"lekamkwamsi\" = things; \"dimdim\" = white; \"mtosiwena\" = ate.\n\nSentence 12: \n\"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\" \n→ \"lekalimati\" = killed; \"natala\" = one; \"bunukwa\" = wild pig; \"nagasisi\" = chief; \"guyau\" = clever.\n\nSo \"guyau\" = clever; \"nagasisi\" = chief → \"nagasisi guyau\" = clever chief.\n\nSentence 13: \n\"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n→ \"navila\" = how many; \"vivila\" = women; \"biyamatasi\" = will look after; \"tau\" = this; \"mtona\" = man.\n\nSo \"vivila biyamatasi tau mtona\" = women who will look after this man.\n\nNow analyze each target sentence:\n\n14. Navila vivila biyamata tomwaya mtona? \n→ \"navila\" = how many; \"vivila\" = women; \"biyamata\" = will look after? → \"biyamatasi\" in 13 → likely \"biyamata\" = will look after; \"tomwaya\" = this; \"mtona\" = man → “how many women will look after this man?” \nThis is parallel to sentence 13 → so translation: “How many women will look after this man?”\n\n15. Bikamkwamsi kweyu vivila minasina. \n→ \"bikamkwamsi\" = that thing? Or \"which\" + thing? \"bikamkwamsi\" = similar to \"bikota\" = that; \"kweyu\" = two? Like \"nayu\" in 5 → \"kweyu\" = two; \"vivila\" = woman? \"minasina\" = fish? \nBut \"minasina\" = number + noun — in sentence 1, \"minasina\" = four fish. \nIn sentence 15: \"vivila minasina\" → could be “two women” if \"vivila\" = women, \"minasina\" = two → but \"minasina\" usually means “four fish” — a number + noun? \nBut \"nayu\" = two pigs, \"nayu bunukwa\" → \"two pigs\" \n\"kweyu\" = two → \"kweyu vivila\" = two women? \nBut \"vivila\" = women → so \"kweyu vivila\" = two women → “which two women”? \nBut \"bikamkwamsi\" = that → “that two women”? \nBut “which” is more likely.\n\nCompare to sentence 5: “Amtona tau lekalimati nayu bunukwa?” → “which man killed two pigs?” \n→ “amtona” = which → “bikamkwamsi” → sounds like “bikota” → “that” → so not “which” → but in 15, “bikamkwamsi” → “that something” → possibly also “that thing”?\n\nBut “kweyu vivila minasina” → “two women” → but “minasina” = four fish → so not numerically consistent.\n\nWait — in sentence 1, “minasina” = “four fish” → so “number + noun” → so “minasina” = four fish.\n\n“nayu” = two pigs → “nayu bunukwa”\n\n“kweyu” = could be two → so “kweyu” = two → “kweyu vivila” = two women → “vivila minasina” → “minasina” = four fish → contradiction.\n\nUnless “vivila minasina” is not structured as number + noun.\n\nBut in sentence 5: “nayu bunukwa” → “two pigs” → so “nayu” = two, “bunukwa” = pigs.\n\nIn sentence 15: “kweyu vivila minasina” → possibly “kweyu” = two, “vivila” = women, “minasina” = fish → no.\n\nBut “vivila” = women → “kweyu vivila” = two women → “minasina” = fish → not matching.\n\nWait — possibilities: \n- “minasina” could be a noun meaning “something” → but in 1, “minasina” = four fish → so number with noun.\n\nBut in 15, “kweyu vivila minasina” → could be “which two women” — but “bikamkwamsi” = that → not “which”.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “bikamkwamsi” = that → “that two women”?\n\nBut “kweyu” = two → so “that two women” → “which two women”?\n\nBut “bikamkwamsi” = that → “that two women” is ungrammatical.\n\nMore likely: “kweyu” = two → “vivila” = women → “minasina” = fish → no.\n\nWait — is “minasina” used in other contexts?\n\nSentence 1: “minasina tetala tau” → “four fish will be caught”\n\nNo other instance of “minasina” with number?\n\nIn sentence 13: “vivila biyamatasi tau mtona” → “women will look after this man”\n\nNo number with “minasina” → only sentence 1.\n\nSo likely “minasina” = four fish → fixed number.\n\nTherefore, in 15, “vivila minasina” cannot mean “two women” → so perhaps “vivila” is not “women”?\n\nBut “vivila” always appears as “women” or “woman” → e.g., sentence 7: “vivila minawena” → woman will see something → “vivila” = woman.\n\nSentence 13: “vivila biyamatasi” → women will look after.\n\nSo “vivila” = women → so “kweyu vivila” = two women → “kweyu” = two → “vivila minasina” → “two women” → but “minasina” is not “fish”?\n\nAlternatives: perhaps “minasina” is used as a general noun — but context shows it's a number + noun.\n\nAnother possibility: “minasina” = “something” → but in sentence 1, “minasina” = four fish → not something.\n\nSo “kweyu vivila minasina” → does not match.\n\nMaybe the structure is “bikamkwamsi” = the one that → “which women”? But “bikamkwamsi” → similar to “bikota” → that → not which.\n\nBut sentence 5: “Amtona” = which → so “which” is marked by “amtona”.\n\nSentence 15: “bikamkwamsi” → only “bikota” or “bigisi” → not “amtona” → so not “which”.\n\nCould it be “that” + “two women”?\n\nBut “that two women” is not idiomatic.\n\nAlternatively, “vivila” might be “something” — but only in context of “minawena” or “minasina”.\n\nNo — all cases show “vivila” as “women”.\n\nTherefore, likely error or mismatch → but only one sentence has two possible translations.\n\nNow sentence 16: Amagudina gwadi lekota?\n\n→ “amagudina” → likely derived from “magudiwena” → “magudiwena” = child → “magudi” = child → “amagudina” = which child?\n\n→ “gwadi” = that → “lekota” = this → “amagudina gwadi lekota” = which that this child?\n\nNo — “gwadi” = that, “lekota” = this → contradiction.\n\nBut in sentence 10: “legisi dakuna makwena gwadi magudiwena” → “that beautiful child”\n\nSo “gwadi magudiwena” = that child.\n\nSo “amagudina” = which child? → “which child that this”?\n\nBut “gwadi” and “lekota” are both demonstratives → “gwadi” = that, “lekota” = this.\n\nSo “amagudina gwadi lekota” → “which that this child” → ungrammatical.\n\nPossibility: “amagudina” = which child → “gwadi” = that → “lekota” = this → so “which that child” → still odd.\n\nPerhaps “amagudina” = which, “gwadi” = that, “lekota” = this → “which that this child” → absurd.\n\nOr “amagudina” = which child → “gwadi” = this → “lekota” = that? No.\n\nStructure: “amagudina” = which + child → so “which child” → “gwadi” = that → not required.\n\nBut “gwadi lekota” = that this → meaningless.\n\nSo may be a postpositive structure — “gwadi lekota” = these?\n\nIn sentence 4: “namwaya minana” → “those canoes” → “namwaya” = those.\n\nIn sentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this; “gwadi” = that.\n\nTherefore “gwadi lekota” = that this → not a natural phrase.\n\nUnless “gwadi” and “lekota” are both part of a noun phrase.\n\nBut “amagudina” = which child → so “which child?” → and then “gwadi lekota” = that this? No.\n\nPerhaps “amagudina” = which, and “gwadi” = that, “lekota” = man → but “lekota” is only used with man in 2.\n\nSentence 2: “lekota dimdim mtona” → “this white man”\n\nSo “lekota” = this man → “dimdim” = white → so “lekota” + noun.\n\nSimilarly, “bikota” = that → + noun → “bikota gwadi” → that child.\n\nIn 16: “amagudina gwadi lekota” → “which that this man”?\n\nNo.\n\nPossibility: “amagudina” = which; “gwadi” = that; “lekota” = man → so “which that man” → but not similar.\n\nBut “lekota” is used only with \"man\".\n\nIn 16, “amagudina gwadi lekota” → “which that man”?\n\nBut “gwadi” = that → so “that man” → “which that man” — unlikely.\n\nPerhaps “gwadi” is attached to “lekota” → “gwadi lekota” = that this → still not.\n\nAlternative: “amagudina” = a form of “which” → like “amtona” → in sentence 5 → “amtona” = which → “amagudina” → possibly same.\n\nSo “amagudina” = which → “gwadi” = that → “lekota” = man → so “which that man” → unclear.\n\nBut “which man” → “amtona tau” → in sentence 5.\n\nSo “amagudina” may be a variant of “which” → so “which man”?\n\nThen “gwadi” → that → so “which that man”?\n\nBut still.\n\nAnother path: look at sentence 17: Tevila tauwau bigisesi gugwadi gudigasisi?\n\n→ “tevila” = how many → like “navila” → “tauwau” = two → “bigisesi” = chiefs → “gugwadi” = that → “gudigasisi” = saw?\n\nWait — “gudigasisi” → like “gweguyau” → “gweguyau” = canoe → so “gudigasisi” = saw?\n\nIn sentence 9: “legisesi gweguyau” = saw canoe.\n\nSo “gudigasisi” = saw.\n\n“gugwadi” = that → “bigisesi” = chiefs → “gugwadi” = that → “gugwadi gudigasisi” = that chiefs saw?\n\nBut “bigisesi” = chiefs → “gugwadi gudigasisi” = that chiefs saw.\n\nSo “tauwau bigisesi gugwadi gudigasisi” = two chiefs that saw?\n\n“tevila” = how many → so “how many [two chiefs that saw something]”?\n\nStructure: “tevila” → how many; “tauwau” → two; “bigisesi” → chiefs → “gugwadi” → that → “gudigasisi” → saw → so “two chiefs that saw”?\n\nBut what is the object? “gugwadi gudigasisi” = that chiefs saw → so it's a verb phrase.\n\nSo the sentence is: “How many two chiefs that saw?” → grammatically odd.\n\n“tevila” likely = how many → followed by noun phrase.\n\nBut “tauwau” = two → so likely “two chiefs” → “bigisesi” = chiefs → so “tauwau bigisesi” = two chiefs.\n\nThen “gugwadi gudigasisi” = that saw → so “two chiefs that saw”?\n\nSo “" + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "planner_index": 14, + "planner_prompt": "You are preparing private strategy memos for diverse attempts at an International Linguistics Olympiad problem. The sampled attempt below may be wrong; use it only to see one possible path and likely failure modes.\n\nPROBLEM:\nSolve this International Linguistics Olympiad question.\n\nReason step by step, using the examples to infer the linguistic pattern. Keep the derivation to roughly 1200 tokens or fewer; when the pattern is clear, stop deriving and answer. Your response must end with one and only one final-answer line, and nothing may follow it:\n\n\\boxed{...}\n\nThe box is a keyed answer record. Write every required unit exactly once, using its exact unit id followed by a colon. Put only that unit's answer after the colon. Separate units with semicolons or line breaks. Do not put reasoning, commentary, alternative guesses, or extra labels inside the box. Do not write any other \\boxed commands.\n\n\nRequired final-answer units:\n- b.1 / 19.: answer for this requested item\n- b.2 / 20.: answer for this requested item\n- b.3 / 21.: answer for this requested item\n- b.4 / 22.: answer for this requested item\n- b.5 / 23.: answer for this requested item\n\nFinal answer shape: \\boxed{b.1: ; b.2: ; b.3: ; b.4: ; b.5: }\n\nProblem 3 (20 points). Here are some sentences in English and their Kilivila translations:\n\n 1. One man will catch these four fish.\n Bibani navasi yena minasina tetala tau.\n 2. This white man arrived.\n Lekota dimdim mtona.\n 3. That child will arrive.\n Bikota gwadi magudiwena.\n 4. This old woman saw those canoes.\n Legisi waga makesiwena namwaya minana.\n 5. Which man killed two pigs?\n Amtona tau lekalimati nayu bunukwa?\n 6. The old women looked after two men.\n Leyamatasi teyu tauwau nunumwaya.\n 7. That clever woman will see something.\n Bigisi kwetala vivila minawena nakabitam.\n 8. How many dogs arrived?\n Navila ka’ukwa lekotasi?\n 9. Which canoe did the chiefs see?\n Amakena waga legisesi gweguyau?\n 10. That beautiful child saw this stone.\n Legisi dakuna makwena gwadi magudiwena gudimanabweta.\n 11. How many things did those white men eat?\n Kwevila lekamkwamsi dimdim mtosiwena?\n 12. The clever chief killed one wild pig.\n Lekalimati natala bunukwa nagasisi guyau tokabitam.\n 13. How many women will look after this man?\n Navila vivila biyamatasi tau mtona?\n\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\n!△ Kilivila belongs to the Oceanic branch of the Austronesian family. It is spoken by approx.\n20,000 people on the Trobriand islands of Papua New Guinea. —Samuel Ahmed\n\nTarget: solve (b) only.\n\nTarget question:\n(b) Translate into Kilivila:\n\n 19. How many canoes did those old women see?\n 20. These four white men will look after this clever child.\n 21. How many children will eat these pigs?\n 22. Which woman caught those beautiful fish?\n 23. Two wild dogs saw that old man.\n\nSAMPLED ATTEMPT:\nStep 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" =\n\nThink privately about the main uncertainty points in this problem: alignment choices, morpheme boundaries, word order, grammatical roles, number-system base and operations, ambiguous glosses, and answer-unit association. Return exactly 4 self-contained solver memos. Each memo should commit to one different correctness-relevant route and include a concrete verification check. Do not include the final answer, do not copy the sampled attempt, and do not mention that a sampled attempt was supplied.\n\nPut each memo inside its own tags.", + "planner_output": "\nFocus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.\n\n\n\nAssume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.\n\n\n\nPropose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.\n\n\n\nRe-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry.\n", + "approaches": [ + "Focus on verb derivation: Identify if \"eat\" is a distinct verb or derived from another morpheme. In sentence 11, \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — the only verb present is implied. But no standalone verb for \"eat\" appears in the data. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau. Thus, \"eat\" is not present. This suggests that \"eat\" may be represented by a verb that is not listed, or that the verb is missing in the translation. However, sentence 21 requires \"will eat\", so a future form must exist. Since \"will look after\" uses \"vivila\", and \"will\" is expressed by \"vivila\" in future contexts, it is plausible that \"will eat\" uses the same future marker. But no \"eat\" verb exists in the data. Therefore, \"eat\" must be a verb not directly given. The only verb that fits \"consume\" or \"eat\" is missing. This is a failure mode: absence of a data point for \"eat\" leads to unverifiable verb assignment. Thus, the translation of 21 is speculative and likely incorrect without a gloss. Verification: In sentence 11, if \"eat\" were present, it would be in the translation. Since it's not, the verb is missing — contradiction. Hence, this approach fails.", + "Assume that verbs are consistent with agent-verb-object structure and that future tense is marked by a specific morpheme. In sentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" — \"vivila\" = will look after. This shows that future action is marked by \"vivila\" in the verb. Similarly, \"will see\" would use a future form. In sentence 4: \"saw\" = \"makesiwena\" — past tense. \"Will see\" is not directly given, but \"vivila\" is used for future. So if \"eat\" is a transitive verb, \"will eat\" might be \"vivila\" + eat-verb. But no \"eat\" verb exists. However, in sentence 1: \"will catch\" = \"yena minasina\" — \"yena\" = will, \"minasina\" = catch. So \"will\" is marked with \"yena\". In sentence 20, \"will look after\" = \"vivila\". So different verbs have different future markers. Thus, \"will eat\" might use a different future marker. But no such marker is present. This inconsistency suggests that the future verb for \"eat\" is not established. Therefore, without a known verb for \"eat\", we cannot derive a correct form. Verification: In all data, verbs for \"eat\" are absent. The only verbs are \"saw\", \"arrived\", \"looked after\", \"killed\". So \"eat\" is not in the lexicon. This indicates a failure to identify a valid base form. Conclusion: 21 cannot be correctly translated without a data point for \"eat\", so this path fails.", + "Propose that \"eat\" is encoded by a verb similar to \"catch\" or \"see\" in structure. In sentence 1: \"catch\" = \"minasina\", and \"will catch\" = \"yena minasina\". In sentence 4: \"saw\" = \"makesiwena\". In sentence 12: \"killed\" = \"guyau\". These are all transitive verbs with a specific root. So \"eat\" might have a root like \"mtona\" or \"kamkwamsi\". But \"mtona\" = man. \"kamkwamsi\" = things. Consider that in sentence 11, \"how many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" — perhaps \"lekamkwamsi\" is both object and verb? Unlikely. Alternatively, the verb \"eat\" might be \"lekamkwamsi\" as a verb, but this is not supported. In no sentence is \"eat\" used. Thus, no evidence. However, in sentence 21, \"children will eat these pigs\" → object is \"pigs\", which may be \"bunukwa\" (pig) from sentence 5. So \"bunukwa\" = pig. \"children\" = \"minawena\". \"will\" = \"vivila\" from sentence 15. So if \"eat\" is absent, we must invent it. But no such verb exists. Verification: In all 13 sentences, no verb for \"eat\" appears. Therefore, this approach fails due to absence of lexical support.", + "Re-express sentence 11 as a structural template: \"How many [X] did [agent] [verb]?\" → \"Kwevila [X] [agent]?\" — but the verb is missing. This implies that the verb \"eat\" is either not present or is encoded in a different form. Since no verb for \"eat\" exists in the data, and since all other verbs are explicitly given, we conclude that \"eat\" is not a standalone verb in Kilivila. This suggests a failure in the assumption that every English verb has a direct translation. Alternatively, \"eat\" might be a derivation of \"consume\" using a root like \"mtona\" or \"minasina\". But no such form appears. In contrast, \"see\" = makesiwena, \"arrive\" = lekotasi, \"look after\" = teyu, \"kill\" = guyau — all distinct. Therefore, \"eat\" must have a unique form. Its absence in the data makes translation of 21 impossible. Verification: The translation for sentence 11 omits the verb, suggesting either a typo or that \"eat\" is not a verb in the language. Since the problem asks for a translation, it must exist. Therefore, this path fails due to lack of verifiable lexical entry." + ], + "anchor_output": "Step 1: Identify linguistic patterns from given English-Kilivila pairs.\n\nFrom sentence 1: \n\"One man will catch these four fish.\" → \"Bibani navasi yena minasina tetala tau.\" \n- \"One man\" = \"Bibani navasi\" \n- \"will catch\" = \"yena minasina\" \n- \"these four fish\" = \"tetala tau\"\n\nNote \"tetala\" = fish, \"tau\" = four. So numerals are marked with suffix \"-tau\", and \"yena\" = will, \"minasina\" = catch.\n\nSentence 5: \n\"How many man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" \n- \"How many\" = \"Amtona\" \n- \"two\" = \"nayu\" \n- \"pigs\" = \"bunukwa\"\n\nSo quantifiers are expressed with \"Amtona\", and numerals are suffixes. \"Nayu\" = two; \"tau\" = four.\n\nSentence 10: \n\"That beautiful child saw this stone.\" → \"Legisi dakuna makwena gwadi magudiwena gudimanabweta.\" \n- \"beautiful child\" = \"gwadi magudiwena\" (magudiwena = child, gwadi = beautiful) \n- \"saw\" = \"dakuna\" \n- \"this stone\" = \"gudimanabweta\"\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n- \"How many\" = \"Navila\" \n- \"women\" = \"biyamatasi\" \n- \"look after\" = \"vivila\" \n- \"this man\" = \"mtona\"\n\nSo again: \"Navila\" = how many, identifies a question with quantifier + noun + action + refers.\n\nPattern: \n- Questions with \"how many X\" use \"Navila\" or \"Amtona\" depending on context. \n- \"Navila\" → how many (in plural/noun group), \"Amtona\" for entity or specific item? \n- \"tau\" often marks quantity (4), \"nayu\" (2), \"mtona\" (man) — looks like numerals are suffixes.\n\nSentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\" \n- \"Navila\" = how many \n- \"dogs\" = \"ka’ukwa\" \n- \"arrived\" = \"lekotasi\" \n\nSo: \"Navila\" appears consistently for \"how many\" questions. Apply to 19.\n\n19. \"How many canoes did those old women see?\" \n- \"how many\" = \"Navila\" \n- \"canoes\" = \"namwaya\" (from sentence 4: \"those canoes\" = \"namwaya\") \n- \"those old women\" = \"legisi\" + \"waga\" (from sentence 4: \"Legisi waga makesiwena namwaya minana\" — \"legisi\" = that, \"waga\" = old) \n- \"see\" = \"makesiwena\" (sentence 4: \"saw\" = makesiwena)\n\nThus, \"Navila namwaya legisi waga makesiwena?\" \nBut in English: \"how many canoes did those old women see?\" \nSo agent = \"those old women\", verb = \"see\", object = \"canoes\"\n\nFrom sentence 4: \"Legisi waga makesiwena namwaya minana\" → \"that old woman saw those canoes\"\n\nSo \"makesiwena\" = saw, and it is used transitively with object.\n\nSo structure: Navila + object + agent + verb?\n\nBut verb must be at end? Look at 8: \"Navila ka’ukwa lekotasi?\" → \"How many dogs arrived?\" → verb is \"lekotasi\" (arrived)\n\nSo in 8: Navila + noun + verb? (not agent)\n\nBut in 4: \"Legisi waga makesiwena namwaya minana\" → agent + adverbial (old) + verb + object\n\nSo verb \"makesiwena\" is in middle or end.\n\nIn 10: \"Legisi dakuna makwena gwadi magudiwena gudimanabweta\" → \"that beautiful child saw this stone\" → structure: agent + verb + object\n\nSo base pattern: [agent] + [verb] + [object] \nWith questions: How many [object] did [agent] [verb]?\n\nSo 19: How many canoes did those old women see? \n→ Navila namwaya legisi waga makesiwena?\n\nYes — \"Navila\" = how many, \"namwaya\" = canoes, \"legisi waga\" = those old women, \"makesiwena\" = saw.\n\nSo b.1: Navila namwaya legisi waga makesiwena?\n\nNow 20: These four white men will look after this clever child.\n\n\"will look after\" = \"vivila\" (sentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" → \"look after\" = \"teyu\" or \"vivila\"?)\n\nSentence 6: \"The old women looked after two men.\" → \"Leyamatasi teyu tauwau nunumwaya\" \n- \"old women\" = \"leyamatasi\" \n- \"look after\" = \"teyu\" \n- \"two men\" = \"tauwau nunumwaya\" → \"tauwau\" = two, \"nunumwaya\" = men\n\n\"teyu\" = look after, confirmed.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" \n\"vivila\" = will look after \nSo \"vivila\" = will look after, verb with future.\n\nSo in 20: These four white men will look after this clever child.\n\nSubject: \"These four white men\" \n\"four\" = \"tau\" \n\"white men\" = \"dimdim mtona\" (sachet 2: \"This white man\" = \"Lekota dimdim mtona\" → dimdim = white, mtona = man)\n\nSo \"tau dimdim mtona\" = these four white men?\n\nThen verb: \"vivila\" = will look after \nObject: \"this clever child\" \n\"clever child\" = \"kwetala\" (sentence 7: \"that clever woman\" = \"Bigisi kwetala vivila minawena\") → \"kwetala\" = clever, \"minawena\" = child\n\nSo \"this\" = \"gwadi\"? In sentence 10: \"this stone\" = \"gudimanabweta\" → likely \"gwadi\" = this\n\nSo \"gwadi kwetala minawena\" = this clever child\n\nThus: tau dimdim mtona vivila gwadi kwetala minawena\n\nBut does \"vivila\" indicate future? Yes, appears in 15 with \"will\".\n\nSo b.2: tau dimdim mtona vivila gwadi kwetala minawena?\n\nNow 21: How many children will eat these pigs?\n\n\"how many\" = Navila \n\"children\" = \"minawena\" (sentence 10 and 7) \n\"will eat\" = \"mtona\"? \"eat\" not directly — check sentence 11: How many things did those white men eat?\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\" \n- \"Kwevila\" = how many \n- \"things\" = \"lekamkwamsi\" \n- \"those white men\" = \"dimdim mtosiwena\" \n- \"ate\" = \"lekamkwamsi\"? Wait no.\n\n\"Kwevila lekamkwamsi dimdim mtosiwena?\" → \"how many things did those white men eat?\" \n→ So \"eat\" is not in verb — possibly \"lekamkwamsi\" = things, \"dimdim mtosiwena\" = white men, but verb?\n\nWait, structure seems off. Perhaps \"lekamkwamsi\" is the verb? Not likely.\n\nAlternative: perhaps \"mtona\" is eat? But \"mtona\" = man.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly verb is missing. Perhaps it's \"mtona\" but \"mtona\" means man.\n\nWait — \"mtona\" is used in \"this man\", \"a man\" — may not be verb.\n\nAnother possibility: \"mtona\" = eat? But no.\n\nLook at sentence 12: \"The clever chief killed one wild pig.\" → \"Lekalimati natala bunukwa nagasisi guyau tokabitam.\"\n\n\"Killed\" = \"nagasisi\"? \"guyau\" = killed? \"guyau\" = kill? \"tokabitam\" = wild pig?\n\nIn 12: \"killed one wild pig\" → \"nagasisi guyau tokabitam\" — seems \"guyau\" = kill, \"tokabitam\" = wild pig.\n\nSo \"killed\" verb is \"guyau\" or \"nagasisi\"?\n\nBut \"guyau\" appears in 12: \"nagasisi guyau tokabitam\" → \"nagasisi\" may be agent (clever chief), \"guyau\" = killed, \"tokabitam\" = wild pig.\n\nSo \"guyau\" = kill → verb.\n\nNow, find \"eat\" verb.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nOnly word left: \"lekamkwamsi?\" likely the object \"things\".\n\nSo verb missing? But in sentence 11, only \"Kwevila\" and the rest?\n\nWait — perhaps it's missing a verb.\n\nBut other sentences have verb.\n\nSentence 12: \"killed\" = \"guyau\"\n\nSentence 10: \"saw\" = \"dakuna\"\n\nSentence 6: \"looked after\" = \"teyu\"\n\nSo what is \"eat\"?\n\nNone directly given. But in sentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nPossibly the verb is implied — \"lekamkwamsi\" = things, and \"dimdim mtosiwena\" = white men, and \"did eat\" is assumed.\n\nBut in other cases, action is explicit.\n\nWait — sentence 13: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau mtona?\" → uses \"vivila\" = will look after\n\nIs there a \"will eat\"?\n\nSentence 21: \"How many children will eat these pigs?\"\n\nSo future tense? Use of future verbs?\n\nNo clear \"will eat\" in data.\n\nBut in sentence 15, \"will look after\" uses \"vivila\"\n\nSo \"will eat\" might use same future marker?\n\nCheck if \"eat\" verb exists.\n\nSentence 11: \"How many things did those white men eat?\" → \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nCould \"lekamkwamsi\" be the verb? But \"lekamkwamsi\" = things.\n\nAlternatively, is there a verb?\n\nNo direct instance of \"eat\" in given sentences.\n\nBut in sentence 4: \"saw\", 2: \"arrived\", 12: \"killed\", 6: \"looked after\"\n\nNo \"eat\".\n\nSo perhaps \"eat\" is encoded as a separate verb.\n\nBut no example.\n\nAlternatively, from sentence 11: the verb is missing — likely \"eat\" is not used in translation data.\n\nBut sentence 21 says \"will eat\" — must have verb.\n\nPossibly the verb is \"kwevila\"? That's \"how many\" — cannot be.\n\nAlternatively, in some cases \"mtona\" = eat? Not found.\n\nWait — in sentence 8: \"arrived\" = \"lekotasi\"\n\nIn sentence 4: \"saw\" = \"makesiwena\"\n\nIn 2: \"arrived\" = \"mtona\"? No — \"Lekota dimdim mtona\" = \"this white man arrived\" — so \"mtona\" = man, not arrive.\n\n\"arrived\" = \"lekotasi\"? Sentence 8: \"How many dogs arrived?\" → \"Navila ka’ukwa lekotasi?\"\n\nYes — \"lekotasi\" = arrived.\n\nSo \"arrived\" = lekotasi\n\n\"will see\" = not given, but \"see\" = \"makesiwena\" in sentence 4\n\nSo \"eat\" must be a different verb.\n\nBut not in data.\n\nUnless \"eat\" is \"mtona\"? No.\n\nWait — sentence 11: \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\n\"Kwevila\" = how many \n\"lekamkwamsi\" = things \n\"dimdim mtosiwena\" = white men\n\nBut what is the verb? Possibly the verb is missing or absent.\n\nBut in sentence 12: \"killed\" is \"guyau\" — so a verb.\n\nIn sentence 10: \"saw\" = \"dakuna\"\n\nIn sentence 6: \"looked after\" = \"teyu\"\n\nNo \"eat\" — so must infer.\n\nCould \"eat\" be \"mtona\"? But \"mtona\" = man.\n\nAnother idea: \"eat\" might be \"minasina\"? In sentence 1: \"catch\" = \"minasina\"\n\nSo \"catch\" = minasina\n\n\"see\" = makesiwena\n\n\"arrive\" = lekotasi\n\n\"look after\" = teyu\n\n\"kill\" = guyau\n\nSo eat must be another verb.\n\nBut not in data.\n\nWait — sentence 11: \"How many things did those white men eat?\" → translated as \"Kwevila lekamkwamsi dimdim mtosiwena?\"\n\nThe verb is missing — likely a typo in problem? Or perhaps \"eat\" is not directly used.\n\nBut the question asks to translate, so must be present.\n\nAlternative: in Kilivila, \"eat\" is formed from a root, and must be inferred.\n\nNo example exists — but look at sentence 5: \"Which man killed two pigs?\" → \"Amtona tau lekalimati nayu bunukwa?\" — no verb.\n\nWait — \"killed\" is not directly verbalized — \"lekalimati\" = man? \"lekalimati\" = one man? \"nayu bunukwa\" = two pigs.\n\n\"Amtona tau\" = how many.\n\nSo in that, \"killed\" is not in the translation — only \"the man\" and \"two pigs\".\n\nSo perhaps the verb \"killed\" is missing or omitted.\n\nBut in sentence 12: \"killed\" is \"guyau\" — \"nagasisi guyau tokabitam\"\n\nSo \"guyau\" = killed.\n\nSo \"eat\" must be a verb — possibly \"mtona\" or another?\n\nIn sentence 7: \"that clever woman will see something\" → \"Bigisi kwetala vivila minawena nakabitam\"\n\n\"vivila\" = will see? But \"vivila\" is used as \"will look after\" — conflict?\n\nSentence 7: \"will see\" — verb is \"nakabitam\"? \"nakabitam\" = something?\n\n\"minawena nakabitam\" = something\n\n\"Bigisi kwetala\" = clever woman\n\n\"vivila\" = \"will see\" or \"will look after\"?\n\nBut \"vivila\" is associated with \"look after\" in sentence 6 and 15.\n\nSentence 6: \"The old women looked after two men\" → \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\"\n\nSentence 15: \"how many women will look after\" → \"Navila vivila biyamatasi tau mtona\" → \"vivila\" = will look after\n\nSentence 7: \"will see something\" → \"vivila minawena nakabitam\" — but \"vivila\" is used with \"see\" — contradiction?\n\nIn sentence 7: \"Bigisi kwetala vivila minawena nakabitam\" — \"Bigisi\" = that, \"kwetala\" = clever, \"vivila\" = will see, \"minawena\" = child, \"nakabitam\" = something?\n\nBut in sentence 6, \"look after\" is \"teyu\", not \"vivila\".\n\nSo probably \"vivila\" = will see, not \"look after\"? Inconsistency.\n\nIn sentence 7: \"will see something\" → \"vivila\" is used, and object is \"minawena nakabitam\"\n\nBut in sentence 15: \"will look after\" → \"vivila\"\n\nSo \"vivila\" cannot mean both.\n\nTherefore, possible that \"vivila\" means \"will see\", and \"teyu\" means \"look after\".\n\nIn sentence 15: \"Navila vivila biyamatasi tau mtona?\" → \"how many women will look after this man?\"\n\nBut if \"vivila\" = will see, then \"will look after\" should be different.\n\nBut in sentence 6: \"Leyamatasi teyu tauwau nunumwaya\" — \"teyu\" = look after\n\nSo \"teyu\" = look after\n\n\"vivila\" = will see (in sentence 7)\n\nSo likely: \"vivila\" = will see, not \"will look after\"\n\nSo in sentence 15: \"Navila vivila biyamatasi tau mtona?\" → should be \"how many women will see this man?\"\n\nBut the English is \"look after\" — contradiction.\n\nTherefore, error in assumption.\n\nSentence 15: \"How many women will look after this man?\" → \"Navila vivila biyamatasi tau 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"method": "redacted_solution_hint_mask5", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "solver_checklist", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-a", + "method": "unit_audit", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "a.1: The thief will strike the donkey; a.2: I bought the doors for me; a.3: I will repair the doors; a.4: will repair the camels to the thief; a.5: I will strike the chicken", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "anti_nearmiss", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_1x4", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "groot_anchor_iid", + "samples": 1, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "iid", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "solver_checklist", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2016-individual-p3-sub-b", + "method": "unit_audit", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "anti_nearmiss", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_1x4", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "groot_anchor_iid", + "samples": 1, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "iid", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "redacted_solution_hint_mask4", + "samples": 4, + "best_score_fraction": 0.2, + "any_positive": true, + "any_exact": false, + "best_boxed_text": "a.1: How many things will this man catch?; a.2: Two things will eat these fish.; a.3: Which child is this?; a.4: How many men will see the wild children?; How many men will the wild children see?; a.5: That man saw those things.", + "matched_units": [ + "a.4" + ], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "solver_checklist", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-a", + "method": "unit_audit", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "a.1", + "a.2", + "a.3", + "a.4", + "a.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "anti_nearmiss", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_1x4", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "b.1: navila namwaya legisi waga makesiwena; b.2: minasina dimdim mtona vivila teyu gwadi kwetala magudiwena; b.3: navila gwadi magudiwena vivila lekamkwamsi minasina bunukwa; b.4: amtona legisi minasina waga dakuna tau; b.5: tetala nayu waga makesiwena dakuna mtona", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "groot_anchor_iid", + "samples": 1, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "iid", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "redacted_solution_hint_mask5", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "solver_checklist", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "b.1: Navila namwaya leyamatasi makesiwena; b.2: tetala dimdim mtona tauwau gwadi kwetala magudiwena; b.3: Navila gwadi mtsiwena waga bunukwa; b.4: amakena legisi navasi waga dakuna minasina; b.5: nayu ka'ukwa makesiwena bikota legisi mtona", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + }, + { + "split": "val", + "record_id": "iol-2021-individual-p3-sub-b", + "method": "unit_audit", + "samples": 4, + "best_score_fraction": 0.0, + "any_positive": false, + "any_exact": false, + "best_boxed_text": "", + "matched_units": [], + "missed_units": [ + "b.1", + "b.2", + "b.3", + "b.4", + "b.5" + ] + } + ], + "positive_samples": 9, + "exact_samples": 3 + } +} diff --git a/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.md b/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.md new file mode 100644 index 0000000000000000000000000000000000000000..b369698c1aee25b2e24dbd4e58b1329c4d7e61d4 --- /dev/null +++ b/benchmark/IOL/ioling_hf/reports/ioling_hint_diversity/Qwen_Qwen3-4B-Instruct-2507__qwen3_4b_trainval_hints_groot_4k.md @@ -0,0 +1,126 @@ +# IOLing Hint Diversity Probe + +- generated: `2026-07-10T23:20:51.241026+00:00` +- model: `Qwen/Qwen3-4B-Instruct-2507` +- samples: `375` +- positive samples: `9` +- exact samples: `3` + +## Method Summary + +| split | method | records | samples | records + | records exact | sample + | sample exact | mean best | format | unique boxes | +| --- | --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | +| train | anti_nearmiss | 9 | 36 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.056 | 3 | +| train | groot_1x4 | 9 | 36 | 2 | 0 | 0.083 | 0.000 | 0.056 | 0.278 | 11 | +| train | groot_anchor_iid | 9 | 9 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.111 | 2 | +| train | iid | 9 | 36 | 1 | 0 | 0.028 | 0.000 | 0.037 | 0.139 | 7 | +| train | redacted_solution_hint_mask0 | 1 | 4 | 1 | 1 | 1.000 | 0.750 | 1.000 | 1.000 | 2 | +| train | redacted_solution_hint_mask1 | 2 | 8 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.125 | 2 | +| train | redacted_solution_hint_mask3 | 1 | 4 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 1 | +| train | redacted_solution_hint_mask4 | 1 | 4 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 1 | +| train | redacted_solution_hint_mask5 | 2 | 8 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.250 | 3 | +| train | redacted_solution_hint_mask6 | 2 | 8 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 1 | +| train | solver_checklist | 9 | 36 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.139 | 6 | +| train | unit_audit | 9 | 36 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.222 | 9 | +| val | anti_nearmiss | 6 | 24 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.042 | 2 | +| val | groot_1x4 | 6 | 24 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.083 | 3 | +| val | groot_anchor_iid | 6 | 6 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 1 | +| val | iid | 6 | 24 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.042 | 2 | +| val | redacted_solution_hint_mask2 | 2 | 8 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.125 | 2 | +| val | redacted_solution_hint_mask4 | 1 | 4 | 1 | 0 | 0.250 | 0.000 | 0.200 | 0.250 | 2 | +| val | redacted_solution_hint_mask5 | 3 | 12 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.000 | 1 | +| val | solver_checklist | 6 | 24 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.083 | 3 | +| val | unit_audit | 6 | 24 | 0 | 0 | 0.000 | 0.000 | 0.000 | 0.042 | 2 | + +## Positive Samples + +### `train` `iol-2011-individual-p1-sub-b` `redacted_solution_hint_mask0` sample `0` + +- score: `1.0` +- matched: `b.1, b.2, b.3, b.4` +- missed: `` + +```text +b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw +``` + +### `train` `iol-2011-individual-p1-sub-b` `redacted_solution_hint_mask0` sample `2` + +- score: `1.0` +- matched: `b.1, b.2, b.3, b.4` +- missed: `` + +```text +b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw +``` + +### `train` `iol-2011-individual-p1-sub-b` `redacted_solution_hint_mask0` sample `3` + +- score: `1.0` +- matched: `b.1, b.2, b.3, b.4` +- missed: `` + +```text +b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: taw¯anæhkæw; b.4: ket¯ohnæw +``` + +### `train` `iol-2011-individual-p1-sub-b` `redacted_solution_hint_mask0` sample `1` + +- score: `0.75` +- matched: `b.1, b.2, b.4` +- missed: `b.3` + +```text +b.1: new¯æpahtan; b.2: kek¯awenæq; b.3: k¯anæhkæ; b.4: ket¯ohnæw +``` + +### `train` `iol-2016-individual-p5-sub-a` `groot_1x4` sample `0` + +- score: `0.3333333333333333` +- matched: `a.1` +- missed: `a.2, a.3` + +```text +a.1: is it in my house; a.2: the field too; a.3: the field too +``` + +### `train` `iol-2016-individual-p5-sub-a` `groot_1x4` sample `2` + +- score: `0.3333333333333333` +- matched: `a.1` +- missed: `a.2, a.3` + +```text +a.1: is it in my house?; a.2: the field too; a.3: the field too +``` + +### `train` `iol-2016-individual-p5-sub-a` `iid` sample `0` + +- score: `0.3333333333333333` +- matched: `a.1` +- missed: `a.2, a.3` + +```text +a.1: is it in my house?; a.2: the field too; a.3: the field too +``` + +### `val` `iol-2021-individual-p3-sub-a` `redacted_solution_hint_mask4` sample `3` + +- score: `0.2` +- matched: `a.4` +- missed: `a.1, a.2, a.3, a.5` + +```text +a.1: How many things will this man catch?; a.2: Two things will eat these fish.; a.3: Which child is this?; a.4: How many men will see the wild children?; How many men will the wild children see?; a.5: That man saw those things. +``` + +### `train` `iol-2008-individual-p5-sub-a` `groot_1x4` sample `0` + +- score: `0.16666666666666666` +- matched: `a.5` +- missed: `a.1, a.2, a.3, a.4, a.6` + +```text +a.1: The hunter came and saw; a.2: Your boy hurt you; a.3: The hunter cured; a.4: The dog hurt and shot; a.5: You came; a.6: The hunter cured a polar bear +``` + diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/NUnitExtension.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/NUnitExtension.meta new file mode 100644 index 0000000000000000000000000000000000000000..0c9988951a1ee743e87c352d88fe574d4ae14c25 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/NUnitExtension.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: 3f9202a39620f51418046c7754f215f0 +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs new file mode 100644 index 0000000000000000000000000000000000000000..e99d4524feef0b1f4818108ee8c135307cbb2326 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs @@ -0,0 +1,32 @@ +using System; +using System.Linq; +using NUnit.Framework; +using NUnit.Framework.Interfaces; +using NUnit.Framework.Internal; + +namespace UnityEditor.TestTools +{ + [AttributeUsage(AttributeTargets.Assembly | AttributeTargets.Class | AttributeTargets.Method)] + internal class RequireApiProfileAttribute : NUnitAttribute, IApplyToTest + { + public ApiCompatibilityLevel[] apiProfiles { get; private set; } + + public RequireApiProfileAttribute(params ApiCompatibilityLevel[] apiProfiles) + { + this.apiProfiles = apiProfiles; + } + + void IApplyToTest.ApplyToTest(Test test) + { + test.Properties.Add(PropertyNames.Category, string.Format("ApiProfile({0})", string.Join(", ", apiProfiles.Select(p => p.ToString()).OrderBy(p => p).ToArray()))); + ApiCompatibilityLevel testProfile = PlayerSettings.GetApiCompatibilityLevel(EditorUserBuildSettings.activeBuildTargetGroup); + + if (!apiProfiles.Contains(testProfile)) + { + string skipReason = "Skipping test as it requires a compatible api profile set: " + string.Join(", ", apiProfiles.Select(p => p.ToString()).ToArray()); + test.RunState = RunState.Skipped; + test.Properties.Add(PropertyNames.SkipReason, skipReason); + } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..66d03bd4ae4870eced7f777740d64b48d4b48b79 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequireApiProfileAttribute.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: a667f6654ad7a9548b8c8e68b51c8895 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs new file mode 100644 index 0000000000000000000000000000000000000000..321a0fe05749a5399cf861297eb5cb1539efaead --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs @@ -0,0 +1,33 @@ +using System; +using System.Linq; +using NUnit.Framework; +using NUnit.Framework.Interfaces; +using NUnit.Framework.Internal; + +namespace UnityEditor.TestTools +{ + [AttributeUsage(AttributeTargets.Assembly | AttributeTargets.Class | AttributeTargets.Method)] + public class RequirePlatformSupportAttribute : NUnitAttribute, IApplyToTest + { + public RequirePlatformSupportAttribute(params BuildTarget[] platforms) + { + this.platforms = platforms; + } + + public BuildTarget[] platforms { get; private set; } + + void IApplyToTest.ApplyToTest(Test test) + { + test.Properties.Add(PropertyNames.Category, string.Format("RequirePlatformSupport({0})", string.Join(", ", platforms.Select(p => p.ToString()).OrderBy(p => p).ToArray()))); + + if (!platforms.All(p => BuildPipeline.IsBuildTargetSupported(BuildTargetGroup.Unknown, p))) + { + var missingPlatforms = platforms.Where(p => !BuildPipeline.IsBuildTargetSupported(BuildTargetGroup.Unknown, p)).Select(p => p.ToString()).ToArray(); + string skipReason = "Test cannot be run as it requires support for the following platforms to be installed: " + string.Join(", ", missingPlatforms); + + test.RunState = RunState.Skipped; + test.Properties.Add(PropertyNames.SkipReason, skipReason); + } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..8493058029924baf310ff47d643e89343d70211e --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/RequirePlatformSupportAttribute.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: d2146428d3f1ad54eb7326c9a44b3284 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs new file mode 100644 index 0000000000000000000000000000000000000000..a0947cbda37d0f307d95ac1c102daee734320aa7 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs @@ -0,0 +1,22 @@ +using System.Linq; +using UnityEditor.Build; + +namespace UnityEditor.TestRunner +{ + // This class is invoked from native, during build + internal class TestBuildAssemblyFilter : IFilterBuildAssemblies + { + private const string nunitAssemblyName = "nunit.framework"; + private const string unityTestRunnerAssemblyName = "UnityEngine.TestRunner"; + + public int callbackOrder { get; } + public string[] OnFilterAssemblies(BuildOptions buildOptions, string[] assemblies) + { + if ((buildOptions & BuildOptions.IncludeTestAssemblies) == BuildOptions.IncludeTestAssemblies || PlayerSettings.playModeTestRunnerEnabled) + { + return assemblies; + } + return assemblies.Where(x => !x.Contains(nunitAssemblyName) && !x.Contains(unityTestRunnerAssemblyName)).ToArray(); + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..f3cd3bd2d9451af4d126f98f2e6630acbc02fc8d --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestBuildAssemblyFilter.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 3411e19edd44cfd46b548b058c3bc36c +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestLaunchers.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestLaunchers.meta new file mode 100644 index 0000000000000000000000000000000000000000..c6a951b371a8506067496afee91d606f0b9807f0 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestLaunchers.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: d64d92e4f04a13e4b99ea8d48e9e8ae9 +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs new file mode 100644 index 0000000000000000000000000000000000000000..b95f63ac0ad2d845aece02bac26adf877201c2bc --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs @@ -0,0 +1,80 @@ +using System; +using System.Reflection; +using System.Text; +using NUnit.Framework.Interfaces; +using NUnit.Framework.Internal; +using UnityEngine; +using UnityEngine.TestRunner.NUnitExtensions; + +namespace UnityEditor.TestTools.TestRunner +{ + [Serializable] + internal class TestResultSerializer + { + private static readonly BindingFlags flags = BindingFlags.NonPublic | BindingFlags.Public | + BindingFlags.Instance | BindingFlags.FlattenHierarchy; + + [SerializeField] public string id; + + [SerializeField] public string fullName; + + [SerializeField] private double duration; + + [SerializeField] private string label; + + [SerializeField] private string message; + + [SerializeField] private string output; + + [SerializeField] private string site; + + [SerializeField] private string stacktrace; + + [SerializeField] private double startTimeAO; + + [SerializeField] private double endTimeAO; + + [SerializeField] private string status; + + [SerializeField] public string uniqueName; + + public static TestResultSerializer MakeFromTestResult(ITestResult result) + { + var wrapper = new TestResultSerializer(); + wrapper.id = result.Test.Id; + wrapper.fullName = result.FullName; + wrapper.status = result.ResultState.Status.ToString(); + wrapper.label = result.ResultState.Label; + wrapper.site = result.ResultState.Site.ToString(); + wrapper.output = result.Output; + wrapper.duration = result.Duration; + wrapper.stacktrace = result.StackTrace; + wrapper.message = result.Message; + wrapper.startTimeAO = result.StartTime.ToOADate(); + wrapper.endTimeAO = result.EndTime.ToOADate(); + wrapper.uniqueName = result.Test.GetUniqueName(); + return wrapper; + } + + public void RestoreTestResult(TestResult result) + { + var resultState = new ResultState((TestStatus)Enum.Parse(typeof(TestStatus), status), label, + (FailureSite)Enum.Parse(typeof(FailureSite), site)); + var baseType = result.GetType().BaseType; + baseType.GetField("_resultState", flags).SetValue(result, resultState); + baseType.GetField("_output", flags).SetValue(result, new StringBuilder(output)); + baseType.GetField("_duration", flags).SetValue(result, duration); + baseType.GetField("_message", flags).SetValue(result, message); + baseType.GetField("_stackTrace", flags).SetValue(result, stacktrace); + baseType.GetProperty("StartTime", flags) + .SetValue(result, DateTime.FromOADate(startTimeAO), null); + baseType.GetProperty("EndTime", flags) + .SetValue(result, DateTime.FromOADate(endTimeAO), null); + } + + public bool IsPassed() + { + return status == TestStatus.Passed.ToString(); + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..96f296036bb400655be541ab58a289238eeccfa4 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestResultSerializer.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 559482fe33c79e44882d3a6cedc55fb5 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRun.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRun.meta new file mode 100644 index 0000000000000000000000000000000000000000..6f6e8cfd23869427ab9027d0b7958159c7bbfd63 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRun.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: 8721cb2237d4a564a94a51f56243bdac +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunner.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunner.meta new file mode 100644 index 0000000000000000000000000000000000000000..d09886b69e5bafba975a100064d33ee53011eff0 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunner.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: 49d4c2ab7ff0f4442af256bad7c9d57c +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs new file mode 100644 index 0000000000000000000000000000000000000000..0be1bceaf8f5106a683adfc9496039c5fb00ba6f --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs @@ -0,0 +1,266 @@ +using System; +using UnityEditor.Callbacks; +using UnityEditor.TestTools.TestRunner.Api; +using UnityEditor.TestTools.TestRunner.GUI; +using UnityEngine; + +namespace UnityEditor.TestTools.TestRunner +{ + /// + /// The TestRunnerWindow class is repsonsible for drawing the Test Runner window. + /// + [Serializable] + public class TestRunnerWindow : EditorWindow, IHasCustomMenu + { + internal static class Styles + { + public static GUIStyle info; + public static GUIStyle testList; + + static Styles() + { + info = new GUIStyle(EditorStyles.wordWrappedLabel); + info.wordWrap = false; + info.stretchHeight = true; + info.margin.right = 15; + + testList = new GUIStyle("CN Box"); + testList.margin.top = 0; + testList.padding.left = 3; + } + } + + private readonly GUIContent m_GUIHorizontalSplit = EditorGUIUtility.TrTextContent("Horizontal layout"); + private readonly GUIContent m_GUIVerticalSplit = EditorGUIUtility.TrTextContent("Vertical layout"); + private readonly GUIContent m_GUIDisablePlaymodeTestsRunner = EditorGUIUtility.TrTextContent("Disable playmode tests for all assemblies"); + private readonly GUIContent m_GUIRunPlayModeTestAsEditModeTests = EditorGUIUtility.TrTextContent("Run playmode tests as editmode tests"); + + internal static TestRunnerWindow s_Instance; + private bool m_IsBuilding; + [NonSerialized] + private bool m_Enabled; + internal TestFilterSettings filterSettings; + + [SerializeField] + private SplitterState m_Spl = new SplitterState(new float[] { 75, 25 }, new[] { 32, 32 }, null); + + private TestRunnerWindowSettings m_Settings; + + private enum TestRunnerMenuLabels + { + PlayMode = 0, + EditMode = 1 + } + [SerializeField] + private int m_TestTypeToolbarIndex = (int)TestRunnerMenuLabels.EditMode; + [SerializeField] + private PlayModeTestListGUI m_PlayModeTestListGUI; + [SerializeField] + private EditModeTestListGUI m_EditModeTestListGUI; + + internal TestListGUI m_SelectedTestTypes; + + private ITestRunnerApi m_testRunnerApi; + + private WindowResultUpdater m_WindowResultUpdater; + + /// + /// Launches the Test Runner window. + /// + [MenuItem("Window/General/Test Runner", false, 201, false)] + public static void ShowWindow() + { + s_Instance = GetWindow("Test Runner"); + s_Instance.Show(); + } + + static TestRunnerWindow() + { + InitBackgroundRunners(); + } + + private static void InitBackgroundRunners() + { + EditorApplication.playModeStateChanged -= OnPlayModeStateChanged; + EditorApplication.playModeStateChanged += OnPlayModeStateChanged; + } + + [DidReloadScripts] + private static void CompilationCallback() + { + UpdateWindow(); + } + + private static void OnPlayModeStateChanged(PlayModeStateChange state) + { + if (s_Instance && state == PlayModeStateChange.EnteredEditMode && s_Instance.m_SelectedTestTypes.HasTreeData()) + { + //repaint message details after exit playmode + s_Instance.m_SelectedTestTypes.TestSelectionCallback(s_Instance.m_SelectedTestTypes.m_TestListState.selectedIDs.ToArray()); + s_Instance.Repaint(); + } + } + + internal void OnDestroy() + { + EditorApplication.playModeStateChanged -= OnPlayModeStateChanged; + } + + private void OnEnable() + { + s_Instance = this; + SelectTestListGUI(m_TestTypeToolbarIndex); + + m_testRunnerApi = ScriptableObject.CreateInstance(); + m_WindowResultUpdater = new WindowResultUpdater(); + m_testRunnerApi.RegisterCallbacks(m_WindowResultUpdater); + } + + private void Enable() + { + m_Settings = new TestRunnerWindowSettings("UnityEditor.PlaymodeTestsRunnerWindow"); + filterSettings = new TestFilterSettings("UnityTest.IntegrationTestsRunnerWindow"); + + if (m_SelectedTestTypes == null) + { + SelectTestListGUI(m_TestTypeToolbarIndex); + } + + StartRetrieveTestList(); + m_SelectedTestTypes.Reload(); + m_Enabled = true; + } + + private void SelectTestListGUI(int testTypeToolbarIndex) + { + if (testTypeToolbarIndex == (int)TestRunnerMenuLabels.PlayMode) + { + if (m_PlayModeTestListGUI == null) + { + m_PlayModeTestListGUI = new PlayModeTestListGUI(); + } + m_SelectedTestTypes = m_PlayModeTestListGUI; + } + else if (testTypeToolbarIndex == (int)TestRunnerMenuLabels.EditMode) + { + if (m_EditModeTestListGUI == null) + { + m_EditModeTestListGUI = new EditModeTestListGUI(); + } + m_SelectedTestTypes = m_EditModeTestListGUI; + } + } + + private void StartRetrieveTestList() + { + if (!m_SelectedTestTypes.HasTreeData()) + { + var listToInit = m_SelectedTestTypes; + m_testRunnerApi.RetrieveTestList(m_SelectedTestTypes.TestMode, (rootTest) => + { + listToInit.Init(this, rootTest); + listToInit.Reload(); + }); + } + } + + internal void OnGUI() + { + if (!m_Enabled) + { + Enable(); + } + + if (BuildPipeline.isBuildingPlayer) + { + m_IsBuilding = true; + } + else if (m_IsBuilding) + { + m_IsBuilding = false; + Repaint(); + } + + EditorGUILayout.BeginHorizontal(); + GUILayout.FlexibleSpace(); + var selectedIndex = m_TestTypeToolbarIndex; + m_TestTypeToolbarIndex = GUILayout.Toolbar(m_TestTypeToolbarIndex, Enum.GetNames(typeof(TestRunnerMenuLabels)), "LargeButton", UnityEngine.GUI.ToolbarButtonSize.FitToContents); + GUILayout.FlexibleSpace(); + EditorGUILayout.EndHorizontal(); + + if (selectedIndex != m_TestTypeToolbarIndex) + { + SelectTestListGUI(m_TestTypeToolbarIndex); + StartRetrieveTestList(); + } + + EditorGUILayout.BeginVertical(); + using (new EditorGUI.DisabledScope(EditorApplication.isPlayingOrWillChangePlaymode)) + { + m_SelectedTestTypes.PrintHeadPanel(); + } + EditorGUILayout.EndVertical(); + + if (m_Settings.verticalSplit) + SplitterGUILayout.BeginVerticalSplit(m_Spl); + else + SplitterGUILayout.BeginHorizontalSplit(m_Spl); + + EditorGUILayout.BeginVertical(); + EditorGUILayout.BeginVertical(Styles.testList); + m_SelectedTestTypes.RenderTestList(); + EditorGUILayout.EndVertical(); + EditorGUILayout.EndVertical(); + + m_SelectedTestTypes.RenderDetails(); + + if (m_Settings.verticalSplit) + SplitterGUILayout.EndVerticalSplit(); + else + SplitterGUILayout.EndHorizontalSplit(); + } + + /// + /// Adds additional menu items to the Test Runner window. + /// + /// The + public void AddItemsToMenu(GenericMenu menu) + { + menu.AddItem(m_GUIVerticalSplit, m_Settings.verticalSplit, m_Settings.ToggleVerticalSplit); + menu.AddItem(m_GUIHorizontalSplit, !m_Settings.verticalSplit, m_Settings.ToggleVerticalSplit); + + menu.AddSeparator(null); + + if (EditorPrefs.GetBool("InternalMode", false)) + { + menu.AddItem(m_GUIRunPlayModeTestAsEditModeTests, PlayerSettings.runPlayModeTestAsEditModeTest, () => + { + PlayerSettings.runPlayModeTestAsEditModeTest = !PlayerSettings.runPlayModeTestAsEditModeTest; + }); + } + + if (PlayerSettings.playModeTestRunnerEnabled) + { + PlayerSettings.playModeTestRunnerEnabled = false; + EditorUtility.DisplayDialog(m_GUIDisablePlaymodeTestsRunner.text, "You need to restart the editor now", "Ok"); + } + } + + internal void RebuildUIFilter() + { + if (m_SelectedTestTypes != null && m_SelectedTestTypes.HasTreeData()) + { + m_SelectedTestTypes.RebuildUIFilter(); + } + } + + internal static void UpdateWindow() + { + if (s_Instance != null && s_Instance.m_SelectedTestTypes != null) + { + s_Instance.m_SelectedTestTypes.Repaint(); + s_Instance.Repaint(); + } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..5cb0e868a55446b368b598e1a0a4838883e41b8f --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindow.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 4dfcd3a631f61d248b7cc0b845d40345 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs new file mode 100644 index 0000000000000000000000000000000000000000..366df2608dedb73871bcde300e56c40bd8007771 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs @@ -0,0 +1,26 @@ +namespace UnityEditor.TestTools.TestRunner +{ + internal class TestRunnerWindowSettings + { + public bool verticalSplit; + + private readonly string m_PrefsKey; + + public TestRunnerWindowSettings(string prefsKey) + { + m_PrefsKey = prefsKey; + verticalSplit = EditorPrefs.GetBool(m_PrefsKey + ".verticalSplit", true); + } + + public void ToggleVerticalSplit() + { + verticalSplit = !verticalSplit; + Save(); + } + + private void Save() + { + EditorPrefs.SetBool(m_PrefsKey + ".verticalSplit", verticalSplit); + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..44bcc5a02a9ed3d480c02bf3f81f0084efe458c1 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/TestRunnerWindowSettings.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 2b301b727225f1941974d69e61a55620 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git 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"Mono.Cecil.Mdb.dll", + "Mono.Cecil.Rocks.dll" + ], + "autoReferenced": false, + "defineConstraints": [] +} \ No newline at end of file diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/UnityEditor.TestRunner.asmdef.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/UnityEditor.TestRunner.asmdef.meta new file mode 100644 index 0000000000000000000000000000000000000000..63c0290042ac35ff1ddfe7a69d230dfcb617186f --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEditor.TestRunner/UnityEditor.TestRunner.asmdef.meta @@ -0,0 +1,7 @@ +fileFormatVersion: 2 +guid: 0acc523941302664db1f4e527237feb3 +AssemblyDefinitionImporter: + externalObjects: {} + userData: + assetBundleName: + 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a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/AssemblyInfo.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/AssemblyInfo.cs new file mode 100644 index 0000000000000000000000000000000000000000..41496773b2f8f31eaf423c639ceda3bc10cd10a7 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/AssemblyInfo.cs @@ -0,0 +1,16 @@ +using System.Reflection; +using System.Runtime.CompilerServices; + +[assembly: AssemblyTitle("UnityEngine.TestRunner")] + +[assembly: InternalsVisibleTo("UnityEditor.TestRunner")] +[assembly: InternalsVisibleTo("DynamicProxyGenAssembly2")] +[assembly: InternalsVisibleTo("Unity.PerformanceTesting")] +[assembly: 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b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/AllocatingGCMemoryConstraint.cs @@ -0,0 +1,128 @@ +using System; +using NUnit.Framework; +using NUnit.Framework.Constraints; +using UnityEngine.Profiling; + +namespace UnityEngine.TestTools.Constraints +{ + /// + /// An NUnit test constraint class to test whether a given block of code makes any GC allocations. + /// + /// Use this class with NUnit's Assert.That() method to make assertions about the GC behaviour of your code. The constraint executes the delegate you provide, and checks if it has caused any GC memory to be allocated. If any GC memory was allocated, the constraint passes; otherwise, the constraint fails. + /// + /// Usually you negate this constraint to make sure that your delegate does not allocate any GC memory. This is easy to do using the Is class: + /// + /// + /// + /// using NUnit.Framework; + /// using UnityEngine.TestTools.Constraints; + /// using Is = UnityEngine.TestTools.Constraints.Is; + /// + /// public class MyTestClass + /// { + /// [Test] + /// public void SettingAVariableDoesNotAllocate() + /// { + /// Assert.That(() => { + /// int a = 0; + /// a = 1; + /// }, Is.Not.AllocatingGCMemory()); + /// } + /// } + /// + /// + public class AllocatingGCMemoryConstraint : Constraint + { + private class AllocatingGCMemoryResult : ConstraintResult + { + private readonly int diff; + public AllocatingGCMemoryResult(IConstraint constraint, object actualValue, int diff) : base(constraint, actualValue, diff > 0) + { + this.diff = diff; + } + + public override void WriteMessageTo(MessageWriter writer) + { + if (diff == 0) + writer.WriteMessageLine("The provided delegate did not make any GC allocations."); + else + writer.WriteMessageLine("The provided delegate made {0} GC allocation(s).", diff); + } + } + + private ConstraintResult ApplyTo(Action action, object original) + { + var recorder = Recorder.Get("GC.Alloc"); + + // The recorder was created enabled, which means it captured the creation of the Recorder object itself, etc. + // Disabling it flushes its data, so that we can retrieve the sample block count and have it correctly account + // for these initial allocations. + recorder.enabled = false; + +#if !UNITY_WEBGL + recorder.FilterToCurrentThread(); +#endif + + recorder.enabled = true; + + try + { + action(); + } + finally + { + recorder.enabled = false; +#if !UNITY_WEBGL + recorder.CollectFromAllThreads(); +#endif + } + + return new AllocatingGCMemoryResult(this, original, recorder.sampleBlockCount); + } + + /// + /// Applies GC memory constraint to the test. + /// + /// An object to apply the GC constraint to. Should be a . + /// A ConstraintResult + /// Throws a if the provided object is null. + /// Throws a if the provided object is not a . + public override ConstraintResult ApplyTo(object obj) + { + if (obj == null) + throw new ArgumentNullException(); + + TestDelegate d = obj as TestDelegate; + if (d == null) + throw new ArgumentException(string.Format("The actual value must be a TestDelegate but was {0}", + obj.GetType())); + + return ApplyTo(() => d.Invoke(), obj); + } + + /// + /// Test whether the constraint is satisfied by a given reference. + /// The default implementation simply dereferences the value but + /// derived classes may override it to provide for delayed processing. + /// + /// The type of the actual value delegate to be tested. + /// A reference to the value delegate to be tested + /// A ConstraintResult + /// Throws a if the provided delegate is null. + public override ConstraintResult ApplyTo(ActualValueDelegate del) + { + if (del == null) + throw new ArgumentNullException(); + + return ApplyTo(() => del.Invoke(), del); + } + + /// + /// The Description of what this constraint tests, for to use in messages and in the ConstraintResult. + /// + public override string Description + { + get { return "allocates GC memory"; } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/AllocatingGCMemoryConstraint.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/AllocatingGCMemoryConstraint.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..0933c8551793245b056615c06a114de882931de3 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/AllocatingGCMemoryConstraint.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: d09858396dd7adb4bbdb22ea0c8c3a37 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs new file mode 100644 index 0000000000000000000000000000000000000000..812b1f06d9e7701acffb6e9f4abc601252b1373e --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs @@ -0,0 +1,14 @@ +using NUnit.Framework.Constraints; + +namespace UnityEngine.TestTools.Constraints +{ + public static class ConstraintExtensions + { + public static AllocatingGCMemoryConstraint AllocatingGCMemory(this ConstraintExpression chain) + { + var constraint = new AllocatingGCMemoryConstraint(); + chain.Append(constraint); + return constraint; + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..13434964a6834e812796415a4185d5204023ca63 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/ConstraintsExtensions.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 68a48d1900320ed458e118415857faf6 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs new file mode 100644 index 0000000000000000000000000000000000000000..ab4ff8e3827e5c5c049fb3fab1ad2d2f812f1b35 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs @@ -0,0 +1,18 @@ +using NUnit.Framework; +using NUnit.Framework.Interfaces; + +namespace UnityEngine.TestTools.TestRunner +{ + internal class InvalidSignatureException : ResultStateException + { + public InvalidSignatureException(string message) + : base(message) + { + } + + public override ResultState ResultState + { + get { return ResultState.NotRunnable; } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..86aee7faa82b6ef468e5dfea199687e42837333d --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/InvalidSignatureException.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 9650d910fcaefb34cb45f121c1993892 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs new file mode 100644 index 0000000000000000000000000000000000000000..c0871ef21a49c74ff7c390098dc049c28492b09f --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs @@ -0,0 +1,10 @@ +namespace UnityEngine.TestTools.Constraints +{ + public class Is : NUnit.Framework.Is + { + public static AllocatingGCMemoryConstraint AllocatingGCMemory() + { + return new AllocatingGCMemoryConstraint(); + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..23ed44a64093b8237695d28b707901a803f72103 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/Is.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 6d5833966abeadb429de247e4316eef4 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs new file mode 100644 index 0000000000000000000000000000000000000000..350bd692ca8a71096523538b5e488489c6932ebb --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs @@ -0,0 +1,78 @@ +using System.Text.RegularExpressions; +using UnityEngine.TestTools.Logging; + +namespace UnityEngine.TestTools +{ + /// + /// A test fails if Unity logs a message other than a regular log or warning message. Use `LogAssert` to check for an expected message in the log so that the test does not fail when Unity logs the message. + /// Use `LogAssert.Expect` before running the code under test, as the check for expected logs runs at the end of each frame. + /// A test also reports a failure, if an expected message does not appear, or if Unity does not log any regular log or warning messages. + /// + /// `LogAssert` lets you expect Unity log messages that would otherwise cause the test to fail. + /// + public static class LogAssert + { + /// + /// Verifies that a log message of a specified type appears in the log. A test won't fail from an expected error, assertion, or exception log message. It does fail if an expected message does not appear in the log. + /// + /// A type of log to expect. It can take one of the [LogType enum](https://docs.unity3d.com/ScriptReference/LogType.html) values. + /// A string value that should equate to the expected message. + /// + /// + /// [Test] + /// public void LogAssertExample() + /// { + /// // Expect a regular log message + /// LogAssert.Expect(LogType.Log, "Log message"); + /// + /// // The test fails without the following expected log message + /// Debug.Log("Log message"); + /// + /// // An error log + /// Debug.LogError("Error message"); + /// + /// // Without expecting an error log, the test would fail + /// LogAssert.Expect(LogType.Error, "Error message"); + /// } + /// + /// + /// + public static void Expect(LogType type, string message) + { + LogScope.Current.ExpectedLogs.Enqueue(new LogMatch() { LogType = type, Message = message }); + } + /// + /// Verifies that a log message of a specified type appears in the log. A test won't fail from an expected error, assertion, or exception log message. It does fail if an expected message does not appear in the log. + /// + /// A type of log to expect. It can take one of the [LogType enum](https://docs.unity3d.com/ScriptReference/LogType.html) values. + /// A regular expression pattern to match the expected message. + public static void Expect(LogType type, Regex message) + { + LogScope.Current.ExpectedLogs.Enqueue(new LogMatch() { LogType = type, MessageRegex = message }); + } + /// + /// Triggers an assertion when receiving any log messages and fails the test if some are unexpected messages. If multiple tests need to check for no received unexpected logs, consider using the attribute instead. + /// + public static void NoUnexpectedReceived() + { + LogScope.Current.NoUnexpectedReceived(); + } + /// Set this property to `true` to prevent unexpected error log messages from triggering an assertion. By default, it is `false`. + /// The value of the ignoreFailingMessages boolean property. + public static bool ignoreFailingMessages + { + get + { + return LogScope.Current.IgnoreFailingMessages; + } + set + { + if (value != LogScope.Current.IgnoreFailingMessages) + { + Debug.LogFormat(LogType.Log, LogOption.NoStacktrace, null, "\nIgnoreFailingMessages:" + (value? "true":"false")); + } + LogScope.Current.IgnoreFailingMessages = value; + } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..7a278a31b0b982627a1802c3af8d5ae6574c71c2 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogAssert.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: c97b794b51780d349a16826a4c7898d7 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogScope.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogScope.meta new file mode 100644 index 0000000000000000000000000000000000000000..284dc6adda8c1c3834b728c25d2b083fbffd96c4 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/LogScope.meta @@ -0,0 +1,8 @@ +fileFormatVersion: 2 +guid: b1d8465ba1376b148bdab58965101f47 +folderAsset: yes +DefaultImporter: + externalObjects: {} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs new file mode 100644 index 0000000000000000000000000000000000000000..8ad39f4460da4950f803524e3423ae054bc4149a --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs @@ -0,0 +1,29 @@ +using NUnit.Framework; +using NUnit.Framework.Interfaces; +using UnityEngine.TestTools.Logging; + +namespace UnityEngine.TestTools.TestRunner +{ + internal class UnexpectedLogMessageException : ResultStateException + { + public LogMatch LogEvent; + + public UnexpectedLogMessageException(LogMatch log) + : base(BuildMessage(log)) + { + LogEvent = log; + } + + private static string BuildMessage(LogMatch log) + { + return string.Format("Expected log did not appear: {0}", log); + } + + public override ResultState ResultState + { + get { return ResultState.Failure; } + } + + public override string StackTrace { get { return null; } } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..7b9e61150fd712b852771097a36279b958a097d3 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnexpectedLogMessageException.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: 5b2eeca598284bd4abb4a15c30df1576 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs new file mode 100644 index 0000000000000000000000000000000000000000..9427cc86ddf5ed209aad199e8f554f2730c795f5 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs @@ -0,0 +1,35 @@ +using NUnit.Framework; +using NUnit.Framework.Interfaces; +using UnityEngine.TestTools.Logging; +using UnityEngine.TestTools.Utils; + +namespace UnityEngine.TestTools.TestRunner +{ + internal class UnhandledLogMessageException : ResultStateException + { + public LogEvent LogEvent; + private readonly string m_CustomStackTrace; + + public UnhandledLogMessageException(LogEvent log) + : base(BuildMessage(log)) + { + LogEvent = log; + m_CustomStackTrace = StackTraceFilter.Filter(log.StackTrace); + } + + private static string BuildMessage(LogEvent log) + { + return string.Format("Unhandled log message: '{0}'. Use UnityEngine.TestTools.LogAssert.Expect", log); + } + + public override ResultState ResultState + { + get { return ResultState.Failure; } + } + + public override string StackTrace + { + get { return m_CustomStackTrace; } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs.meta new file mode 100644 index 0000000000000000000000000000000000000000..1019924b3e3dc04711c5e00bb93b75ca0913b082 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnhandledLogMessageException.cs.meta @@ -0,0 +1,11 @@ +fileFormatVersion: 2 +guid: a8ed4063f2beecd41a234a582202f3c4 +MonoImporter: + externalObjects: {} + serializedVersion: 2 + defaultReferences: [] + executionOrder: 0 + icon: {instanceID: 0} + userData: + assetBundleName: + assetBundleVariant: diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnityTestTimeoutException.cs b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnityTestTimeoutException.cs new file mode 100644 index 0000000000000000000000000000000000000000..6e4243ef73e987a76161543d349b9d5d3c69f135 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnityTestTimeoutException.cs @@ -0,0 +1,28 @@ +using NUnit.Framework; +using NUnit.Framework.Interfaces; + +namespace UnityEngine.TestTools.TestRunner +{ + internal class UnityTestTimeoutException : ResultStateException + { + public UnityTestTimeoutException(int timeout) + : base(BuildMessage(timeout)) + { + } + + private static string BuildMessage(int timeout) + { + return string.Format("Timeout value of {0}ms was exceeded", timeout); + } + + public override ResultState ResultState + { + get { return ResultState.Failure; } + } + + public override string StackTrace + { + get { return ""; } + } + } +} diff --git a/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnityTestTimeoutException.cs.meta b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/Assertions/UnityTestTimeoutException.cs.meta new file mode 100644 index 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b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.test-framework@1.1.22/UnityEngine.TestRunner/NUnitExtensions/ActionDelegator.cs @@ -0,0 +1,79 @@ +using System; +using System.Linq; +using UnityEngine.TestRunner.NUnitExtensions.Runner; +using UnityEngine.TestTools.Logging; +using UnityEngine.TestTools.TestRunner; + +namespace UnityEngine.TestTools.NUnitExtensions +{ + /// + /// This class delegates actions from the NUnit thread that should be executed on the main thread. + /// NUnit thread calls Delegate which blocks the execution on the thread until the action is executed. + /// The main thread will poll for awaiting actions (HasAction) and invoke them (Execute). + /// Once the action is executed, the main thread releases the lock and executino on the NUnit thread is continued. + /// + internal class ActionDelegator : BaseDelegator + { + private Func m_Action; + public object Delegate(Action action) + { + return Delegate(() => { action(); return null; }); + } + + public object Delegate(Func action) + { + if (m_Aborted) + { + return null; + } + + AssertState(); + m_Context = UnityTestExecutionContext.CurrentContext; + + m_Signal.Reset(); + m_Action = action; + + WaitForSignal(); + + return HandleResult(); + } + + private void AssertState() + { + if (m_Action != null) + { + throw new Exception("Action not executed yet"); + } + } + + public bool HasAction() + { + return m_Action != null; + } + + public void Execute(LogScope logScope) + { + try + { + SetCurrentTestContext(); + m_Result = m_Action(); + if (logScope.AnyFailingLogs()) + { + var failingLog = logScope.FailingLogs.First(); + throw new UnhandledLogMessageException(failingLog); + } + if (logScope.ExpectedLogs.Any()) + throw new UnexpectedLogMessageException(LogScope.Current.ExpectedLogs.Peek()); + } + catch (Exception e) + { + m_Exception = e; + } + finally + { + m_Action = null; + m_Signal.Set(); + } + } + } +} diff --git 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